24 years CAT Topic-wise Solved Papers (2017-1994) with 6 Online Practice Sets 11th edition - Shipra Agarwal Deepak Agarwal

UNIT - I : QUANTITATIVE ABILITY

CHAPTER 1 : NUMBER SYSTEM — Types of Numbers; Surds and Indices; Arithmetic Calculations; Division and Divisibility Test; Simplification and Rationalization; HCF and LCM; Fractions; Comparison of Fractions; Numeration Systems; Conversion between Numeration Systems. CHAPTER 2 : SET THEORY — Sets and their Representations; Types of Sets; Subsets; Venn Diagrams; Operations on Sets. CHAPTER 3 : FUNCTIONS — Relations; Types of Relations; Functions; Domain, Co-domain and Range; Inverse Trigonometric Functions; Real Valued Functions; Arithmetic Combinations of Functions; Different types of Functions; Composition of Functions. CHAPTER 4 : AVERAGE, RATIO & PROPORTION — Average; Mixture Problems; Unitary Ratio; Comparison of Two or More Ratios; Composition of Ratios; Ratios Applications; Direct and Inverse Variation Alligation; Partnership. CHAPTER 5 : ALGEBRA-1 — Elementary Algebra; Algebraic Expressions; Basic Rules of Algebra; Equations and Solutions; Equation involving Fractional Expressions; Polynomial Equations; Equations with Fractions or Absolute Values; Simplifying Radicals; Rational Exponents; Problems Based on Ages. CHAPTER 6 : ALGEBRA-2 — Sequence and Series; Sum of Numbers; Logarithm; Arithmetic Geometric and Harmonic Mean; Progressions. CHAPTER 7 : PERCENTAGE, PROFIT & LOSS — Value and Percentage; Comparing Percentages; Simple and Compound Interest; Profit and Loss. CHAPTER 8 : GEOMETRY — Basic Concepts in Geometry; Classification of Triangles; Quadrilateral; Co-ordinate Geometry; Equations of Parallel and Perpendicular Lines; Bisectors of Angles between two lines;

Concurrence of Straight Lines; General Equation of Circles; Position of point with respect to a Circle. CHAPTER 9 : MENSURATION — Polygon; Circle; Surface Areas Volumes and Areas of Solids; Cube and Cuboid; Cylinder; Sphere; Pyramid; Conversion of Solid from One Shape to Another. CHAPTER 10 : TIME, DISTANCE & WORK — Time and Distance; Time, Work and Wages; Pipes and Cisterns; Calendar and Clocks; Problems on Trains, Boats, Aeroplane, Streams and Races. CHAPTER 11 : PERMUTATION, COMBINATION & PROBABILITY — Fundamental Principle of Counting; Distinguishable Permutations; Combination; Difference between Permutation and Combination; Counting Formulae for Combination; Division and Distribution of Objects; Random Experiments; Event; Probability of atleast one of the n Independent Events; Baye’s Formula; Total Probability Theorem.

UNIT - II : DATA INTERPRETATION, DATA SUFFICIENCY & REASONING CHAPTER 12 : LINE & BAR CHART — Caselet Based Problems on Line Chart; Bar Chart (Histogram); Mix of both. CHAPTER 13 : PIE CHART — Caselet Based Problems on Pie Chart. CHAPTER 14 : DATA TABULATION — Caselet Based Problems on Data Tables; Combination of Data Table with other graph. CHAPTER 15 : DATA SUFFICIENCY — Questions based on Mathematical data and Logical Reasoning. CHAPTER 16 : LOGICAL REASONING — Questions based on Fact, Judgement and Inference; Syllogism; Sentence and Conclusion; Arguments.

CHAPTER 17 : ANALYTICAL REASONING — Arrangement; Conditional Analysis; Relationships and Associations; Categorisation; Optimisation; Mathematical Reasoning; Decision Making.

UNIT - III : VERBAL AND READING COMPREHENSION CHAPTER 18 : VOCABULARY — Synonyms and Antonyms; Analogy; Odd One Out; Dictionary definition and Usage; Contextual Use of Word; Fillers. CHAPTER

CHAPTER

19 : GRAMMAR — Spot the Error; Sentence Improvement; Best way of writing the sentence; Grammatical incorrect or inappropriate sentences; Fill in the Blanks. 20 : PARAGRAPH CONSTRUCTION — Parajumbles; Coherent paragraph; Missing or deleted part of sentences; Sentence Completion. 21 : CRITICAL REASONING — Questions based on Information of Passage; Description of the unseasonable man in the passage; Essence of the text. 22 : READING COMPREHENSION Based on SOCIAL SCIENCES — Passages based on History, Geography, Psychology, Political Thoughts, Sociology, Economy and Business Contemporary Issues etc. 23 : READING COMPREHENSION Based on NATURAL SCIENCES — Passages based on Physical Sciences and Life Science, Natural Phenomenon, Astronomy etc. 24 : READING COMPREHENSION Based on HUMANITIES — Passages based on Literature, Criticism Art, Philosophy etc.

CAT 2017 Solved Paper Question numbers: (1 to 6) The passage below is accompanied by a set of six questions. Choose the best answer to each question. Understanding where you are in the world is a basic survival skill, which is why we, like most species come hard- wired with specialised brain areas to create cognitive maps of our surroundings. Where humans are unique, though, with the possible exception of honeybees, is that we try to communicate this understanding of the world with others. We have a long history of doing this by drawing maps- the earliest versions yet discovered were scrawled on cave walls 14,000 years ago. Human cultures have been drawing them on stone tablets, papyrus, paper and now computer screens ever since. Given such a long history of human map–making, it is perhaps surprising that it is only within the last few hundred years that north has been consistently considered to be at the top. In fact, for much of human history, north almost never appeared at the top, according to Jerry Brotton, a map historian... “North was rarely put at the top for the simple fact that north is where darkness comes from,” he says. “West is also very unlikely to be put at the top because west is where the sun disappears.” Confusingly, early Chinese maps seem to buck this trend. But, Brotton, says, even though they did have compasses at the time, that isn’t the reason that they placed north at the top. Early Chinese compasses were actually oriented to point south, which was considered to be more desirable than deepest darkest north. But in Chinese maps, the Emperor, who lived in the north of the country was always put at the top of the map, with everyone else, his loyal subjects, looking up towards him. “In Chinese culture the Emperor looks south because it’s where the winds come from, it’s a good direction. North is not very good but you are in a position of subjection to the emperor, so you look up to him,” says Brotton.

Given that each culture has a very different idea of who, or what, they should look up to it’s perhaps not surprising that there is very little consistency in which way early maps pointed. In ancient Egyptian times the top of the world was east, the position of sunrise. Early Islamic maps favoured south at the top because most of the early Muslim cultures were north of Mecca, so they imagined looking up (south) towards it. Christian maps from the same era (called Mappa Mundi) put east at the top, towards the Garden of Eden and with Jerusalem in the centre. So when did everyone get together and decide that north was the top? It’s tempting to put it down to European explorers like Christopher Columbus and Ferdinand Megellan, who were navigating by the North Star. But Brotton argues that these early explorers didn’t think of the world like that at all. “When Columbus describes the world it is in accordance with east being at the top,” he says. “Columbus says he is going towards paradise, so his mentality is from a medieval mappa mundi.” We’ve got to remember, adds Brotton, the at the time. “no one knows what they are doing and where they are going.” 1. Which one of the following best describes what the passage is trying to do? (a) It questions an explanation about how maps are designed. (b) It corrects a misconception about the way maps are designed. (c) It critiques a methodology used to create maps (d) It explorers some myths about maps 2. Early maps did NOT north at the top for all the following reasons EXCEPT (a) North was the source of darkness (b) South was favoured by some emperors (c) East and south were more important for religious reasons for some civilisations. (d) East was considered by some civilisations to be a more positive direction 3. According to the passage, early chinese maps placed north at the top because

(a) The Chinese invented the compass and were aware of magnetic north. (b) They wanted to show respect to the emperor. (c) The Chinese emperor appreciated the winds from the south. (d) North was considered the most desirable direction. 4. It can be inferred from the passage that European explorers like Columbus and Magellan. (a) Set the precedent for north-up maps. (b) Navigated by the compass. (c) Used an eastward orientation for religious reasons. (d) Navigated with the help of early maps. 5. Which one of the following about the northern orientation of modern maps is asserted in the passage? (a) The biggest contributory factor was the understanding of magnetic north. (b) The biggest contributory factor was the role of European explorers. (c) The biggest contributory factor was the influence of Christian maps. (d) The biggest contributory factor is not stated in the passage. 6. The role of natural phenomena in influencing map-making conventions is seen most clearly in (a) Early Egyptian maps (b) Early Islamic maps (c) Early Chinese maps (d) Early Christian maps The passage below is accompanied by a set of six questions. Choose the best answer to each question. I used a smartphone GPS to find my way through the cobblestoned maze of Geneva’s Old Town, in search of a handmade machine that changed the world more than any other invention. Near a 13th– Century cathedral in this Swiss city on the shores of a lovely lake, I found what I was looking for: a Gutenberg printing press. “This was the Internet of its day – at least as influential as the iphone,” said Gabriel de Montmollin, the director of the Museum of the

Reformation, toying with the replica of Johann Gutenberg’s great invention. [Before the invention of the printing press] it used to take four monks…up to a year to produce a single book. With the advance in movable type in 15th-Century Europe, one press could crank out 3,000 pages a day. Before long, average people could travel to places that used to be unknown to them – with maps! Medical information passed more freely and quickly, diminishing the sway of quacks… The printing press offered the prospect that tyrants would never be able to kill a book or suppress an idea. Gutenberg’s brainchild broke the monopoly that clerics had on scripture. And later, stirred by pamphlets from a version of that same press, the American colonies rose up against a king and gave birth to a nation. So, a question in the summer of this 10th anniversary of the iPhone: has the device that is perhaps the most revolutionary of all time given us a single magnificent idea? Nearly every advancement of the written word through new technology has also advanced humankind. Sure, you can say the iPhone changed everything. By putting the world’s recorded knowledge in the palm of a hand, it revolutionized work, dining, travel and socializing. It made us more narcissistic – here’s more of me doing cool stuff ! – and it unleashed an army of awful trolls. We no longer have the patience to sit through a baseball game without that reach to the pocket. And one more casualty of Apple selling more than a billion phones in a decade’s time: daydreaming has become a lost art. For all of that, I’m Still waiting to see if the Iphone can do what the printing press did for religion and democracy… the Geneva museum makes a strong case that the printing press opened more minds than anything else…. It’s hard to imagine the French or American revolutions without those enlightened voices in pirnt…. Not long after Steve Jobs introduced his iPhone, he said the bound book was probably headed for history’s attic. Not so fast. After a period of rapid growth in e-books, something closer to the medium for Chaucer’s volumes has made a great comeback. The hope of the iPhone, and the Internet in general, was that it would free people in closed societies. But the failure of the Arab Spring, and

the continued suppression of ideas in North Korea, China and Iran, has not borne that out…. The iPhone is still young. It has certainly been “One of the most important, world–changing and successful products in history,” as Apple C.E.O. Tim Cook said, But I’m not sure if the world changed for the better with the iPhone– as it did with the printing press–or merely changed. 7. The printing press has been likened to the Internet for which one of the following reasons? (a) It enabled rapid access to new information and the sharing of new ideas. (b) It represented new and revolutionary technology compared to the past. (c) It encouraged reading among people by giving them access to thousands of books. (d) It gave people access to pamphlets and literature in several languages. 8. According to the passage, the invention of the printing press did all of the following EXCEPT (a) Promoted the spread of enlightened political views across countries. (b) Gave people direct access to authentic medical information and religious texts. (c) Shortened the time taken to produce books and pamphlets. (d) Enabled people to perform various tasks simultaneously. 9. Steve Jobs predicted which one of the following with the introduction of the iPhone? (a) People would switch from reading on the Internet to reading on their iPhones. (b) People would lose interest in historical and traditional classics. (c) Reading printed books would become a thing of the past. (d) The production of e-books would eventually fall. 10. “I’m still waiting to see if the iPhone can do what the printing press did for religion and democracy.” The author uses which one of the following to indicate his uncertainty? (a) The rise of religious groups in many parts of the world.

(b) The expansion in trolling and narcissism among users of the Internet. (c) The continued suppression of free speech in closed societies. (d) The decline in reading habits among those who use the device. 11. The author attributes the French and American revolutions to the invention of the printing press because (a) Maps enabled large numbers of Europeans to travel and settle in the American continent. (b) The rapid spread of information exposed people to new ideas on freedom and democracy. (c) It encouraged religious freedom among the people by destroying the monopoly of religious leaders on the scriptures. (d) It made available revolutionary strategies and opinions to the people. 12. The main conclusion of the passage is that the new technology has (a) Some advantages, but these are outweighed by its disadvantages. (b) So far not proved as successful as the printing press in opening people’s minds. (c) Been disappointing because it has changed society too rapidly. (d) Been more wasteful than the printing press because people spend more time daydreaming or surfing. The passage below is accompanied by a set of six questions. Choose the best answer to each question. This year alone, more than 8,600 stores could close, according to industry estimates, many of them the brand- name anchor outlets that real estate developers once stumbled over themselves to court. Already there have been 5,300 retail closings this year…. Sears Holdings – which owns Kmart – said in March that there’s “substantial doubt” it can stay in business altogether, and will close 300 stores this year. So far this year, nine national retail chains have filed for bankruptcy. Local jobs are a major casualty of what analysts are calling, with only a hint of hyperbole, the retail apocalypse. Since 2002,

department stores have lost 448,000 jobs, a 25% decline, while the number of store closures this year is on pace to surpass the worst depths of the Great Recession. The growth of online retailers, meanwhile, has failed to offset those losses, with the ecommerce sector adding just 178,000 jobs over the past 15 years. Some of those jobs can be found in the massive distribution centers Amazon has opened across the country, often not too far from malls the company helped shutter. But those are workplaces, not gathering places. The mall is both. And in the 61 years since the first enclosed one opened in suburban Minneapolis, the shopping mall has been where a huge swath of middle–class America went for far more than shopping. It was the home of first jobs and blind dates, the place for family photos and ear piercings, where goths and grandmothers could somehow walk through the same doors and find something they all liked. Sure, the food was lousy for you and oceans of parking lots encouraged car–heavy development, something now scorned by contemporary planners. But for better or worse, the mall has been America’s public square for the last 60 years. So what happens when it disappears? Think of your mall. Or think of the one you went to as a kid. Think of the perfume clouds in the department stores. The fountains splashing below the skylights. The cinnamon wafting from the food court. As far back as ancient Greece, Societies have congregated around a central marketplace. In medieval Europe, they were outside Cathedrals, For half of the 20th century and almost 20 years into the new one, much of America has found their agora on the terrazzo between Orange Julius and Sbarro, Waldenbooks and the Gap, Sunglass Hut and Hot Topic. That mall was an ecosystem unto itself, a combination of community and commercialism peddling everything you needed and everything you didn’t: Magic Eye Posters, Wind catchers, Air Jordans….. A growing number of Americans, however, don’t see the need to go to any Macy’s at all. Our digital lives are frictionless and

13.

14. (a) (b) (c) (d) 15. (a) (b) (c) (d) 16. (a) (a) (a) (a)

ruthlessly efficient, with retail and romance available at a click. Malls were designed for leisure, abundance, ambling. You parked and planned to spend some time. Today, much of that time has been given over to busier lives and second jobs and apps that let you swipe right instead of haunt the food court. Malls, Says Harvard business professor Leonard Schlesinger, “were built for patterns of social interaction that increasingly don’t exist. The Central idea of this passage is that: (a) The closure of malls has affected the economic and social life of middle-class America. (b) The advantages of malls outweigh their disadvantages. (c) Malls used to perform a social function that has been lost. (d) Malls are closing down because people have found alternate ways to shop. Why does the author say in paragraph 2, ‘the massive distribution centers Amazon has opened across the country, often not too far from malls the company helped shutter’? To highlight the irony of the situation. To indicate that malls and distribution centers are located in the same area. To show that Amazon is helping certain brands go online. To indicate that the shopping habits of the American middle class have changed. In Paragraph 1, the phrase “real estate developers once intumbled over themselves to court” suggests that they took brand-name anchor outlets to court. no longer pursue brand–name anchor outlets. collaborated with one another to get brand-name anchor outlets. were eager to get brand–name anchor outlets to set up shop in their mall. The author calls the mall an ecosystem unto itself because people of all ages and from all walks of life went there. people could shop as well as eat in one place. it was commercial space as well as a gathering place. it sold things that were needed as well as those that were not.

17. Why does the author say that the mall has been America’s public square? (a) Malls did not bar anybody from entering the space. (b) Malls were a great place to shop for a huge section of the middle class. (c) Malls were a hangout place where families grew close to each other. (d) Malls were a great place for everyone to gather and interact. 18. The author describes ‘perfume clouds in the department stores’ in order to (a) evoke memories by painting a picture of malls. (b) describe the smells and sights of malls. (c) emphasise that all brands were available under one roof. (d) show that malls smelt good because of the various stores and food court. The passage below is accompanied by a set of three questions. Choose the best answer to each question. Scientists have long recognised the incredible diversity within a species. But they thought it reflected evolutionary changes that unfolded imperceptibly, over millions of years. That divergence between populations within a species was enforced, according to Ernst Mayr, the great evolutionary biologist of the 1940s, when a population was separated from the rest of the species by a mountain range or a desert, preventing breeding across the divide over geologic scales of time. Without the separation, gene flow was relentless. But as the separation persisted, the isolated population grew a part and speciation occurred. In the mid-1960s, the biologist Paul Ehrlich–author of the Population Bomb (1968) – and his Stanford University colleague Peter Raven challenged Mayr’s ideas about speciation. They had studied checkerspot butterflies living in the Jasper Ridge Biological Preserve in California and it soon became clear that they were not examining a single population. Through years of capturing, marking and then recapturing the butterflies, they were able to prove that within the population, spread over just 50

acres of suitable checkerspot habitat, there were three groups that rarely interacted despite their very close proximity. Among other ideas, Ehrlich and Raven argued in a now classic paper from 1969 that gene flow was not as predictable and ubiquitous as Mayr and his cohort maintained and thus evolutionary divergence between neighboring groups in a population was probably common. They also asserted that isolation and gene flow were less important to evolutionary divergence than natural selection (when factors such as mate choice, weather, disease or predation cause better-adapted individuals to Survive and pass on their successful genetic traits). For example, Ehrlich and Raven suggested that, without the force of natural selection, an isolated population would remain unchanged and that, in other scenarios, natural selection could be strong enough to overpower gene flow... 19. Which of the following best sums up Ehrlich and Raven’s argument in their classic 1969 paper? (a) Ernst Mayr was wrong in identifying physical separation as the cause of species diversity. (b) Checkerspot butterflies in the 50-acre Jasper Ridge Preserve formed three groups that rarely interacted with each other. (c) While a factor, isolation was not as important to speciation as natural selection. (d) Gene flow is less common and more erratic than Mayr and his colleagues claimed. 20. All of the following statements are true according to the passage EXCEPT (a) Gene flow contributes to evolutionary divergence. (b) The Population Bomb questioned dominant ideas about species diversity. (c) Evolutionary changes unfold imperceptibly over time. (d) Checkerspot butterflies are known to exhibit speciation while living in close proximity. 21. The author discusses Mayr, Ehrlich and Raven to demonstrate that (a) evolution is a sensitive and controversial topic.

(b) Ehrlich and Raven’s ideas about evolutionary divergence are widely accepted by scientists. (c) the causes of speciation are debated by scientists (d) checkerspot butterflies offer the best example of Ehrlich and Raven’s ideas about speciation. Question Numbers: (22 to 24) The passage below is accompanied by a set of three questions. Choose the best answer to each question. Do sports mega events like the summer Olympic Games benefit the host city economically? It depends, but the prospects are less than rosy. The trick is converting... several billion dollars in operating costs during the 17day fiesta of the games into a basis for long-term economic returns. These days, the summer Olympic Games themselves generate total revenue of $4 billion to $5 billion, but the lion’s share of this goes to the International Olympics Committee, the National Olympics Committees and the International Sports Federations. Any economic benefit would have to flow from the value of the games as an advertisement for the city, the new transportation and communications infrastructure that was created for the games, or the ongiong use of the new facilities. Evidence suggests that the advertising effect is far from certain. The infrastructure benefit depends on the initial condition of the city and the effectiveness of the planning. The facilities benefit is dubious at best for buildings such as velodromes or natatoriums and problematic for 100,000-seat Olympic stadiums. The latter require a conversion plan for future use, the former are usually doomed to near vacancy. Hosting the summer games generally requires 30-plus sports venues and dozens of training centers. Today, the Bird’s Nest in Beijing sits virtually empty, while the Olympic Stadium in Sydney costs some $30 million a year to operate. Part of the problem is that Olympics planning takes place in a frenzied and time=pressured atmosphere of intense competition with the other prospective host cities-not optimal conditions for contemplating the future shape of an urban landscape. Another

part of the problem is that urban land is generally scarce and growing scarcer. The new facilities often stand for decades or longer. Even if they have future use, are they the best use of precious urban real estate? Further, cities must consider the human cost. Residential areas often are razed and citizens relocated (without adequate preparation or compensation). Life is made more hectic and congested. There are, after all, other productive uses that can be made of vanishing fiscal resources. 22. The central point in the first paragraph is that the economic benefits of the Olympic Games (a) are shared equally among the three organising committees. (b) accrue mostly through revenue from advertisements and ticket sales. (c) accrue to host cities, if at all, only in the long term. (d) are usually eroded by expenditure incurred by the host city. 23. Sports facilities built for the Olympics are not fully utilised after the Games are over because (a) their scale and the costs of operating them are large. (b) their location away from the city centre usually limits easy access. (c) the authorities do not adapt them to local conditions (d) they become outdated having being built with little planning and under time pressure. 24. The author feels that the Games place a burden on the host city for all of the following reasons EXCEPT that (a) they divert scarce urban land from more productive uses. (b) they involve the demolition of residential structures to accommodate sports facilities and infrastructure. (c) the finances used to fund the Games could be better used for other purposes. (d) the influx of visitors during the games places a huge strain on the urban infrastructure. Correct:3 Wrong:1 The passage given below is followed by four summaries. choose the option that best captures the author’s position.

25. To me, a “classic” means precisely the opposite of what my predecessors understood: a work is classical by reason of its resistance to contemporaneity and supposed universality, by reason of its capacity to indicate human particularity and difference in that past epoch. The classic is not what tells me about shared humanity–or, more truthfully put, what lets me recognize myself as already present in the past, what nourishes in me the illusion that everything has been like me and has existed only to prepare the way for me. Instead, the classic is what gives access to radically different forms of human consciousness for any given generation of readers, and thereby expands for them the range of possibilities of what it means to be a human being. (a) A classic is able to focus on the contemporary human condition and a unified experience of human consciousness. (b) A classic is a work seeks to resist particularity and temporal difference even as it focuses on a common humanity. (c) A classic is a work exploring the new, going beyond the universal, the contemporary, and the notion of a unified human consciousness. (d) A classic is a work that provides access to a universal experience of the human race as opposed to radically different forms of human consciousness. The passage below is followed by four summaries. Choose the option that best captures the author’s position. The passage given below is followed by four summaries. Choose the option that beslt captures the author’s position. 26. A translator of literary works needs a secure hold upon the two languages involved, supported by a good measure of familiarity with the two cultures. For an Indian translating works in an Indian language into English, finding satisfactory equivalents in a generalized western culture of practices and symbols in the original would be less difficult than gaining fluent control of contemporary English. When a westerner works on texts in Indian languages the interpretation of cultural elements will be the major challenge, rather than control over the grammar and

essential vocabulary of the language concerned. It is much easier to remedy lapses in language in a text translated into English, than flaws of content. Since it is easier for an Indian to learn the English language than it is for a Briton or American to comprehend Indian culture, translations of Indian texts is better left to Indians. (a) While translating, the Indian and the westerner face the same challenges but they have different skill profiles and the former has the advantage. (b) As preserving cultural meanings is the essence of literary translation Indians’ knowledge of the local culture outweighs the initial disadvantage of lower fluency in English. (c) Indian translators should translate Indian texts into English as their work is less likely to pose cultural problems which are harder to address than the quality of language. (d) westerners might be good at gaining reasonable fluency in new languages, but as understanding the culture reflected in literature is crucial, Indians remain better placed. The passage given below is followed by four summaries. Choose the option that best captures the author’s position. 27. For each of the past three years, temperatures have hit peaks not seen since the birth of meteorology, and probably not for more than 110,000 years. The amount of carbon dioxide in the air is at its highest level in 4 million years. This does not cause storms like Harvey- there have always been storms and hurricanes along the Gulf of Mexico- but it makes them wetter and more powerful. As the seas warm, they evaporate more easily and provide energy to storm fronts. As the air above them warms, it holds more water vapour. For every half a degree Celsius in warming, there is about a 3% increases in atmospheric moisture content. Scientists call this the ClausiusClapeyron equation. This means the skies fill more quickly and have more to dump. The storm surge was greater because sea levels have risen 20 cm as a result of more than 100 years of humanstorm surge was greater because sea levels have risen 20 cm as a result of more than 100 years of human–related

(a) (b)

(c)

(d)

28.

(A) (B) (C) (D) (E) 29.

global warming which has melted glaciers and thermally expanded the volume of seawater. The storm Harvey is one of the regular, annual ones from the Gulf of Mexico; global warming and Harvey are unrelated phenomena. Global warming does not breed storms but makes them more destructive,; the Clausius-Clapeyron equation, though it predicts potential increase in atmospheric moisture content, cannot predict the scale of damage storms might wreck. Global warming melts glaciers, resulting in seawater volume expansion; this enables more water vapour to fill the air above faster. Thus, modern storms contain more destructive energy. It is naive to think that rising sea levels and the force of tropical storms are unrelated; Harvey was destructive as global warming has armed it with more moisture content, but this may not be true of all storms. The five sentences (labelled A, B, C, D, E) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer. The process of handing down implies not a passive transfer, but some contestation in defining what exactly is to be handed down. Wherever Western scholars have worked on the Indian past, the selection is even more apparent and the inventing of a tradition much more recognizable. Every generation selects what it requires from the past and makes its innovations, some more than others. It is now a truism ot say that traditions are not handed down unchanged, but are invented. Just as life has death as its opposite, so is tradition by default the opposite of innovation. The five sentences (labelled A, B, C, D, E) given in this question, when properly sequenced, form a coherent paragraph.

(A)

(B) (C) (D) (E) 30.

(A) (B) (C)

(D)

Each sentence is labelled with a number. Decide on the proper order for the sentenes and key in this sequence of five numbers as your answer. Scientists have for the first time managed to edit genes in a human embryo to repair a genetic mutation, fuelling hopes that such procedures may one day be available outside laboratory conditions. The cardiac disease causes sudden death in otherwise healthy young athletes and affects about one in 500 people overall. Correcting the mutation in the gene would not only ensure that the child is healthy but also prevents transmission of the mutation to future generations. It is caused by a mutation in a particular gene and a child will suffer from the condition even if it inherits only one copy of the mutated gene. In results announced in Nature this week, scientists fixed a mutation that thickens the heart muscle, a condition called hypertrophic cardiomyopathy. The five sentences (labelled A, B, C, D, E) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer. The study suggests that the disease did not spread with such intensity, but that it may have driven human migrations across Europe and Asia. The oldest sample came from an individual who lived in southeast Russia about 5,000 years ago. The ages of the skeletons correspond to a time of mass exodus from today’s Russia and Ukraine into western Europe and central Asia, suggesting that a pandemic could have driven these migrations. In the analysis of fragments of DNA from 101 Bronze Age skeletons for sequences from Yersinia pestis, the bacterium that causes the disease, seven tested positive.

(E) DNA from Bronze Age human skeletons indicate that the black plague could have emerged as early as 3,000 BCE, long before the epidemic that swept through Europe in the mid1300s. 31. The five sentences (labelled A, B, C, D, E) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer. (A) This visual turn in social media has merely accentuated this announcing instinct of ours, enabling us with easy-to-create, easy-to-share, easy-to-store and easy-to-consume platforms, gadgets and apps. (B) There is absolutely nothing new about us framing the vision of who we are or what we want, visually or otherwise, in our Facebook page, for example. (C) Turning the pages of most family albums, which belong to a period well before the digital dissemination of self-created and self-curated moments and images, would reconfirm the basic instinct of documenting our presence in a particular space, on a significant occasion, with others who matter. (D) We are empowered to book our faces and act as celebrities within the confinement of our respective friend lists, and communicate our activities, companionship and locations with minimal clicks and touches. (E) What is unprecedented is not the desire to put out newsfeeds related to the self, but the ease with which this broadcast operation can now be executed, often provoking (un) anticipated responses from beyond one’s immediate location. 32. Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. (a) People who study children’s language spend a lot of time watching how babies react to the speech they hear around them.

(b) They make films of adults and babies interacting, and examine them very carefully to see whether the babies show any signs of understanding what the adults say. (c) They believe that babies begin to react to language from the very moment they are born. (d) Sometimes the signs are very subtle-slight movements of the baby’s eyes or the head or the hands. (e) You’d never notice them if you were just sitting with the child, but by watching a recording over and over, you can spot them. 33. Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. (a) Neuroscientists have just begun studying exercise’s impact within brain cells-on the genes themselves. (b) Even there, in the roots of our biology, they’ve found signs of the body’s influence on the mind. (c) It turns out that moving our muscles produces proteins that travel through the bloodstream and into the brain, where they play pivotal roles in the mechanisms of our highest thought processes. (d) In today’s technology-driven, plasma-screened-in world, it’s easy to forget that we are born movers– animals, in fact–because we’ve engineered movement right out of our lives. (e) It’s only in the past few years that neuroscientists have begun to describe these factors and how they work, and each new discovery adds awe-inspiring depth to the picture. 34. Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. (a) The water that made up ancient lakes and perhaps an ocean was lost. (b) Particles from the Sun collided with molecules in the atmosphere, knocking them into space or giving them an electric charge that caused them to be swept away by the solar wind.

(c) Most of the planet’s remaining water is now frozen or buried, but clues over the past decade suggested that some liquid water, a presumed necessity for life, might survive in underground aquifers. (d) Data from NASA’S MAVEN orbiter show that solar storms stripped away most of Mars’s once-thick atmosphere. (e) A recent study reveals how Mars lost much of its early water, while another indicates that some liquid water remains. Question Numbers: (35 to 38) Healthy Bites is a fast food joint serving three items; burgers, fries and ice cream. It has two employees Anish and Bani who prepare the items ordered by the clients. Preparation time is 10 minutes for a burger and 2 minutes for an order of ice cream. An employee can prepare only one of these items at a time. The fries are prepared in an automatic fryer which can prepare up to 3 portions of fries at a time, and takes 5 minutes irrespective of the number of portions. The fryer does not need an employee to constantly attend to it, and we can ignore the time taken by an employee to start and stop the fryer; thus, an employee can be engaged in preparing other items while the frying is on. However fries cannot be prepared in anticipation of future orders. Healthy Bites wishes to serve the orders as early as possible. The individual items in any order are served as and when ready; however, the order is considered to be completely served only when all the items of that order are served. The table below gives the orders of three clients and the times at which they placed their orders:

35. Assume that only one client’s order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared. At what time is the order placed by Client 1 completely served?

(a) (b) (c) (d) 36.

10 : 17 10 : 10 10 : 15 10 : 20 Assume that only one client’s order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared. At what time is the order placed by Client 3 completely served? (a) 10 : 35 (b) 10 : 22 (c) 10 : 25 (d) 10 : 17 37. Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier. At what time is the order placed by Client 2 completely served? (a) 10 : 10 (b) 10 : 12 (c) 10 : 15 (d) 10 : 17 38. Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier. Also assume that the fourth client came in only at 10 : 35. Between 10: 00 and 10 : 30, for how many minutes is exactly one of the employees idle? (a) 7 (b) 10 (c) 15 (d) 23 Question Numbers: (39 to 42) A study to look at the early learning of rural kids was carried out in a number of villages spanning three states, chosen from the North East (NE), the West (W) and the South(S). 50 four-year old kids each were sampled from each of the 150 villages from NE, 250 villages from W and 200 villages from S. It was found that of the

30000 surveyed kids 55% studied in primary schools run by government (G), 37% in private schools (P) while the remaining 8% did not go to school (O). The kids surveyed were further divided into two groups based on whether their mothers dropped out of school before completing primary education or not. The table below gives the number of kids in different types of schools for mothers who dropped out of school before completing primary education:

It is also known that: I In S, 60% of the surveyed kids were in G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school. (II) In NE, among the O kids, 50% had mothers who had dropped out before completing primary education. (III) The number of kids in G in NE was the same as the number of kids in G in W. 39. What percentage of kids from S were studying in P? (a) 37% (b) 6% (c) 79% (d) 56% 40. Among the kids in W whose mothers had completed primary education, how many were not in school? (a) 300 (b) 1200 (c) 1050 (d) 1500 41. In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were

not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P, in the second region, all such kids were in G now, while in the third region, 50% of such kids has now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools. What number of the surveyed kids now were in G in W? (a) 6000 (b) 5250 (c) 6750 (d) 6300 42. In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P, in the second region, all such kids were in G now, while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools. What percentage of the surveyed kids in S, whose mothers had dropped out before completing primary education, were in G now? (a) 94.7% (b) 89.5% (c) 93.4% (d) Cannot be determined from the given information Question Numbers (43 to 46) Applicants for the doctoral programmes of Ambi Institute of Engineering (AIE) and Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test (CET). The test has three sections. Physics (P), Chemistry (C), and Maths (M). Among those appearing for CET, those at or above the 80th percentile in at least two sections, and at or above the 90th

For (a) (b) (c)

(d) BIE

43. (a) (c) (d) 44.

percentile overall, are selected for Advanced Entrance Test (AET) conducted by AIE. AET is used by AIE for final selection. the 200 condidates who are at or above the 90th percentile overall based on CET, the following are known about their performance in CET. No one is below the 80th percentile in all 3 sections. 150 are at or above the 80th percentile in exactly two sections. The number of candidates at or above the 80th percentile only in P is the same as the number of candidates at or above the 80th percentile only in C. The same is the number of candidates at or above the 80th percentile only in M. Number of candidates below 80th percentile in P. Number of candidates below 80th percentile in C. Number of candidates below 80th percentile in M = 4:2:1. uses a different process for selection. If any candidate is appearing in the AET by AIE, BIE considers their AET score for final selection provided the candidate is at or above the 80th percentile in P. Any other candidate at or above the 80th percentile in P in CET, but who is not eligible for the AET, is required to appear in a separate test to be conducted by BIE for being considered for final selection. Altogether, there are 400 candidates this year who are at or above the 80th percentile in P. What best can be concluded about the number of candidates sitting for the separate test for BIE who were at or above the 90th percentile overall in CET? 3 or 10 (b) 10 5 7 or 10 If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, what is the number of candidates who are at or above the 90th percentile overall and at or above the 80th percentile in both P and M in CET?

45. If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, then how many candidates were shortlisted for the AET for AIE? 46. If the number of candidates who are at or above the 90th percentile overall and also are at or above the 80th percentile in P in CET, is more that 100, how many candidates had to sit for the separate test for BIE? (a) 299 (b) 310 (c) 321 (d) 330 Questions Numbers: (47 to 50) Simple Happiness index (SHI) of a country is computed on the basis of three parameters: social support (S), freedom to life choices (F) and corruption perception (C). Each of these three parameters is measured on a scale of 0 to 8 (integers only). A country is then categorised based on the total score obtained by summing the scores of all the three parameters, as shown in the following table:

Following diagram depicts the frequency distribution of the scores is S, F and C of 10 countries-Amda, Benga, Calla, Delma, Eppa, Varsa, Wanna, Xanda, Yanga and Zooma:

Further, the following are known:

(a)

Amda and Calla jointly have the lowest total score, 7, with identical scores in all the three parameters. (b) Zooma has a total score of 17. (c) All the 3 countries, which are categorised as happy, have the highest score in exactly one parameter. 47. What is Amda’s score in F? 48. What is Zooma’s score in S? 49. Benga and Delma, two countries categorized as happy, are tied with the same total score. What is the maximum score they can have? (a) 14 (b) 15 (c) 16 (d) 17 50. If Benga scores 16 and Delma scores 15, then what is the maximum number of countries with a score of 13? (a) 0 (b) 1 (c) 2 (d) 3 Question Numbers : (51 to 54) There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular-skilled employees (RE). During the next five months, the division has to complete five projects every month. Out of the 25 projects, 5 projects are “challenging”, while the remaining ones are “standard”. Each of the challenging projects has to be completed in different months. Every month, five teams T1, T2, T3, T4 and T5, work on one project each. T1, T2, T3, T4 and T5 are allotted the challenging project in the first, second, third fourth and fifth month, respectively. The team assigned the challenging project has one more employee than the rest. In the first month, T1 has one more SE than T2, T2 has one more SE than T3, T3 has one more SE than T4, and T4 has one more SE than T5. Between two successive months, the composition of the teams changes as follows.

(a) The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange. one RE is shifted from the former team to the latter team. (b) After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T4 to T2. Each standard project has a total of 100 credit points, while each challenging project has 200 credit points. The credit points are equally shared between the employees included in that team. 51. The number of times in which the composition of team T2 and the number of times in which composition of team T4 remained unchanged in two successive months are. (a) (2, 1) (b) (1, 0) (c) (0, 0) (d) (1, 1) 52. The number of SE in T1 and T5 for the projects in the third month are, respectively. (a) (0, 2) (b) (0, 3) (c) (1, 2) (d) (1, 3) 53. Which of the following CANNOT be the total credit points earned by any employee from the projects? (a) 140 (b) 150 (c) 170 (d) 200 54. One of the employees named Aneek scored 185 points. Which of the following CANNOT be true? (a) Aneek worked only in teams T1, T2, T3 and T4. (b) Aneek worked only in teams T1, T2, T4 and T5.

(c) Aneek worked only in teams T2, T3, T4 and T5. (d) Aneek worked only in teams T1, T3, T4 and T5. Question Number 55 to 58 In a square layout of size 5m × 5m, 25 equal-sized square platforms of different heights are built. The height (in metres) of individual platforms are as shown below:

Individuals (all of same height) are seated on these platforms. We say an individual A can reach an individual B if all the three following conditions are met: (i) A and B are in the same row or column (ii) A is at a lower height than B (iii) If there is/are any individual(s) between A and B, such individual (s) must be at a height lower than that of A. Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5. Rows in the layout are numbered from top to bottom and columns are numbered from left to right. 55. How many individuals in this layout can be reached by just one individual? (a) 3 (b) 5 (c) 7 (d) 8 56. Which of the following is true for any individual at a platform of height 1 m in this layout? (a) They can be reached by all the individual in their own row and column?

(b) (c) (d) 57.

They can be reached by at least 4 individuals. They can be reached by at least one individual. They cannot be reached by anyone. We can find two individuals who cannot be reached by anyone in (a) the last row (b) the fourth row (c) the fourth column (d) the middle column 58. Which of the following statements is true about this layout? (a) Each row has an individual who can be reached by 5 or more individuals. (b) Each row has an individual who cannot be reached by anyone. (c) Each row has at least two individuals who can be reached by an equal number of individuals. (d) All individuals at the height of 9 m can be reached by at least 5 individuals. Question Numbers : (59 to 62) A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule. The underlying principle that they are working on is the following. Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day. 59. If the underlying principle is to satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is. (a) 45 (b) 90 (c) 180 (d) 135

60. Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and /or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is. (a) 54 (b) 120 (c) 96 (d) 60 61. Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4, having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following. (I) Both cities are in G1 (II) Between A and any city in G2 (III) Between B and any city in G3 (IV) Between C and any city in G4 Then the minimum number of direct flights that satisfies the underlying principle of the airline is. 62. Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further suppose that direct flights are allowed only between two cities satisfying one of the following. (A) Both cities are in G1 (B) Between a and any city in G2 (C) Between b and any city in G3 (D) Between c and any city in G4 However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or G4.

What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose? 63. Directions (Qs. 63-66) Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes).On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute. The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order. 63. How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department? 64. If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-N-B and a car that takes the route A-M-B? (a) 1 (b) 0.1 (c) 0.2 (d) 0.9 65. A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and AM-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the AN-B route.

66.

(a) (b) (c) (d) 67. 68.

69.

70.

How many cars would the police department order to take the AM-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.) A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and AM-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the AN-B route. If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.) 26 32 29.9 30 Arun’s present age in years is 40% of Barun’s. In another few years, Arun’s age will be half of Barun’s. By what percentage will Barun’s age increase during this period? A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job? An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group? A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had

71.

72. (a) (b) (c) (d) 73.

departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train’s departure. The distance (in km) from his home to the railway station is Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi’s savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is `59500, then Ravi’s total monthly savings (in `) is If a seller gives a discount of 15% on retail price, She still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%? Give a discount of 5% on retail price. Give a discount of 2% on retail price. Increase the retail price by 2%. Sell at retail price. A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

(a) (b) (c) (d) 3 : 2 74. Suppose, C1, C2, C3, C4 and C5 are five companies. The profits made by C1, C2 and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of `19 crore more than C1, then the total profit (in `) made by all five companies is (a) 438 crore (b) 435 crore (c) 348 crore (d) 345 crore

75. The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is (a) 35 (b) 50 (c) 60 (d) 65 76. A stall sells popcorn and chips in packets of three sizes : large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio (a) 1 : 1 (b) 8 : 7 (c) 4 : 3 (d) 6 : 5 77. In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bougth the good ones. His overall profit is (a) 6% (b) 8% (c) 10% (d) 12% 78. If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit? (a) 30% (b) 25% (c) 24% (d) 28%

79. If a and b are integers of opposite signs such that (a + 3)2 : b2 = 9 : 1 and (a – 1)2 : (b – 1)2 = 4 : 1, then the ratio a2 : b2 is (a) 9 : 4 (b) 81 : 4 (c) 1 : 4 (d) 25 : 4 80. A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is (a) 9.5 (b) 10 (c) 4.5 (d) 6 81. The area of the closed region bounded by the equation |x| + |y| = 2 in the two-dimensional plane is (a) 4π (b) 4 (c) 8 (d) 2π 82. From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is (a) (b) (c) (d) 83. Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC.

(a) (b) (c) (d) 84.

(a) (b) (c) (d) 85.

86.

87. (a) (b) (c) (d) 88. (a) (b) (c) (d)

Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is 9π – 18 18π 9π 9 A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to 10 50 60 20 A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is Suppose, log3 x = log12 y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6 G is equal to 2a a/2 a If x + 1 = x2 and x > 0, then 2x4 is

89. The value of

is equal to

(a) (b) (c) (d) 90. If 92x–1 – 81x–1 = 1944, then x is (a) (b) (c) (d) 91. (a) (b) (c) (d) 92. 93.

94. 95.

3 9/4 4/9 1/3 The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y < 12, and z < 12 is 101 99 87 105 For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied? If f1 (x) = x2 + 11x + n and f2 (x) = x, then the largest positive integer n for which the equation f1 (x) = f2 (x) has two distinct real roots, is If a, b, c and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2 is Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K and O so as to form a triangle?

96. The shortest distance of the point 1| + |x + 1| is

from the curve y = |x –

(a) 1 (b) 0 (c) (d) 97. If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is (a) 2 : 3 (b) 3 : 2 (c) 3 : 4 (d) 4 : 3 98. In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers? (a) 16 (b) 20 (c) 14 (d) 15 99. If f(x) =

and g(x) = x2 – 2x – 1, then the value of g (f(f(3)))

is (a) 2 (b) (c) 6 (d) 100. Let a1, a2...., a2n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ... + a2n = 1830, then what is the smallest positive integer m such that m(a1 + a2 + ... + an) > 1830? (a) 8 (b) 9

ANSWERS 1.

(b) The starting part of the passage talks about the history of map making. It is then mentioned how North being considered a bad direction was never put at the top in ancient times. Putting North at the top is a fairly recent phenomenon. It is further discussed about the reasons for putting North on the top and how the reasons of different people putting North at the top were different than that of the opinion of people today. So, it can be concluded by saying that the passage is focusing on clearing the misconception behind North being put at the top in the maps. Hence, option (b) is the most suitable answer. (b) It is clearly mentioned in the passage that Chinese emperors who lived in the North was always put at the top of the map with everyone else looking towards him. Hence, option (b) is the correct choice. (b) Options A and D can straightaway be eliminated. It is stated in the passage that Chinese compasses pointed towards magnetic South and South was considered a more desirable direction. On the other hand, option C is true i.e. not the reason behind putting North at the top. It is also mentioned in the passage that since the emperor lived in the North direction, maps depicted him above his subjects. Therefore, North was placed at the top to show respect to the emperor. Hence, option B is correct. (c) Option A can straightaway be eliminated. The author states that though one might think that the trend of putting North at the top was set by these explorers; however, this is not true. Both options B and D are incorrect. It is stated in the passage that the explorers used to navigate with the help of the North Star. It is said in the passage that when Columbus describes the world it is in accordance with East being at the top, he says “Columbus says he is going towards

(d)

(a)

(d)

paradise, so his mentality is from a medieval mappa mundi.” Hence, it can be inferred that statement C holds true. It is discussed in the passage how in the early maps, North was traditionally not put on the top. The author clearly proves the role of the compass and European explorers in placing North at the top of maps as wrong. So, option A and B gets eliminated. The author further says that East was placed at the top of Christian maps thus, option C is incorrect. The author contradicts all known explanations behind putting North on the top but does not give any explanation of his own and therefore, option D is correct. In the passage, it is stated that early Egyptian maps placed East on the top as it was the position of sunrise. Hence, it can be asserted that natural phenomena dictated the mapmaking convention. Therefore, option A is correct. Option B and D are wrong because map-making conventions were decided by religious factors and not natural phenomena. Option C also gets eliminated on the premise that the orientation was a result of their desire to honour their emperor. Hence, the correct option to choose is option A. The first paragraph clearly mentions printing press as the internet of its day. The second paragraph explains how printing press was helpful in spreading ideas and information. Therefore, it is evident that printing press is linked to the internet because it enabled rapid access to new information and the sharing of new ideas. Therefore, option A is the correct choice. Option (b) is true as it can be inferred from the sentence “Medical information passed more freely and quickly diminishing the sway of quacks” and “Gutenberg’s brainchild broke the monopoly that clerics had on scriptures.” Option (a) is true as it can be inferred from the sentence “And later stirred by pamphlets from a version of that same press, the American colonies rose up against a king and gave birth to a nation” and “it’s hard to imagine the French or American revolutions without those enlightened

(c)

10. (c)

11.

(b)

12. (b)

voices in print”. Option (c) is true and it can be inferred from the sentence “Before the invention of the printing press, it used to take four months up to a year to produce a single book. With the advance in movable type in 15th-century Europe, one pres could crank out 3,000 pages a day”. The statement in option (d) has not been stated anywhere in the entire passage. Referring to the line “Not long after Steve Jobs introduced his iPhone, he said that bound book was probably headed for history’s attic”, it can be inferred that Steve Jobs predicted that reading printed books would become a thing of the past. Hence, option (c) is the correct choice. In the passage, the author is of the view that iPhone has not fulfilled its potential as a piece of revolutionary technology. He further says that it was expected that iPhone could prove to be helpful in liberating people in closed societies. Moreover, the failure of the Arab Spring and continued suppression in places like North Korea indicates that this has not happened. Hence, the ‘continued suppression of free speech in closed societies’ is used by the author to indicate why he is still uncertain about the potential of iPhone, therefore, option (c) is correct. With the help of the line “it’s hard to imagine the French or American revolutions without those enlightened voices in pint”, we can eliminate option (a) and (c). Among options (b) and (d), (b) correctly exhibits the points made by the author i.e. the printing press allowed the spread of enlightened voices and as a result, people were exposed to new ideas on freedom and democracy. Option (d) can be eliminated because the passage does not mention any revolutionary ‘strategies’. Thus, option (b) is the correct choice. The main theme of the passage is that iPhone has failed in doing anything to make the society more liberated or enlightened which the Gutenberg printing press did. This point has been mentioned in option (b). The author has not

emphasised on the advantage or disadvantage of new technology hence, option (a) gets eliminated. The author is not of the view that the society has rapidly changed as a result of new technology, moreover, he believes that nothing really has changed as a result of it. He further says that people no longer are daydreaming as a result of new technology. Hence option (d) which is contradicting the facts given in the passage can be eliminated. 13. (c) 14. (a) 15. (b) 16. (c) 17. (d) 18. (a) 19. (c) 20. (b) 21. (c) 22. (c) 23. (a) 24. (d) 25. (c) 26. (c) 27. (c) 28. edacb 29. aebdc 30. edabc 31. cbade 32. (c) 33. (d) 34. (a) 35. (b) As the item which take the maximum time is burger, client I will be completely served by 10.00 + 10 min = 10 : 10 36. (c) Client–1 10 : 00 – 10 : 10 (burger) Client–2 10 : 10 – 10 : 15 (fries) Client–3 10 : 15 – 10 : 25 (burger) 37. (a) Client 1 – 10 : 00 – 10 : 10 (Anish)

Client 2 – 10 : 05 – 10 : 10 (Bani) The second client can be served by 10 : 10 38. (b) 10 : 02 – 10 : 05 (Bani) – 3 minutes 10 : 10 – 10 : 17 (Anish/Bani) – 7 minutes Total time = 3 + 7 = 10 minutes. Sol. (39 – 42) 39. (a) With the table given for kids in different schools whose mothers had dropped out of school we will be adding another value for each value already present and the new value will represent the number of kids in different types of schools for kids whose mothers completed primary education.

300 + 3400 = 3700 i.e

= 37%

40. (a) In W, 300 kids whose mothers had completed primary education were not in school. 41. (a) As there were initially 2400 students who were not in school and now 1200 of them are in G, with the mentioned percentages the only possibility is 50% of students in W, 25% of students in NE and 100% of students in S who were not going to school shifted to G. ∴ 50% of W = 50% of 1500 = 750 25% of NE = 25% of 600 = 150 100% of S = 100% of 300 = 300 ⇒ Total = 750 + 150 + 300 ⇒ 1200 ∴ now 4200 + 1050 + 750 = 6000 students were in G is W. 42. As explained in the previous question, all 300 in S who were not going to school, now shifted to G. Now of the 5700 students whose mothers had dropped out in S regions, 5400 are in G.

i.e =

= 94.70%

43. (a) The number of candidates sitting for separate test far BIE who were at or above 90th percentile in CET (a) is either 3 or 10.

From 1, h = 0. From 2, d + e + f =150 From 3, a = b = c Since there are a total of 200 candidates, 3a + g = 200 –150 = 50 From 4, (2a + f) : (2a + e) : (2a + d) = 4 : 2 : 1 Therefore, 6a + (d + e + f) is divisible by 4 + 2 + 1 = 7. Since d + e + f =150, 6a + 150 is divisible by 7, i.e., 6a + 3 is divisible by 7. Hence, a = 3, 10,17, . .. Further, since 3a + g = 50, a must be less than 17. Therefore, only two cases are possible for the value of a, i.e.. 3 or 10. We can calculate the values of the other variables for the two cases. a = 3 or 10 d = 18 or 10 e = 42 or 40 f = 90 or 100

g = 41 or 20 Among the candidates who are at or above 90th percentile, the candidates who are at or above 80th percentile in at least two sections are selected for AET. Hence, the candidates represented by d, e, f and g are selected for AET. BIE will consider the candidates who are appearing (for AET and are at or above 80th percentile in P. Hence, BIE will consider the candidates represented by d, e and g, which can be 104 or 80. BlE will conduct a separate test for the other students who are at or above 80th percentile in P. Given that there are a total of 400 candidates at or above 80th percentile in P, and since there are 104 or 80 candidates at or above 80th percentile in P and are at or above 90th percentile overall, there must be 296 or 320 candidates at or above 80th percentile in P who scored less than 90th percentile overall. 44. (60) From the given condition. 9 is a multiple of 5, Hence. g = 20. The number of candidates at or above 90th percentile overall and at or above 80th percentile in both P and M .= e + g = 60. 45. (170) In this case, g = 20. Number of candidates shortlisted for AET = d + e + f + g =10 + 40 + 100 + 20 = 170 46. (a) From the given condition, the number of candidates at or above 90th percentile overall and at or above 80th percentile in P in CET =104. The number of candidates who have to sit for separate test = 296 + 3 = 299 47. (1) The given data can be represented in a table as follows.

A and C had a total score of 7, with identical scores in all these parameters. So it can only be 1, 2 and 4 or 3 and 1. As Zooma has a score of 17, and all three countries in the happy category had the highest score in exactly one parameter, he can only have a 7 in F, 6 in S and 4 in C as a score of 7 in S and 6 in C would be the scores of the other two countries and he cannot have a 7, 7 and 5 as there is no country which scored a 5 in C Amda can have a distribution of 3, 3, 1 or 4, 2, 1. In either case the only possible score of F is 1 as no other parameter has a scare of 1 for two countries. 48. (b) As explained before Zooma’s score in C has to be 6. 49. (b) In the table given, among the highest scores, a score of 7 in F, 6 in S and 4 in S were the score of Zoom. The best possible scores remaining for Benga and Dalma would be

As it is given that both had the some total score it can only be 15 for both, i.e. Benga’s score in S or F was one less than the maximum possible.

50. (b) Considering the score of Zoom, Benga and Delma as 17, 16 and 15, we get

If Benga score 16 and Dalma score 15 (as illustrated in the previous solution) the maximum possible values remaining are

51. (b) Given that there are 10 SE and 11 RE In the first month, since T1 has one more SE than T2, who in turn has one more SE than T3,... till T5, the number of SEs in T1, T2, T3, T4 and T5 must be 4, 3, 2, 1 and 0. Also, the team that is assigned the challenging project has one more employees than the rest. Hence, the team that is assigned the challenging project will have 5 employees, while the other teams will have 4 employees. Since T1 is assigned the challenging project in the first month, T1 will have 5 employees, and the other teams will have 4 employees each. The following table provides the composition of the teams in the first month:

In the second month, T2 will be allotted the challenging project. From a, two SEs will be transferred from Tl to T2. One RE is transferred from T2 to T1. From b, one SE will be transferred from T1 to T5, one RE will be transferred from T5 to T1. Similar transfers will happen between T2 and T4. The following table provides the number of employees in each team in the second month:

In the third month, T3 will be allotted the challenging project. From a, two SEs will be transferred from T2 to T3. One RE is transferred from T3 to T2. From b, one SE will be transferred from T1 to T5, one RE will be transferred from T5 to T1. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2. The following table provides the number of employees in each team in the third month:

In the fourth month, T4 will be allotted the challenging project. From a, two SEs will be transferred from T3 to T4. One RE is transferred from T4 to T3.

From b, one SE must be transferred from T1 to T5. However, since there are no SEs in T1, this will not happen. Also, one SE must be transferred from T2 to T4 and one RE must be transferred from T4 to T2. However, there are no REs in T4. Hence, this transfer will not happen. The following table provides the number of employees in each team in the fourth month: In the fifth month, T5 will be allotted the challenging project. From a, two SEs will be transferred from T4 to T5. One RE is transferred trom T5 to T4. From b, one SE must be transferred from T1 to T5. However, since there are no SEs in T1, this will not happen. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2. The following table provides the number of employees in each team in the fifth month.

The composition of T2 did not change once between the third and the fourth months. The composition of T4 changed between any two successive months.

Hence, the answer is (1, 0). 52. (a) Given that there are 10 SE and 11 RE. In the first month, since T1 has one more SE than T2, who in turn has one more SE than T3.... till T5, the number of SEs in T1, T2, T3, T4 and T5 must be 4, 3, 2, 1 and 0. Also, the team that is assigned the challenging project has one more employee than the rest. Hence, the team that is assigned the challenging project will have 5 employees, while the other teams will have 4 employees. Since T1 is assigned the challenging project in the first month, T1 will have 5 employees, and the other teams will have 4 employees each. The following table provides the composition of the teams in the first month:

In the second month, T2 will be allotted the challenging project. From a, two SEs will be transferred from T1 to T2. One RE is transferred from T2 to Tl. From b, one SE will be transferred from T1 to T5, one RE will be transferred from T5 to T1. Similar transfers will happen between T2 and T4. The following table provides the number of employees in each team in the second month:

In the fourth month, T4 will be allotted the challenging project. From a. two SEs will be transferred from T3 to T4. One RE is transferred from T4 to T3.

From b, one SE must be transferred from T1 to T5. However, since there are no SEs in Tl, this will not happen. Also, one SE must be transferred from T2 to T4 and one RE must be transferred from T4 to T2. However, there are no REs in T4. Hence, this transfer will not happen. The following table provides the number of employees in each team in the fourth month: In the fifth month, T5 will be allotted the challenging project. From a, two SEs will be transferred from T4 to TS. One RE is tranferred from T5 to T4. From b, one SE must be transferred from T1 to T5. However, since there are no SEs in T1, this will not happen. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2. The following table provides the number of employees in each team in the fifth month:

Number of SE in T1 in third month = 0 Number of SE in T5 in third month = 2. Hence, the answer is (0, 2) 53. (b) Given that there are 10 SE and 11 RE In the first month, since T1 has one more SE than T2, who in turn has one more SE than T3, .. till T5, the number of SEs in T1, T2, T3, T4 and T5 must be 4, 3, 2, 1 and 0. Also, the team that is assigned the challenging project has one more employee than the rest. Hence, the team that is assigned the challenging project will have 5 employees, while the other teams will have 4 employees.

Since Tl is assigned the challenging project in the first month, Tl will have 5 employees, and the other teams will hove 4 employees each. The following table provides the composition of the teams in the first month:

In the second month, T2 will be allotted the challenging project. From a, two SEs will be transferred from T1 to T2. One RE is transferred from T2 to T1. From b, one SE will be transferred From T1 to T5, one RE will be transferred from T5 to Tl. Similar transfers will happen between T2 and T4. The following table provides the number of employees in each team in the second month:

In the third month, T3 will be allotted the challenging project. From a, two SEs will be transferred from T2 to T3. One RE is transferred from T3 to T2. From b, one SE will be transferred from Tl to T5, one RE will be transferred from T5 to T1. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2.

The following table provides the number of employees in each team in the third month:

In the fourth month, T4 will be allotted the challenging project. From a, two SEs will be transferred from T3 to T4. One RE is transferred from T4 to T3.

Also, one SE must be transferred from T2 to T4 and one RE must be transferred from T4 to T2. However, there are no REs in T4. Hence, this transfer will not happen. The following table provides the number of employees in each team in the fourth month: In the fifth month, T5 will be allotted the challenging project. From a, two SEs will be transferred from T4 to T5. One RE is transferred from T5 to T4. From b. one SE must be transferred from Tl to T5. However, since there are no SEs in T1 this will not happen. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2.

The following table provides the number of employees in each team in the fifth month:

Given that challenging projects has 200 credits and standard projects have 100 credits. In each type of project the credits are equally shared by the employees in the team. Hence, for a challenging project an employee earns 200/5 = 40 credits. For a standard project, an employee earns 100/4 = 25 credits. For the five months, on employee can work in five challenging projects OR four challenging projects and one standard project OR three challenging projects and two standard projects OR two challengmg projects and three challenging projects OR one challenging project and four standard projects OR five standard projects. In each case, an employee Will earn 200 or 185 or 170 or 155 or 140 or 125 credits. Hence. it is not possible for an employee to earn 150 credits. 54. (d) Given that there are 10 SE and 11 RE In the first month, since Tl has one more SE than T2, who in turn has one more SE than T3,... till T5, the number of SEs in T1, T2, T3, T4 and T5 must be 4, 3, 2, 1 and 0. Also, the team that is assigned the challenging project has one more employee than the rest. Hence, the team that is assigned the challenging project will have 5 employees, while the other teams will have 4 employees. Since T1 is assigned the challenging project in the first month, Tl will have 5 employees, and the other teams will have 4

employees each. The following table provides the composition of the teams in the first month:

In the second month, T2 will be allotted the challenging project. From a, two SEs will be transferred from Tl to T2. One RE is transferred from T2 to T1. From b, one SE will be transferred from T1 to T5, one RE will be transferred from T5 to Tl. Similar transfers will happen between T2 and T4. The following table provides the number of employees in each team in the second month:

In the third month, T3 will be allotted the challenging project. From a, two SEs will be transferred from T2 to T3. One RE is transferred from T3 to T2. From b, one SE will be transferred from Tl to T5, one RE will be tramferred from T5 to Tl. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2. The following table provides the number of employees in each team in the third month:

In the fourth month, T4 will be allotted the challenging project. From a, two SEs will be transferred from T3 to T4. One RE is transferred from T4 to T3.

From b, one SE must be transferred from T1 to T5. However. Since there are no SEs in T1, this will not happen. Also, one SE must be transferred from T2 to T4 and one RE must be transferred from T4 to T2. However, there are no REs in T4. Hence, this transfer will not happen. The following table provides the number of employees in each team in the fourth month: In the fifth month, T5 will be allotted the challenging project. From a, two SEs will be transferred from T4 to T5. One RE is transferred from T5 to T4. From b, one SE must be transferred from Tl to T5. However, since there are no SEs in Tl, this will not happen. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2. The following table provides the number of employees in each team in the fifth month:

Since Aneek secured 185 credits he worked in four challenging projects and one standard project. Option A: Aneek could have worked in Tl in first month an challenging project, T2 in second month (in challenging project), T3 in third month (in challenging project), T4 in fourth month (in challenging project) and fifth month (in standard project). Hence, this is possible. Option B: Aneek could have worked in T1 in first month (in challenging project), T2 in second month (in challenging project), T4 in third month (in standard project), T4 in fourth month (in challenging project) and T5 in fifth month (in challenging project). Hence, this is possible. Option C: Aneek could have worked in T2 in first month (in standard project), T2 in second month (in challenging project), T3 in third month (in challenging project), T4 in fourth month (in challenging project) and T5 in fifth month (in challenging project). Hence, this is possible. Option D: Aneek could hove worked in T1 in first month (in challenging project). He can work in Tl or T5 in the second month. In either case, he cannot work in T3 without working in T2 first. In if we assume, he worked in T3 in the first month, he could not have worked in four teams in the five months. Similarly, we can rule out the other possibilities for this option. Hence, this is the answer. 55. (c) The height of the platforms given is as below

The number of person who can be reached by just one individual is circled

A total of 7 persons can be reached by just one individual. 56. (d) For individual at a platform of height 1, they cannot be reached by anyone as candition (ii) will be violated. 57. (c) the height of the platforms given as below.

Only in the fourth column can we find two individuals who can not be reached by anyone. In the fourth column the individual at height 2 and the individual at height 1 can not be reached by any one. 58. (c) According to platform height tableStatement 1 is wrong as no individual in row 1 can be reached by 5 or more Same as statement 2 and 1 wrong Only statement 3 correct. 59. (c) Number of ways of selecting two cities from ten cities - 10C2

= Hence the minimum no. of flights that must be scheduled = 45 × 4 = 180 60. (c) Let the ten cities be represented by A through J. Among these ten cities, consider A, B and C to be hubs and the other seven cities to be non-hub cities. It is given that any direct flight should originate and terminate at a hub. Total flight from D = 4 × 3 = 12 [ Only for A, B, C] Non hub city flight = 12 × 7 = 84 [ for other then A, B, C] Total flight = 12 + 84 = 96 61. (40) Given that G1 has the cities A, B and C. G2, G3 and G4 have 3, 2 and 2 cities respectively. From the given conditions, we can see that a city in G2 cannot be connected by a direct flight to a city in G3 or G4. Hence, for a person to travel from a city in G2 to a city in G3 or G4, all the citres in G2 must be connected to A and from A, he can travel to B or C to travel to a city G3 or G4 respectively. Hence, the 3 cities in G2 must be connected to A between each pair of cities there must be four flights. Hence, there must be 4 × 3 = 12 flights between cities in G2 and A. Since there are 2 cities in G3, there must be 2 × 4 = 8 flights between cities in G3 and 8. Since there are 2 cities in G4, there must be 2× 4 = 8 flights between cities in G4 and C. Also, the cities in G1, i.e., A, B and C must be connected to each other Hence, there must be an additional 4 × 3 = 12 flights between these three cities. Therefore, the total minimum number of direct flights that must be scheduled =12 + 8 + 8 + 12 = 40 62. (4) It is given that the cities in G2 will be assigned to G3 or G4. However, this, by itself, will not result in any reduction in the number of flights because the cities in G2 will still have to be connected to either 8 or C.

However, it is also given that there are now flights between A and C. Hence, the 4 flights that would have been scheduled in the previous case, will now not be scheduled. Hence, the reduction in the number of flights can be a maximum of 4. 63. (2) As there are four cars and as the time through each route is nearly the same, two cars should go through A–M–B and the other two through A–N–B. In case three cars are directed to go through any of the routes, one of the three cars can break the police order and reduce its travel time.

64. (b)

According to the police order 2 cars each would pass through A–M–B and A–N–B. Then time taken through A–M–B = 29.9 and time taken through A–N–8 = 30.0 ∴ Difference = 0.1 65. (2) Original time (A–N–B) = 21 + 12 = 33 (three cars) New time = 12 + 20.9 = 32.9 If one car is directed through M–N, one of the car directed through M–B can break the Police order and go through M– N and save time as shown– original time (A–M–B) = 12 (3 cars) + 20.9 = 32.9 New time (A–M–N–B) = 12 + 8 + 12 = 32 Minutes ∴ Only two cars must be directed through M–N

Such that any car breaking the Police order can not reduce the travel time. 66. (b) When all cars follow the Police order the time taken would be A–M–B (1 car) = 12 + 20 = 32 minutes. A –M–N–B (2 cars) = 12 + 8 + 12 = 32 minutes. A–N–B (1 car) = 20 + 12 = 32 minutes. 67. (20) Let Barun’s age be = 10x Arun’s age will be = 4x. The difference of these age in 6x When Arun’s age is 50% of Barun’s age, this difference also would be 50% i.e. Barun’s age at that stage would be 12x. It would be increase by 20% 68. (15) Work ⇒ [1 + 2 + 3 + ... n] = 1

⇒ ⇒

∑n = 120

⇒

= 120

⇒ n = 15 69. (11) Number of people in the group can not exceed = 11 70. (20)

⇒

D = S×(T + 1/6) D = 12 71. (70,000)

= 20 km

Let total monthly salary = ` x, Now f.d = x/2 stocks = 0.3 × Bank A/c = –

– 0.3 × = 59500

x = 70, 000 72. (d) Let retail price be 100 Discount = 15 S.P = 85 C.P =

for make 2 % profit

C.P =

for making 20% profit

The seller must sell at the retail price 73. (b) Let the speed of the boat in still water and the speed of the river be u and v respectively u=x v=y

or u : v =

74. (a)

[multiply by 9

in first row and multiply by 5 in second row] c5 – c1 = 19, the numbers above are the actual profits the total profit = 438 crore. 75. (d) Let the no. of boys appearing for the admission test be b % of candidates who get admission. = 35% 76. (a) Let the total no. of popcorn pockets in stock be total no. of chips pockets in stock = T required ratio =

= 77. (b)

=1:1 Let the price of each good mango be = x

price of medium quality mango = Total cost price = 80 x +

= 100x

Total selling price = 120 × 0.9x =108x over all profit = 8% 78. (d) Let the printed price be P if 40% discount is given, selling price = 0.6 × 60P = 36P

In order to make a profit of 20% the selling price Total C.P = = 30P Ten toys are destroyed in the fire, the remaing toys are sold at a price such that the same amount of profit is made as in the conditional caseProfit make on remaining toys = 6P total selling P of remaining toys = 36P Discount = 50P – 36P = 14P Discount = 28% 79. (d)

= 9 and

we get 4 cases a + 3 = 3b a + 3 = – 3b a – 1 = 2b – 2 a – 1 = 2b – 2 a + 3 = – 3b a – 1 = – 2b + 2 a + 3 = – 3b a – 1 = – 2b + 2 Solved each case i.e. a = – 15 b=–6 ∴ 80. (a)

(i) (ii) (i) (ii) (i) (ii) (i) (ii)

Let the average score of the boys in the midsemester examination be b average score of the girls = b + s in the exam, average score of the girl = b + 5 – 3 =b+2

average score of the entire class increased by 2 and is hence + 2 i.e b + 5 Average score of the boys = b + 9.5 ⇒

Increase in average of boy is 9.5

81. (c)

Area = =8

82. (b)

Area of GBC =

Area of remaing part = = = =

(area of ∆ABC) × Area of ∆ABC

83. (b)

enclosed Area = Area of semi circle BQC with centre O – Area of Arc BPC with O Now, Area of triangle ABC + BPCO (Arc) = Area of Quarter circle (ABPC)

Area of BPCO = 9π –18 Put the value in equation (i) enclosed Area = = 18 sq cm 84. (b) Volume ratio of 5 smaller and original cube = 1:1 : 8 : 27 : 27 : 64 side ratio of 5 smaller and original cube =1:1:2:3:3:4 Surface area ratio of 5 smaller and original cube = 1 : 1 : 4 : 9 : 9 : 16 Sum of smaller cube (surface area) = 24 parts. big cube = 16 parts. The sum is 50% greater. 85. (6) The height of cylinder (h) = 3 volume = 9π πr2h = 9π r= radius of the ball (R) = 2 height of O (centre of ball) a = 1 (say)

height of topmost point = n + a + R =3+1+2=6 86. (24) In a 3, 4, 5 triangle the length of the altitude to the Hypotenuse =

= 2.4

therefore in a 15, 20, 25 triangle it is 1.2. This is the shortest distance from A to BC. At 60 km/hr i.e. 1 km/min It would be take 24 min to cover 24 km. 87. (a) log3x = a, x = 3a log12y = a, y = 12a xy = 36a G xy = G = 6a ∴ log6 G = a 88. (d) x2 – x – 1 = 0 x= 2x4 =

( =7+3

89. (c) =

–7

= =– ⇒ 90. (b)

1 – 1/6 ⇒

92x–1 – 81x–1 = 1944 = 1944

92x

= 1944

x > 0)

92x – 2 = 243 ⇒ 34x – 4 = 35 4x – 4 = 5 ⇒ x = 91. (b)

x = 25 + y + z Possible value table below. 27 ≤ x ≤ 40

The no. of solution is 1 + 2 + ... + 12 + 11 + 10 = 99 92. (11) (n – 5)(n – 10) –3 (n – 2) ≤ 0 ⇒ n2 – 18n + 56 ≤ 0 (n – 4) (n – 14) ≤ 0 As n is an integer n can be 4, 5, 6, 7 .... 14 have 11 values. 93. (24) x2 + 11x + n = x ⇒ x2 + 10x + n = 0 x2 + 10x + 25 = 0 has real and equal roots. x2 + 10x + n = 0 where n > 25 has complex roots. maximum value of n for real roots = 24 94. (2) a + b + c + d = 30 (a – b)2 + (a – c)2 + (a – d)2 would have minimum if a = 8, b = 8, c = 7, d = 7, or a = 8 b = 7, c = 8, d = 7 or a = 7, b = 8, c = 7, d = 8, or a = 7, b = 7, c = 8, d = 8. or a = 8, b = 7, c = 7, d = 8 or a = 7, b = 8, c = 8 d = 7 minimum value = 1 + 1 = 2

95. (160)

Total 11 point formed triangle = 11C3 – colinear point group = =

–5

–5 ⇒ 165 – 5 = 160

96. (a)

97. (a)

shortest distance according graph = 1 y = |x – 1| + | x + 1 | let x, – 1 ≤ x ≤ 1 y=–x+1+x+1⇒y=2 (a + 6d)2 = (a + 2d)(a + 16d) a2 + 12ad + 36d2 = a2 + 18ad + 32d2 4d2 = 6ad =

⇒a:d=2:3

98. (a)

After giving are eraser to each of the 4 kids there are 3 left, They can split 2, 1 or 1, 1, 1 (No kid can get 4) so, 4p2 + 4c3 = 16 ways. 99. (a)

f (x) = g (x) = x2 – 2x – 1 f (3) =

⇒

g (f ( f (3))) = (3)2 – 3 × 2 – 1 = 9 – 6 – 1 = 9 – 7 = 2 100. (b) a1 = 3, a2 = 7, d = 4 Sn = Sn = S3n

(2a + (n – 1)d)

(2 × 3 +(n – 1)4) ⇒

⇒ n(2n + 1)

(6 + (3n – 1) 4) = 1830

n(6n + 1) = 610 6n + n – 610 = 0 solved, n = 10 Now, m (a1 + a2 + .... an) > 1830 2

m> m > 8.7 ⇒ m > 9

⇒m>

1. (a) (b) (c) (d) 2.

(a) (b) (c) (d) 3. (a) (b) (c) (d) 4.

What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24? (1994) 264 259 269 None of these Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12 and 16 will leave the same remainder 4 (1994) 137 1361 140 172 Two positive integers differ by 4 and sum of their reciprocals is 10/21. Then one of the number is (1995) 3 1 5 21 Three bells chime at an interval of 18, 24 and 32 minutes respectively. At a certain time they begin to chime together. What length of time will elapse before they chime together again? ( 1995)

(a) (b) (c) (d) 5. (a) (b) (c) (d) 6. (a) (b) (c) (d) 7.

(a) (b) (c) (d) 8.

2 hours 24 minutes 4 hours 48 minutes 1 hour 36 minutes 5 hours For the product n(n+1)(2n+1), n ∈ N, which one of the following is not necessarily true? (1995) It is always even. Divisible by 3. Always divisible by the sum of the square of first n natural numbers Never divisible by 237. The remainder obtained when a prime number greater than 6 is divided by 6 is (1995) 1 or 3 1 or 5 3 or 5 4 or 5 Cost of 72 hens is ` .....96.7..... Then, what will be the cost of hen, where two digits in place of “ ....... ” are not visible or are written inillegible handwriting? (1995) ` 3.23 ` 5.11 ` 5.51 ` 7.22 Three consecutive positive even numbers are such that thrice the first number exceeds double the third number by 2 then the third number is (1995)

(a) (b) (c) (d)

10 14 16 12

–

divisible

(1995) (a) (b) (c) (d) 10. (a) (b) (c) (d) 11. (a) (b) (c) (d)

13 31 5 None of these If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be (1996) 7, 8 8, 0 5, 8 None of these If n is any odd number greater than 1, then n(n2 – 1) is ( 1996) divisible by 48 always divisible by 24 always divisible by 6 always None of these

12. Find

the

value

(1996) (a) 13/7 (b) 15/7 (c) 11/21 (d) 17/28 Directions for questions 13 & 14 : Read the information given below and answer the questions that follow :

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs 1148, but the inventory reduced by 54. 13. What is the actual price per piece ? (1996) (a) (b) (c) (d) 14.

82 41 56 28 What

the

actual

quantity

sold

(1996) (a) (b) (c) (d) 15.

(a) (b) (c) (d) 16.

28 14 82 41 If n is an integer, how many values of n will give an integral value of (16n2 + 7n + 6) / n? (1997) 2 3 4 None of these A student, instead of finding the value of 7/8th of a number, found the value of 7/18th of the number. If his answer differed from the actual one by 770, find the number. (1997)

(a) (b) (c) (d)

1584 2520 1728 1656

17. If m and n are integers divisible by 5, which of the following is not necessarily true? (1997) (a) m – n is divisible by 5 (b) m2 – n2 is divisible by 25 (c) m + n is divisible by 10 (d) None of these 18. Which of the following is true? (1997) (a) (b) (c) (d) None of these 19. P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R. (1997) (a) 5 (b) 7 (c) 9 (d) 11 20. A, B and C are defined as follows : (1997)

Which of the following is true about the value of the above three expressions? (a) All of them lie between 0.18 and 0.20

(b) (c) (d) 21.

(a) (b) (c) (d) 22.

(a) (b) (c) (d) 23.

I. II. III. (a) (b) (c) (d) 24. (a) (b) (c)

A is twice of C C is the smallest B is the smallest P and Q are two integers such that (PQ) = 64. Which of the following cannot be the value of P + Q? (1997) 20 65 16 35 Five digit numbers are formed using only 0,1,2,3,4 exactly once. What is the difference between the maximum and minimum number that can be formed? (1998) 19800 41976 32976 None of these n3 is odd. Which of the following statements is/are true? (1998) n is odd n2 is odd n2 is even I only II only I and II only I and III only (BE)2 = MPB, where B, E, M and P are distinct integers, then M =? (1998) 2 3 9

(d) None of these 25. Three wheels can complete respectively 60,36,24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again? (1998) (a) 5/2 seconds (b) 5/3 seconds (c) 5 seconds (d) 7.5 seconds 26. A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29. (1998) (a) 5 (b) 4 (c) 1 (d) Cannot be determined 27. A is the set of positive integers such that when divided by 2,3,4,5 and 6 leaves the remainders 1,2,3,4 and 5 respectively. How many integer(s) between 0 and 100 belongs to set A? (1998) (a) 0 (b) 1 (c) 2 (d) None of these 28. Number of students who have opted the subjects A, B, C are 60, 84, 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions? (1998) (a) 28 (b) 60

the

digit

the

unit

place

251

(1998) (a) (b) (c) (d) 30.

(a) (b) (c) (d) 31. I. II. III. (a) (b) (c) (d) 32.

2 8 1 4 A hundred digit number is formed by writing first 54 natural numbers in front of each other as 12345678910111213.................5354. Find the remainder when this number is divided by 8 (1998) 4 7 2 0 If n = 1 + x, where ‘x’ is the product of four consecutive positive integers, then which of the following statements is/are true? ‘n’ is odd ‘n’ is prime ‘n’ is perfect square (1999) I only II only III only I & III only

(1999) (a) 1246789 (b) 12345321 (c) 1111111

(d) 111111111 33. When 784 remainder?

divided

342,

what

the

(1999) (a) (b) (c) (d) 34.

0 1 49 341 A, B, C are three distinct digits. AB is a two digit number and CCB is a three digit number such that (AB)2 = CCB where CCB > 320. What is the possible value of the digit B? (1999) (a) 1 (b) 0 (c) 3 (d) 9 35. For the given pair (x, y) of positive integers, such that 4x – 17y = 1 and x 1000, how many integer values of y satisfy the given conditions (1999) (a) 55 (b) 56 (c) 57 (d) 58 36. Convert 1982 in base 10 to base 12 (2000) (a) 1129 (b) 1292 (c) 1192 (d) 1832 37. Let D be a recurring decimal of the form D = 0.a1 a2 a1a2a1a2.............where a1 and a2 lie between 0 and 9. Further at most one of them is zero. Which of the following numbers

(a) (b) (c) (d) 38. (a) (b) (c) (d) 39. (a) (b) (c) (d) 40.

(a) (b) (c) (d) 41.

(a) (b)

necessarily produces an integer when multiplied by D? (2000) 18 198 100 288 P is the product of all the prime numbers between 1 to 100. Then the number of zeroes at the end of P are (2000) 1 24 0 none of these N = 1421 × 1423 × 1425 what is the remainder when N is divided by 12? (2000) 0 1 3 9 xn is either –1 or 1 & n 4; If then n can be (2000) odd even prime can’t be determined There are two integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder. What is the value of n? (200 0) 298 307

(c) 461 (d) can’t be determined 42. If x, y and z are odd integers then which of the following is necessarily false? (2000) (a) xyz is odd (b) (x – y) z is even (c) (x – y) (z + y) x is even (d) (x – y – z) (x + z) is odd 43. is divisible by (a) 44.

(a) (b) (c) (d) 45.

(a) (b) (c) (d) 46.

(2000) both 3 and 13 (b) both 7 and 17 (c) both 3 and 17 d) both 7 and 13 Out of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least (2001) 5 103 6 Cannot be determined In a 4 - digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number? (2001) 5 8 1 4 Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by

540. product?

What

the

new

(2001) (a) (b) (c) (d) 47.

1050 540 1440 1590 In a number system the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes (2001) (a) 406 (b) 1086 (c) 213 (d) 691 48. Every ten years the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri (2001) Chota Hazri has 4,522 fewer males than Mota hazri. Mota Hazri has 4,020 more females than males. Chota Hazri has twice as many females as males. Chota Hazri has 2,910 fewer females than Mota Hazri. What is the total number of males in Chota Hazri? (a) 11264 (b) 14174 (c) 5632 (d) 10154 49. Let x, y and z be distinct integers. x and y are odd positive, and z is even positive. Which one of the following statements can not be true? (2001) (a) y is even

(b)

is odd

(c) (x – z)y is odd (d) is even 50. Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is (2002) (a) (b) (c) (d) 51.

24 54 34 45 When be

2256

divided

the

remainder

would

(2002) (a) (b) (c) (d) 52.

1 16 14 None of these At a book store, “MODERN BOOK STORE” is flashed using neon lights. The words are individually flashed at intervals of seconds respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is (2002)

(a) (b) (c) (d) 53.

49.5 seconds 73.5 seconds 1742.5 seconds 855 seconds After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same

number? (2002) (a) (b) (c) (d) 54.

80 76 41 53 If u, v, w and m are natural numbers such that um + vm = wm, then one of the following is true (2002)

(a) (b) (c) (d) None of these 55. 76n – 66n, where by

integer

divisible

(2002) (a) (b) (c) (d) 56.

(a) (b) (c) (d) 57.

(a)

13 127 559 All of these A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals (2003C) 31 63 75 91 How many even integers n, where are divisible neither by seven nor by nine? (2003C) 40

(b) (c) (d) 58.

37 39 38 The number of positive integers n in the range that the product is not divisible by n is

such

(2003C) (a) (b) (c) (d) 59.

5 7 13 14 What ?

the

remainder

when

divided

(2003) (a) 0 (b) 2 (c) 3 (d) 4 Directions for Questions 60 to 62 : Answer the questions on the basis of the information given below. The seven basic symbols in a certain numeral system and their respective values are as follow : I = 1 , V = 5 , X = 10, L = 50, C = 100, D = 500, and M = 1000 In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols. For example , XXVII = 10 + 10 + 5 + 1 + 1= 27. An exception to the left to right reading occurs when a symbol is followed immediately by a symbol of greater value; then, the smaller value is subtracted from the larger. For example, XLVI = (50 – 10) + 5 + 1 = 46.

60. The is

value

the

numeral

MDCCLXXXVII

(2003) (a) (b) (c) (d) 61.

1687 1787 1887 1987 The is

value

the

numeral

MCMXCIX

(2003) (a) (b) (c) (d) 62.

I. II. III. IV. (a) (b) (c) (d) 63.

(a) (b) (c) (d)

1999 1899 1989 1889 Which of the following can represent the numeral for 1995? (2003) MCMLXXV MCMXCV MVD MVM only I and II only III and IV only II and IV only IV What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7? (2004) 666 676 683 777

64. Let x and y be positive integers such that x is prime and y is composite. Then (2004) (a) y – x cannot be an even integer (b) xy cannot be an even integer. (c) (x + y)/x cannot be an even integer (d) None of the above statements is true. 65. Let n( > 1) be a composite integer such that is not an integer. Consider the following statements (2004) I : n has a perfect integer-valued divisor which is greater than 1 and less than . II : n has a perfect integer-valued divisor which is greater than but less than n Then, (a) Both I and II are false (b) I is true but II is false (c) I is false but II is true (d) Both I and II are true 66. Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer? (2004) (a) (b) (c) (d)

67. If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is (2004) (a) one (b) two (c) three (d) more than three 68. The remainder, when (1523 + 2323) is divided by 19, is (2004 - 2 marks) (a) 4 (b) 15 (c) 0 (d) 18 69. If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of (2005) (a) 0 (b) 1 (c) 69 (d) 35 70. The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B–A is perfectly divisible by 7, then which of the following is necessarily true? (2005 - 2 marks) (a) 100 < A < 299 (b) 106 < A < 305 (c) 112 < A < 311 (d) 118 < A < 317 71. The rightmost non-zero digit of the number 302720 is (2005 - 2 marks)

(a) (b) (c) (d)

1 3 7 9

72.

then (2005) (a) (b) (c) (d) R > 1.0 73. For a positive integer n, let pn denote the product of the digits of n, and sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which pn + sn = n is (2005) (a) 81 (b) 16 (c) 18 (d) 9 74. If x = –0.5, then which of the following has the smallest value? (2006) (a) (b) (c)

(d) 2x

(e)

75. Which one among 21/2, 31/3, 41/4, 61/6 and 121/12 is the largest? (2006) (a) 21/2 (b) 31/3 (c) 41/4 (d) 61/6 (e) 121/12 76. Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? (2007) (a) 1 (b) 3 (c) 2 (d) 4 (e) 0 77. How many pairs of positive integers m, n satisfy where

(a) (b) (c) (d) (e) 78.

odd

integer

less

than

60? (2007) 3 6 4 7 5 The integers 1, 2, ...., 40 are written on a blackboard. The following operation is then repeated 39 times; In each repetition, any two numbers, say a and b, currently on the blackboard are

(a) (b) (c) (d) (e) 79.

(a) (b) (c) (d) (e)

erased and a new number a + b – 1 is written. What will be the number left on the board at the end? (2008) 820 821 781 819 780 How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed? (2008) 499 500 375 376 501

80. What

are

the

last

two

digits

? (2008) (a) (b) (c) (d) (e) 81.

21 61 01 41 81 How many numbers are there between 0 and 1000 which on division by 2, 4, 6, 8 leave remainders 1, 3, 5, 7 respectively? (2009) (a) 21 (b) 40 (c) 41

(d) 39 82. N! is completely divisible by 1352.What is sum of the digits of the smallest such number N? (2009) (a) 11 (b) 15 (c) 16 (d) 19 83. If ‘x’ is a real number then what is the number of solutions for the equation (2009) (a) (b) (c) (d) 84. (a) (b) (c) (d) 85.

(a) (b) (c) (d) 86.

0 1 2 3 If S = 12 – 22 + 32 – 42 + ..... – 20002 + 20012, then what is the value of S? (2009) 2001300 2003001 2010301 2000031 If 7103 is divided by 25, then the remainder is (2009) 20 16 18 15 In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in the third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also include four animals grazing in all the three sectors are now transported to another zoo, find the total number of animals. (2009)

(a) (b) (c) (d) 87.

(a) (b) (c) (d) 88.

(a) (b) (c) (d) 89.

38 56 54 None of the above A person closes his account in an investment scheme by withdrawing ` 10,000. One year ago he had withdrawn ` 6000. Two years ago he had withdrawn ` 5000. Three years ago he had not withdrawn any money. How much money had he deposited approximately at the time of opening the account 4 years ago, if the annual simple interest is 10% ? (2009) ` 15600 ` 16500 ` 17280 None of these P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R. (2009) 5 7 9 11 If ‘n’ is a natural number then the greatest integer less than or equal to

(a) (b) (c) (d) 90.

(2010)

even. odd. even when ‘n’ is even and odd when ‘n’ is odd. even when ‘n’ is odd and odd when ‘n’ is even. If x and y are positive integers, then the last digit of which of the following is same as the last digit of the sum of x and y? (2010) (a) x7 + y7

(b) (c) (d) 91.

(a) (b) (c) (d) 92. (a) (b) (c) (d)

x13 + y13 x20 + y20 None of these If ‘a’ is one of the roots of x5– 1 = 0 and a ≠1, then what is the value of a15 + a16 + a17 +.......a50? (2010) 1 5a 35 None of these What is the number of non-negative integer solutions for the equation x2 – xy + y2 = x + y? (2010) 3 4 1 None of these

93. The

last

digit

is (2010) (a) (b) (c) (d) 94.

0 4 8 2 Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide ` 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to ` 21 lakhs each when they reach the age of 21. He is looking for plan that will give him a simple interest per annum. The rates of interest of the plans for his younger son and elder son should be

(2010) (a) 5% and 7.5% respectively

(b) (c) (d) 95.

8% and 12% respectively 10% and 15% respectively 20% and 30% respectively Let S denote the infinite sum , where | x | < 1 and the coefficient equals

Then

(2010)

(a) (b) (c) (d) 96.

is a sequence where

X≠1 (2011) What is the least value of X for which HCF (Numerator, Denominator) = 1 for each term of the given sequence? (a) 17 (b) 13 (c) 11 (d) None of these 97. A positive integer is equal to the square of the number of factors it has. How many such integers are there? (2011) (a) 1 (b) 2 (c) 3

(d) Infinite 98. (x – 1)(x – 2)(x – 3) = 6y. How many integer solutions exist for the given equation? (2011) (a) 0 (b) 1 (c) 2 (d) More than 2 99. All the two-digit natural numbers whose unit digit is greater than their ten’s digit are selected. If all these numbers are written one after the other in a series, how many digits are there in the resulting number? (2012) (a) 90 (b) 72 (c) 36 (d) 54 100. There are five consecutive integers a, b, c, d and e such that a < b < c < d < e and a2 + b2 + c2 = d2 + e2. What is/are the possible value(s) of b? ( 2012) (a) 0 (b) 11 (c) 0 and – 11 (d) –1 and 11. 101. A sequence of terms is defined such that What is the value of (2012) (a) 2551 (b) 2753 (c) 2601 (d) 2451 102. 500! + 505! + 510! + 515! is completely divisible by 5n, where n is a natural number. How many distinct values of n are

possible? (2012) (a) 120 (b) 121 (c) 124 (d) 125 103. The number 44 is written as a product of 5 distinct integers. If ‘n’ is the sum of these five integers then what is the sum of all the possible values of n?

(a) (b) (c) (d)

(2012) 11 23 26 32

104. Arrange

the

numbers

and

ascending

order. (2013) (a) (b) (c) (d) None of these 105. If E = 3 + 8 + 15 + 24 + … + 195, then what is the sum of the prime factors of E? (2013) (a) 29 (b) 31 (c) 33 (d) 23

106. ‘ab’ is a two-digit prime number such that one of its digits is 3. If the absolute difference between the digits of the number is not a factor of 2, then how many values can ‘ab’ assume? (2013) (a) 5 (b) 3 (c) 6 (d) 8 107. The number of factors of the square of a natural number is 105. The number of factors of the cube of the same number is ‘F’. Find the maximum possible value of ‘F’. (2013) (a) 208 (b) 217 (c) 157 (d) 280 108. How many natural numbers divide exactly one out of 1080 and1800, but not both? (2013) (a) 20 (b) 42 (c) 24 (d) 36 109. If f(n) = 14 + 24 + 34 + ... + n4, then how can 14 + 34 + 54 + ... + (2n – 1)4 be expressed? (2014) (a) f(2n – 1) – 16 × f(n) (b) f(2n – 1) – 8 × f(n) (c) f(2n) – 16 × f(n) (d) f(2n) – 8 × f(n) 110. The number of APs with 5 distinct terms that can be formed from the first 50 natural numbers is (2014) (a) 325

(b) 300 (c) 375 (d) 288 111. The ratio of two numbers whose sum is 600 is 7 : 8. What is the LCM of the given two numbers? (2014) (a) 1120 (b) 560 (c) 2240 (d) 1152 112. The sequence P1, P2, P3, ..... is defined by P1 = 211, P2 = 375, P3 = 420, P4 = 523, and Pn = Pn−1 – Pn− 2 + Pn − 3 – Pn − 4 for all n 5. What will be the value of P531 + P753 + P975? (2014) (a) 898 (b) 631 (c) 364 (d) 544 113. Find the number of ways in which a batsman can score 100 runs by scoring runs in 2’s, 4’s and 6’s, such that he hits at least one double, one boundary and one six. (2014) (a) 184 192 1. 2.

(b) (d) 208

185

(c)

(b) Required no. = LCM of ( 8, 11, 24 ) –5 = 264 – 5 = 259 (d) Suppose least no. be x or 1856 – x = n (336)+ 4 we should take n = 5 so that n(336) is nearest to 1856and n (336)< 1856 1856 – x = 1680 + 4 = 1684 x = 1856 – 1684 = 172 (a) Let two positive integers be x and y. ∴ x–y=4 .....(i)

and 4. 5. 6.

.....(ii)

It is clear from second equation that x and y will be3 and 7. (b) L.C.M of 18, 24 and 32 = 288 Hence they would chime together after every 288 min. or 4 hrs. 48 min. (d) It is clear that for n = 237 the expression n(n + 1)(2n + 1) is divisible by 237. Hence option (d) is not necessarily true. (b) It is clearly 1 or 5 Example : 7 divided by 6 leaves remainder 1 11 divided by 6 leaves remainder 5 13 divided by 6 leaves remainder 1. (c) Multiply each option by 72 and find out the result which matches the visible digits. Clearly we see (b) Let be the 3 consecutive numbers then, 3 (x – 2) = 2 (x + 2) + 2 (according to the question) or Hence, the 3rd no. is 14. (b)

which is divisible by 31 10. (b) According to the question, the number is divisible by 8 and 9. For the number to be divisible by 8, its last three digits have to be divisible by 8. This 960 and 968 can be the possibilities. For the number to be divisible by 9, the sum of the digits of the number should be divisible by 9. Hence, it can be possible if B = 8 and A = 9 and ifB = 0 and A = 8. Hence, (8, 0) is the possible values of A and B. 11. (b) n is an odd no. > 1 ∴ The minimum possible value of n = 3 2 n (n – 1) = 3 × 8 = 24

Hence, n(n2 – 1) is divisible by 24 always

12. (b)

For Qs. 13-14. Let quantity sold = q ; price = p and p’, q’ be the wrong price and quantity respectively and q’ = q + 54 pq = sales = Rs 1148 = p’q’ .....(i) 13. (b) As q is an integer, both p and p’ must divide 1148. Now checking the options : (a) 1148 is divisible by 82 and 28 but does notsatisfy (i) (b) 1148 is divisible by 41 and also by 14. It givesq = 28 and satisfies (i) (c) 1148 is divisible by 56 and not by 65 and does not satisfy (i). (d) 1148 is also divisible by 28 and 82 but does not satisfy (i). 14. (a) From option (b) of previous question, 28 is the quantity sold and the price is Rs 41. Alternatively : q’ = q + 54, which is only possible in case of 28 and 82 as given in options.

q = 28 and q’ = 82. Therefore p = 15. (c)

( n is an integer)

Hence, to become the entire expression an integer be an integer and

can be an integer

for n = 1, n= 2, n= 3 and n = 6 Hence, n will have only four values. 16. (a) Let the number be x

∴ x = 1584 17. (c) If m & n are integers divisible by 5. Then, (m + n) might be or might not be divisible by 10. The only number satisfying the given condition212 = 441. So, B = 1. 35. (d) , and given that Hence we can say that i.e., y 235 Further also note that every 4th value of y (e.g. 3, 7, 11, ......) will give an integer value of x. So, number of values of y =

= 58

should

36. (c) Thus, 1982 (10) = 1192 (12) 37. (b) Multiplied by 100 on both side 100D = a1a2 . D

38.

39.

40.

41.

Required number should be the multiple of 99. So we can get an integer when multiplied by D. Hence, 198 is the required number. (a) There are only 2 prime numbers 5 & 2 between 1 & 100 which when multiplied will give zero in the end. Thus there will be only one zero at the end of the product of given number. (c) , when these numbers are divided by 12 we have remainders as 5, 7, 9. The product of remainders when divided by 12 gives 3 as its remainder. Thus when N divided by 12remainder is 3 (b) Every term in the question is either 1 or –1. In order to have zero the number of terms must be even. Note that there are n number of terms. (since the first term in each product varies from x1 to xn). So n has to be even. (b) Let the common remainder be x. Then numbers(34041 – x) and (32506 – x) would be completely divisible by n. Hence the difference of the numbers (34041 – x) and (32506 – x) will also be divisible by n or (34041 – x – 32506 + x) = 1535 will also be divisibleby n. Now, using options we find that 1535 is divisible by 307.

42. (d) Consider in which first term is odd and second term is even and the product of even and odd is always even. ∴ It is necessarily false. 43. (c) N = 553 + 173 – 723 = (54 + 1)3 + (18 – 1)3 – 723 or N = (51 + 4)3 + 173 – (68 + 4)3 These two different forms of given expression is divisible by 3 and 17 both. Alternatively: Let a = 55, b = 17, c = –72 ∴ a + b + c = 55 + 17 – 72 = 0 ∴ a3 + b3 + c3 = 3abc = 3(55) (17) (–72) Hence it is divisible by 3 and 17 both. 44. (a) 128 boxes of oranges each has 120 144 oranges Since we have only 25 options of number of oranges i.e. oranges can count from 120, 121....144, and total boxes are 128. So the boxes with same number of oranges will be boxes. 45. (a) Let ABCD be the 4-digit number According to the question, we have .....(1) .....(2) .....(3) (1) – (2) gives B – D = D Putting in (3), or 3D = 4A + 2D or D = 4A & B = 8A Putting these values in (2), C = A + 4A = 5A This can only be true for A = 1, hence C = 5. 46. (d) Let the other multiplier be x ∴ New product = (53 × 30) = 1590

47. (a) The product of 44 and 11 is 484. But given product of 44 and 11 = 3414 (in number system) Here, This equation is satisfied only when x = 5. In decimal system, the number 3111 can be written as 406 = [3 × 53 + 1 × 52 + 1 × 51 + 1 × 50] 48. (c) Let the total no. of males in Chota Hazri be x. According to the question, No. of female in Chota Hazri = 2x

According to the question, x = 5632 49. (a) x, y, z > 0; x and y are odd, z is even Note : [odd – Even is odd], [odd – odd is even], [odd × odd is odd] Since, (x – z) is odd is also odd and is odd can not be even. 50. (b) Suppose D = 24 ∴ S = (2 + 4)2 = 36 According to the Question If D = 54 then therefore D is 54 51. (a) Consider = 1764 – 64C1.1763.1 +

C2 (17)62 12 +.......+ 64C64.10.1 (Using binomial theorem) For example: If m = 5 and n = 10 then m + n = 15 which is not divisible by 10.

But if m = 5, n = 25 then m + n = 30 which is divisible by 10. 18. (b)

while

Hence, 19.

(c) Let P, Q and R be n, n + 2 and n + 4 respectively in ascending order. According to the Question 3n = 2(n + 4) – 3 = 2n + 5 ∴ n=5 Thus, R = 5 + 4 = 9

20. (d) 21. 22. 23. 24.

25.

;

∴ B is the smallest. (d) Given PQ = 64 = 1 × 64 = 2 × 32 = 4 × 16 = 8 × 8. Corresponding values of P + Q are 65, 34, 20, 16. Therefore, P + Q cannot be equal to 35. (c) Maximum no. = 43210 Minimum no. = 10234 Hence, difference = 43210 – 10234 = 32976 (c) If n3 is odd then n and n2 will also be odd. (b) (BE)2 = MPB If LHS has square, then according to question unit’s digit of RHS can be 0, 1, 4, 5, 6, 9 If B = 0, then (BE)2 cannot be a three digit number If B ≠ 1 then LHS exceeds 3 digits and is not compatible with RHS. So B = 1 ∴ E = 1 or 9 1 is rejected since B & E are distinct integers hence BE = 19 ∴ M = 3 (c) 1st wheel makes 1 rev. per sec 2nd wheel makes

rev. per sec

3rd wheel makes

rev. per sec

In other words 1st, 2nd and 3rd wheel take 1,

and

seconds

respectively to complete one revolution. L.C.M of 1,

and

Hence, after every 5 seconds the red spots on all the three wheels touch the ground. 26. (a) Dividend = Divisor × Quotient + Remainder = 899 Q + 63 Dividend = 29 × 31Q + 29 × 2 + 5 = 29(31Q + 2) + 5 Hence, remainder = 5 when same no. is divided by 29. 27. (b) Note that, Hence, the required number will be of the form LCM of (2, 3, 4, 5, 6) n – 1 where n is any integer. LCM of 2, 3, 4, 5, 6 is 60. Hence the elements of A will be of the form 60n – 1, where n is any integer. Only for n is equal to 1 the number (60 – 1= 59) will be between 0 and 100. Hence, only one integer between 0 and 100 belongs to A. 28. (d) For Subject A – 60 students; Subject B – 84 students; Subject C – 108 students HCF of 60, 84 and 108 is 12. So, each room contain 12 students at minimum. But each room contains students of only 1 subject So, number of rooms

= 21

29. (b) The digit in the unit’s place of 251 is equal to the remainder when 251 is divided by 10. 25 = 32 leaves the remainder 2 when divided by 10. Then 250 = (25)10 leaves the remainder 210 = (25)2 which in turn leaves the remainder 22 = 4.

Then 251 = 250× 2, when divided by 10, leaves the remainder 4 × 2 = 8. Alternatively:

(16)12 gives one’s digit 6 23 = 8 ∴ (16)12 × 23 = one’s digit 6 × 8 = one’s digit = 8. 30. (c) Given number Since 1000 = 8 × 125 So, remainder when 354 divided by 8 be 2 Required remainder = 2. 31. (d) Let the four consecutive number be (a – 2), (a – 1), a,(a + 1). Multiplying these, we get , which will always be even. By the problem we add 1. Thus the expression becomes odd. This is also the perfect square of

, which is .

You can also take any four consecutive numbers and check for the validity. 32. (d) Square root of given number = 111111111 Alternatively: Using Pattern As 112 = 121 1112 = 12321 11112 = 1234321 (111111111)2 = 12345678987654321 33. (b)

is always divisible as it is in the form of . 34. 68.

69.

70.

Hence, the remainder is 1. (a) (AB)2 = CCB. Put value of ‘a’ starting from 3, we will have 3, 5 and 7 as the only set of prime numbers satisfying the given relationships. (c) The expression becomes (19 – 4)23 + (19 + 4)23.All the terms except the last one contains 19 and the last terms get cancelled out. Hence the remainder obtained on dividing by 19 will be 0. Alternatively : an + bn is always divisible by (a + b), if n is odd Here n is odd (23). So the given expression is divisible by 15 + 23 = 38, which is a multiple of 19. (a) Remember that, a3 + b3 = (a + b) (a2 + b2 – ab) x = (163 + 173 + 183 + 193) x = (163 + 193) + (173 + 183) x = (16 + 19) (162 + 192 – 16 × 19) + (17 + 18) (172 + 182 – 17 × 18) x = 35[162 + 192 – 16 × 19 + 172 + 182 – 17 × 18] x = 35 × (Even number) Hence, x is divisible by 70 and leaves remainder as zero. (b) Let the 3 digits of number A be x, y and z Hence A = 100x + 10y + z On reversing the digits of number A, we get the number B i.e., z y x. ∴ B = 100z + 10y + x As B>A⇒z>x ...(i) B – A = 99z – 99x = 99(z – x)

As 99 is not divisible by 7 so (z – x) has to be divisible by 7. ...(ii) Using (i) & (ii), the only possible values of z and x are(8, 1) and (9, 2) So the minimum and maximum range of A are 108 and 299, which 71. (a) The number 302720 will have 2720, zero’s. For the right most non-zero digit we have to check the power cycle of 3 and find when their multiplication again leads to a 3 as the right most digit. 31 = 3; 32 = 9; 33 = 27; 34 = 81; 35 = 243 Hence, 3 will appear after every fourth power of 3. Hence, 302720 = 32720 × 102720 = (34)680 × 102720 As the number 2720 is an exact multiple of 4, hence the last digit will be 1 similar to what we find in 34. 72. (d) As xn – yn is divisible by x – y if n is odd. xn – yn = (x – y) (xn – 1y0 + xn – 2y1 +..........+ x0yn – 1) Hence numerator becomes = (30 – 29) (3064 +........+2964) = 3064+........+ 2964

Clearly the numerator is greater than the denominator. Hence R > 1.0 73. (d) The no. can be 2 or 3 digit. Firstly let n be the two digit no. Therefore, n = 10x + y pn + sn = n ⇒ xy + x + y = 10 x + y ⇒ xy – 9x = 0 ⇒ y = 9 as x 0 So the numbers can be 19, 29.........99, i.e., 9 values. For 3 digits n = 100x + 10y + z ⇒ xyz + x + y + z = 100x + 10y + z ⇒

xyz = 99x + 9y

It can be verified using various values of y that this equation do not have any solution. E.g. : For y = 9, x(z – 11) = y which is not possible.So in all 9 integers. 74. (b) Putting the value of x = – 0.5 in all the options. (a)

(b)

(c)

(d)

(e) So, clearly (b) is smallest. 75. (b) In this question it is advisable to raise all the numbers to the power of 12, so the numbers become, or

64, 81, 64, 36, 12

So, 31/3 is the largest. 76. (a) Since in the four digits number first two digits are equal and the last two digits are also equal, therefore we can suppose that the digit at the thousand and hundred place each be x and the digit at the tenth and unit place each be y. Hence, the four digits number = 1000x + 100x + 10y + y = 11(100x + y) This number 11(100x + y) will be perfect square, if100x + y is of the form 11n, where n is a perfect square Now 100x + y = 11n y = 11n – 100x On checking, we get for the value n = 64 (a perfect square) only, y = 704 – 100x, for which a single digit positive integral value 7 of x, the value of y = 4, which is the single digit positive integer. There is no single digit positive integral value of y for any other single positive integral value of x for the equation y = 704 –

100x Hence, 7744 is the only for digits number. 77. (a) 12n + 48m – mn – 576 = – 576 ...(i) Since n is an odd, therefore, (n – 48) is an odd. Also – 576 is an even, therefore (m – 12) is definitely even. Now n is an odd integer less than 60. Hence, on checking, we get all possible value of n are 49, 51 and 57. Therefore, there are three value of n 78. (c) 1 + 2 + 3 + ..... + 40 = = K + 1, where K contains all the multiple terms of 17. Therefore when 2256 is divided by 17, remainder would be 1. Alternatively: When (i) (ii)

Remainder is 1 if n is even. Remainder is x if n is odd. ∴ Remainder is 1.

52. (c) Full name of the bookstore can be read again by taking LCM of the times seconds 53. (d) According to the question the required no. is 3[4 (7x + 4) + 1] + 2 = 84x + 53 So the remainder is 53, when the same number is divided by 84. Alternatively: Let no. be x

x = 3m + 2 m = 4n + 1 n = 7P + 4 Let last quotient = P = 1 x = 3 × 45 + 2 = 137 ∴ 137 84 = R (53) Hence remainder = 53. 54. (c) We have where u, v, w, m are natural numbers Take u = 2, v = 4, w = 6; then This will be true if m = 1 and 1 < min ( 2, 4 , 6) = 2 Hence, m < min (u, v, w) 55. (d) where n is integer > 0 Let n = 1, then This number is divisible by 127, 559 and 13. 56. (d) 63 and 75 are ruled out as their last digit can’t be 1. Converting to base 2, 3, and 5, we get 31 = (11111)2 = (1011)3 = (111)5. Taking 91 = (1011011)2 = (1010)3 = (331)5. In 2 out of 3 cases, the first digit is 1, hence (d). 57. (c) Total even nos. between 100 and 200 (including 100 and 200) = 51 Even nos. divisible by 7 = 7 Even nos. divisible by 9 = 6 There is a common no. divisible both by 7 and 9 = 126 Hence total nos. which are divisible neither by 7 nor by 9 ∴ Even integers n, are divisible neither by 7 nor by 9 = 51– 12 = 39 58. (b) Consider the prime numbers between 12 and 40, which are 13, 17, 19, 23, 29, 31 and 37.

Given product is not divisible by these 7 prime numbers. 59. (d)

; to find the remainder

Let us divide the different powers of 4 by 6 and find the remainder. So remainder for 41 = 4, 42 = 4, 43 = 4, 44 = 4,45 = 4, 46 = 4 and so on. From this we know that remainder for any power of 4 will be 4 only. 60. (b) M D C C L X X X V I I = 1000 + 500 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 = 1787 61. (a) 1000 + 900 + 90 + 9 = 1999 62. (c) M C M L X X V = 1975, M C M X C V = 1995, M V D = 1000 + (500 – 5) = 1495, M V M = 1995 Clearly II and IV can represent the numeral for 1995 63. (b) Number is of the form = 7n + 3; n = 1 to 13 So, Alternatively: No. arc = 10, 17, 24, ............, 94 94 = 10 + (n – 1) × 7

= 676 64. (d) x is prime say 7 y is not prime but composite no. say 8, 9, 21 (a) 9 – 7 = 2

(b) 7 × 8 = 56

(c)

Put x = 2 and y = 6 and check for the options.

By hit and trial all the 3 options can be proved wrong 65. (d) Let n = 6 Therefore Now, the divisor of 6 are 1, 2, 3 If we take 2 as divisor then Statement I is true. If we take 3 as divisor then i.e. Therefore statement II is true 66. (d) Given a = 6b = 12c = 27d = 36e Multiplied and Divide by 108 in whole expression

(say) ⇒ a = 108, b = 18, c = 9, d = 4, e = 3 So it is clear that

contains a number

not an integer 67. (a) a, a + 2, a + 4 are prime numbers. 2(x2– xy + y2) = 2(x + y) ⇒ 2x2 – 2xy + 2y2 = 2(x + y) (x – y)2 + x2 + y2 = 2x + 2y (x –y)2 + (x – 1)2 + (y – 1)2 = 2 ↓ ↓ ↓ 0 1 1 → (A) 1 0 1 → (B) 1 1 0 → (C) Integer solutions for (x, y): Case 1: (0, 0) and (2, 2) Case 2: (1, 2) and (1, 0) Case 3: (2, 1) and (0, 1) So there are six non-negative integer solutions. 93. (b) Consider 34n = (81)n = (1 + 80)n = 1 + 80q, q ∈ N

which is

∴

= 380q + 1 = (81)20q . 3

Since the last digit of (81)20q is 1, so the last digit of

1 is 1 × 3 + 1 = 4 94. (d) For the younger child ` 7.5 lakh should become 21 lakhs in 9 years. Hence, Amount = Principal + Simple Interest 21 = P + 21 = 7.5 21 × 100 = 7.5 × 100 + 7.5 × R1 × 9 7.5 × R1 × 9 = (21 – 7.5) 100 R1 =

= 20%

Similarly, for the elder son, ` 7.5 lakh should become in 6 years. Hence, Amount = Principal + Simple Interest 21 = 7.5 21 × 100 = 7.5 × 100 + 7.5 × R2 × 6 7.5 × R2 × 6 = (21 – 7.5) × 100 R2 = 95. (a) From option (a), Using Binomial here

= 30%

this is same series as given Thus, option (a) is correct answer. 96. (d) The general term is of the form . n(n + 2) is always divisible by (n + 2). So we can say that n(n + 2) ± 1would never be divisible by (n + 2). If we put X = –1, the numerator and denominator of all the terms would be co-prime. 97. (b) One such number is 1 which has no factor other than itself. If the number has only one prime factor i.e. it is of the form pa where p is a prime number and a is a natural number, then according to the question: (a + 1)2 = pa This is possible only if a = 2 and p = 3. So the number is 9. If the number has two prime factors then it would be of the type pa × qb, where p and q are two distinct prime numbers. Then according to the question: (a + 1)2 (b + 1)2 = pa × qb This is possible only if p and q are both 3. Since they are different, this is not a valid case. So there would no such case with two or more prime factors. So there are only two such integers - 1 and 9. 98. (b) In the given equation the right hand side contains the powers of 2 and 3 only; therefore the left hand side should contain the powers of 2 and 3 only. Since (x – 1)(x – 2)(x – 3) is a product of three consecutive numbers, it will always contain either one or two multiples of 2 and one multiple of 3. Lets make two cases: (1) If (x – 1) and (x – 3) are multiples of 2: Let (x – 1) be equal to 2k; then (x – 3) is equal to 2(k + 1). Now k and (k + 1) should both contain powers of 2 or 3 only. This is possible with k = 1, 2 or 3. Also if any of k or (k + 1) is a

multiple of 3, (x – 2) will not be a multiple of 3 or 2. So again it will not satisfy. (2) If (x – 2) is a multiple of 2: Here (x – 1) and (x – 3) will both be odd, out of which only one will be a multiple of 3. Hence the other number will be a multiple of an odd number other than 3. So the equation can be satisfied only if that other odd number is 1. Hence taking one odd number as 1 we get 1 × 2 × 3 which is equal to 6. Hence the equation is satisfied for x = 4 only. 99. (b) Here find the number of two–digit natural numbers such that unit digit is greater than their ten’s digit. In such natural numbers, we cannot take 0 or 1 in units place. When we take 2 at unit’s place, we obtain only 1 Such number is 12. When we take 3 at unit’s place, we obtain 2 such numbes are 13 and 23. When we take 9 at unit’s place, we obtain 8 such numbers. So, number of such numbers is (1 + 2 + 3 + .... + 8) = 36 Hence, the required number has 72 digits. 100. (d) Let first integer = (x – 1), then Second integer = x; so..... on According to question. ⇒ (x – 1)2 + x2 + (x + 1)2 = (x + 2)2 + (x + 3)2 ⇒ x2 + 1 – 2x + x2 + x2 + 1 + 2x = x2 + 4 + 2.x.2 + x2 + 9 + 2.x.3 ⇒ 3x2 + 2 = x2 + 4 + 4x + x2 + 9 + 6x Since at each time any two numbers a and b are erased and a single new number (a + b – 1) is writen. Hence, each one is subtracted and this process is repeated 39 times. Therefore, number left on the board at the end = 820 – 39 = 781. 79. (d) All the numbers greater than 999 but not greater than 4000 are four digits number. The number of numbers between 999 and 4000 = 3 × 5 × 5 × 5 = 375

80.

81.

82.

83.

Since one number 4000 will also be included. Hence number of toal number greater than 999 but not greater than 4000 = 375 + 1 = 376 (c) 70 = 01 (7)1 = 07 (7)2 = 49 (7)3 = 243 (7)4 = 2401 (7)5 = 16807 (7)6 = 117649 (7)7 = 823543 (7)8 = 5764801 Here we see last two digit 01 is repeated when power of (7)0 is increased by 4 each time. Now 2008 ÷ 4 = 502 Hence when power of (7)0 increases 502 times by 4 (each time), then we get that 01 is the last two digits in the number (7)2008. (c) We can see that the difference between the divisor and the respective remainder is the same in each division i.e. 2 – 1 =4–3=6–5=8–7=1 Hence the general form of such numbers will be LCM(2, 4, 6 and 8) K – 1 = 24K – 1, where ‘K’ is any natural number. Hence the numbers are 23, 23 + 1 × 24, 23 + 2 × 24, ......, 23 + 40 × 24 A total of 41 such numbers are there between 0 and 1000. (c) The number needs to be less than 13 × 52 = 676. The highest power of 13 in 676! is 56. The power of 13 in the smallest such number needs to be exactly 52. If we subtract 13 × 3 = 39 from 676, we get 637. The number 637! will be the smallest number of type N! that is completely divisible by 1352. The sum of the digits of 637 is 16. (a) x4 + 16 is always greater than x4 and x2 is always greater than x2 – 4. Hence,

will

always

greater

than

–

is greater than x2 – 4.

So the given two expressions can never be equal for any real value of x. 84. (b) S = 20012 – 20002 + 19992 – 19982 + .... + 32 – 22 + 12 =(2001 + 2000)(2001– 2000) + (1999 + 1998) (1999 – 1998) ..... + (3 + 2)(3 – 2) +1 = 2001 + 2000 + 1999 + 1998 +.... + 3 + 2 + 1 ⇒ 85. (c) We have, 7103 = 7 (49)51 = 7 (50 – 1)51 = 7 (5051 – 51C1 5050 + 51C2 5049 – ... – 1) = 7 (5051 – 51C1 5050 + 51C2 5049 – ...) – 7 + 18 – 18 = 7 (5051 – 51C1 5050 + 51C2 5049 – ...) – 25 + 18 = k + 18 (say) where k is divisible by 25, ∴ remainder is 18. 86. (c) From the Venn diagram, it follows that n (sector I ) = 42, n (sector II) = 34, n (sector III) = 20 n (I ∩ II) = 24, n (II ∩ III) = 10, n (I ∩ III) = 12, n (I ∩ II ∩ III) = 4 Now using the formula, we get n (I ∪ II ∪ II) = 42 + 34 + 20 – 24 – 10 – 12 + 4 = 54. 87. (a) Let the money be deposited at the time of opening the account be m. So after 1 year (i.e. 3 years ago) it would amount to 1.1m.

Since no money was withdrawn at this point, after 2 years i.e. 2 years ago) it would amount to 1.2m. At this point, the person withdraws Rs. 5000. Hence his principal for the next year = (1.2m – 5000). Next year, he earns 10% interest on this, which will amount of 1.1 (1.2m – 5000) = (1.32m – 5500). At this point, he withdraws Rs. 6000. Hence his principal for the next year would be (1.32m – 11500). He earns 10% interest on this, which amounts to 1.1 (1.32m – 11500) = (1.452m – 12650). But this is equal to Rs. 10000. Hence m = Rs. 15600. 88. (c) Let P, Q and R be n, n + 2 and n + 4 respectively in ascending order. According to the Question 3n = 2(n + 4) – 3 = 2n + 5 ∴ n=5 Thus, R = 5 + 4 = 9 89. (b) Putting n = 1, we get

whose integral part is

9. Putting n = 2, we get 25 + 19 + whose integral part is 25 + 19 + 43 which is again an odd number. Now, through the options it can be judged that the greatest integer must always be an odd number. 90. (b) The cyclicity of each digit from 0 to 9 is a factor of 4. Hence any digit raised to a power of the type 4k + 1 will always end in the same digit. Hence the answer is x13 + y13. 91. (a) a15 + a16 + a17 + .... + a50| Sum = a15 {1 + a + a2 + ..... a35} where a ≠ 1 Since a is the root of equation x5 – 1 = 0, a5 – 1 = 0 ⇒ a5 = 1 So, Sum

(d) (x2 – xy + y2) = (x + y) Multiplying both sides by 2: Again, P6 = P5 – P4 + P3 – P2 ⇒ P6 = – P1 P7 = – P2 , Similarly, P8 = – P3 P9 = – P4 P10 = – P5 The sequence repeats its terms after every 10 terms. Here, we observe following pattern P531 = P(530 + 1) = P1 = 211 P753 = P(750 + 3) = P3 = 420 P975 = P(970 + 5) = P5 = 267 So, P531 + P753 + P975 = 211 + 420 + 267 = 898. 113. (a) Let the batsman scored a 2’s, b 4’s and c 6’s. ⇒ 2a + 4b + 6c = 100 ⇒ a + 2b + 3c = 50. ...(i) When c = 1, (i) becomes a + 2b = 47 ⇒ a = 47 – 2b ....(ii) Since a ≥ 1 and b ≥ 1, the number of solutions of (ii) is 23. When c = 2, (i) becomes a + 2b = 44 ⇒ a = 44 – 2b ...(iii) Since a ≥ 1 and b ≥ 1, the number of solutions of (iii) is 21. When c = 3, (i) becomes a + 2b = 41 ⇒ a = 41 – 2b ...(iv) Since a ≥ 1 and b ≥ 1, the number of solutions of (iv) is 20. When c = 4, (i) becomes a + 2b = 38 ⇒ a = 38 –2b ...(v) Since a ≥ 1 and b ≥ 1 , the number of solutions of (v) is 18. Thus, we see a pattern emerging. ∴ The total number of ways = 23 + 21 + 20 + 18 + ... + 3 + 2 = 184. 92.

114. (d)

Here, we take the 1st option, a delete all perfect squares and perfect cubes, then a total of 22 perfect square will be deleted (12, 22 ........ 222) and a total of 7 perfect cubes will be deleted (13 23,.... 73) and Two numbers are common in between them viz. 16 and 26 which are perfect squares as well as perfect cubes Thus, 500 is the (500 – 22 – 7 + 2) = 473 rd term. So, 476th term = 500 + 3 = 503. 115. (c) Here,343b = 676 ⇒ 73b = 262 Now, 7a = 26 ⇒ 73b = (7a)2 ⇒ 2a = 3b 116. (c) In order to maximize the power of 2 in the product, one of the ten numbers has to be 64 as this is the highest two– digit number of the form 2k, where k is a natural number. There has to be maximum number of multiples of 8 among the ten numbers. In a set of ten consecutive natural numbers, there can be a maximum of two numbers that will be a multiple of 8. The possible sets of ten consecutive natural numbers that satisfy the aforementioned conditions are 55 to 64, 56 to 65, 63 to 72 and 64 to 73. The highest power of 2 in the product of any of these sets of ten numbers will be 13. 117. (245)Let x be the initial quantity of wine in the vessel. y litres of content is removed twice. The part of wine left is

Now in 98 L of sample 18 L is wine which is same as part of the solution

⇒

⇒ x = 245.

118. (d) x = L.C.M. of (7, 8, 9) – 3 = 504 – 3 = 501 x3 + 2x2 + x – 3 = (x – 1) (x + 1) (x + 2) –1 = 500 × 502 × 503 – 1 Remainder when 500 × 502 × 503 – 1 is divided by: 11 = 4 3=0 4=3 Required remainder = least possible number which when divided by 11, 3 and 4 leavs remainder 4, 0 and 3 respectively. Such least no. is 15. 119. (12) For the amount to get tripled, the increase is 200% of the principal. If it happens in 24 years then it will take 12 years for the increase to be 100% of the principal. 120. (b) P = 15100 (1 × 2 × 3 × .... × 100) = 15100 × 100! Highest power of 2 in P = 97 (2 will be deciding factor for number of zeroes because number of lives will be greater than number of zeroes in this number) Q = 2520×50 (1 × 2 × 3x .... × 50) = 52000 × 50! Highest power of 2 in θ = 47 So Highest power of 2 in = 2 × 97 + 1767 – 47 = 1914 Hence, number of zeroes = 1914. 121. (b) Solve by option.

Option (a): If the product of the digits is 6. then the factors of 6 are 1,2, 3 and 6. This combination of digits is not suitable. So it is not the answer. Option (b): If the product of the digits is 8, then the factors of 8 are 1, 2, 4 and 8. So only possible combination is 1, 1, 2, 4. Hence, the number is 4112. It is suitable for answer. Similarly, we can check options (c) and (d). ⇒ 3x2 + 2 = 2x2 + 10x + 13 ⇒ 3x2 + 2 – 2x2 – 10x – 13 = 0 ⇒ x2 – 10x – 11 = 0 ⇒ x2 – 11x + x – 11 = 0 ⇒ x (x – 11) + 1 (x – 11) = 0 ⇒ (x + 1) (x – 11) ∴ x = –1 or 11 101. (c) Sum of a0 + a1 + .... + a50 = 1 + 3 + .... + 101 =

= 2601.

102. (c) 500! + 505! + 510! + 515! = 500! (1 + 5k) (where k is a natural number) So (5k + 1) won’t be a multiple of 5. Minimum value of n for which 500 ! is divisible by 5n = 1. Maximum value of n for which 500! is divisible by 5n

= 100 + 20 + 4 = 124 Hence, there are 124 possible values of n. 103. (a) Prime factorization of 44 is = 2 × 2 × 11 To express 44 as product of five distinct integers So, we’ll have to put 1 and –1. The only possible way comes out to be: 44 = 2 × (–2) × 11 × 1 × (–1) In this case the value of n would be 11 which is also the only possible value. 104. (c) LCM of 6, 4 and 3 = 12

Multiply by 12 of each number in power ⇒ ⇒ 214, 39, 58 So, ascending order is 58 > 39 > 214 or 52/3 > 33/4 >27/6 105. (b) E = 3 + 8 + 15 + 24 + .... + 195 = 1 × 3 + 2 × 4 + 3 × 5 + 4 × 6 + .... + 13 × 15 ∴ Tn = n (n + 2) and n = 13 ∴E= =

= 1001

= 7 × 11 × 13 Hence the sum of the prime factors of E = 7 + 11 + 13 = 31. 106. (b) Since ‘ab’ is a two - digit prime number and one of its digit is 3, it can assume any of the values among 13, 23, 31, 37,43, 53, 73 and 83. As the absolute difference between the digits of the number is not a factor of 2, the number among the obtained numbers that satisfy the aforementioned condition are 37, 73 and 83. Hence, the number of values that ‘ab’ can assume is 3. 107. (d) Let the number be N. In order to maximize the number of factors of N3, N2 must be expressed as a product of as many prime factors as possible. No. of factors of N2 = 105 = 3 × 5 × 7 where a = 2 b = 4 c = 6 then power original number = (2 + 1) (4 + 1) (6 + 1) ∴ N2 = (a)2 (b)4 (c)6, where a, b and c are prime numbers. ∴ N3 = (a)3 (b)6 (c)9 Where N = ap bq cr no = (p + 1) (q + 1) (r + 1) Hence, the number of factors of N3 = (3 + 1) × (6 + 1) × (9 × 1) = 4 × 7 × 10 = 280.

108. (a) 1080 = 23 × 33 × 51 (where N = apbqcr ∴ No. of factors (p + 1) (q + 1) (r + 1) ∴ No. of factors of 1080 (3 + 1) (3 + 1) (1 + 1) = 4 × 4 × 2 = 32 1800 = 23 × 32 × 52 (where N = apbqcr ∴ No. of factor (p + 1) (q + 1) (r + 1) ∴ Number of factor of 1800 = (3 + 1)(2 + 1)(2 +1) = 4 × 3 × 3 = 36 ∴ HCF of 1080 and 1800 = 23 × 32 × 5 where N = ap, bq, cr No. of factors HCl = (p + 1)(q + 1)(r +1) ∴ No. of factors HCF of two numbers = (3 + 1) (2 + 1) (1 + 1) = 4 × 3 × 2 = 24 So, the required number of divisors = (32 + 36) – 2 × 24 = 20 109. (c)

f(2n) = 14 + 24 + 34 + 44 + 54 +.... + (2n)4

⇒ f(2n) = (14 + 34 + 54 + .... + (2n – 1)4) + (24 + 44 + 64 + .... + (2n)4) ∴ 14 + 34 + 54 + ..... + (2n – 1)4 = f(2n) – (24 + 44 + 64 + .... + (2n)4) = f(2n) – 24 × (14 + 24 + 34 + .... + n4) = f(2n) – 16 × f(n) 110. (d) For d = 1, Total = 46 (1, 2, 3, 4, 5), (2, 3, 4, 5, 6) ............(46, 47, 48, 49, 50) For d = 2, total = 42 (1, 3, 5, 7, 9), (2, 4,6, 8, 10)......... (42, 44, 46, 48, 50) For d = 3, total = 38 (1, 4, 7, 10, 13) (2, 5, 8, 11, 14) ........ (38, 41, 44, 47, 50) For d = 12, total = 2 (1, 13, 25, 37, 49) (2, 14, 26, 38, 50) So total = 46 + 42 + 38 ..........2

Possible APs = (2 + 46) = 288. 111. (c) Let the two numbers be x and y according to question, x + y = 600 and x + y = 600 ...(i) ⇒ 8x – 7y = 0

...(ii)

From equation (i) and (ii) x = 280 and y = 320 ∴ LCM of 280 and 320 = 2240 112. (a) Put n = 5, in the given relation then, P5 = 267 122. (c) Let n be xyz and since n is odd z can take only odd values i.e. 1, 3, 5 and 9 Now, x ≤ y and x ≥ z

∴ Total number of elemenls in P = 95. 123. (a) x = 10690 – 4990 (xn – an) is divisible by both (x – a) and (x + a) whenever n is even ⇒ (10690 – 4990) is divisible by both 57 and 155 57 = 19 × 3 155 = 31 × 5 Therefore, (10690 – 4990) will be divisible by (19 × 31) = 589 as well. Also, note that (10690– 4990) will be odd and options (b) and (c) are even. Hence, they can be rejected. 124. (b) 1000 = 23 × 53 and 2000 = 24 × 53 Since LCM (c, a) and LCM (b, c) is 24 × 53 and LCM (a, b) = 23 × 53, so the factor 24 must be present in c. Hence c = 24 × 5x, where x ranges from 0 to 3 Therefore, there are four possible values of C.

Since, HCF of (a, b) = K × 53, it means a = 2y × 53 b = 2z × 53 x = 0 to 3, y = 0, then z = 3 → 4 cases. x = 0 to 3, y = 1, then z = 3 → 4 cases. x = 0 to 3, y = 2, then z = 3 → 4 cases. x = 0 to 3, y = 3, then z = 3 → 4 cases. x = 0 to 3, y = 3, then z = 2 → 4 cases. x = 0 to 3, y = 3, then z = 1 → 4 cases. x = 0 to 3, y = 3, then z = 0 → 4 cases. Hence, total cases = 28. 125. (31) Let the four numbers are XA, XB, XC and XD respectively where X is the common factor of each pair of numbers and A, B, C, D are prime to each other. Then, 310 = 2 × 5 × 31 651 = 31 × 21 = 3 × 7 × 31 ∴ GCF (310, 651) = 31 ∴ highest common factor of all = 31 126. (a) Here, 74 = 2401 ∴ 7700 = (74)175 = (2401)175 Any power of 2401 will end with 1 as the units digit and 0 as the tens digit. ∴ When it is divided by 100, the remainder is 1. 127. (d) Let the 4-digit sequence be abcd. In base 6, this represents 216a + 36b + 6c + d and each of a, b, c, d is less than 6. In base 10, it represents 1000a + 100b + 10c + d. Given 4(216a + 36b + 6c + d) = 1000a + 100b + 10c + d ⇒136a = 44b + 14c + 3d...(A) By trial a = 1, b = 2, c = 3, d = 2 If a = 2, the LHS = 272 [If we consider b = 5, we need 272 – 220 or 52 from 14c + 3d (c, d)=(2, 8) but 8 is not a proper digit in base 6.

If a= 3, the LHS = 408, while 44b + 14c + 3d can at the most be (44 + 14 + 3) 5 or 305. ∴ There are no other possible values that satisfy (A)] ∴ abcd = 1232 and a + b + c + d = 8 128. (b) Remainder [N/625] = = = 129. (b) Here, 120 ≤ n ≤ 240. 120 = 23 (3)(5) and 240 = 24 (3)(5) So, the prime factors involved in 120 and 240 are the same. So, number of co-primes of 240 lying between 120 and 240 = φ (240) – φ (120). = = 130. (d) Let the number of girls be 2x and number of boys be x. Girls getting admission = 0.6 x Boys getting admission = 0.45 x Number of students not getting admission = 3x – 0.6x – 0.45x = 1.95x Alternatively, Let the no. of boys appearing for the admission test be b % of candidates who get admission.

Directions for questions 1 to 3 : Read the information given below and answer the questions that follow : Ghoshbabu is staying at Ghosh Housing Society, Aghosh Colony, Dighoshpur, Calcutta. In Ghosh Housing Society 6 persons read daily Ganashakti and 4 read Anand Bazar Patrika; In his colony there is no person who reads both. Total number of persons who read these two newspapers in Aghosh Colony and Dighoshpur is 52 and 200 respectively. Number of persons who read Ganashakti in Aghosh Colony and Dighoshpur is 33 and 121 respectively; while the persons who read Anand Bazar Patrika in Aghosh Colony and Dighoshpur are 32 and 117 respectively. 1. (a) (b) (c) (d) 2.

(a) (b) (c) (d) 3.

(a) (b)

Number of persons in Dighoshpur who read only Ganashakti is (1994) 121 83 79 127 Number of persons in Aghosh Colony who read both of these newspapers is (1994) 13 20 19 14 Number of persons in Aghosh Colony who read only one newspaper (1 994) 29 19

(c) 39 (d) 20 Directions for questions 4 & 5 : Read the information given below and answer the questions that follow : There are three different cable channels namely Ahead, Luck and Bang. In a survey it was found that 85% of viewers respond to Bang, 20 % to Luck, and 30% to Ahead. 20% of viewers respond to exactly two channels and 5% to none. 4.

(a) (b) (c) (d) 5.

(a) (b) (c) (d) 6.

(a) (b) (c) (d)

What percentage of the viewers responded to all three ? (1995) 10 12 14 None of these Assuming 20% respond to Ahead and Bang and 16% respond to Bang and Luck, what is the percentage of viewers who watch only Luck ? (1995) 20 10 16 None of these In a locality, two-thirds of the people have cable-TV, one-fifth have VCR, and one-tenth have both, what is the fraction of people having either cable -TV or VCR ? (1996) 19/30 3/5 17/30 23/30

Directions for questions 7 to 9 : Read the information given below and answer the questions that follow : A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN. 7.

(a) (b) (c) (d) 8.

(a) (b) (c) (d) 9.

(a) (b) (c) (d) 10.

What is the maximum percentage of people who can watch all the three channels? (1997) 12.5 8.5 17 Insufficient data If 5% of the people watched DD and CNN, 10% watched DD and BBC, then what per cent of the people watched BBC and CNN only? (1997) 2% 5% 8.5% Can’t be determined Referring to the previous question, how many per cent of the people watched all the three channels? (1997) 3.5% 0% 8.5% Can’t be determined In a political survey, 78% of the politicians favour at least one proposal. 50% of them are in favour of proposal A, 30% are in favour of proposal B and 20% are in favour of proposal C. 5% are in favour of all three proposals. What is the percentage of

people proposal?

favouring

than

one

(1999) (a) (b) (c) (d) 11.

16 17 18 19 There where

are

two

disjoint

sets

and

(2000) such that S1 ∪ S2 forms the set of natural number. Also (a) (b) (c) (d) 12.

(a)

& g (1) < g (2) < g(3) and f (n) = g ((g (n)) + 1 then what is g (1)? 0 1 2 can’t be determined Let ‘f’ be a function from set A to set B for a set, XCB define f–1 (X) = Then which of the following is necessarily true for a subset U of X? (2000) (b) (c) (d)

Directions for questions 13 to 16 : Read the information given below and answer the questions that follow : A and B are two sets (e.g. A = mothers, B = women). The elements that could belong to both the sets (e.g. women who are mothers) is given by the set C = A.B. The elements which could belong to either A or B, or both, is indicated by the set D = A B. A set that does not contain any elements is known as null

set, represented by (for example, if none of the women in the set B is a mother, then C = A.B. is a null set , or C = ). Let ‘V’ signify the set of all vertebrates; ‘M’ the set all mammals; ‘D’ dogs, ‘F’ fish; ‘A’ alsatian and ‘P’, a dog named Pluto. 13. Given that X = M.D is such that X = D, which of the following is true? (2001) (a) All dogs are mammals (b) Some dogs are mammals (c) X = (d) All mammals are dogs 14. If Y = F.(D.V), is not a null set, it implies that : (2001) (a) All fishes are vertebrates (b) All dogs are vertebrates (c) Some fishes are dogs (d) None of these 15. If Z = (P.D) M, then (2002) (a) The elements of Z consist of Pluto the dog or any other mammal (b) Z implies any dog or mammal (c) Z implies Pluto or any dog that is a mammal (d) Z is a null set 16. If P.A = and P A = D, then which of the following is true? (2002) (a) Pluto and alsatians are dogs (b) Pluto is an alsatian (c) Pluto is not an alsatian (d) D is a null set 17. Let T be the set of integers { 3, 11, 19, 27 .....451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S

(a) (b) (c) (d) 18.

is 003) 32 28 29 30 Consider the sets

= {n, n + 1, n + 2, n + 3, n + 4}, where n =

1, 2, 3, ............... , 96. How many of these sets contains 6 or any integral multiple thereof (i.e. any one of the numbers 6, 12, 18,............)? (2004) (a) 80 (b) 81 (c) 82 (d) 83 Directions for Questions 19 to 21 : Answer the questions on the basis of the tables given below. Two binary operations ⊕ and * are defined over the set {a , e, f, g, h} as per the following tables :

Thus, according to the first table f ⊕ g = a , while according to the second table g *h = f, and so on. Also, let f 2 = f * f , g 3 = g * g * g, and so on. 19. What is the smallest positive integer n such that gn = e? (2003) (a) 4 (b) 5 (c) 2 (d) 3 20. Upon simplification, f [f * {f (f * f)}] equals (2003) (a) e (b) f (c) g (d) h 21. Upon

simplification,

equals (2003) (a) (b) (c) (d) 22.

e f g h A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popularoptions — air-conditioning, radio and power windows - were already installed. The survey found (2003) 15 had air conditioning 2 had air conditioning and power windows but no radios 12 had radio 6 had air-conditioning and radio but no power windows

11 had power windows 4 had radio and power windows 3 had all three options. What is the number of cars that had none of the options? (a) 4 (b) 3 (c) 1 (d) 2 23. 70 per cent of the employees in a multinational corporation have VCD players, 75 per cent have microwave ovens, 80 per cent have ACs and 85 per cent have washing machines. At least what percentage of employees has all four gadgets? (2003) (a) 15 (b) 5 (c) 10 (d) Cannot be determined 24. A survey was conducted of 100 people to find out whether they had read recent issues of Golmal, a monthly magazine. The summarized information regarding readership in 3 months is given below: (2006) Only September : 18; September but not August: 23; September and July : 8; September : 28; July : 48; July and August : 10; None of the three months : 24. What is the number of surveyed people who have read exactly two consecutive issues (out of the three)? (a) 7 (b) 9 (c) 12 (d) 14 (e) 17

25. S1 800}

{2,

....................

(2009) S2 = {3, 6, 9, 12, .................. 900} If S3 = S1∪ S2, then what will be the 105th element of S3 if all its elements are arranged in increasing order? (a) 120 (b) 630 (c) 158 (d) 198 26. In a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the rule. So he arranges the uranium stack the way he wanted. What is the number of hazardous combinations of uranium in a stack of 5? (2010) (a) 3 (b) 7 (c) 8 (d) 10 27. For constructing the working class consumer price index number of a particular town, the following weights corresponding to different group of items were assigned : Food-55, Fuel-15, Clothing -10, Rent -8 and Miscellaneous-12. It is known that the rise in food prices is double that of fuel and the rise in miscellaneous group prices is double that of rent. In October 2006, the increased D.A. by a factory of that town by 182% fully compensated for the rise in prices of food and rent but did not compensate for anything else. Another factory of the same locality increased D.A. by 46.5%, which compensated for the rise in fuel and miscellaneous groups.

Which is the correct combination of the rise in prices of food, fuel, rent and miscellaneous groups? (2011) (a) 320. 14, 159.57, 95.64, 166.82 (b) 317.14 , 158.57, 94 .64, 189.28 (c) 311.14, 159.57, 90 .64, 198.28 (d) 321.14, 162.57, 84.46, 175.38 28. Let S = {1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12}. The number of subsets of S comprising composite number(s) only and that of those comprising prime number(s) only are N1 and N2 respectively. What is the absolute difference between N1 and N2? (2013) (a) 0

(b) (d) 24

(c)

29. Find the range of ‘x’ if (2014) (a) x < –4 (b) (x > 4) ∪ (x < –4) (c) (x < – 4) ∪ (–2 < x < 2) ∪ (x > 4) (d) –2 < x < 2

(b) Suppose G and A are represented by Ganashakti and Anand Bazar Patrika respectively

Given that n(G A) = 200

No. of persons in Dighospur who read only Ganashakti .

(a)

Given that , n(G

A) = 52

(a)

Here,

n(A∪L∪B) = n(A) + n(L) + n(B) – n(A ∩ L) – n(L ∩ B) – n(B ∩ A) + n(A ∩ L ∩ B)

or 5.

(d) Percentage of viewers who watch only Luck

(d) Fraction of people who watch Cable-TV only

Fraction of people who have VCR only

Fraction of people having either cable TV or VCR

Alternatively:

(b) We solve such question from venn diagram. For max. percentage of people who watch all three channels, we consider that there are no such people who watch only two channels. Let x personals of viewers responded all the three channels.

According to the given conditions,

Hence, 8.5% of people watched all the three channels.

(a)

Let x viewers watch all the three channels. Let y viewers watch CNN and BBC only. From venn diagram : y=4 ∴ 2% of viewers watch BBC and CNN only. 9. (d) From the previous question data, we can’t determine how many people watched all the three channels. The data are insufficient. 10. (b) or This includes three times. Percentage of people favouring more than one proposal = 27 – 5 × 2 = 17 11. (b) It is given that f(n) = g(g(n)) + 1 Therefore,

Also,

shows that the function g(x) is an increasing function. So for a natural number n,

Thus,

for every n

or is the least number in Now, S1 ∪ S2= set of natural numbers. Therefore, 1 in S1 ∪ S2 is the smallest number. Thus, g(1) = 1. 12. (c) We have i.e., if there is an x such that f (x) is in X then x belongs to this set f–1(X). Now, if and f (u) = v for some (U). i.e., Thus every element in U is in The option (a) is possible but it is not true in every case as shown in the following example. Let f (x) = x2, defined on the set of integers and let U = {–3, ,2, – 1, 1, 2, 3} which is not same as U. 13. (a) X = M.D. X=D It clearly shows that all dogs are mammals. 14. (c) Y= F ∩ (D ∩ V) is not a null set means some F’s are D’s and some D’s are V’s. That means some fishes are dogs. 15. (a) P.D. = A dog which name is Pluto This contains Pluto the dog or any other mammal. 16. (c) Pluto is not an alsatian. Pluto and alsatians constitutes the dogs. 17. (d) T = {3, 11, 19, 27 ....467} is an AP with a=3 and d = 8.To find number of terms, we use the formula for nth term : a + (n – 1) d = 3 + (n – 1) 8 = 467.

Hence, n = 59. S = subset in which not sum of two elements = 470 . So, S can be a set in which either the first half or the second half of the terms are present. So number of maximum possible elements in S = 18. (a) Sets starting from 1, 7, 13..... does not contain multipleof 6. Now 1, 7, 13, 19..... forms an A.P. ⇒ Tn = 1 + (n–1)6 ≤ 96 ⇒ 6n ≤ 101 ⇒ n = 16 ∴ No. of sets which doesn’t contain the multiple of 6 = 96 – 16 = 80. 19. (a) ∴n=4 20. (d) =h 21. (a) Clearly, a10 = a

Now, =

= ( a * f)

e=a

e = e.

22. (d)

Total cars having any one of AC, radio or power windows = 4 + 6 + 3 + 2 + 1 + 2 + 5 = 23 Cars with no options = 25 – 23 = 2. 23. (c) Employees who doesn’t have VCD = 100 – 70 = 30% Employees who doesn’t have MWO = 100 – 75 = 25% Employees who doesn’t have AC = 100 – 80 = 20% Employees who doesn’t have WM = 100 – 85 = 15% ∴ Total employees who doesn’t have atleast one of the four equipments = 30 + 25 + 20 + 15 = 90% ∴ Percentage of employees having all four gadgets = 100 – 90 = 10%. 24. (b) Putting the given information in the form of a venn diagram, we get

; n(only S) = 18 n(S but not A) = 23 =

To find the people who have read exactly 2 consecutive issues (out of 3) we shall find the people reading J & A and A & S. Hence required no. = 7 + 2 = 9. 25. (c) Starting from 1, in every set of 6 consecutive natural numbers there will be 4 elements that belong to S3 (e.g. 2, 3, 4, 6). So we can say that the 104th element of S3 will be The next element i.e. the 105th element will 26.

27. 28.

29.

be 158. (c) For a stack of 5 cubes to be hazardous atleast 3 cubes of uranium have to be together. So there are 3 cases: Case I: 3 uranium and 2 lead cubes are present. They can be arranged in 3 ways (with the uranium cubes at positions (1, 2, 3 or 2, 3, 4 or 3, 4, 5) when uranium is together. Case II: 4 uranium & 1 lead cube: If the 4 uranium cubes are together then they can be arranged in 2 ways (UUUUL and LUUUU). If 3 uranium cubes are together then they can be arranged in 2 ways (UULU, and ULUUU). CaseIII: 5 uranium cubes which can be arranged in 1 way. So in all 3 +4 + 1 = 8 ways. (b) The rise in food prices is double that of fuel prices and the rise in miscellaneous groups prices is double that of rent. Only option ‘b’ satisfies the above criteria. (c) Here set S has 6 composite and 4 prime numbers. The number of subsets of S comprising composite numbers only = 26 – 1 The number of subset of S comprising prime numbers only 24 – 1 Hence, the required difference = (26 – 1) – (24 – 1) = (63 – 15) = 48. (c) There would be two cases. They are as follows : Case I : x ≥ 0 ...(i)

The inequality becomes,

⇒ (x – 2) < 0.5 (x – 2)2 ⇒ (x – 2)2 – 2 (x – 2) > 0 ⇒ (x – 2) (x – 4) > 0 ⇒ x > 4 or x < 2 Using (i), the range becomes x > 4 or 0 ≤ x < 2 Case II : x < 0 The inequality becomes,

...(ii) ...(iii)

⇒ ⇒ 2 (x + 2) + (x + 2)2 > 0 ⇒ (x + 2) (x + 4) > 0 ⇒ x > – 2 or x < – 4 Using (iii), the range becomes –2 < x < 0 or x < – 4 ...(iv) Combining (ii) and (iv), The range is (x < – 4) ∪ (–2 < x < 2) ∪ (x > 4).

Directions for questions 1 & 2 : Read the information given below and answer the questions that follow : If md (x) = | x |, mn (x, y) = minimum of x and y and Ma (a, b, c, ....) = maximum of a, b, c, .... 1. Value of Ma [md (a), mn (md(b), a), mn (ab, md(ac))] where a = –2, b = –3, c = 4 is (1994) (a) 2 (b) 6 (c) 8 (d) –2 2. Given that a > b then the relation Ma [md (a), mn (a, b)] = mn [a, md (Ma (a, b))] does not hold if (1994) (a) a < 0, b < 0 (b) a > 0, b > 0 (c) a > 0, b < 0, | a | < | b | (d) a > 0, b < 0, |a | > | b | Directions for questions 3 to 6 : Read the information given below and answer the questions that follow : If f (x) = 2x + 3 and 3.

fog

, then (x)

= (1994)

(a) 1 (b) gof(x) (c)

(d) 4.

For 3)

what

value

(x)

–

? (1994)

(a) (b) (c) (d) 5.

–3 1/4 –4 None of these What is ? (1994) (a) x (b) x2

value

What (x)?

the

value

fo(fog)

(gof)

(1994) (a) x (b) x 2 (c) 2x + 3 (d) Directions for questions 7 to 10 : Read the information given below and answer the questions that follow : le (x, y) = least of (x, y) mo (x) = |x| me (x, y) = maximum of (x, y)

7. (a) (b) (c) (d) 8.

Find the value of at a = –2 and b = –3. (1995) 1 0 5 3 Which of the following must always be correct for a, b > 0 (1995)

(a) (b) (c) (d) 9.

For

what

values

me (199

5) (a) (b) (c) (d) a = 3 10. For what values of a le (a2 – 3a, a – 3) < 0 ? (1995) (a) 1 < a < 3 (b) a < 0 and a < 3 (c) a < 0 and a 3 (d) a < 0 or a > 3 11. Largest value of min (2 + x2, 6 – 3x), when x > 0 is (1995) (a) 1 (b) 2 (c) 3

(d) 4 Directions for questions 12 & 13 : Read the information given below and answer the questions that follow : A,S, M and D are functions of x and y, and they are defined as follows : A (x, y) = x + y S (x, y) = x – y M (x, y) = xy D (x, y) = x / y where y 0. 12. What is the value of M(M(A(M(x, y), S (y, x)), x), A (y,x)) for x =2 ,y=3? (1996) (a) 50 (b) 140 (c) 25 (d) 70 13. What is the value of S[M(D(A(a, b),2), D(A(a, b),2)),M(D(S(a,b),2), D(S(a, b), 2))] ? (1996) (a) (b) ab (c) (d) a/b Directions for questions 14 to 16 : Read the information given below and answer the questions that follow : The following functions have been defined : la (x, y, z) = min (x + y, y + z) le (x, y, z) = max (x – y, y – z) ma (x, y, z) = (½) [le (x, y, z) + la (x, y, z)] 14. Given that x > y > z > 0, which of the following is necessarily true? (1997) (a) la (x, y, z) < le (x, y, z) (b) ma (x, y, z) < la (x, y, z)

(c) ma (x, y, z) < le (x, y, z) (d) cannot be determined 15. What is the value of ma (10, 4, le (la (10, 5, 3), 5, 3)) ? (1997) (a) 7.0 (b) 6.5 (c) 8.0 (d) 7.5 16. For x = 15, y = 10 and z = 9, find the value of : le (x, min (y, x – z), le (9, 8, ma (x, y, z))) (1997) (a) 5 (b) 12 (c) 9 (d) 4 Directions for questions 17 to 19 : Read the information given below and answer the questions that follow : The following operations are defined for real numbers a # b = a + b if a and b both are positive else a # b = 1. a b = (ab)a+b if ab is positive else a b = 1. 17. (2 # 1) / (1 2) = (1998) (a) 1/8 (b) 1 (c) 3/8 (d) 3 18. {((1 # 1) # 2) – (101.3 log10 0.1)}/(1 2) = (1998) (a) 3/8 (b) 4 log10 0.1/8 (c) (4 + 101.3)/8 (d) cannot be determined

19. ((X # – Y)/(– X Y)) = 3/8, then which of the following must be true? (1998) (a) X = 2, Y =1 (b) X > 0, Y < 0 (c) X and Y both are positive (d) X and Y both are negative Directions for questions 20 to 22 : Read the information given below and answer the questions that follow : If x & y are real numbers, the functions are defined as . Now with 20.

(a) (b) (c) (d) 21.

the help of this information answer the following questions. Which of the following will be necessarily true? (1999) G (f(x, y), F (x, y)) > F (f(x, y), G (x, y)) F (F (x, y), F (x, y)) = F (G(x, y), G(x, y)) F (G(x, y), (x + y)) ≠ G(F (x, y), (x + y)) F (f (x, y), f (x, y)) = G (F(x, y), f(x, y)) If y = x, which of the following will give x2 as the final value ? (1999)

(a) f (x, y) G (x, y)4 (b) G (f(x, y) f (x, y), F (x, y)/8 (c) –F (x, y) G (x, y)/log216 (d) –f (x, y) G (x, y) F (x, y)/F (3x, 3y) 22. What (a) 2 (b) –2 (c) 1 (d) –1

will

the

final

value ?

given

the

function (1999)

Directions for questions 23 to 26 : Read the information given below and answer the questions that follow : Any function has been defined for a variable x, where range of Mark (a) if Mark (b) if Mark (c) if

F1(x) = –F (x) F1(x) = F (–x) F1(x) = –F (–x)

Otherwise mark (d).

23.

(1999)

24.

(1999)

25.

(1999)

26.

(1999)

27. There is a set of ‘n’ natural numbers. The function ‘H’ is such that it finds the highest common factor between any two numbers. What is the minimum number of times that the function has to be invoked to find the H.C.F. of the given set of numbers? (1999) (a) 1/2 n (b) n – 1 (c) n (d) None of these Directions for questions 28 & 29 : Read the information given below and answer the questions that follow : Certain relation is defined among variable A & B. Using the relation answer the questions given below : @ (A, B) = average of A and B \ (A, B) = product of A and B x (A, B) = the result when A is divided by B 28. The sum of A and B is given by (2000) (a) \ (@ (A, B), 2)

(b) (c) (d) 29.

@ (\ (A, B),2) @ (X (A, B), 2) None of these The average

and

given

(2000) (a) @ ( × ( \ ( @ (A, B), 2), C ), 3) (b) (c) (d) Directions for questions 30 to 32 : Read the information given below and answer the questions that follow : x and y are non-zero real numbers is real otherwise = (x +y)2 is real, otherwise = –(x + y) 30. For which of the following is f (x ,y) necessarily greater than g (x, y)? (2000) (a) x and y are positive (b) x and y are negative (c) x and y are greater than–1 (d) None of these 31. Which of the following is necessarily false ? (2000) (a) (b) (c) (d) None of these 32. If f then

(x,

y) (2000)

(x,

(a) (b) (c) (d) 33.

(a) (b) (c) (d) 34.

x=y x+y=1 x + y = –2 Both b and c Which of the following equations will best fit for the given data ? (2000)

y = ax + b y = a + bx +cx2 y = e ax + b None of these If then, what is the value of f (1, 2) ? (2000) (a) 1 (b) 2 (c) 3 (d) 4 Directions for questions 35 to 37 : Read the information given below and answer the questions that follow : Graphs of some functions are given. Mark the correct options from the following: (a) f (x) = 3f (–x) (b) f (x) = f (–x) (c) f (x) = –f (–x) (d) 6f (x) = 3f (–x) for x > 0

35.

(2000)

36.

(2000)

37.

(2000) Directions for questions 38 to 40 : Read the information given below and answer the questions that follow : Functions m and M are defined as follows:

m(a, b, c) = min (a + b, c, a) M(a, b, c) = max (a + b, c, a) 38. If a = – 2, b = – 3 and c = 2 what is the maximum between and ?(2000) (a) (b) (c) (d) 39. (a) (b) (c) (d) 40. (a) (b) (c) (d)

3/2 7/2 –3/2 –7/2 If a and b, c are negative, then what gives the minimum of a and b? (2000) m (a, b, c) –M (–a, a, –b) m (a+ b, b, c) none of these What is m (M(a–b, b,c), m (a + b,c,b) , –M (a,b,c)) for a = 2, b= 4, c = 3? (2000) –4 0 –6 3

Directions for questions 41 & 42 : Read the information given below and answer the questions that follow : f(x) = 1/(1 + x) if x is positive = 1 + x if x is negative or zero f n (x) = f (f n – 1(x)) 41.

(a) 1/5

(2000) (b) 1/6 (d) 1/8

42. If be (a) 2/3 (c) 3/5 (d) 4 43. If

–1

what

f 5(x)

will

(2000) (b) 1/2

then

(x)

(y)

is (2002) (a) f (x + y) (b) (c) (d) 44. Suppose, for any real number x, [x] denotes the greatest integer less than or equal to x. Let L (x, y) = [x] + [y] + [x + y] and R(x,y)= [2x] + [2y]. Then it’s impossible to find any two positive real numbers x and y for which (2002) (a) L(x, y) = R (x, y) (b) L(x, y) R(x, y) (c) L(x, y) < R (x, y) (d) L(x, y) > R(x, y) 45. Let g (x) = max (5–x, x + 2). The smallest possible value of g (x) is (2003C) (a) 4.0 (b) 4.5 (c) 1.5 (d) None of these

46. Let , where x is a real number, attains a minimum at? (2003C) (a) x = 2.3 (b) x = 2.5 (c) x = 2.7 (d) None of these 47. When the curves y = log10 x and y = x–1 are drawn in the x-y plane, how many times do they intersect for values ? (200 3C) (a) Never (b) Once (c) Twice (d) More than twice. 48. Consider the following two curves in the xy- plane; ; . (2003C) Which of the following statements is true for ? (a) The two carves intersect once (b) The two curves intersect twice (c) The two curves do not intersect (d) The two curves intersect thrice 49. On January 1, 2004 two new societies, S1 and S2, are formed, each with n members. On the first day of each subsequent month, S1 adds b members while S2 multiplies its current number of members by a constant factor r. Both the societies have the same number of members on July 2, 2004. If b = 10.5n, what is the value of r? (2004) (a) 2.0 (b) 1.9 (c) 1.8 (d) 1.7

50. If f (x) = x3 – 4x + p, and f (0) and f (1) are of opposite signs, then which of the following is necessarily true? (2004) (a) – 1 < p < 2 (b) 0 < p < 3 (c) – 2 < p < 1 (d) – 3 < p < 0 51. Let f (x) = ax2 – b | x |, where a and b are constants. Then at x = 0, f (x) is (2004) (a) maximized whenever a > 0, b > 0 (b) maximized whenever a > 0, b < 0 (c) minimized whenever a > 0, b > 0 (d) minimized whenever a > 0, b < 0 Directions for Questions 52 and 53 : Answer the questions on the basis of the information given below : f1 (x)= x 0 x 1

x) f2(x)

=1 =0 f2 (x) for all x f3 (x) for all x

x 1 otherwise =

f1(–

–

f4 (x) = f3(– x) for all x 52. How many of the following products are necessarily zero for every x ? (2004 - 2 marks) , , (a) (b) (c) (d)

0 1 2 3

53. Which of the true? (2004 - 2 marks) (a) f4(x) = f1(x) for all x

following

necessarily

(b) f1(x) = – f3(–x) for all x (c) f2(– x) = f4(x) for all x (d) f1(x) + f3(x) = 0 for all x 54. Let g(x) be a function such that g(x + 1) + g(x – 1) = g(x) for every real x. Then for what value of p is the relation g(x + p) = g(x) necessarily true for every real x? (2005 - 2 marks) (a) 5 (b) 3 (c) 2 (d) 6 55. The graph of y – x against y + x is as shown below. (All graphs in this question are drawn to scale and the same scale is used on each axis).

Which of x?

the

following

shows

the

graph

y against (2006)

(a)

(b)

(c)

(d)

(e)

56. Let f(x) = max (2x + 1, 3– 4x), where x is any real number. Then the minimum possible value of f(x) is (2006)

(a) (b) (c) (e) 57.

1/3 1/2 2/3(d) 4/3 5/3 A quadratic function f (x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10? (2007) (a) –105 (b) –119 (c) –159 (d) –110 (e) –180 Directions for questions 58 and 59 : Mr. David manufactures and sells a single product at a fixed price in a niche market. The selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x units is 240 + bx + cx2, where b and c are some constants. Mr. David noticed that doubling the daily production from 20 to 40 units increases the daily production cost by

However, an increase in daily production from 40 to 60 units results in an increase of only 50% in the daily production cost. Assume that demand is unlimited and that Mr. David can sell as much as he can produce. His objective is to maximize the profit 58. How many units should Mr. David produce daily? (2007) (a) 150 (b) 130 (c) 100 (d) 70 (e) Cannot be determined 59. What is the maximum daily profit, in rupees, that Mr. David can realize from his business? (2007)

(a) (b) (c) (d) (e) 60.

760 620 920 840 Cannot be determined Suppose, the seed of any positive integer n is defined as follows : seed (n) = n, if n < 10 = seed (s (n)), otherwise, where s (n) indicates the sum of digits of n. For example, seed (7) = 7, seed (248) = seed (2 + 4 + 8) = seed (14) = seed (1 + 4) = seed (5) = 5 etc. How many positive integers n, such that n < 500, will have seed (n) = 9? (2008) (a) 39 (b) 72 (c) 81 (d) 108 (e) 55 61. Let f (x) be a function satisfying f (x) f (y) = f (xy) for all real x, y. If f (2) = 4, then what is the value of

(2008)

(a) 0 (b) (c) (d) 1 (e) cannot be determined 62. [x] = Greatest integer less than or equal to x {x} = x – [x]. How many real values of x satisfy the equation 5[x] + 3{x} = 6 + x? (2009) (a) 0

(b) (c) (d) 63.

1 2 More than 2 A function f(x) is defined for all real values of x as 2f(x) + f (1 – x) = x2. What is the value of f(5)? (2009) (a) 10 (b) 17 (c) (d) Cannot be determined 64. In the X-Y plane two distinct lines are drawn parallel to the line 3y – 4x = 15, each at a distance of 3 units from the given straight line. What are the lengths of the line segments of these two lines lying inside the circle x2 + y2 = 25? (2010) (a) 6 and 8 (b) 0 and 8 (c) 0 and 10 (d) 8 and 10 65. A function f(x) is defined for all real values of x as f(x) = ax2 + bx + 1. It is also known that f (5) = f(k) = 0, where k is not equal to 5. If a < 0, then which of the following is definitely correct? (2010) (a) b < 0 (b) b > 0 (c) k < 0 (d) k > 0 66. The graph of ‘3 – x’ against ‘y + 5’ is as shown below. (All the graphs in this question are drawn to scale and the same scale has been used on each axis.)

(2010)

Which of the following shows the graph of y against x?

(a)

(b)

(c)

(d)

67. Consider the expression (a2 + a + 1)(b2 + b + l)(c2 + c + 1)(d2 + d + l) (e2 + e + l)

abcde Where a, b, c, d and e are positive numbers. The minimum value of the expression is (2010) (a) 3 (b) 1 (c) 10 (d) 243 68. If mxm – nxn = 0, then what is the value of

in terms of xn ?

(2010)

(a) (b) (c) (d) 69. If

(a) (b) (c) (d) 70.

then

(m,

(n,

0 (20 10) only when m = n only when m ≠ n only when m = – n for all m and n There are three coplanar parallel lines. If any p points are taken on each of the lines, then find the maximum number of triangles with the vertices of these

points. (2010) p2 (4p – 3) p3 (4p – 3) p (4p – 3) p3 If three positive real numbers a, b and c (c > a) are in Harmonic Progression, then log (a + c) + log (a – 2b + c) is equal to: (2010) (a) 2 log (c – b) (b) 2 log (a – c) (c) 2 log (c – a) (a) (b) (c) (d) 71.

(d) log a + log b + log c 72. When ‘2’ is added to each of the three roots of x3 – Ax2 + Bx – C = 0, we get the roots of x3 + Px2 + Qx – 18 = 0. A, B, C, P and Q are all non-zero real numbers. What is the value of (4A + 2B + C)? (2011) (a) (b) (c) (d) 73.

10 – 10 11 Cannot be determined The shaded portion of figure shows the graph of which of the following ? (2011)

(a) x (y – 2x) ≥ 0 (b) x (y – 2x) ≤ 0 (c) (d) 74. Let f be an injective map with domain{x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false. f(x) = 1, f(y) ≠ 1, f(z) ≠ 2. The value of f –1(1) is (2011) (a) x (b) y (c) z (d) None of the above 75. A function f(x) is defined for real values of x as: What f(x)? (a) (b) (c)

(2012)

the

domain

(d) 76. A function F(n) is defined as

for all natural

numbers ‘n’. If F(1) = 2, then what is the value of [F(1)] + [F(2)] + …………+ [F(50)]? (Here, [x] is equal to the greatest integer less than or equal to ‘x’) (2012) (a) 51 (b) 55 (c) 54 (d) None of these 77. At how many points do the graphs of intersect each other? (2013) (a) 0 (b) (d) 3

and y = x2 – 4

78. If f(x) = (secx + cosecx)(tanx − cotx) and in the range of

(c)

then f(x) lies (2013)

(a) (b) (c) (d) None of these 79. Let f(x) = ax2 + bx + c, where a, b and c are real numbers and a ≠ 0. If f(x) attains its maximum value at x = 2, then what is the sum of the roots of f(x) = 0?

(a) 4

(2013) –2

(b) (c) 8 (d) –4 80. ‘f’ is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(–7) = 7, then the value of f(–49) + f(49) is (2014) (a) 7 (b) 14

(c) 0 (d) 49 81. The coordinates of two diagonally opposite vertices of a rectangle are (4, 3) and (-4,-3). Find the number of such rectangle(s), if the other two vertices also have integral coordinates. (2015) (a) 1 (b) 4 (c) 5 (d) 10 82. If log 2x = 2 log (x + 1), find the number of real values of x?. (2015) 83. If where [x] denotes the greatest integer less than or equal to x, then (2016) (a) 96 n < 104 (b) 104 < − n < 107 (c) 107 n < 111 (d) 111 n < 116 84. Consider two figures A and D that are defined in the co-ordinate plane. Each figure represents the graph of a certain function, as defined below: A: D: If the are enclosed by A and D is O. Which of the following is a possible value of (a, d) : (2016) (a) (2,1) (b) (−2, 1) (c) (−2, 3) (d) (2 ,3) 85. The area of the closed region bounded by the equation |x| + |y| = 2 in the two-dimensional plane is (2017) (a) 4π (b) 4 (c) 8 (d) 2π

(b)

= 6. 2.

(a) or 2 = –2 relation does not hold for a = –2 and b = –3 or a < 0, b < 0

(b) And

Clearly (c)

or 5.

(b) From Q. 3 we have Therefore above expression becomes (x). (x) = x2. (c) we have, So given expression reduces to f (x) that is 2x + 3. (a) Find Given Now, And

= 8.

Hence, (d) (a)

. which is false.

(b) which is again false. (c) or

which is false

(d) or TRUE 9. (a) To solve this, take arbitrary values of a in the specified In option (a), 0 < a < 3, take a = 1. Then me(a2 – 3a, a – 3) < 0 ⇒ me(–2, –2) < 0 ⇒ –2 < 0, which is true In option (b), a < 0, take a = –2. Then me(a2 – 3a, a– 3) < 0 ⇒ me(10,–5) < 0 ⇒ 10 < 0,which is false In option (c), a > 3, take a = 4. Then me (a2 – 3a, a – 3) < 0 ⇒ me (4, 1) < 0 ⇒ 4 < 0, which is false In option (d), a = 3 then me(a2 – 3a, a – 3) < 0 ⇒ me (0, 0) < 0 ⇒ 0 < 0, which is false ∴ Option (a) is right one. 10. (a,b)In option (a), take a = 2 In option (b), take a = –1 Again take a = 2 which true In option (c), take a = 3

range

which is false In option (d), take a = 4 which is false. Hence options (a) and (b) are correct. 11. (c) Equating 2 + x2 = 6 – 3x

But x > 0. So, x = 1 Thus, 2 + x2 = 3 and 6 – 3x = 3 It means the largest value of function min (2 + x2, 6 – 3x) is 3. 12. (d)

)

13. (b)

14.

(d) Since x > y > z > 0

and le = max (x – y, y – z) we cannot find the value of la and le. Therefore we can’t say whether la > le or le > la Hence, we can’t comment, as data is insufficient. 15. (b) la (10, 5, 3) = 8; le (8, 5, 3) = 3

16. (c) ma ( 15, 10, 9 )

[5 + 19] = 12

min (10, 6) = 6 ; le (9, 8, 12) = 1; le (15, 6, 1) = 9. 17. (c)

18. (d) Here, (1 # 1) # 2 = (1 + 1) # 2 = 2 + 2 = 4 And But

which is –ve,

so the operation (ab)a + b fails. 19. (b) Equating with a # b = a + b : Option (a) : b = –Y = –1 Operation fails for –ve value of b. Option (b) : b = –Y > 0 at Y < 0 a=X>0 ∴ = (a + b) (ab)–(a + b) Operation succeeds. Option (c) : b = – Y < 0 as Y > 0 Operation fails. Option (d) : a = X < 0 as X < 0 Operation fails. Hence option (b) is correct. 20. (b) f(x, y) = |x + y| F(x, y) = – f(x, y) = – |x + y| G(x, y) = – F(x, y) = |x + y| We will check all the options one by one. Option (a) :

0 > – 2 |x + y| which is invalid when x + y = 0 Option (b) :

which is true. Option (c) :

which is not valid when x = 0, y = 0. Option (d) :

which is not valid when x = 1, y = 0 etc. Hence option (b) is correct. 21. (c) Consider option (a) : as x = y Consider option (b) :

as x = y Consider option (c) :

as – F (x, y) . G(x, y) = – [–|x + y| . |x + y|] = 4x2 for x = y. And log216 = = 4, which gives value of (c)as x2. Consider option (d) :

as x = y 22. (a) Solving the given function from innermost bracket, we obtain

23. (d) From the graph F1(x) = F(x) for but, F1(x) = –F(x) for . No option of (a, b, c) satisfy this condition. 24. (d) From the graphs, F1(x) = –F(x) and also F1(x) = F(–x). So, both (a) and (b) are satisifed which is not given in any of the option. 25. (d) By observation F1(x) = – F(x) and also F1(x) = F(–x). So, both (a) and (b) are satisfied. Since no option is given, mark (d) as the answer. 26. (c) By observation F1(x) = –F(–x). This can be checked by taking any value of x say 1, 2. So, answer is (c). 27. (b) Out of n numbers, HCF of 1st and 2nd numbers can be calculated by invoking the function once. Then HCF of this HCF and 3rd number can be calculated by invoking the function 2nd time and so on.

Each time the function is invoked, instead of two numbers we are left with one, i.e., one number is eliminated. Getting the final HCF means eliminating(n – 1) numbers and thus function has to be invoked(n – 1) times. 28. (a) From the given conditions, we obtain @ \ (A, B) = B × A And

∴

29. (d)

30. (d) We know that

Taking option (a) :

when x and y are positive Thus for x + y > 1, (x + y) 0.5 < (x + y)2 Therefore, Taking option (b) : x and y are negative Take

Clearly, f (x, y) < g (x, y) Taking option (c) : Using option (a) or (b), we get f (x, y) < g (x, y) Hence option (d) is correct. 31. (c) When statement (a) is true. When x, y < –1, again statement (b) is true. When x, y > 1, x + y > 1, hence f (x,y) < g (x,y). Thus statement (c) given is necessarily false. 32. (b) When x + y =1 we have i.e., Thus correct answer is (b). 33. (b) At x = 1, y = 4; and x = 2, y = 8 4 = a + b and 8 = 2a + b a = 4, b = 0 So, y = ax + b y = 4x

given

The other values do not satisfy this last equation. so option (a) is not fit. Similarly, we may find that option (c) is also not fit. But option (b) is absolutely fit. 34. (d) Put x = 0, Put y = 2, . 35. (b) As graph is symmetrical about y axis, we can say function is even, so 36. (d) We see from the graph. Value of f (x) in the left region is twice the value of f (x) in the right region. So, or 37. (c) f (–x) is replication of f (x) about y axis, –f (x) is replication of f (x) about x-axis and –f (–x) is replication of f (x) about y axis followed by replication about x-axis . Thus given graph is f (x) = –f (–x). For Qs. 38-41. Putting the actual values in the functions, we get the required answers. 38. (c) m (a, b, c) = –5, M(a, b, c) = 2

And So

is maximum and maximum value is –

3/2. 39. (c) Suppose a = –1, b = –2, c = –4 Then m (a, b, c) = min (a + b, c, a) = min(–3, –4, –1) = –4; –M (–a, a, –b) = –max (0, –b, –a) = – max(0, 2, 1) = –2; m (a+b, b, c)

= min (a + 2b, c, a + b) = min(–5, –4, –3) = –5 Clearly option (c) is correct. 40. (c) Here, M (a – b, b, c) = max (a, c, a – b) = max (2, 3, –2) = 3 m (a + b, c, b) = min (a + b + c, b, a + b) = min (9, 4, 6) = 4 And –M (a, b, c) = –max (a + b, c, a) = – max (6, 3, 2) = – 6 ∴ m (M (a – b, b, c), m (a + b, c, b), –M (a, b, c)) = m (3, 4, – 6) = min (3 + 4, – 6, 3) = –6. 41. (d)

as x is positive ; ; . Thus

42. (c) When x is negative, f(x) = 1 + x ; ; ; and 43. (b)

and ∴

[Divide and multiply the numerator & denominator by (1 + xy)]

44. (d) [x] means if x = 5.5, then [x] = 5 L[x, y] = [x] + [y] + [x + y], R(x, y) = [2x] + [2y] Relationship between L (x, y) and R (x, y) can be found by putting various values of x and y. Put x = 1.6 and y = 1.8. L (x, y) = 1 + 1 + 3 = 5 and R (x, y) = 3 + 3 = 6 So, (b) and (c) are wrong. If x = 1.2 and y = 2.3. L(x, y) = 1 + 2 + 3 = 6 and R (x, y) = 2 + 4 = 6 Or R(x, y) = L(x, y) , so (a) is not true We see that (d) will never be possible 45. (d) g (x) = max (5 – x, x + 2). Drawing the graph,

The bold lines representing the function g (x) intersect one another at a unique point. It clearly shows that the smallest value of g (x) = 3.5.

46. (b) f (x) =

can attain minimum value

when either of the three terms = 0. Case I : When Value of f (x) = 0.5 + 1.6 = 2.1. Case II : When Value of f (x) = 0.5 + 0 + 1.1 = 1.6. Case III : When |3.6 – x| = 0 x = 3.6 Value of f (x) = 1.6 + 1.1 + 0 =2.7. Hence the minimum value of f (x) is 1.6 at x=2.5. 47. (b) The curves can be plotted as follows :

We see that they meet once. 48. (d) Solving the given two curves, we get x3 + x2 + 5 = x2 + x + 5 ⇒ x3 – x = 0 ⇒ x = 0, 1, –1 All these three points lie in . At x = 0, y = 0 + 0 + 5 = 5; y = 0 + 0 + 5 = 5 ⇒ Point = (0, 5)

At x = 1, y = 13 + 12 + 5 = 7; y = 12 + 1 + 5 = 7 ⇒ Point = (1, 7) At x = –1, y = (–1)3 + (–1)2 + 5 = 5; y = (–1)2 – 1 + 5 = 5 ⇒ Point = (–1, 5) Hence, the two curves intersect at three points. 49. (a) Using the given conditions, we find the following number of members on the indicated date:

Since, on July 2, 2004, number of members of each society are same. ∴ n + 6b = nr6 ......(i) But Putting b = 10.5 n in (i), we obtain n + 6 × 10.5 n = nr6 or 64 n = nr6 or r = 2. 50. (b) f (x) = x3 – 4x + p f (0) = p (positive) Let p > 0 .......(ii) f (1) = p – 3 (which will be negative) ⇒ p – 3 < 0 or p < 3 .......(ii) From (i) and (ii) 0 < p < 3. Again let p < 0 (iii) then p – 3 > 0 (iv) From (iii) and (iv) : 3 0, then f1(–x) = 0 and if x < 0 then f1(x) = 0 f2(x)f3(x) = f1(–x)[–f2(x)] = f1(–x)[–f1(–x)] = 0 if x 0and < 0 if x < 0 f2(x)f4(x) = f1(–x) f3(–x) = f1(–x) [–f2(–x)] = –f1(–x) f1(x) = 0 (As above) So all of them are zero. (b) f4(x) = f3(–x) = –f2(–x) = –f1(x) So, (a) and (c) are not true. –f3(–x) = f2(–x) = f1(x), i.e., option (b) is true. (d) g(x + 1) + g(x – 1) = g(x) ⇒ g(x + 1) = g(x) – g(x – 1) Using x = x + 5 ⇒ g(x + 6) = g(x + 5) – g(x + 4) = g(x + 4) – g(x + 3) – g(x + 4) = –g(x + 3) = –[g(x + 2) – g(x + 1)] = –g(x + 2) + g(x + 1) = –g(x + 1) + g(x) + g(x + 1) = g(x) Hence p = 6. (d) All graphs in this question are drawn to scale and same scale is used on each axis. By inspection of the graph of (y – x) against (y + x), you can find that angle of inclination of the graph (line) is more than 45°. ∴ Slope of the line = tan (45° + θ), where 0° < θ < 45°

[By componendo and dividendo] Hence slope of the graph (line) of y against x

Now, 0° < θ < 45°. 0 < tan θ < 1

By inspection of the graph (line) of y against x, you can find that the slope of the graph of y against x is less than –1 only in option (d). Alternative Method : In the normal xy-plane, the graph of y – x = 0 is a line passing through the origin and bisects quadrant I and III of the x–y plane. The graph of y + x = 0 is a line passing through the origin and bisects the II and IV quadrants of x – y plane. So line y – x = 0 and y + x = 0 are perpendicular to each other like the lines x = 0 and y = 0. Also x = 0 and y = 0 repersent y-axis and x-axis. In the same way y – x = 0 and y + x = 0 reprersent (y + x) axis and (y – x) axis respectively as shown in the graph.

Here dotted line is the graph drawn in the question.If we observe this dotted line with respect to x- andy-axis, it looks like

So the option (d) is correct. 56. (e) f(x) = max (2x + 1, 3 – 4x) The minimum possible value in this case will be when 2x + 1 = 3 – 4x. The reason for this is that the ‘max’ function will only take the higher value out of 2x + 1 and 3 – 4x. So for minimum value of f(x) 2x + 1 = 3 – 4x At

57. (c) Let the quadratic function be ax2 + bx + c At x = 0, ax2 + bx + c = 1 c=1 At x = 1, ax2 + bx + c = a + b + c = 3 or a + b = 2...(i) As the function attains maxima at x = 1, so or

...(ii)

Using (i) and (ii), we get a = – 2 and b = 4 At x = 10, ax2 + bx + c = – 2(102) + 4 × 10 + 1 = – 200 + 41 = – 159. 58. (c) Cost function, C(x) = 240 + bx + cx2 When production changes from 20 to 40 units, then C(40) – C(20) = 3.C(40) – 5.C(20) = 0 3[240 + 40b + 1600c] – 5[240 + 20b + 400c] = 0 140c + b = 24 ...(i) When production changes from 40 to 60 units, then C(60) – C(40) = 2.C(60) – 3.C(40) = 0 2[240 + 60b + 3600c] – 3[240 + 40b + 1600c] = 0 480 + 120b + 7200c – 720 – 120b – 4800c = 0 2400c – 240 = 0

b = 10

[Putting

Cost function, Profit function, P(x) = R(x) – C(x) P(x) = 30x –

in (i)]

On differentiating we get, ...(ii) Put P’(x) = 0, for maxima or minima x = 100 Again differentiating equation (ii), we get

Hence, profit is maximum when production = 100 units 59. (a) Maximum daily profit = P(100) = – 1000 + 2000 – 240 = Rs 760 60. (e) The given function can be described as seed (n) = Sum of the digits of n. Here, we have to find the number of positive integers n such that n < 500 and sum of the digits of n = 9. So, the number n will be 9, 18, 27, .... and so on but less than 500. Actually these are the numbers divisible by 9 but less than 500. Now,

= 55.55 .....

Hence, required number of n = 55. 61. (b) f (x). f (y) = f (x.y) ⇒ p (0) . p (1) = p (0) ∴ p (1) = 1 Now, p (2) .

= p (1)

⇒ ∴ 62.

(a) {x} = x – [x]

. or {x} + [x] = x

The given equation 5[x] + 3{x} = 6 + x ⇒2[x] + 3([x] + {x}) = 6 + x reduces to 2[x] + 3x = 6 + x or 2[x] + 2x = 6 or [x] + x = 3 ...(i) Since 3 and [x] are both integers, in the above equation x must also be an integer. ⇒ [x] = x Hence, 2x = 3 or No satisfactory solution in equation ...(i) 2 63. (c) 2f(x) + f(1 – x) = x Replacing x by (1 – x) in the above equation, we get:2f(1 – x) + f(x) = (1 – x)2 Solving the above pair of equations, we get:

Thus, 64.

Let the new lines drawn parallel to 3y – 4x – 15 = 0 be L1 and L2. Distance of L1 from origin = 3 + 3 = 6 units Distance of L2 from origin = 3 – 3 = 0 units The circle x2 + y2 = 25 has a radius of 5 units. Hence line segment of L1 lying outside the circle will be of zero length (L1 does not cut the circle). Chord cut by L2 will be diameter = 10 units 65. (c) It can be concluded that 5 and k are the two distinct roots of the equation ax2 + bx + 1 = 0.

Also, product of the roots Hence, 5k < 0 ⇒ k < 0. 66. (c) The given graph must be of an equation of type

y + 5 = kx – 3k y = kx – (3k + 5) This is the equation of a line in the x-y plane, whose slope (k) is greater than zero and it has a negative intercept (of length 3k + 5) on the y-axis. Only one graph satisfies the condition. 67. (d)

....By AM – GM relation

Hence,

a or

Similarly, a similar relation for b, c, d and e and then multiplying, we get

68. (a) mxm = nxn ∴ xm =

∴ Given

69. (d) put

, f (x + k, x – k) = 8xk

put x + k = A, x – k = B or

and

Now, f (A, B) = f (A, B) = 2 (A2 – B2) ; f (B, A) = 2 (B2 – A2) then f (m, n) + f (n, m) = 0 for all m, n 70. (a) The number of triangles with vertices on different lines The number of triangles with 2 vertices on one line and the third vertex on any one of the other two lines p

= 3C1 ( C2 × 2 C1) = 6p.

= 3p2 (p – 1)

∴ the required number of triangles = p3 + 3p2 (p – 1) = 4p3 – 3p2 = p2 (4p – 3) (The work “maximum” shows that no selection of points from each of the three lines are collinear). 71. (c) Since a, b, c are in H.P. ∴

, ⇒ b (a + c) = 2ac

Now log (a + c) + log (a – 2b + c) = log [(a + c){(a + c) – 2b}] = log [(a + c)2 – 2b (a + c)] = log [(a + c)2 – 2 × 2ac] = log (a – c)2 or log (c – a)2 = 2 log (a – c) or 2 log (c – a) ∴ log (a + c) + log (a – 2b + c) = 2 log (c – a)

72. (a) Let the roots of the equation x3 – Ax2 + Bx – C = 0 be α, β, γ respectively. So the roots of x3 + Px2 + Qx – 18 = 0 will be α + 2, β + 2, γ + 2. (α +2)(β +2)(γ +2) = 18 ⇒ 4(α + β + γ) +2 (αβ + βγ + γα) + αβγ + 8 =18 ⇒ 4A + 2B + C = 10 73. (a) Each of the answer choices in the form of the product of two factors on the left and a “≥ 0” or “ ≤ 0” on the right. The product will be negative when the two factors have opposite signs, and it will be positive when the factors have the same sign. Choice (a), for example, has a “≥ 0”, so you’ll be looking for other factors to have the same sign. Either : x ≥ 0 and y – 2x ≥ 0 ⇒ x ≥ 0 and y ≥ 2x or x ≤ 0 and y – 2x ≤ 0 ⇒ x ≤ 0 and y ≤ 2x The graph of x ≥ 0 and y ≥ 2x looks like this :

The graph of x ≤ 0 and y ≤ 2x looks like this.

Together, they make the graph in the figure. 74. (b) There are following three cases arise : Case (I) : When is correct then

and

clearly the mapping f is not injective (i.e., not one-one) Hence this case is not possible. Case (II) : When is correct then Hence z mapped to 2 but x and y or mapped to 2 or 3 or one of them mapped to 2 and the other mapped to 3.

Clearly in all the above 4 sub-cases, we see that the mapping f is not injective (i.e. not one-one). Hence, this case is not possible. Case (III) : If is correct then Hence y mapped 1 but x mapped 2 or 3 Whereas y mapped 1 or 3. The possible four mapping are as follows :

Clearly in sub case (c), the mapping is injective (i.e., one-one). Hence this case is possible and 75. (c)

f(x) =

= Base of the logarithmic function 5 – |x| > 0 and 5 – |x| ≠ 1 So, x ∈ (–5, –4) ∪ (–4, 4) ∪ (4, 5) ...(i) Also, (x–1) (x–2) (x–4) must be greater than zero as well So, x ∈ (1, 2) ∪ (4, ∞) ...(ii) Combining (i) and (ii) : x ∈ (1, 2) ∪ (4, 5) 76. (a)

Given that F(n – 1) =

and F(1) = 2.

For n = 2 : F(1) = ⇒ F(2) =

Similarly, we can find the values of F(3), F (4), F (5) as

and

respectively. ⇒ F(n) = From this we can say that every term except [F(1)], of the series [F(1)] + [F (2)] + .... + [F (50)] is equal to 1 as for ‘n’ > 0, F (n) lies between 1 and 2. Therefore, [F (1)] + [F (2)] + .... + [F (50)] = 51. Hence, option (a) is the correct choice. 77. (d) The graphs of the two functions are shown below: If a > 0 in any parabolic function then parabola open up side

From the above figure, it is obvious that the graphs of the two functions intersect at three points. 78. (b) Convert into sine form this is a increasing function At x =

, f(x) = 0

At x =

, f(x) = ∞

Hence, f(x) lies in the range of (0, ∞) 79.

(a)

The sum of the roots of ax2 + bx + c = 0 is

By differentiating we get 2ax + b = 0 ax2 + bx + c attains its maximum value at x = ∴

Hence, the sum of the roots = 4. 80. (b) Let us assume f(0) = K, where ‘K’ is a constant. Then, f(0 + y) = f(0.y) = f(0) = K and f(x + 0) = f(x.0) = f(0) = K.

This proves that the function is a constant function. Thus, the value of f(–49) = f (49) = 7 Hence, f(–49) + f(49) = 14.

81. (c)

Other two vertices will make two right angled triangles with AB as the common hypotenuse. So they must lie on the circle with AB as the diameter and O as the centre. Radius of that circle will be 5 units. There will be 5 such pairs in which both the coordinates are integers. [(5, 0), (–5, 0), [(4, 3), (4, – 3)], [(–3, 4), (3, –4)] [(–3, –4), (3, 4)] and [(0 5), (0, –5)] 82. (0) Clearly, x > 0 So, 2x = x2 + 2x + 1 ⇒ 0 = x2 + 1 Here, no any real roots. Hence, there are no solutions. 83. (c) [log10 x] = 0, for any value of x ∈ {1, 2, ......9), ...(1) Similarly [log10x] = 1, for x ∈ {10, 11, 12 ... 99}...(2) and [log10x] = 2, for x ∈ {100, 101, 102, ... 999} ...(3) Now consider, then [log101] + [log102] + [log103] ... [log10 n] = 0 (i.e., ≠ n) Hence the expression given in the question cannot be satisfied. Now consider, then [log101] + [log102] ... [log10n]

From (1) and (2), the above expression becomes (0 + 0 ... 9 times) + (1 + 1 + ... (n – 9) times) = n – 9 Using the same approach, for 100 ≤ n ≤ 999, [log 101] + [log102] ... [log 10n] = 90 + 2(n – 99) If can be seen that, only for the third case i.e., 100 ≤ n ≤ 999, can the expression given in the question be satisfied. Hence 90 + 2(n – 99) = n ⇒ n = 198 – 90 = 108 ∴107 ≤ n < 111. 84. (b) The lines represented by A where a > 0 and when a < 0 are given in the following figures

The area enclosed by A and D would be zero if d < |a|. In choice (b), d = 1 and a = – 2 i.e., d < |a|. If a > 0, then the only case when the area enclosed by A and D will be zero, is when d = 0.

85. (c)

Area = =8

AVERAGE, RATIO & PROPORTION Directions for questions 1 to 3 : Read the information given below and answer the questions that follow : Alphonso, on his death bed, keeps half his property for his wife and divides the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs 1,575,000. 1.

What was property?

the

worth

the

total

(1994) (a) Rs 30 lakh (b) Rs 8 lakh (c) Rs 18 lakh (d) Rs 24 lakh 2.

What share?

was (1994)

(a) Rs 4 lakh (b) Rs 12 lakh (c) Rs 6 lakh

Carl’s

original

(d) Rs 5 lakh 3.

What was the ratio of the property owned by the widows of the three sons, in the end? (1994) (a) 7 : 9 : 13 (b) 8 : 10 : 15 (c) 5 : 7 : 9 (d) 9 : 12 : 13 4.

A man buys spirit at Rs 60 per litre, adds water to it and then sells it at Rs 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%? (1994)

(a) 9 : 1 (b) 10 : 1 (c) 11 : 1 (d) None of these 5.

Two liquids A and B are in the ratio 5 : 1 in container 1 and in container 2, they are in the ratio 1:3, what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1:1? (1996) (a) 2 : 3 (b) 4 : 3 (c) 3 : 2 (d) 3 : 4 Directions for questions 6 to 8 : Read the information given below and answer the questions that follow : There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each.

(a) (b) (c) (d) 7. (a) (b) (c) (d) 8. (a) (b) (c) (d)

(a) (b) (c) (d)

The groups A and C are combined to form group D. What is the average weight of the students in group D? (1997) more than the average weight of A more than the average weight of C less than the average weight of C Cannot be determined If one student from Group A is shifted to group B, which of the following will be true? (1997) The average weight of both groups increases The average weight of both the groups decreases The average weight of the class remains the same Cannot be determined If all the students of the class have the same weight, then which of the following is false? (1997) The average weight of all the four groups is the same. The total weight of A and C is twice the total weight of B. The average weight of D is greater than the average weight of A. The average weight of all the groups remains the same even if the number of students are shifted from one group to another. The average marks of a student in ten papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest. (1997) 55 60 62 Can’t be determined

10. The value of each of a set of silver coins varies as the square of its diameter, if its thickness remains constant, and it varies as the thickness, if the diameter remains constant. If the diameters of two coins are in the ratio 4 : 3, what should the ratio of their thicknesses be if the value of the first is 4 times that of the second? (1997) (a) 16 : 9 (b) 9 : 4 (c) 9 : 16 (d) 4 : 9 11. I have one rupee coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio 2.5 : 3 : 4. If the total amount with me is Rs 210. Find the number of one rupee coins. (1998) (a) 90 (b) 85 (c) 100 (d) 105 12. There are two containers : the first contains 500 ml of alcohol, while the second contains 500 ml of water. Three cups of alcohol from the first container is removed and is mixed well in the second container. Then three cups of this mixture is removed and is mixed in the first container. Let ‘A’ denote the proportion of water in the first container and ‘B’ denote the proportion of alcohol in the second container. Then, (1998) (a) A > B (b) A < B (c) A = B (d) Cannot be determined 13. Mr Launcher plans to launch a new TV channel called Dekha Dekhi (DD). He envisages a viewership of 42%. He plans to

(a) (b) (c) (d) 14.

(a) (b)

capture the viewership from CAT TV and MAT TV, which currently hold viewership of 35% and 48%, each having a distinct and separate target audience. In what ratio should he capture the target audience of the two channels (1999 ) 6:7 7:6 1:1 8:9 There are seven consecutive natural numbers such that the average of the first five is n. Then average of all seven numbers will be? (2000) n n+1

where k is a positive constant.

(d) 15. Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took 1/3 of the mints, but returned four because she had a momentary pang of guilt. Fatima then took1/4 of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl? (2001) (a) 38 (b) 31 (c) 41

(d) None of these 16. Three maths classes: X, Y and Z take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average for all the three classes? (2001) (a) 81 (b) 81.5 (c) 82 (d) 84.5 17. A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 (a) (b) (c) (d) 18.

(a) (b)

. What

was the number erased? (2001) 7 8 9 None of these A change making machine contains 1 rupee, 2 rupee and 5 rupee coins. The total number of coins is 300. The amount is Rs 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by Rs 40. The total number of 5 rupee coins is (2001) 100 140

(c) 60 (d) 150 19. At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs 120 exactly. At the same place it would cost Rs 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries? (2001) (a) Rs 31 (b) Rs 41 (c) Rs 21 (d) Cannot be determined 20. Mayank, Mirza, Little and Jaspal bought a motorbike for $60.00. Mayank paid one half of the sum of the amounts paid by the other boys, Mirza paid one third of the sum of the amounts paid by the other boys; and Little paid one fourth of the sum of the amounts paid by the other boys. How much did Jaspal have to pay? (2002) (a) 15 (b) 13 (c) 17 (d) None of these 21. Using only 2, 5, 10, 25 and 50 paise coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise, and Rs 1.01 to three different persons? (2003) (a) 19 (b) 20 (c) 17

(d) 18 22. In a coastal village, every year floods destroy exactly half of the huts. After the flood water recedes, twice the number of huts destroyed are rebuilt. The floods occurred consecutively in the last three years namely 2001, 2002 and 2003. If floods are again expected in 2004, the number of huts expected to be destroyed is (2003) (a) Less than the number of huts existing at the beginning of 2001 (b) Less than the total number of huts destroyed by floods in 2001 and 2003 (c) Less than the total number of huts destroyed by floods in 2002 and 2003 (d) More than the total number of huts built in 2001 and 2002 Directions for questions 23 & 24 : Read the information given below and answer the questions that follow : A certain perfume is available at a duty-free shop at the Bangkok International Airport. It is priced in the Thai currency Baht but other currency are also acceptable. In particular, the shop accepts Euro and US Dollar at the following rates of exchange : US Dollar 1 = 41 Bahts, Euro 1 = 46 Bahts The perfume is priced at 520 Bahts per bottle. After one bottle is purchased, subsequent bottles are available at a discount of 30%. Three friends S, R and M together purchase three bottles of the perfume, agreeing to share the cost equally. R pays 2 Euros. M pays 4 euros and 27 Thai Bahts and S Pays the remaining amount in US Dollars. 23. How much does R owe to S in Thai Baht? (2003C) (a) 428

(b) (c) (d) 24.

416 334 324 How much Dollars?

does

owe

(2003C) (b) (c) (d) 25.

(a) (b) (c) (d) 26.

(a) 3 4 5 6 A milkman mixes 20 litres of water with 80 litres milk. After selling one-fourth of this mixture, he adds water to replenish the quality that he has sold. What is the current proportion of water to milk? (2004) 2:3 1:2 1:3 3:4 A sprinter starts running on a circular path of radius r metres. Her average speed (in meters/minute) is r during the first 30 seconds,

during next one minute,

during next 2 minutes,

during next 4 minutes, and so on. What is the ratio of the

(a) (b) (c) (d)

time taken for the nth round to that for the previous round? (2004 - 2 marks) 4 8 16 32

27. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be: (2006) (a) 101 : 88 (b) 87 : 100 (c) 110 : 111 (d) 85 : 98 (e) 97 : 84 28. If of

and ?

, then what is the value (2006)

(a) (b) (c) (d) (e) 29. Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight–member joint family is nearest to (2007)

(a) (b) (c) (d) (e) 30.

(a) (b) (c) (d)

24 years 23 years 22 years 21 years 25 years On 1st January, 2000 the average age of a family of 6 people was ‘A’ years. After 5 years a child was born in the family and one year after that the average age was again found to be ‘A’ years. What is the value of ‘A’? (Assume that there are no other deaths and births.) (2009) 25 35 37 39

31. Three truck drivers, Amar, Akbar and Anthony stop at a road side eating joint. Amar orders 10 rotis, 4 plates of tadka, and a cup of tea. Akbar orders 7 rotis, 3 plates of tadka, and a cup of tea. Amar pays ` 80 for the meal and Akbar pays ` 60. Meanwhile, Anthony orders 5 rotis, 5 plates of tadka and 5 cups of tea. How much (in `) will Anthony pay? (2009) (a) 75 (b) 80 (c) 95 (d) 100 32. Two different solutions of honey, milk and water are mixed with each other three times in varying proportions. The concentration of honey and milk in the three resulting solutions are found to be (10%, 16%), (12%, 12%) and (16%, x%) respectively. What is the value of x? (2010)

(a) (b) (c) (d) 33.

4 7 8 10 The average age of a couple is 25 years. The average age of the family just after the birth of the first child was 18 years. The average age of the family just after the second child was born was 15 years. The average age of the family after the third and the fourth children (who are twins) were born was 12 years. If the present average age of the family of six persons is 16 years, how old is the eldest child ? (2010) (a) 6 years (b) 7 years (c) 8 years (d) 9 years 34. The letters of the English alphabet, in the order A to Z, are made to represent 26 numbers which are in Arithmetic Progression. The sum of the numbers representing A, C and E is 36 while that of A, C, E and G is 60. What is the sum of the numbers representing B, D, F and H? (2011) (a) 96 (b) 66 (c) 72 (d) 84 35. Three men are gambling in Casino Royal. They start with sums of money in the ratio 7 : 6 : 5 and finish with sums of money in the ratio 6 : 5 : 4, in the same order as before. One of them won $ 12. How many dollars did he start with ? [The three men gambled amongst each other

only] (a) 36.

(a) (b) (c) (d)

(2012) $1080 (b) $420 (c) $210 (d) None of these The ratio of alcohol to water in an alcohol-water solution is 9 : 1. The rate of evaporation per hour of alcohol and water on boiling is 20% and 5% respectively. The minimum number of hours for which the solution needs to be boiled so as it contains at least 18% of water? (2013) 3 4 3.5 4.5

37. There are 40 students in a class. A student is allowed to shake hand only once with a student who is taller than him or equal in height to him. He can’t shake hand with anyone who is shorter than him. Average height of the class is 5 feet. What is the difference between the maximum and minimum number of handshakes that can take place in the class? (2015) (a) (b) 361 (c) (d) 38. A certain sum of money is made up of Re. 1, 50 paise and 25 paise coins. The ratio of the number of these coins is 5 : 6 : 8. Then, 3/5th of the Re. 1 coins are changed to 50 paise and 25 paise coins, such that the ratio of the total number of these coins in the same order became 1: 2. Now, half of the 50 paise coins

are changed to Re. 1 coins and all the 25 paise coins are changed to Re. 1 and 50 paise coins in the ratio 7: 4. What is the ratio of the Re. 1 and 50 paise coins at the end of the conversions? (Note:- If you change a Re.1 coin into 50 paise coins, then you will get two coins of 50 paise for a Re. 1 coin.) (2015) (a) 11 : 23 (b) 16 : 13 (c) 54 : 71 (d) None of these 39. Arun’s present age in years is 40% of Barun’s. In another few years, Arun’s age will be half of Barun’s. By what percentage will Barun’s age increase during this period? (2017) 40. Suppose, C1, C2, C3, C4 and C5 are five companies. The profits made by C1, C2 and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of `19 crore more than C1, then the total profit (in `) made by all five companies is (2017) (a) 438 crore (b) 435 crore (c) 348 crore (d) 345 crore 41. A stall sells popcorn and chips in packets of three sizes : large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio (2017) (a) 1 : 1 (b) 8 : 7

(c) 4 : 3 (d) 6 : 5 42. A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is (2017) (a) 9.5 (b) 10 (c) 4.5 (d) 6 1.

(d) Let the total property of Alphonso be Rs x. After hise demise, First distribution Wife got

and each son got

;

2nd distribution After demise of Ben, Ben’s wife got Carl and Dave got

3rd distribution Carl’s bequest Carl’s widow gets

and Dave get

∴ Dave’s total property 4th distribution

When Dave dies his mother gets

and

Dave’s widow gets Mother’s total property is So, or ∴ 2.

Total property was Rs 24 lakh.

(a) Carl’s original share

and x = 24 lakh

∴ Share 3.

(b) Ben’s widow gets

= 2 lakh

Carl’s widow gets Dave’s widow gets Required ratio 4.

(b) Cost of mixture, C.P = S.P – Profit Let C.P. of mixture be Rs x per litre. or or

⇒

Fraction of pure spirit in the mixture

∴ Fraction of water in mixture Hence, ratio of spirit to water 5.

(d) Let the ratio in which the contents of the two containers are mixed be x : y Hence, we have

(d) Average weight of the students in group D cannot be determined since we do not know the average weight of each student. The given data is insufficient to compare its average with other groups. 7. (c) If one student from group A is shifted to group B, still there is no effect on the whole class. In any case, the no. of students inside the class is same. Hence the average weight of the class remains same. 8. (c) Since all the students of the class have the same weight, then the average of weight of any group of any no. of students will be the same as that of each students weight. Hence, the average weight of D cannot be greater than average weight of A. 9. (b) Let the lowest marks be x Then, ⇒ x + 92 = 152 ∴ x = 60 10. (b) Let the diameters and thickness of the two coins be D1T1 and D2T2 respectively Value of coin 1 : value of coin 2 = 4 : 1

or 11.

(d) Let the no. of one rupee, fifty paise and twenty five paise coins be 2.5x, 3x and 4x respectively. So, 2.5x × 1 +

∴ 1 Re coins = 2.5 × 42 = 105 12. (c) Let capacity of each cup be 100 ml After first operaton, first container will have 200 ml of alcohol and second container will have 300 ml alcohol and 500 ml water. Ratio of water to alcohol in the second container = 5 : 3. After second operation, the quantity of water and alcohol left would be

and

respectively in the first container. and the quantity of water and alcohol in the first container is 187.5 ml and (200 + 112.5) ml = 312.5 ml hence, ratio of water and alcohol = 187.5 : 312.5 = 3 : 5 and the ratio of alcohol to water = 5 : 3. Hence, on comparing ratio of water and alcohol in both the containers we find that A = B. 13. (a) This is an alligation problem where the mean rate is given as 42% i.e. % of viewership for Dheka-Dheki and the other two rates are 35% i.e., % of viewership of the CAT TV and 48% i.e., % viewership of MAT TV respectively.

Hence, the ratio in which he captures the target audience is 6 : 7. 14. (b) If n is the average of 5 natural numbers. Therefore n should be the middle term. Then the first five numbers will

n – 2, n – 1, n, n + 1, n + 2 Now, , n + 4 will be all seven no. ∴ Hence, new average will be (n + 1). 15. (d) Let number of mints = x Sita took :

; Fatima took :

;

Eswari took : ∴

Mints remaining in the bowl

= = 17

∴ x = 48. 16. (b) Let no. of students in classes X, Y and Z = x, y and z respectively. ....(i) and

....(ii)

We have to find From (i) 4x = 3y or From (ii) 5y = 4z or

;

∴

Required average

17. (a) Let number erased be x The average of the remaining no. = Here n = 69 and x = 7 satisfy the above equation. 18. (b) Let number of 1 rupee coins = x; 2 rupees coin = y and 5 rupees coin = z x + y + z = 300 ...(i) ...(ii) ...(iii) or y = 40 + x Multiply (i) by 5 and subtract (ii), 540 = 4x + 3y put y = 40 + x 549 = 4x + 3x + 120 or 420 = 7x or x = 60, y = 100 & z = 140 19. (a) Let the cost of burger, shake and one order of fries be x, y and z respectively. According to question ....(i) and ....(ii) Subtracting (i) from (ii), ....(iii) Multiplying (i) by 4, (ii) by 3 and subtracting (ii) from (i) We get, = –13.5 ....(iv)

Adding (iii) and (iv), we get, = 31 20. (b) Let Mayank Paid $ x, Mirza Paid $ y, Little paid $ z , Jaspal paid $ u According to question ;

and

Given x + y + z + u = 60, u =? So,

x + y + z + u = 60 ⇒ 20 + 15 + 12 + u = 60 ∴ u = 60 – 47 = 13 21. (a) For minimum number of coins 78 paise 69 paise 101 paise 50 × 1 50 × 1 50 × 1 10 × 2 10 × 1 25 × 1 — 5×1 10 × 2 2×4 — — — 2×2 2×3 Total = 7 Total = 5 Total = 7 ∴ Total number of coins = 19 22. (c) Let total number of huts in beginning of year 2001 are 100, then we find the following table.

Expected to be destroyed = Option (c) ⇒ 23. (d) Cost of perfume bottle in Bahts = 520 + 2 [70 % of 520] = 1248 Bahts Cost to each friend =

R pays 2 Euros = 2 × 46 = 92 Bahts M pays = S pays = 1248 – (211 + 92) = 945 Bahts R owes S = 416 – 92 = 324 Bahts 24. (c) M owes = (416 – 211) = 205 Bahts. Converting into dollars we get

= 5 dollars.

25. (a) Ratio of water and milk in mixture = 20 : 80 = 1 : 4 25% of mixture is sold ∴ amount of water in mixture = 15l & amount of milk in mixture = 60l In new mixture ratio of water and milk = (15 + 25) : 60 =2:3 26. (c) Distance covered by the sprinter in

minutes, 1 minutes,

2 minutes, 4 minutes, and so on

i.e., sprinter covers

distance in each round of time.

Time taken to cover the first round

Time taken to cover the second round

= 8 + 16 + 32 + 64 = 120 minutes The ratio of nth to (n – 1)th round = ratio of any two consecutive rounds. ∴ Required ratio 27. (e) This problem can be easily solved by adding the Denominator and Numerator of all the ratios and checking whether it is prime or not. [Note : Ratios are such that any of its integral multiples will not be < 300] (a) 189, is divisible by 3. (b) 187, is divisible by 11. (c) 221, is divisible by 17. (d) 183, is divisible by 3. (e) 181, is prime. 28. (a)

for a = 1, b = 3 for b = 3, for

,d=3

for d = 3, e = 1 for e = 1, f = 4

29. (a) Ten years ago, sum of the ages of 8 people of the family = 231 years Age of the members before 8 years who died after3 years = 60 – 3 = 57 years. And age of the member before 8 years, who died after6 years = 60 – 6 = 54 years Sum of ages of the two children in the current year = 7 + 4 = 11 years

Sum of the ages of 8 members in the current year = (Sum of ages of 6 members before 10 years) + 6 × 10 + (Sum of ages of two children in the current year) = 231 – (57 + 54) + 60 + 11 = 291 Hence, average age 30.

= 24 years (Approx).

(c) Total age of the 6 people on 1st January 2000 = 6A Total sum of ages (including child’s) of the family after 5 years = 6(A + 5) = 6A + 30 Total sum of ages (including child’s) of the family after 6 years = 6A + 30 + 7 = 6A + 37 Average =

Hence, 7A = 6A + 37 or A = 37. 31. (d) Let cost of one roti, one tadka, and one tea be ` x, y, z respectively ∴ 10x + 4y + z = 80 7x + 3y + z = 60 ∴ 10x + 4y = 80 – z .... (i) 7x + 3y = 60 – z .... (ii) Solving this, we get x = z/2 and y = Now we required 5x + 5y + 5z = 32. (a)

= 5 × 20 =

100

Let the %age of honey and milk in the two solutions be (a%, b%) and (c%, d%) respectively. According to the question:

Solving, we get, 16a – ad – 160 + 10d = 10b – 160 – bc + 16c So, ad – bc = 16a – 10b – 16c + 10d ...(1)

Similarly from the second and third proportions we can say that ad – bc = 12a – 12b – 12c + 12d. ...(2) and ad – bc = xa – 16b – xc + 16d ...(3) From (1) and (2), we get Also from (2) and (3), we get

Hence, 8 = 12 – x and x = 4. 33. (d) The total age of the family at the birth of first child = 18 × 3 = 54 While the total age of the couple at marriage = 25 × 2 = 50. ⇒ The years from marriage till the first child’s birth =

= 2 years.

The total age of family at the birth of the second child = 15 × 4 = 60 years. ⇒ Second child was born= Similarly the twins were born =

= 2 years after the first. = 3 years.

After the second child and today the twins are 4 years old. ( average age of the family became 16 years from 12 years) ∴ Age of eldest son = 4 + 3 + 2 = 9 years. 34. (c) Let the number representing A be a, and the common difference be d. ⇒ a + (a + 2d) + (a + 4d) = 36 ...(i) and (A + C + E + G) – (A + C + E) = 60 – 36 ⇒ G = 24 ⇒ a + 6d = 24 ...(ii) From (i) and (ii)

(3a + 6d) – (a + 6d) = 12 ⇒ 2a = 12 ⇒ a = 6 and d = 3 So, B + D + F + H = 4a + 16d = 24 + 48 = 72 35. (b) Let the total amount involved in this game in $K. The first person has

in the beginning and

in the end.

Thus he won something. Second person has

in the beginning and

in the end.

So he neither gains nor loses. At this point it is very clear that third person loses something. ⇒ ⇒

= 12

So, K = 1080 So, the winner must have started. with $ 420. 36. (b) Let the required number of hour be h.

∴

Going through the options, h = 4 comes out to be the correct answer. 37. (d) If all are of equal height. number of handshakes = 40C2. If all are of different heights, number of handshakes = 0 ∴ Required difference = 40C2 – 0 = 40C2. 38. (b) Let the number of Re. 1,50 paise and 25 paise coins be 360, 432 and 576 respectively (ratio 5 : 6 : 8). Re. 1 50 paise 25 paise 360 432 576

I transaction: 3/5 th of Re. 1 coins changed 216 coins of Re. 1 would be changed with 144 coins of 50 paise and 576 coins of 25 paise (so that total 50 paise coins = 576 and total 25 paise coins = 1152 in the ratio 1 : 2) Re. 1 50 paise 25 paise 144 576 1152 II transaction: Half of 50 paise coins to Re. 1 and all 25 paise coins to Re. 1 and 50 paise in the ratio 7:4 Half of 50 paise coins ⇒ 144 coins of Re. 1 1152 coins of 25 paise ⇒ 224 coins of Re. 1 and 128 coins of 50 paise Re. 1 50 paise 25 paise 512 416 0 Ratio = 512 : 416 =16 : 13. 39. (20) Let Barun’s age be = 10x Arun’s age will be = 4x. The difference of these age in 6x When Arun’s age is 50% of Barun’s age, this difference also would be 50% i.e. Barun’s age at that stage would be 12x. It would be increase by 20%

40. (a)

[multiply by 9 in first row and multiply by 5 in second row] C5 – C1 = 19, the numbers above are the actual profits ∴ The total profit = 438 crore. 41. (a) Let the total no. of popcorn pockets in stock be T Total no. of chips pockets in stock = T Required ratio =

=1:1

42. (a) Let the average score of the boys in the midsemester examination be b Average score of the girls = b + s in the exam, Average score of the girl = b + 5 – 3 =b+2 Average score of the entire class increased by 2 and is + 2 i.e b + 5 Average score of the boys = b + 9.5 ⇒ Increase in average score of boys is 9.5

where

is (a) (b) (c) (d) 2.

to zero 1 –1 abc If one root of has

(a) (b) (c) (d) 3. I. II. (a) (b) (c) (d) 4. (a) (b) (c)

then, equal

(1994)

is 4, while the equation equal

roots,

then

the

value

is (1994) 49/4 4/49 4 1/4 Nineteen years from now Jackson will be 3 times as old as Joseph is now. Joseph is three years younger than Jackson. (1994) Jackson’s age now Joseph’s age now I > II I < II I = II Nothing can be said What is the value of m which satisfies 3m2 – 21m + 30 < 0 ? (1995) m < 2 or m > 5 m>2

(d) 5.

The

value

of (1995)

(a) (b) (c) (d) 6. (a) (b) (c) (d) 7.

(a) (b) (c) (d) 8. (a) (b) (c) (d) 9. (a)

100 105 125 75 One root of x2 + kx – 8 = 0 is square of the other. Then the value of k is (1995) 2 8 –8 –2 Once I had been to the post-office to buy stamps of five rupees, two rupees and one rupee. I paid the clerk ` 20, and since he did not have change, he gave me three more stamps of one rupee. If the number of stamps of each type that I had ordered initially was more than one, what was the total number of stamps that I bought? (1996) 10 9 12 8 Given the quadratic equation x2 – (A – 3)x – (A – 7), for what value of A will the sum of the squares of the roots be zero? (1996) –2 3 6 None of these Which of the following values of x do not satisfy the inequality at all? (1996)

(b) (c) (d) 10. Out of two-thirds of the total number of basket-ball matches, a team has won 17 matches and lost 3 of them. what is the maximum number of matches that the team can lose and still win three-fourths of the total number of matches, if it is true that no match can end in a tie ? (1996) (a) 4 (b) 6 (c) 5 (d) 3 11. If the roots, x1 and x2, of the quadratic equation x2 – 2x + c = 0 also satisfy the equation 7x2 – 4x1 = 47, then which of the following is true? (1997) (a) c = – 15 (b) x1 = –5, x2 = 3 (c) x1 = 4.5, x2 = –2.5 (d) None of these 12. One year payment to a servant is Rs. 90 plus one turban. The servant leaves after 9 months and receives Rs. 65 and a turban. Then find the price of the turban (1998) (a) Rs. 10 (b) Rs. 15 (c) Rs. 7.5 (d) Cannot be determined 13. You can collect Rubies and Emeralds as many as you can. Each Ruby is worth Rs. 4crores and each Emerald is worth of Rs. 5crore. Each Ruby weights 0.3 kg. and each Emerald

(a) (b) (c) (d) 14. (a)

weighs 0.4 kg. Your bag can carry at the most 12 kg. What you should collect to get the maximum wealth? (1998) 20 Rubies and 15 Emeralds 40 Rubies 28 Rubies and 9 Emeralds None of these then what is the minimum value of q / r? (1999) –2

(b) (c) (d) 15. The expenses of a boarding school depends upon the fixed cost and variable cost. Variable cost varies directly as the number of students. If the expenses per student were Rs. 600 for 50 students and Rs. 700 for 25 students then what are the expenses for 100 students? (1999) (a) 50000 (b) 60000 (c) 57500 (d) 55000 16. then which of the following holds good ? (2000) (a) (b)

(c) x > – (d) None of these 17. A, B and C are 3 cities that form a triangle and where every city is connected to every other one by at least one direct roots. There are 33 routes direct & indirect from A to C and there are 23 direct routes from B to A. How many direct routes are there from A to C ? (200 0) (a) 15 (b) 10 (c) 20 (d) 25 18. If the equation has three real roots then (a) (b) (c) (d) 19.

which of the following is true? a = 1l a 1 b=1 b 1

(2000)

, then the value of

is (2000)

(a) (b) (c) (d) 20. (a) (b) (c) (d)

0.6 0.2 0.36 0.4 If x > 5 and y < – 1, then which of the following statements is true? (2001) (x + 4y) > 1 x > – 4y – 4x < 5y None of these

21. Two men X and Y started working for a certain company at similar jobs on January 1, 1950. X asked for an initial salary of Rs. 300 with an annual increment of Rs. 30. Y asked for an initial salary of Rs. 200 with a rise of Rs. 15 every six months. Assume that the arrangements remained unaltered till December 31, 1959. Salary is paid on the last day of the month. What is the total amount paid to them as salary during the period? (2001) (a) Rs. 93,300 (b) Rs. 93,200 (c) Rs. 93,100 (d) None of these 22. x and y are real numbers satisfying the conditions 2 < x < 3 and – 8 < y < – 7. Which of the following expressions will have the least value? (2001) 2 (a) x y (b) xy2 (c) 5xy (d) None of these 23. m is the smallest positive integer such that for any integer , the quantity –7 + 11n – 5 is positive. What is the value of m? (2001) (a) 4 (b) 5 (c) 8 (d) None of these 24. Let x, y be two positive numbers such that x + y = 1. Then, the minimum value of (a) 12 (b) 20

(2001)

– b. If

, then

– 2a

is divisible by (2001) (a) 15 (b) 20 (c) 24 (d) none of these 26. Ujakar and Keshab solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation? (2001) (a) (6, 1) (b) (– 3, – 4) (c) (4, 3) (d) (– 4, – 3) Directions for questions 27 & 28 : Read the information given below and answer the questions that follow : The batting average (BA) of a test batsman is computed from runs scored and innings played - completed innings and incomplete innings (not out) in the following manner : r1 = number of runs scored in completed innings n1 = number of completed innings r2 = number of runs scored in incomplete innings n2 = number of incomplete innings. BA = To better assess a batsman’s accomplishments, the ICC is considering two other measures MB A1 and MB A2 defined as follows : MB

max

. MB

27. Based on the information provided which of the following is true? (2001) (a) MB BA MB (b) (c) (d) 28.

BA MB MB MB BA MB None of these An experienced cricketer with no incomplete innings has a BA of 50. The next time he bats, the innings is incomplete and he scores 45 runs. It can be inferred that (2001) (a) BA and MB A1 will both increase (b) BA will increase and MB A2 will decrease (c) BA will increase and not enough data is available to assess change in MB A1 and MB A2 (d) None of these 29. If x, y and z are real numbers such that, x + y + z = 5 and xy + yz + zx = 3 (2002) What is the largest value that x can have? (a) 5/3 (b) (c) (d) None of these 30. If I. II. III. (a) (b) (c) (d)

then

statements are necessarily true? x=2y x=2z 2x = z Only I Only II and III Only I and II None of these

which

the

following (2002)

31. The number of real roots of the equation

where A

and B are real numbers not equal to zero simultaneously is (2002) (a) (b) (c) (d) 32.

None 1 2 1 or 2 If pqr

the

value

the is

to (a) p + q + r

expression equal

(2002)

(b) (c) 1 (d) 33. A piece of string is 40 centimeters long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized piece and the shortest piece is 23 centimeters shorter than the longest piece. Find the length of the shortest piece. (2002) (a) 27 (b) 5 (c) 4 (d) 9 34. Three pieces of cakes of weight respectively are to be divided into parts of equal weights. Further, each part must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be

entertained? (2002) (a) (b) (c) (d) 35.

54 72 20 None of these Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that ? (2003C) ; ;

(a) (b) (c) (d) 36. The number of (a) (b) (c) (d) 37.

(a)

non-negative real roots of

equals (2003C) 1.0 1 2 3 Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true? (2003C) The minimum possible value of is

(b) The minimum possible value of

(d) The maximum possible value of is 38. Let p and q be the roots of the quadratic equation . What is the minimum possible value of

? (2003C) (a) (b) (c) (d) 39.

0 3 4 5 If the product of n positive real numbers is unity, then their sum is necessarily (2003C) (a) a multiple of n (b) equal to (c) never less than n (d) a positive integer 40. Given that

and w =

, then which of the following is necessarily true? (2003C) (a) (b) (c) (d) 41. If

are

distinct

positive

real

numbers

then would

(a) (b) (c) (d) 42.

be (2003C) greater than 4 greater than 5 greater than 6 None of the above. A test has 50 questions. A student scores 1 mark for a correct answer, –1/3 for a wrong answer, and 1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student can not be less than

(2003C) (a) (b) (c) (d) 43.

6 12 3 9 The number of roots common between the two equations + 4x + 5 = 0 and

(a) (b) (c) (d)

+ 7x + 3 = 0 is

(a) (b) (c) (d) 46.

(2003)

0 1 2 3

44. A real number x satisfying 1 – (a) (b) (c) (d) 45.

< x

3 +

, for every

positive integer n, is best described by (2003) 1 t and II. If x > z, then y < t Which of the following is necessarily true? (2015) (a) If x < y, then z < t (b) If x > z then x – y < z + t (c) If x > y + z, then z > y (d) None of these 89. If 3x + y + 4 = 2xy, where x and y are natural numbers, then find the ratio of the sum of all possible values of x to the sum of all possible values of y. (2015)

(a) (b) (c) (d) 90. Find the solution set for [x] + [2x] + [3x] = 8, where x is a real number and [x] is the greatest integer less than or equal to x. (2015) (a) (b) (c) (d) None of these 91. If x2 + (x + 1) (x + 2) (x + 3) (x + 6) = 0, where x is a real number, then one value of x that satisfies this equation is (2015) (a) (b) (c) (d) 0 92. If the roots of the equation (x + 1) (x + 9) + 8 = 0 are a and b, then the roots of the equation (x + a) (x + b) – 8 = 0 are (2016) (a) 1 and 9 (b) – 4 and – 6 (c) 4 and 6 (d) Cannot be determined 93. If S?

find

the

value

(2016)

(a) 24/90 (b) 242/900 (c) 245/900 (d) 200/729 94. If the sum to infinity of the series 2 +(2 – d) 2/3+ (2 + d) 4/9 + (2 + 3d) 8/27 + .... is 5/2, what is the value of d? (2016) (a) 7/12 (b) –7/12 (c) – 5/12 (d) 5/12 95. Suppose, log3 x = log12 y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6 G is equal to (2017) (a) (b) 2a (c) a/2 (d) a 96. The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y < 12, and z < 12 is (2017) (a) 101 (b) 99 (c) 87 (d) 105 97. For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied? (2017) 2 98. If f1 (x) = x + 11x + n and f2 (x) = x, then the largest positive integer n for which the equation f1 (x) = f2 (x) has two distinct real roots, is (2017) 99. If a, b, c and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2 is 100. If f(x) = is (a) 2

and g(x) = x2 – 2x – 1, then the value of g (f(f(3))) (2017)

(b) (c) 6 (d)

(b) Take any value of a, b, c such that a + b + c = 0 where say substituting these values in =

(a) Given x2 + px + 12 = 0 Since, x = 4 is the one root of the equation, therefore x = 4 will satisfy this equation Other quadratic equation becomes (By putting value of p) 2

Its roots are equal, so, b = 4ac ⇒ 49 = 4q 3.

(a) Let present age of Jackson be x years and then present age of Joseph = x – 3 After 19 years Jackson’s age = (x + 19) years and x + 19 = 3 (x – 3) x + 19 = 3 x –9 2x = 28, x = 14 Jackson’s age = 14 years Joseph’s age = 14 – 3 = 11 years I > II According to the question: or x – 3y = 38

So only from above equation x and y cannot be found. (c) (factorize)

Case I : Case II : nothing common Hence, 2 < m < 5 5.

(a) We know, [using, a3 + b3 = (a + b) (a2 + b2 – ab)] ( on comparing with given information a = 55, b = 45)

(d) Given Let a and b be the roots of given equation andb = a2 (given) Sum of roots .....(i) Product of roots

Using a = –2 in (i) , –k = –2 + 4 = 2 or k = –2 (a) The number of stamps that were initially bought were more than one of each type. Hence, the total number of stamps = = 10 (d) Let the roots be m and n. The given quadratic equation can be written as ax2 + bx + c = 0

where The sum of the roots is and the product of the roots is (mn) The sum of the squares of the roots = m2 + n2 =

On solving, we get, A2 – 4A – 5 = 0 A2 – 5A + A – 5 = 0 A(A – 5) + 1(A – 5) = 0 (A + 1) (A – 5) = 0 A = 5 or –1 None of these values are given in the options. (a) Given inequality is

This gives ( x > 2) as one range and (x < 1) as the other. or x < 2 as one range and x > 1 as the other. In between these two extremes, there is no value of x which satisfies the given inequality. 10. (a) Let total number of matches be x . Hence, to win to win

of the total number of matches, the team has matches.

Hence, if team loses 4 more matches, it can still win

of the

matches. 11. (a) 7x2 – 4x1 = 47 x1 + x2 = 2 Solving 11x2 = 55 x2 = 5 & x1 = –3 ∴ c = –15 12. (a) Let turban be of cost Rs. x. So, payment to the servant= 90 + x for 12 month Payment for 9 months = 65 + x

13. (b) Basically, the question is of weights, so let us analyse them. 4 Rubies weight as much as 3 Emeralds Cost of 4 Rubies = 16 crores Cost of 3 Emeralds = 15 crores ∴ All Rubies, multiple of 4 allowed, is the best deal,so

14. (a) When

Now,

is min. then q = min. and r = max.

∴ Minimum value of –2 is given which is the least among the given values. 15. (d) Let a and X be the fixed cost and constant of proportionality respectively. The expenses are given by Z. E = a + nx

....(1)

Where n = no. of students Again,

....(2)

Subtracting (2) from (1),

Now, E = 5000 + 100 × 500 = Rs. 55,000 for 100 stds. 16. (d) Given, y > – 1 i.e. if y is positive no. then product of x and y also positive. But any option does not give xy is +ve. By putting different values of x and y we see that none of these three hold good. 17. (b) Let the no. of direct routes from A to B be x, from A to C be z and that from C to B be y. Then the total no. of routes from A to C are = xy + z = 33. Since the no. of direct routes from A to B are 23,∴ x = 23. Therefore, 23y + z = 33. Then y must take value 1 and then z = 10. Hence, 10 routes are direct from A to C. 18. (d) Let f(x) = x3 – ax2 + bx – a =0 In the given equation, there are 3 sign changes, therefore, there are at most 3 positive real roots. In f (–x), there is no sign change. Thus, there is no negative real root. i.e. if α, β and γ are the roots then they are all positive and we have

f(x) = (x – α) (x – β) (x – γ) = 0 and

Thus, 19. (d) x – y = + 0.2 or (x – y)2 = 0.04. Also, x2 + y2 = 0.1 (since x2 + y2 > 0) And solving these two we get, 2xy = 0.06. From this we can find value of x + y which comes out to be +0.4 or – 0.4 and we get |x| + |y| = 0.4. 20. (d) x > 5 and y < –1 (i) x > 5 and 4y < – 4 so x + 4y < 1 (ii) Let x > – 4y be true or – 4y > 4 So, x > 4, which is not true as given x > 5. So, is not necessarily true. (iii)

and

It is not necessary that as –4x can be greater than 5y, since 5y < –5. Hence none of the options is true. 21. (a) For total salary paid to X = 12 × (300 + 330 + 360 + 390 + 420 + 450 + 480 + 510 + 540 + 570) =

[sum of A.P.]

= = Rs. 52, 200 For total salary paid to Y = 6 × [200 + 215 + 230 + 245 + 260 .. 20 terms ] = [sum of A.P.] = = Rs. 41, 100 Total sum of both = Rs. 93, 300 22. (c) 2 < x < 3 and –8 < y < –7 4 < x2 < 9 and – 8 < y < – 7 While Hence, 5xy is the least because xy2 is positive 23. (d) Let = Now, (n – 1)2 is always positive. And for n < 5, the expression gives a negative quantity. Therefore, the least value of n will be 6. Hence m = 6. 24. (c) Given, x + y = 1 Then, Minimum value of x2 + y2 occur when x = y [ x + y = 1] Put Minimum value = 25. (c)

So, this is divisible by 24 for

26. (a) Ujakar’s equation (sum of roots = 7, product of roots = 12) equation (sum of roots = 5, product of roots = 6) Hence, the correct equation is

Keshab’s

So, roots are 6 and 1. 27. (d) Clearly BA > MBA1 and MBA2 < BA as So, option (a), (b) and (c) are neglected. see because

and which is always

true. So, none of the answers match 28. (b) Initially BA = 50, BA increases as numerator increases with denominator remaining the same. decreases as average of total runs decreases from 50, as runs scored in this inning are less than 50. 29. (c) We know, (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)

or (5)2 = x2 + y2 + z2 + 2 × 3 ⇒ x2 + y2 + z2 = 19 For maximum value of x, y = z = 0 but both cannot be zero at the same time as xy + yz + zx ≠ 0 So, x2 < 19 ∴ x can be

as x2 =

30. (c) Put

.....(i)

This is not necessarily true Put y = z in (i) we get, or (i) is true for Therefore, only I and II satisfy the given result 31. (d) If only A = 0 then there is only one root If only B = 0 then there is only one root If both A and B are not zero then, there would be two roots (because quadratic equation forms) ∴ Required number roots be 1 or 2 32. (c) pqr = 1 (given)

= =

(

pqr = 1)

33. (c) Let the length of shortest piece be x cm. Then length of longest piece be 23 + x and length of middle piece be According to question, or or x = 4 cm. 34. (d) The required weight of each part would be the HCF of given prices of cakes So,

HCF =

Now, total number of parts

= 10 + 15 + 16 = 41 35. (a) Solving from the choices, =0

For no other choices above condition is satisfied, hence option (a) is correct. 36. (c) It is clear that the equation 2x – x – 1 = 0 is satisfied by x = 0 and 1 only. For x > 1, f(x) = 2x – x – 1 start increasing. Hence, there are 2 non-negative real roots. 37. (b) The minimum value of (By putting m = 1) Since, a + b + c + d = 5. We have, a = b = c = 1 and d = 2. Then, 38. (d) Given equation is Sum of the roots, p + q = α – 2 Product of the roots pq = – α – 1 Now, p2 + q2 = (p+q)2 – 2pq = (α – 2)2 + 2 (α + 1) = ( α – 1 )2 + 5 Hence, the minimum value of p2 + q2 will be 5 39. (c) The numbers must be reciprocals of each other. For example Hence, the sum is greater than the product of numbers. 40. (b) Substitute the extreme values in the given equation :

v = 1, u = –0.5, z = –2. Then w =

= 4.

Only option (b) gives this. 41. (c) Simply substitute x = 1, y = 2 and z = 3 in the expression we get

which is greater than 6.

42. (c) Let x be the number of questions answered correctly, y be wrong attempts and hence (50 – x – y) becomes the number of questions not attempted. Then, net score – or

. or y = 7x – 242.

We get y = 3 for x = 35, which is the minimum value of y as for any value of x > 35, y starts increasing. 43. (a) Subtract the both equations, we get

Roots 1 and 2 do not satisfy any of the original equation. In case there is a common root, it will be the root of the subtracted equation. Therefore there is no common root between both the given equations. 44. (c) Given inequality is … (1) For any positive n, … (2) Add 3 to each part in inequality (2), we get

… (3) Again from inequality (2), we get (multiply (–1) in each part) (Add 1 in each part) … (4) From inequalities (1), (3) and (4), we get 45. (c) 5x + 19y = 64 We see that if y = 1, we get an integer solution x = 9, Now if y changes (increases or decreases) by 5, x will change (decrease or increase) by 19 Looking at options, if x = 256, we get, y = 64 Using these values we see option a, b and d which are eliminated and also that there exists a solution for 250 < x < 300. 46. (b) For real roots

For b2 = 4, no. of solution = 1 For b2 = 9, no. of solution = 2 For b2 = 16, no. of solution = 4 Total no. of solutions = 4 + 2 + 1 = 7 47. (b)

Let ⇒ a z (a – z) = 8 ⇒ az2 – a2z + 8 = 0 For, z to be real , b2 – 4ac 0 ∴ a4 – 32a 0 ⇒ a3 32

Hence, minimum possible value of y = 22/3 48. (d) Let

.....(1) For

[putting in equation (1)] or 28 < x < 60 49. (d)

and

In the above equation, all the options a, b & c are possible but not necessarily true. 50. (b) (given)

Consider 51. (c) Equation x + y = xy can be satisfied for (x, y) ≡ (0, 0),(2, 2) Hence, total no. of integer pairs (0 and 2) = 2 52. (c) There are 2 cases, first, the given condition will be satisfied only when a, b and c are equal and second, when a + b + c = 0. Case (i) : If a = b = c = 1, we getr = 1/2, Case (ii) : when a + b + c = 0, then we get the value of r = – 1. There are no other values that r can take. Hence (c) is the correct option. 53. (d) The expression can be written as

⇒ 2y2 + 7y = 3 + y ⇒ 2y2 + 6y – 3 = 0

(as y cannot be negative)

54. (c)

(x – k)2 + y2 = 1, represents a circle with centre (k, 0) and radius = 1. For a positive unique solution the line y = x will be tangent to the circle at point P. OA2 = AP2 + OP2

55. (c) The given expression can be reduced to

Putting the values of x in the options we find that

is the

correct option. Therefore, .......(1)

L.H.S. =

(from (1)) = R.H.S. 56. (d) Cost of a male operator per call

Cost of a female operator per call As cost of a female operator is cheaper so he shall employ maximum no. of females, i.e., 12 and let x be the no. of male operators employed. ∴ 12 × 50 + x × 40 = 1000 or 40x = 1000 – 600 = 400 ⇒ x = 10 ⇒ Males employed = 10 For Qs. 57-58.

Let the free luggage be ‘s’ kg and excess luggage possessed by Raja and Praja be ‘r’ and ‘p’ kg respectively. 2s + r + p = 60 ......(1) Again let the charge for excess luggage be ` x/kg. For Raja, rx = 1200 ......(2) and for Praja, px = 2400 ......(3) or

......(4)

If the entire luggage belongs to one only, then only ‘s’ will be the free luggage and s + r + p will be the charge for excess luggage (s + r + p)x = 5400 or (s + 3r)x = 5400 ......(5) Dividing (5) by (2),

......(6) Using in (1),

12s = 60 × 3 or s = 15 kg Again 2 × 15 + 3r = 60 r = 10 kg and p = 20 kg 57. (d) Praja’s luggage = s + p = 15 + 20 = 35 kg 58. (d) Free luggage = s = 15 kg. 59. (b) Let one of the nos. be 10x + y Reversing the digits it become 10y + x. As per question. 10y + x – (10x + y) = 18 9(y – x) = 18 or y – x = 2

So, it will be possible in all the cases where the difference between the two digits = 2. So, the nos. are 13, 24, 35, 46, 57, 68, 79. Hence the no. of such two-digit numbers apartfrom 13 is 6. 60. (a) Put

or or or

61. (e)

Equating the powers of 2 and 3 or x = 5 and

or y = 2

Using x = 5 and y = 2 in equation

; Which is true hence correct 62. (b) 2x + y = 40;

; x, y

I+

This problem can be solved by putting various values for x and y. Starting from x = 1. The above equation can be solved till x = 13. At x = 13, y = 14 which is > x. But above this value of x, it becomes greater than y so the condition is violated. 63. (c) Let the first number be 10 x + y.

So the other numbers would be 10 x + y + 2, 10x + y + 4, 10x + y + 6 (S) Sum = 40x + 4y + 12 This is divisible by 10 or S = It means 4y + 12 has to be divisible by 10 and y is odd (1, 3, 5, 7, 9). This condition can be fulfilled by 7 only. So the numbers become = 10x + 7, 10x + 9, 10x + 11, 10x + 13. Now using the options and finding whether the sum divided by 10 is a perfect square or not. For (a), the nos. are 17, 19, 21, 23 not a perfect square. (b), can not be the no. as none of the 4 nos. have 5 as last digit. For (c), the nos. are 37, 39, 41, 43 , perfect square For (d) the nos. are 67, 69, 71, 73 , not a perfect square For (e), the nos. are same as for (d). 64. (d) On 100th day of 2007, Price per kg of Darjeeling Tea = 100 + 0.10 × 100 = Rs. 110 Price per kg of Ooty Tea = 89 + 0.15 × 100 = Rs. 104 Therefore, there will be a day after 100th day of 2007, on which prices of the two tea varieties will be same, let it be the xth day after the 100th day 110 = 89 + 0.15 (100 + x) 110 = 89 + 15 +

Hence, the day on which the prices of the two varieties of the tea are same = 140th day = 20th may, 07. 65. (e) Let the original amount of the cheque be x rupees and y paise. Hence, original cheque amount = (100x + y) paise The amount paid by bank teller = (100y + x) paise According to the given question, 100y + x – 50 = 3(100x + y)

On checking, we get if x = 18 (a positive integer), then only y has an positive integral value 56. Hence, original amount of the cheque = Rs. 18.56 i.e., over rupees18 but less than rupees 19. 66. (b) Quantity of rice purchased by first customer kg Hence, remaining quantity of rice after first customer kg

Remaining quantity of rice after second customer kg Remaining quantity of rice after third customer

Since, no rice is left after third customer,

x = 7. 67. (a) Let the three consecutive positive integers are x – 1, x and (x + 1) Then, (x – 1) + x2 + (x + 1)3 = (x – 1 + x + x + 1)2 ⇒ x (x2 – 5x + 4) = 0 ⇒ x (x –4) (x – 1) = 0 ⇒ x ≠ 0, ∴ = 1 or 4 If x = 1, then the three consecutive positive integers are 0, 1, 2, which is not possible (as ‘0’ is not a positive integers). If x = 4, then the three consecutive positive integers are 3, 4, 5. ∴ m = 3. 68. (b) Let roots are (n – 1), n and (n + 1) Sum of the roots = b (n – 1) n + n (n + 1) + (n + 1) (n – 1) = b ⇒ n2 – n + n2 + n + n2 – 1 = b ⇒ 3n2 – 1 = b The value of b will be minimum when the value of n2 is minimum i.e., n2 = 0 Hence, minimum value of b = – 1. 69. (b) f (x) = ax2 + bx + c Since 3 is a root of f (x) = 0 ∴ f (3) = 0 ⇒ 9a + 3b + c = 0 ...(i)

Now f (5) = – 3 f (2) 25a + 5b + c = – 3 (4a + 2b + c) ⇒ 37a + 11b + 4c = 0 ...(ii) Multiply equation (i) by 4 and subtract it from equation (ii) we get 37a + 11b + 4c = 0 36a + 12b + 4c = 0 – – – a–b=0 ⇒ a=b Now sum of the roots If other root be n, then n+3=–1 ∴ n=–4 Hence the root = – 4. 70. (e) From the solution of previous questions, a = b and roots are 3 and – 4 Now, f (3) = 9a + 3b + c = 0 ⇒ 12a + c = 0 [ a = b] f ( – 4) = 16a – 4b + c = 0 ⇒ 12a + c = 0 [ a = b] And f (5) = – 3 f (2) ⇒ 25a + 5b + c = – 3 (4a + 2b + c) ⇒ 37a + 11b + 4c = 0 ⇒ 48a + 4c = 0 [ a = b] ⇒ 12a + c = 0 71. (c) As p, q, r are non-negative integers, the maximum will be achieved when the value of each variable is closed to each other. i.e. p, q, r are 3, 3, 4 (not necessarily in the same order). Hence the value of pq + qr + pr + pqr

=3×3+3×4+3×4+3×3×4 = 9 + 12 + 12 + 36 = 69 72.

where x lies in

the interval (0, 1).Since (1.25)3 = 1.953125 and (1.3)3 = 2.197, it can be concluded that

belongs to the interval

(1.25, 1.3). Hence, a = 1. This implies that

lies in the interval

(0.25, 0.3). The only possible value of b = 3. 73. (b) Let α, β are roots of

Now

74. (a) We have x = 1 + 2a + 3a2 + 4a3 + ⇒ ax = a + 2a2 + 3a3 + Subtracting (2) from (1), we get

.......(1) .......(2)

(1 – a) x = 1 + a + a2 + a3 +...=

[sum of an infinite G.P.]

⇒x=

.......(3)

Next y = 1 + 3b + 6b2 + 10b3 b × y = b + 3b2 + 6b3 + 10b4 Subtracting (5) from (4) we get,

.......(4) .......(5)

(1 – b)y = 1 + 2b + 3b2 + 4b3 +....=

[shown above]

⇒y=

.......(6)

From (3) we get 1 – a =

or a = 1 –

From (6) we get 1 – b =

or b = 1 –

. .

Now, 1 + ab + (ab)2 + (ab)3 +.......... =

75. (d) r + t = 2s would be correct option as s is the average of r and t.

76. (c)

(x – k)2 + y2 = 1, represents a circle with centre (k, 0) and radius = 1. For a positive unique solution the line y = x will be tangent to the circle at point P. OA2 = AP2 + OP2 77. (a)

Let,

So, ∴ bx – ay = kbc ...(i) ay – cz = kac ...(ii) cz – bx = kab ...(iii) On addition of (i), (ii) and (iii) We get, K (ab + bc + ca) = 0 or, ab + bc + ca = 0. 78. (c) Quadratic equation ax2 + bx + c = 0 must have two roots which may or may not be identical. Let f(x) = ax2 + bx + c. f(1) = a (1)2 + b(1) + c =a+b+c=0 So, x = 1 is definitely a root of ax2 + bx + c = 0. Product of roots of ax2 + bx + c = 0 is

So if one of the roots is 1 then the other root must be 79. (b)

Let the fund value follow the quadratic polynomial f(x) = ax2 + bx + c. When x = 0, f (x) =10 ⇒ c =10 When x = 2, f(x) = 5 ⇒ 4a + 2b + 10 = 5 ⇒ 4a + 2b = – 5 ...(i) When x = 4, f(x) = 15 ⇒ 16a + 4b + 10 = 15 ⇒ 16a + 4b = 5 ...(ii)

Solving (i) and (ii), we get a=

b= ∴

Required difference

= 80. (a)

= 70 (x – 2) is a factor of R(x) ∴ R (2) = 0 ⇒ m(2)3 – 100 (2)3 + 3n = 0 ⇒ 8m – 400 + 3n = 0 ⇒m=

m and n are positive integers, so n must be a multiple of 8. i.e. n = 8, 16, 24, ....., 128, then we get m = 47, 44, 41, ....,2 respectively. So, the number of ordered pairs (m, n) is 16. 81. (d) General term expansion of (a2 + b)13 = To get coefficient of a12 b8 (a2)6 b8 where 6 + 8 ≠ 13. So the term is not possible 82. (d) Here, (x – 1) (x – 2) (x – 3) = 0 ⇒ (x2 – 3x + 2) (x – 3) = 0 ⇒ x3 – 6x2 + 11x – 6 = 0 According to question, x = 3, an = –6, a1 = –6 Substitute the above values in the option, Option (a) : (–6)3 ≥ 33 × – 6 ⇒ – 216 ≥ – 168 This is incorrect, thus option (a) is incorrect. Opiton (b) : 33 ≥ (–6)3 × –6 27 ≥ 64 This is incorrect, thus option (b) is incorrect.

Option (c) : (–6)3 ≥ 33 × – 6 ⇒ –216 ≥ – 168 This is incorrect, thus option (c) is incorrect. Thus, none of the options is necessarily true. 83. (a) We obtain the sum of all the coefficients of a polynomial by equating all the variables to 1. Here by putting x = 1 in the polynomial, the required sum comes out to be zero. 84. (d) The equations formed by the roots of the equation (x – a) (x – b)(x – c) can be as follows: (i) (x – a)(x – b) ⇒ Roots are a, b (ii) (x – b)(x – c) ⇒ Roots are b, c (iii) (x – c)(x – a) ⇒ Roots are c, a (iv) (x – a)2 ⇒ Roots are a, a (v) (x – b)2 ⇒ Roots are b, b (vi) (x – c)2 ⇒ Roots are c, c Adding all these roots, we get 4(a + b + c). 85. (a) nth term of the series can be written as = = = Put n = 1,2 , .... 10 to get

= 86. (c) According to question, x (x – 3) = –1 cubing on both side. ⇒ x3 (x – 3)3 = (–1)3 ⇒ x3 (x 3– 27 – 9x2 + 27x) = – 1

⇒ x3 (x3 – 18) + x3 (–9 – 9x2 + 27x) = –1 ⇒ x3 (x3 – 18) – 9x3 (x2 – 3x + 1) = –1 ⇒ x3 (x3 – 18) – 9x3 (–1 + 1) = –1 ⇒ x3 (x3 – 18) = –1 87. (c) Take roots as 2, 2 ⇒r=–4&s=4 ⇒ 88.

= + ve (R > 0)

(c)

By assuming the values of x, y, z and t, (a) and (b) can be very easily ruled out. Checking option (c), if x > y + z. then x > y and x > z (since all numbers are positive). So, using statements I and II, x > z > t > y. So, option (c) is correct. 89. (d) 3x + y + 4 = 2x y ⇒ 3x + 4 = y (2x – 1) ⇒y= When x = 6 ⇒ y = 2 When x = 1 ⇒ y = 7 These two are the only possible pairs of values of x and y. Where x and y are natural numbers. ∴ Required ratio =

90. (c) By observing we can find that x > 1 and x < 2. Else the RHS ≠ 8. So the combinations are [x] = 1, [2x] = 2 or 3. [3×] = 4 or 5 The combinations that give RHS = 8 are 1 + 2 + 5 or 1 + 3 + 4. For any value of x, the case of “1 + 2 + 5” is not possible. Hence it has to be the case of “1 + 3 + 4”. Which will occur when

and x
25 has complex roots. maximum value of n for real roots = 24 99. (2) a + b + c + d = 30 (a – b)2 + (a – c)2 + (a – d)2 would have minimum ifa = 8, b = 8, c = 7, d = 7, or a = 8 b = 7, c = 8, d = 7 or a = 7, b = 8, c = 7, d = 8, or a = 7, b = 7, c = 8, d = 8. or a = 8, b = 7, c = 7, d = 8 or a = 7, b = 8, c = 8 d = 7 minimum value = 1 + 1 = 2 100. (a) f (x) = g (x) = x2 – 2x – 1 f (3) =

⇒

g (f ( f (3))) = (3)2 – 3 × 2 – 1 = 9 – 6 – 1 = 9 – 7 = 2

the

base

is (1994) (a) (b) (c) (d) 2.

3 3/2 7/2 None of these If

find

the

value

x. (1994) (a) (b) (c) (d) 3.

1 0 2 None of these If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13; then the numbers could be in the ratio (1994)

(a) (b) (c) (d) 4.

12 : 13 1/12 : 1/13 4:9 2:3 Fourth term of an arithmatic progression is 8. What is the sum of the first 7 terms of the arithmatic progression? (1994) (a) 7 (b) 64

(c) 56 (d) Can’t be determined 5. Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man carried out the job starting with the stone in the middle, carrying stones in succession, thereby covering a distance of 4.8 km. Then the number of stones is (1994) (a) 35 (b) 15 (c) 29 (d) 31 6. If log2 [log7 (x2 – x + 37)] = 1, then what could be the value of x? (1997) (a) 3 (b) 5 (c) 4 (d) None of these Directions for Questions 7 to 9 : These questions are based on the situation given below : There are fifty integers a1, a2, ....... a50, not all of them necessarily different. Let the greatest integer of these fifty integers be referred to as G, and the smallest integer be referred to as L. The integers a1through a24 form sequence S1, and the rest form sequence S2. Each member of S1 is less than or equal to each member of S2. 7. All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true? (1999)

(a) Every member of S1 is greater than or equal to every member of S2. (b) G is in S1. (c) If all numbers originally in S1 and S2 had the same sign, then after the change of sign, the largest number of S1 and S2 is in S1 (d) None of the above 8. Elements of S1 are in ascending order, and those of S2 are in descending order. a24 and a25are interchanged then which of the following statements is true (1999) (a) S1 continues to be in ascending order. (b) S2 continues to be in descending order. (c) S1 continues to be in ascending order and S2 in descending order. (d) None of the above 9. Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1an integer x.Then x cannot be less than (1999) (a) 210 (b) The smallest value of S2 (c) The largest value of S2 (d) (S1 – S2) Directions for questions 10 to 12 : Read the information given below and answer the questions that follow : There are m blue vessels with known volumes V1, V2,....., Vm arranged in ascending order of volumes, where V1 is greater than 0.5 litres and Vm is less than 1 litre. Each of these is full of water. The water is emptied into a minimum number of white empty vessels each having volume 1 litre. If the volumes of the vessels increases with the value of lower bound 10–1.

10. What m?

the

maximum

possible

value

(1999) (a) (b) (c) (d) 11.

(a) (b) (c) (d) 12.

(a) (b) (c) (d) 13.

7 8 9 10 If m is maximum then what is the minimum number of white vessels required to empty it? (1999) 7 6 5 8 If m is maximum then what is range of the volume remaining empty in the vessel with the maximum empty space? (1999) 0.45 – 0.55 0.55 – 0.65 0.1 – 0.75 0.75 – 0.85 Find the following sum (2000)

(a)

(b)

(c)

(d) 14. of a 100 is

for n being a natural number. The value (2000)

(a) 5 × 299 + 6 (b) 5 × 299 – 6 (c) 6 × 299 + 5 (d) 6 × 299 – 5 15. All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice? (2001) (a) 44 (b) 45 (c) 10 (d) 12 16. If a, b, c and d are four positive real numbers such that abcd = 1 , what is the minimum value of (1 + a) (1 + b) (1 + c) (1 + d)? (2001) (a) 4 (b) 1 (c) 16 (d) 18 17. For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence? (2001) (a) (b) (c) (d) 18.

147 76 123 Cannot be determined The nth element of a series is represented as Xn = (–1)n Xn – (200 1 2) If X0 = x and x > 0 then which of the following is always true

(a) Xn is positive if n is even (b) Xn is positive if n is odd (c) Xn is negative if n is even (d) None of these 19. Let S denote the infinite sum where

1, then the value of the expression can

never

(a) (b) (c) (d)

be –1 – 0.5 0 1

(2005 - 2 marks)

36. Consider a sequence where the nth term, tn =

, n = 1, 2,...

The value of t3×t4×t5×.....×t53 equals: (2006) (a) (b) (c) (d) (e) 37. If logy x =(a . log z y) = (b . logx z) = ab, then which of the following pairs of values for (a,b) is not possible? (2006) (a) (–2,1/2) (b) (1, 1) (c) (0.4, 2.5) (d) (π, 1/π) (e) (2, 2) 38. Consider the set S = {1, 2, 3, ..., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements? (2006) (a) 3

(b) (c) (d) (e) 39.

(a) (b) (c) (d) (e)

4 6 7 8 A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible? (2006) 3 4 5 6 7

Directions for Qs. 40 and 41 : Let a1 = p and b1 = q, where p and q are positive quantities. Define an = pbn–1, bn = qbn–1, for evenn > 1, and an = pan–1, bn = qan–1, for odd n > 1. 40. Which of the following best describes an + bn for even n? (2007) (a) (b) (c) (d) (e)

41. If p =

and q =

+ bn < 0.01?

, then what is the smallest odd n such that an (2007)

(a) (b) (c) (d) (e) 42.

15 7 13 11 9 Consider the set S = {2, 3, 4,..., 2n+1}, where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y? (2007) (a) 2008 (b) 0 (c) 1 (d) (e) 43. A function f (x) satisfies f (1) = 3600 and f (1) + f (2) + ... + f (n) = n2 f (n), for all positive integers n > 1. What is the value of f (9)? (200 7) (a) 120 (b) 80 (c) 240 (d) 200 (e) 100 44. What is the number of distinct terms in the expansion of (a + b + c)20? (2008) (a) 231

(b) (c) (d) (e) 45.

253 242 210 228 Find the sum

(2 008) (a) (b) (c) (d) (e) 46. The number of common terms in the two sequences 17, 21, 25, ...., 417 and 16, 21, 26, ...., 466 is (2008) (a) 78 (b) 19 (c) 20 (d) 77 (e) 22 47. x and y are real numbers such that y = |x – 2| – |2x – 12| + |x – 8|. What is the least possible value of y? (2009) (a) 6(b) 2 (c) –2 (d) None of these

48. If log (0.57) = is :

, then the value of log 57 + log (0.57)3 + log (2009)

(a) 0.902 (b) (c) 1.902 (d) 49. If a, b and c are three real numbers, then which of the following is not true? (2009) (a) (b) (c) (d) 50. If a = b2 = c3 = d4 then the value of loga (abcd) would be : (2010) (a) log a 1 + log a 2 + log a 3 + log a 4 (b) loga 24 (c) (d) 51. If log165 = m and log53 = n, then what is the value of log36 in terms of ‘m’ and ‘n’? (2011) (a) (b) (c) (d) Cannot be determined

52. If x + y = 1, then what is the value of (x3 + y3 + 3xy)? (2012) (a) 1 (b) 3 (c) 9 (d) –1 53. If

(a) (b) (c) (d)

the maximum value of X for n = 8 is : 1 + log10 24 log10 56 1 + log10 7 1 + log10 48

54. A ray of light along the line axis to become a ray along the line

, where p ≤ n, then (2014)

gets reflected on the x(2014)

(a) (b) (c) (d) 55. If log32, log3(2x – 5) and log3

(a) (b) (c) (d) 56.

are in Arithmetic

Progression, then x is equal to (2014) 2 3 2 or 4 2 or 3 P1, P2, P3, ..., P11 are 11 friends. The number of balls with P1 through P11 in that order is in an Arithmetic Progression. If the sum of the number of balls with P1, P3, P5, P7, P9 and P11 is 72,

what is the number of balls with P1, P6 and P11 put together? (2014) (a) 24 (b) 48 (c) 36 (d) Cannot be determined 4 4 57. If x – y = 15, where x and y are natural numbers, then find the value of the expression x4 + y4. (2015) 58. Two positive real numbers, a and b, are expressed as the sum of m positive real numbers and n positive real numbers respectively as follows: a = s1 + s2 +…+ sm and b = t1 + t2 +…+ tn If [a] = [s1] + [s2] +…+ [sm] + 4 and [b] = [t1 ] + [t2 ] +…+ [tn] + 3, Where [x] denotes the greatest integer less than or equal to x, what is the minimum possible value of m +n? (2016) (a) 6 (b) 10 (c) 8 (d) 9 59. If x + 1 = x2 and x > 0, then 2x4 is (2017) (a) (b) (c) (d) 60. The to (2017) (a) (b) (c)

value

equal

(d) 61. If 92x–1 – 81x–1 = 1944, then x is (2017) (a) (b) (c) (d) 62.

(a) (b) (c) (d) 63.

(a) (b) (c) (d) 1.

3 9/4 4/9 1/3 If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is (2017) 2:3 3:2 3:4 4:3 Let a1, a2...., a2n be an arithmetic progression with a1 = 3 and a2 = 7. If a1 + a2 + ... + a2n = 1830, then what is the smallest positive integer m such that m(a1 + a2 + ... + an) > 1830? (2017) 8 9 10 11 (c)

= =

(b)

use loga x = b ⇒ ab = x ∴

or By componendo & dividendo

Taking square root on each side

Again by componendo & dividendo or 4.

=4:9

(d) Suppose there are n stones are placed. So, there are (2n + 1) stones, on each side of middle stone To pick up and return at middle point the man will travel 20m for 1st, 40 m for 2nd, and so on. Therefore total distance (4.8 km) is given by 2400 = 20[1 + 2+ 3 + ...... n]

No. of stones = 2n + 1 = 30 + 1 = 31 (c) Given Use logp x = y

72 = x2 – x + 37 =0

For Qs. 7-9. S1 = a1, a2, ..........a24 S2 = a25................a50 And we also know that L which is the least number has to be in S1 and G which is the greatest number must be in S2. 7. (d) With the change in the sign of the members of S1 nothing definitely can be said because if both the sequences contain negative number then each term of S1 will be greater than each term of S2. So the answer must be none of these.

(a) With the interchanging of a24 and a25 still the sequence of S1 will be in ascending order because each term of S2 is either greater than or equal to each term of S1. 9. (d) x must be equal to the greatest difference in the value of members of S1 and S2. 10. (d) The lower bound is 0.5 and increases with 0.05. It forms an Arithmetic progression, where 0.05 is the common difference and 0.5 is the first term. The last term is less than 1 and hence it is 0.95. To find the no. of terms in the series use the formulae for nth term i.e., Tn = a + (n – 1)d. Where ‘a’ is the first term and ‘d’ is the common difference. Hence the value of n comes as 10. Maximum possible value of m is 10. 11. (d) To find the minimum number of white vessel requied to empty the vessel for maximum possible value of m i.e. 10, we have to use the formula of sum of n terms of this A.P. series. Sum to n terms is given by , where n is the number of terms in the series. For this sum, . Hence, minimum number of white vessels is 8 as the capacity of white vessel is 1 litre. 12. (c) From the above solution we can see that the eighth vessel is empty by 0.75 litres and hence that is the upper limit for the range. Further for the lower limit, make all the vessels equally full, which makes them all 0.1 parts empty. So, the option that satisfies the above condition is (c).

13. (d) nth term, , n = 1, 2, .......10

14. (d) This can be solved by going through options. The general term of the series formed will be 6(2n – 1) + 1 which again will be written as 6 × 2n – 1 – 5. So the hundredth term of the series will be 6 × 299 – 5. 15. (c) Let total number of pages be x and page number which was added twice be y. Then, Sum of x numbers =

...(1)

For integral value of ‘x’, b2 – 4ac should be perfect square. ∴

(

x cannot be negative; neglecting –80)

Putting x = 44 in (1) ∴ But sum of total pages = 1000 ∴ Page number which was added twice = y = 1000 – 990 = 10.

16. (c)

(For numbers 1 & a) ∴ Minimum value of

= (

abcd = 1)

(

x > 0)

17. (c) Given,

...(i)

Here x7 = 29 and x6 = 18 satisfy (i) Now, x8 = x7 + x6 = 47 and x9 = 47 + 29 = 76 and

x10 = 76 + 47 = 123.

18. (d) Put n = 1, As

therefore, none of these option is correct. 19. (a) From option (a),

Using Binomial here

this is same series as given Thus, option (a) is correct answer. 20. (b) Let x1, x2...........x10 are two digit + ve numbers Let digits of x10 are interchanged

original after interchanging According to question,

21. (d) Since the child missed the number so actual result would be more than 575. Therefore we choose n such that

For n2 + n – 1150 = 0, So, least value of n is 34 ∴ correct answer Missing no. = 595 – 575 = 20 22. (b) log3

= =

= ⇒ N9 =

23. (c) We know, nth term of an A.P is Tn = a + (n – 1)d. Hence, we get, 3rd + 15th term = (a + 2d) + (a + 14d) = 2a + 16d. Similarly, sum of 6, 11 and 13th terms = (a + 5d) + (a + 10 d) + (a + 12d) = 3a + 27d. Now, 2a + 16d = 3a + 27d Hence, a + 11d = 0. This means that the 12th term is zero. 24. (d) This represents an AP with the first term as 1 and common difference as 1. Sum of terms =

which must be close to 288.

By hit and trial , we get for n = 23, Sum =

24th

alphabet is x, hence the 288th term is ‘x’. 25. (d) In an AP, the three terms a, b and c are relatedas 2b = a+c Hence , 2

Substitute the choices, only x = 3 satisfies the above condition 26. (c) The number of balls in each layer is 1, 3, 6, 10.....(each term is sum of natural numbers upto 1, 2, 3 ..... n digits). (

∴

no. of total balls = 8436)

After solving, we get, n = 36 27. (a) There are 2 n – j students who answered wrongly. For j = 1, 2, 3.....n, The number of students will be in GP with base 2. Hence, 1 + 2 + 22+.....2n – 1 = 4095. Using the formula, 2n = 4095 + 1

, we get

n =12

28. (c)

.....(i) .....(ii)

Subtracting (ii) from (i), .....(iii) .....(iv) Subtracting (iv) from (iii),

This becomes a GP with the first term =

andcommon ratio

= 1/7 or

29. (d)

n terms

30. (a) Let given numbers a, a + d, a + 2d, .......... are in A.P.

⇒ 11 (a + 5d) = 19 (a + 9d) ⇒ 19a – 11a = – 171 d + 55 d ⇒ 8a = – 116 d ⇒ 2a = – 29 d ⇒ 2a + 29d = 0 ∴

31. (b) Let

⇒ log10 x = ± 2 ⇒ x = 102 or 10–2 32. (c) a1 = 81.33; a2 = – 19; a3 = a2 – a1; a4 = a3– a2; a5 = a4 – a3 and so on ∴ a1 + a2 + a3 +............... + ∞ = a1 + a6001 = a1 + a2 = 81.33 – 19 = 62.33 u

33. (b) x = 256 Taking log to the base 2 on both sides u log2x = log2 256 = log2 28 = 8 log22= 8

Let log2 x = a ⇒ Equation becomes, 3

⇒ a – 6a + 12a – 8 = 0 ⇒a=2

(from given value of ‘a’) (a – 2) = 0 3

log2 x = 2

∴ There is only one solution. 34. (c) an + 1 = 3an + 4n – 2 Given, a1 = 1 = 31 – 2 a2 = 3 × 1 + 4 – 2 = 5 = 32 – 4 a3 = 3 × 5 + 4 × 2 – 2 = 21 = 33 – 6 or an = 3n – 2n ⇒ a100 = 3100 – 2 × 100 = 3100 – 200 35. (d) Let

We know, or A < 1 So, A can now be 1. 36.

(a)

;

Thus, = = 37. (e) or or

......(1)

and

......(2)

and

......(3) =

or ......(4) Putting the options in condition 4, we see that it is not satisfied only when a = 2and b = 2. 38. (d) We know, the last term, Here,

, a = 1, 1000 = 1+ (n – 1)d or

999 = (n – 1)d

An AP with the elements of the set S will be possible only when 999 will be divisible by (n – 1) where . So, we need to find the factors of 999, which are 3, 9, 27, 37, 111, 333, 999. An AP is possible for all the 7 above factors of 999 with n = 4, 10, 28, 38, 112, 334 and 1000 elements. 39. (d) This is an AP problem with common difference, d = – 3 Sum of AP = (

total children = 630)

or 2an + n(n – 1)(– 3) = 630 × 2 = 1260 or or Now using all the options given, we find that (a) For n = 3, a = 213 and the AP is 213, 210, 207. (b) For n = 4, a = 162 and the AP is 162, 159, 156, 153 (c) For n = 5, a = 132, and the AP is 132, 129, 126, 123, 120. (d) For n = 6, a = 117.5 which is not possible (e) For n = 7, a = 99 and the AP is 99, 96, 93, 90, 87, 84, 81. 40. (b) a1 = p, b1 = q a2 = pb1, b2 = qb1 a2 = pq, b2 = q2 ...(i) Now, a3 = pa2, b3 = qa2 a3 = p2q, b3 = pq2 Now, a4 = pb3, b4 = qb3 a4 = p2q2, b4 = pq3 ...(ii) Now, a5 = pa4, b5 = qa4 a5 = p3q2, b5 = p2q3 Now, a6 = pb5, b6 = qb5 a6 = p3q3 , b6 = p2q3 ...(iii) On viewing the equation (i), (ii) and (iii) For even integral value of n, we conclude that

41. (e) a1 = pq0, b1 = p0q ...(iv) a3 = p2q, b3 = pq2 ...(v) a5 = p3q2, b5 = p2q3 ...(vi) On viewing the above equations (v), (vi) and (vii) for odd integral value of n, we conclude that

Now checking for option n = 9, we get a9 + b9 = p4 . q4 (p + q)

= 0.0024 < 0.01 = 9 42. (c)

f (1) + f (2) +....+ f (n) = n2 f (n) f (1) + f (2) +....+ f (n–1) = n2 f (n) – f (n) Σ f (n – 1) = (n2 – 1) f (n)

43. (b)

⇒ f (1) = 3600 f (2) = f (3) = f (4) = f (5) = f (6) = f (7) = f (8) =

f (9) =

44. (a) (a + b + c)20 = [(a + b) + c]20 = 20C0 (a + b)20. c0 + 20c1 (a + b)19. c + 20C2 (a + b)18.c2 + ...... + 20c19(a + b).c19 + 20c20 (a + b)0c20

Since, number of terms in a binomial expansionfor natural number index is one more than the indexi.e., (n + 1). Hence, if we further expand the each terms except the last term we get total number of distinct terms = 21 + 20 + 19 + ...... + 2 + 1 45. (a)

46. (c) The given first sequence can be written as 17 + (n – 1) 4 i.e., 4n + 13, where n = 1, 2, 3 ...., 101

The given second sequence can be written as16 + (m – 1) 5 i.e., 5m + 11 where m = 1, 2, 3, .... 91 For common terms, 4n + 13 =5m + 11

For positive integral value of m, the unit digit of the number n will 2 or 7. Hence, total possible value of n = 2,7, 12, 17, .... , 97 i.e., 20 values of n. Hence, there will be 20 common terms in given two sequences. 47. (c) The value of y will be minimum at all values of x ≤ 2. 48. (a) log (0.57) = ⇒ log 57 = 1.756 [ mantissa will remain the same] log 57 + log (0.57)3 + log = log 57 + 3 log

+ log

= log 57 + 3 log 57 – 3 log 100 + =

log 57 –

log 100 =

× 1.756 –

log 57 –

log 100

×2

= 7.902 – 7 = 0.902. 49. (c) This can be checked by taking arbitrary values of a and b in the given terms. Taking a = 2 and b = 3, we conclude that (c) is not true. 50. (c) Let a = b2 = c3 = d4 a = b2

Similarly, Consider, =

(By putting values)

51. (a)

...(i) ...(ii)

From equations (i) and (ii), we get

Let log36 be equal to k; therefore,

52. (a)

Given that x + y = 1 ⇒x+y–1=0 ⇒ x3 + y3 – 1 = – 3xy (a3 + b3 + c3 = 3abc if a + b + c = 0) ⇒ x3 + y3 + 3xy = 1 53. (c) X = (log10 1 + log10 2 + ... + log10 n) – (log10 1 + log10 2 + .... + log10 p) – (log10 1 + log10 2 + .... + log10 (n – p)) ⇒ X = log10 n! – log10 p! – log10 (n – p)! log (m × n) = log m + log n log

= log m – log n

⇒X= X is maximum when ⇒

is maximum.

is maximum, i.e. 8Cp is maximum

⇒p=4 ⇒ X = log10

= log10 70 = 1 + log10 7.

54. (c) Take –y in place of y Then equation is =

⇒y= 55. (b) According to question, log3 (2x – 5) – log3 2 = log3

⇒

⇒ Let 2x = a ⇒ ⇒ a2 – 10a + 25 = 2a – 7 ⇒ a2 – 12a + 32 = 0 ⇒ (a – 4) (a – 8) = 0 ⇒ a = 4 or 8 ∴ x = 2 or 3 Hence, 2x – 5 = –1,

– log3 (2x – 5)

when x = 2, which is not possible. ∴ x = 3. Or All numbers are in AP, 2 log3 (2x – 5) = log3 2 + log3 (2x – 7/2) Suppose 2x = t 2 log3 (t – 5) = log3 2 + log3 (t – 7/2) ⇒ log3 (t – 5)2 = log3 (2t – 7) ⇒ (t – 5)2 = 2t – 7 ⇒ t2 – 10t + 25 = 2t – 7 ⇒ t2 – 12t + 32 = 0 ⇒ t = 4.8 x 2 = 4.8 ∴ x = 2, 3. 56. (c) Let the number of balls with Pi = ai (i = 1 to 11) a1 + a3 + a5 ...... + a11 = 6 (a6) = 72. As a6 would be the arithmetic mean of these 11 numbers and 2(a6) = (a1 + a11) = (a2 + a10) = (a3 + a9) = (a4 + a8) = (a5 + a7) ∴ a1 + a6 + a11 = 3 (a6) = 36 57. (17)

x4 – y4 = 15 (where (a2 – b2) = (a + b) (a – b)

∴ (x2 – y2) (x2 + y2) = 15 ⇒ (x2 – y2) (x2 + y2) = 1 × 15 = 3 × 5 ⇒ x2 – y2 = 3 and x2 + y2 = 5 (because x and y are natural numbers) ∴ 2x2 = 8

⇒ x2 = 4 ∴ y2 = 1 ∴ x4 + y4 = 42 + 12 = 17. 58. (d) If a positive number a is expressed as the sum of two positive numbers s1 and s2 then [a] could be at the most 1 more than [s1] + [s2], i.e., the fractional parts of s1 and s2 together, can provide at most 1. Similarly, the fractional parts of s1, s2, s3, s4, s5 can together, provide at most 4. Conversely, if [a] is 4 more than [s1] + [s2] + [s3] + [s4] + [sm], then m has to be at least 5. Similarly, the least value of n is 4. ∴ (m + n)min = 5 + 4 = 9 59. (d) x2 – x – 1 = 0 x= 2x4 =

( =7+3

60. (c) =

–7=

=– ⇒ 1 – 1/6 ⇒ 61. (b) 92x–1 – 81x–1 = 1944 = 1944 92x

= 1944

x > 0)

92x – 2 = 243 ⇒ 34x – 4 = 35 4x – 4 = 5 ⇒ x = 62. (a) (a + 6d)2 = (a + 2d)(a + 16d) a2 + 12ad + 36d2 = a2 + 18ad + 32d2 4d2 = 6ad =

⇒a:d=2:3

63. (b) a1 = 3, a2 = 7, d = 4 Sn =

(2a + (n – 1)d)

Sn =

(2 × 3 +(n – 1)4)

S3n ⇒

⇒ n(2n + 1)

(6 + (3n – 1) 4) = 1830

n(6n + 1) = 610 6n2 + n – 610 = 0 solved, n = 10 Now, m (a1 + a2 + .... an) > 1830 m>

⇒m>

m > 8.7 ⇒ m > 9

(a) (b) (c) (d) 2.

(a) (b) (c) (d) 3.

I. II. (a)

The number of votes not cast for the Praja Party increased by 25% in the National General Elections over those not cast for it in the previous Assembly Polls, and the Praja Party lost by a majority twice as large as that by which it had won the Assembly Polls. If a total of 2,60,000 people voted each time, how many voted for the Praja Party in the Assembly Elections? (1994) 1,10,000 1,50,000 1,40,000 1,20,000 A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much per cent above the cost price were his wares listed? (1994) 100% 80% 75% 66 2/3% Last week Martin received $ 10 in commission for selling 100 copies of a magazine. Last week Miguiel sold 100 copies of this magazine. He received his salary of $ 5 per week plus a commission of 2 percent for each of the first 25 copies sold, 3 percent for each of next 25 copies sold and 4 percent for each copy thereafter. ($1 = 100 cents) (1994) Martin’s commission in the last week Miguiel’s total income for last week I > II

(b) I < II (c) I = II (d) Nothing can be said 4. A person who has a certain amount with him goes to the market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount as taxi fare and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is (1995) (a) (b) (c) (d) 5.

(a) (b) (c) (d) 6.

36 40 15 20 Ram purchased a flat at ` 1 lakh and Prem purchase a plot of land worth ` 1.1 lakh. The respective annual rates at which the prices of the falt and the plot increased were 10 % and 5%. After two years they exchanged their belongings and one paid the other the difference. Then... (1995) Ram paid Rs. 275 to Prem Ram paid Rs. 475 to Prem Ram paid Rs. 2750 to Prem Prem paid Rs. 475 to Ram The rate of inflation was 1000%. Then, what will be cost of an article, which costs 6 units of currency now, two years from now? (1995)

(a) (b) (c) (d) 7.

666 660 720 726 A man invests ` 3000 at a rate of 5% per annum. How much more should he invest at a rate of 8%, so that he can earn a

total ?

per

annum (1995)

(a) (b) (c) (d) 8.

(a) (b) (c) (d) 9.

(a) (b) (c) (d) 10.

(a) (b) (c) (d)

Rs. 1200 Rs. 1300 Rs. 1500 Rs. 2000 2/5 of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q and P lost by 2 votes. Then the total number of voters is (1995) 100 110 90 95 I sold two watches for Rs. 300 each, one at a loss of 10% and the other at a profit of 10%. What is the per cent loss (–) or the per cent profit (+) that resulted from the transaction ? (1996) (+) 10 (–) 1 (+) 1 0 The price of a Maruti Car rises by 30% while the sales of the car come down by 20%. What is the per cent change in the total revenue? (1996) –4 –2 +4 +2

11.

The cost of a diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond. (1996) (a) Rs. 1.4 lakh (b) Rs. 2.0 lakh (c) Rs. 1.0 lakh (d) Rs. 2.1 lakh 12. I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I had paid. What percent of the total paid by one was paid for the pens? (1996) (a) 37.5% (b) 62.5% (c) 50% (d) None of these Directions for questions 13 & 14 : Read the information given below and answer the questions that follow : A watch dealer incurs an expense of Rs. 150 for producing every watch. He also incurs an additional expenditure of Rs.30, 000, which is independent of the number of watches produced. If he is able to sell a watch during the season, he sells it for Rs. 250. If he fails to do so, he has to sell each watch for Rs. 100. (1996) 13. If he is able to sell only 1200 out of the 1500 watches he has made in the season, then in the season he has made a profit of (a) Rs. 90, 000 (b) Rs.75.000 (c) Rs. 45,000 (d) Rs. 60,000

14. If he produces 1500 watches, what is the number of watches that he must sell during the season in order to break even, given that he is able to sell all the watches produced? (1996) (a) 500 (b) 700 (c) 800 (d) 1,000 15. Instead of a metre scale cloth merchant uses a 120 cm scale while buying but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20 per cent of cash payment, what is his overall per cent profit? (1996) (a) 20% (b) 25% (c) 40% (d) 15% 16. A student gets an aggregate of 60% marks in five subjects in the ratio 10:9:8:7:6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the exam? (1997) (a) 2 (b) 3 (c) 4 (d) 5 17. After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many per cent above the cost price does he mark his goods? (1997) (a) 28.56% (b) 35%

(c) 22.22% (d) None of these 18. Fresh grapes contain 90% water while dry grapes contain 20% water. What is the weight of dry grapes obtained from 20 kg of fresh grapes? (1997) (a) 2 kg (b) 2.5 kg (c) 2.4 kg (d) None of these 19. A man earns x % on the first 2000 rupees and y % on the rest of his income. If he earns Rs. 700 from Rs. 4000 and Rs. 900 from Rs. 5000 of income, find x (1997) (a) 20 (b) 15 (c) 25 (d) None of these 20. One bacterium splits into eight bacteria of the next generation. But due to environment only 50% of one generation can produce the next generation. If the seventh generation number is 4096 million, then what is the number in first generation? (1998) (a) 1 million (b) 2 million (c) 4 million (d) 8 million Directions for questions 21 & 22 : Read the information given below and answer the questions that follow : A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international

scenario, cost of the German Mark increased by 30% and that of USA Dollar increased by 22%. Due to market conditions the selling price cannot be increased beyond 10%. Then 21. What is the maximum current gain possible? (1998) (a) 10% (b) 12.5% (c) 0% (d) 7.5% 22. If the USA Dollar becomes cheap by 12% over its original cost and the cost of German Mark increased by 20%. The selling price is not altered. What will be the gain? (1998) (a) 10% (b) 20% (c) 15% (d) 7.5% 23. In a company 40% are male, out of which 75% earn a salary of 25,000 plus. If 45% of the employees 25,000 plus salaries, what is the fraction of female employees earning less than or equal to 25,000? (1999) (a) 1/4 (b) 3/7 (c) 3/4 (d) 5/9 Directions for questions 24 to 28 : Answer the questions based on the following information. ABC Ltd. produces widgets for which the demand is unlimited and they can sell all of their production. The graph below describes the monthly variable costs incurred by the company as a function of the quantity produced. In addition, operating the plant for the first shift results in a fixed monthly cost of ` 800. Fixed

monthly costs for second shift operation is estimated at ` 1,200. Each shift operation provides capacity for producing 30 widgets per month. Variable cost

Note : Average unit cost,

24.

(a) (b) (c) (d) 25.

(a) (b)

and marginal

cost, MC is the rate of change in total cost for unit change in quantity produced. Total production in July is 40 units. What is the approximate average unit cost for July? (2000) 3,600 90 140 115 ABC Ltd. is considering increasing the production level. What is the approximate marginal cost of increasing production from its July level of 40 units ? (2000) 110 130

(c) 150 (d) 160 26. From the data provided it can be inferred that, for production levels in the range of 0 to 60 units. (2000) (a) MC is an increasing function of production quantity (b) MC is a decreasing function of production quantity (c) initially MC is a decreasing function of production quantity, attains a minimum and then it is an increasing function of production quantity (d) None of the above 27. Suppose that each widget sells for Rs. 150. What is the profit earned by ABC Ltd. in July ? (2000) (Profit is defined as the excess of sales revenue over total cost) (a) 2,400 (b) 1,600 (c) 400 (d) 0 28. Assume that the unit price is Rs. 150 and profit is defined as the excess of sales revenue over total costs. What is the monthly production level of ABC Ltd. at which the profit is highest ? (2000) (a) 30 (b) 50 (c) 60 (d) 40 29. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is (2001)

(a) (b) (c) (d) 30.

(a) (b) (c) (d) 31.

(a) (b) (c) (d) 32.

(a)

2 3 4 5 A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people, the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited? (2001) Rs. 300 Rs. 250 Rs. 400 Rs. 500 The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices by X %, then a while later he reduces all the new prices by X %. After one such up-down cycle, the price of a painting decreased by Rs. 441. After a second up-down cycle the painting was sold for Rs. 1944.81. What was the original price of the painting? (2001) 2756.25 2256.25 2500 2000 Davji Shop sells Samosas in boxes of different sizes. The Samosas are priced at ` 2 per Samosa up to 200 Samosas. For every additional 20 Samosas, the price of the whole lot goes down by 10 paise per Samosa. What should be the maximum size of the box that would maximise the revenue? (2002) 240

(b) (c) (d) 33.

(a) (b) (c) (d) 34.

300 400 None of these At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q % of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true? (2003C) p=q pq p = q/2 A leather factory produces two kinds of bags, standard and deluxe bag. The profit margin is Rs. 20 on a standard bag and Rs. 30 on a deluxe bag. Every bag must be processed on machine A and on machine B. The processing times per bag on the two machines are as follows:

The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit? (2003C) (a) Standard 75 bags, Deluxe 80 bags (b) Standard 100 bags, Deluxe 60 bags (c) Standard 50 bags, Deluxe 100 bags (d) Standard 60 bags, Deluxe 90 bags. Directions for Questions 35 & 36 : Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three

options, each of which can be utilized fully or partially in conjunction with others. Option A: Invest in a public sector bank. It promises a return of +0.10%. Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%. Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%. 35. The maximum guaranteed return to Shabnam is (2007) (a) 0.30% (b) 0.25% (c) 0.10% (d) 0.20% (e) 0.15% 36. What strategy will maximize the guaranteed return to Shabnam? (2007) (a) 30% in option A, 32% in option B and 38% in option C (b) 100% in option A (c) 36% in option B and 64% in option C (d) 64% in option B and 36% in option C (e) 1/3 in each of the three options 37. There are three water-alcohol solutions A, B and C whose alcohol concentrations are 50%, 60% and 70% respectively. x ml of A, (x + 2) ml of B and (x + 3) ml of C are mixed. If the alcohol concentration of the resultant mixture is 65%, then x lies in the range (2009) (a) 0.1 to 0.5 (b) 0.5 to 0.9

(c) 0.9 to 1.4 (d) 1.4 to 1.9 38. In an examination, the average marks obtained by students who passed was x %, while the average of those who failed was y %. The average marks of all students taking the exam was z %. Find in terms of x, y and z, the percentage of students taking the exam who failed. (2009) (a) (z – x) / (y – x) (b) (x – z) / (y – z) (c) (y – x) / (z – y) (d) (y – z) / (x – z) 39. Ramit sold a table at a profit of 15%. Had he bought it at 10% less and sold it for ` 21 less, he would have gained 25%. At what price (in `) had he bought the table? (2010) (a) 800 (b) 840 (c) 420 (d) 640 40. 10% of the voters did not cast their vote in an election between two candidates. 10% of the votes polled were found invalid. The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters list was : (2011) (a) 25000 (b) 33000 (c) 35000

(d) 40000 41. A contractor did not have space in his garage for 8 of his trucks. He, therefore, increased the size of his garage by 50% which gave him space for 8 more trucks than he owned altogether. How many trucks did he own? (2012) (a) 32 (b) 48 (c) 40 (d) 45 42. The list price of an article was increased by 10%. It was then decreased by 10%. If the final price became `. 20, then find the initial list price (in `.) (2012) (a)

(b)

(c)

(d) 43. A shopkeeper sells four qualities of rice A, B, C and D having cost price ` 40/kg, ` 55/kg, ` 50/kg and ` 65/kg respectively. Ankit purchased ‘a’ kg of A and ‘b’ kg of B to make ‘a + b’ kg of a new quality ‘E’ of rice worth ` 50/kg. Then he purchased ‘c’ kg of C and ‘d’ kg of D to make ‘c + d’ kg of a new quality ‘F’ of rice worth ` 60/kg. Finally he took ‘x’ kg of rice and ‘y’ kg of rice from ‘E’ quality of rice and ‘F’ quality of rice respectively to make ‘x + y’ kg of rice worth ` 53/kg. Ensuring that a, b, c, d, x and y are all integers then what is the minimum value of a + b + c + d + x + y in kg? (2014) (a) (b) (c) (d)

28 22 16 26

44. A trader used to make 5% profit on an item by selling it at the usual marked price. One day, he tripled the marked price of the item and finally offered a discount of 30%. Find the percentage profit he made on the item that day. (2014) (a) (b) (c) (d) 45.

120.5% 100% 94.5% None of these An empty metal container (without its handle) weighs 15% of what it weighs when completely filled with a particular liquid. After adding the handle, the weight of the fully filled container increases by 5%. If the weight of a partly filled container is

the completely filled container with the handle attached, then what fraction of container is utilized? (2014) (a) (b) (c) (d) 46. The percentage volumes of milk in three solutions A, B and C from a geometric progression in the order. If we mix the first, second and third solutions in the ratio 2 : 3 : 4 by volume, we obtain a solution containing 32% milk. If we mix them in the ratio 3 : 2 : 1, by volume, we obtain a solution containing 22% milk, What is the percentage of milk in A ? (2014) (a) 6%

(b) 12% (c) 18% (d) 24% 47. There are two factories – A and B – in Kaarobaarnagar. In factory A, the number of male employees is 50% more than that of female employees. In factory B, the number of female employees is 40% less than that of male employees. The number of female employees in factory B is 60 more than that of male employees in factory A. Which of the following cannot be the total number of male employees in the two factories put together? (2014) (a) 204 (b) 180 (c) 320 (d) 300 48. A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13 % and 10 % respectively, find the profit percentage on the whole. (2015) (a) 11.5% (b) 12% (c) 12.5% (d) Data insufficient 49. The total cost of 2 pencils, 5 erasers, and 7 sharpeners is ` 30, while 3 pencils and 5 sharpeners cost ` 15 more than 6 erasers. By what amount (in `) does the cost of 39 erasers and 1 sharpener exceed the cost of 6 pencils? (2016) (a) 20 (b) 30 (c) It does not exceed (d) Cannot be determined

50. Balram, the local shoe shop owner, sells four types of footwear – Slippers (S), Canvas Shoes (C), Leather Shoes (L) and Joggers (J). The following information is known regarding the cost prices and selling prices of these four types of footwear: (2016) (i) L sells for ` 500 less than J, which costs ` 300 more than S, Which, in turn, sells for `200 more than L. (ii) L costs ` 300 less than C, which sells for ` 100 more than S, which, in turn, costs ` less than C. If it is known that Balram never sells any item at a loss, then which of the following is true regarding the profit percentages earned by Balram on the items L, S, C and J represented by l, s, c and j (a)

(b)

(c)

(d) 51. Some friends planned to contribute equally to jointly buy a CD player. However, two of them decided to withdraw at the last minute. As a result, each of the others had to shell out one rupee more than what they had planned for. If the price (in `) of the CD player is an integer between 1000 and 1100, find the number of friends who actually contributed? (2016) (a) 21 (b) 23 (c) 44 (d) 46 52. Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi’s savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is `59500, then Ravi’s total monthly savings (in `) is (2017) 53. If a seller gives a discount of 15% on retail price, She still makes a profit of 2%. Which of the following ensures that she makes a profit of

20%? (2017) (a) (b) (c) (d) 54.

Give a discount of 5% on retail price. Give a discount of 2% on retail price. Increase the retail price by 2%. Sell at retail price. In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bougth the good ones. His overall profit is (20 17) (a) 6% (b) 8% (c) 10% (d) 12% 55. If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit? (2017) (a) 30% (b) 25% (c) 24% (d) 28% 56. If a and b are integers of opposite signs such that (a + 3)2 : b2 = 9 : 1 and (a – 1)2 : (b – 1)2 = 4 : 1, then the ratio a2 : b2 is (2017)

(a) (b) (c) (d)

9:4 81 : 4 1:4 25 : 4

(c) Suppose no. of people voted in Assembly for Praja Party = x and no. of people voted in national polls for Praja Party = y Then, people not voted in assembly for Praja Party = 2,60,000 – x People not voted in national polls for Praja Party = 2,60,000 – y Party won assembly polls by a margin = 2x – 2,60,000 Lost vote in national polls by a margin = 2,60,000 – 2y Given that,

(2,60,000 – x)

......(i) Also given, 2x + y = 3,90,000 y = 3,90,000 – 2x ......(ii) From (i) and (ii) we get x = 1,40,000, y = 110,000 So, No. of votes for the Praja party in the assembly elections are 140, 000.

(a) If listed price of article be Rs. 100 then discounted price be Rs. 80 (since discount = 20%) After offering 16 articles to a dozen Price of 16 articles = 80 × 12 Price of one article Profit = 20 % Cost price x (say) = 60 – x ×

Per cent above the cost price 3.

= 100%

(a) Miguel’s

income = $ 8.25

Martin’s commission = $ 10 Thus, Martin’s commission > Miguiel’s income (d) Let the price of an orange and a mango be Rs. ‘x’ andRs. ‘y’ respectively. Then, As he buys only for 90% of the amount he can buy a miximum of mangoes. But he buys only 20 mangoes and remain oranges. Hence, 36 mangoes = 20 mangoes

oranges

∴ No. of oranges purchased = 20 (a) Ram’s flat value after 2 years = Prem’s flat value after 2 years = 1.1(1 + 0.05)2= 1.1(1.05)2

Difference = 1.1(1.05)2 – 1.12 lakh

Ram paid Rs. 275 to prem (d) Cost of article after 2 years

(a) Voters to vote for Voters to vote for On the last day Voters voted for Voters voted for As P lost by 2 votes,

Alternatively Let total voters be 100 Voters to vote for P = 40 Voters to vote for Q = 60 On the last day Voters voted for

P= Voters voted for Q=

∴ P lost by 51 – 49 = 2 votes Hence, total voters = 100. (b) Let cost price of 1st watch be CP1 and 2nd watch be CP2 Then CP of 1st watch = CP of 2nd watch = ∴ Total CP = 333.33 + 272.72 = Rs. 606.05 Total SP = Rs. 600 ∴ % loss Alternatively: There is always loss and Loss %

10. (c) Let initial price = x and sales = y Then, total revenue = xy After price rise Price = ∴ Change in revenue

% change

= + 4%

Alternatively: Change in Price = + 4% 11. (c) Let the weight of the diamond be 10 units. Hence the cost will vary by 102 i.e. cost = 100 x After the diamond is broken, the cost becomes i.e., 30 x. Thus,

∴ Original cost = Rs. 1,00,000 12. (b) Let the price of a pen, pencil and eraser be Rs. x, y and z respectively. ...(i) ...(ii) Multiply (i) by 2, ...(iii) Subtracting (ii) from (iii) we have, 4x = 0.5A

∴ For 5 pens, amount paid = 0.125A × 5 = 0.625A Hence, 62.5 % of total amount paid by me For Qs. 13-14. Let watch dealer makes x watches then Total cost price = 30,000 + 150x Selling price of per watch = 250 in season or S = 100 otherwise 13. (b) CP = 30,000 + 2,25,000 = 2,55,000

SP = 1200 × 250 + 300 × 100 = 3,30,000 Profit = 3,30,000 – 2,55,000 = Rs. 75000 14. (b) Let he sells x watches at Rs. 250 watches sells at Rs. 100

or = 700 watches 15. (a) Let the cost of cloth per cm be Rs. x As he uses 120 cm scale, so, he has 120 cm cloth cost incurred = 100x. While selling he uses 80 cm scale, so actually he charges for

cm of cloth

Amount obtained after 20% discount = ∴ Profit = 16. (c) Let maximum marks be 100 Hence his average = 60 Let his marks be 10x, 9x, 8x, 7x, 6x respectively in 5 subjects i.e. 10x + 9x + 8x + 7x + 6x = 60% of 5 × 100 =

......(i)

Solving we get his marks were 75, 67.5, 60, 52.5, 45 Since passing marks are 50 He passed in 4 subjects 17. (a) Let the C.P be Rs. 100 and selling price be Rs. x Discount

or 114.78

= 128. 56 ∴ Price above the cost price = Rs. 28.56 = 28.56% Alternatively: Price above the cost price

18. (b) 100 kg of fresh grapes have 90 kg water and 100 kg of dry grapes have 20 kg water 20 kg fresh grapes have

water

i.e, 2 kg non water For dry grapes non- water material If any grapes are x kg ⇒ 19. (b) According to question .....(i)

and 900

....(ii)

Solving from (i) and (ii) we get y = 20 and x = 15 20. (a) Let n1 be the bacteria in 1st generation

Hence,

= 4n1

Similarly,

= 42 n1

∴ Hence 1 million 21. (a) Let cost of component A and B be Rs. 30 and Rs. 50 respectively. Then cost of production = Rs. (30 + 50 + 20), whereRs. 20 contributes to the other expenses, assuming total production cost Rs. 100. Since, profit is 20%. Hence, selling price = Rs. 120. Now, new cost price of component A =

Rs. 39

New cost price of component B =

Rs. 61

New production cost (other expenses do not change) = (39 + 61 + 20) = Rs. 120 Since new S.P. = 120 ×

= 132

∴ New profit % 22. (b) New cost of component A = 30 × New cost of component B = 50 ×

. = Rs. 36 = Rs. 44

New production cost = Rs. (36 + 44 + 20) = Rs. 100 New selling price is same. Hence profit = 120 – 100 = 20 or 20%.

23. (c) Let total no. of employees be Emplyees who get 25000 plus salaries = 45 Male emplyees = 40 Female emplyees = 60 Male employees who get 25000 plus salaries = 30 Female employees who get 25000 plus salaries = 15 Female employees who get less than or equal to 25000 = (60 – 15) = 45 i.e., 24. (c) Cost in shift operation = 800 + 1200 = Rs. 2,000 Variable cost for 40 units = Rs. 3,600 Approximate average unit cost for July

25. (b) The only change for change of production from 40 to 41 is the variable cost which is Rs. (3730 –3600) = Rs.130. 26. (c) The trend for MC is varying and is just the reverse condition as that stated in C. Take some values and check. 27. (c) Total sales revenue = Rs. (150 × 40) = Rs. 6,000 Total production cost = Rs. (3600 + 2000) = Rs. 5600. So profit = Rs. 400 28. (c) Profit is highest when there is no second shift. 29. (c) Let Maximum marks be 100. Hence, his average = 60 Let marks in subjects be 6x, 7x, 8x, 9x and 10x According to question, (6 + 7 + 8 + 9 + 10 ) x = 60 × 5 ⇒ (40)x = 300 ∴ Hence, his marks, supposing the maximum marks to be 100 for each subject = 75 , 67.5, 60, 52.5, 45 Hence, he got above 50% in 4 subjects

30. (a) Let the total donors be = x 60% of donors pay 75% of the amount. ∴ Total amount raised = Remaining amount = 25% Now, 25% of the amount is raised by 40% of the donors. Therefore, average donation of these people = 31. (a) In first up-down cycle, the reduction price is Rs. 441. According to this, option (b) and (d) are removed. Now we see the option (c), if the original price isRs. 2500, then after first operation, the price will be 2500 – 441 = Rs. 2059 In second operation, it will come down around Rs. 400. So the value is not equivalent to Rs.1944.81. Hence, Rs. 2756.25 is the correct option. Alternatively : Let the initial price be Rs. A. Then, ...(i) and

...(ii)

From (i) and (ii)

32. (b) For 200 Samosas prices = 2 × 200 = Rs. 400 For 220 Samosas prices = 1.90 × 220 = Rs. 418

For 240 Samosas prices = 1.80 × 240 = Rs. 432 For 260 Samosas prices = 1.70 × 260 = Rs. 442 For 280 Samosas prices = 1.60 × 280 = Rs. 448 For 300 Samosas prices = 1.50 × 300 = Rs. 450 For 320 Samosas prices = 1.40 × 320 = Rs. 448 Hence we see that revenue increase when size increases up to 300. After 300 revenue reduces therefore maximum size for maximise the revenue = 300 Samosas 33. (c) Shephard adds p % of 108 goats every year and sellsq % of It is observed that the goats sold is a percentage of a higher quantity as compared to the goats added. Hence, if he has 108 goats left, it means he should have added more (higher percentage of small quantity) than he sold. Hence, p > q. 34. (a) Let the standard bags produced be ‘s’ and deluxe bags produced bE ‘d’ For machine A, ......(i) For machine ......(ii) Solving for s and d from (i) and (ii) we get, s = 75 and d = 80 ∴ Profit, P = 20s + 30d = 75 × 20 + 80 × 30 = 1500 + 2400 = 3900 This is the maximum profit meeting the complete machine availability constraints. The options (c) & (d) do not satisfy equations (i) and (ii). Profit in option (b), which is less than option (a). 35. (d) Investment in option A will fetch + 0.10% return. We need to compare this return with the return from the rise and fall in the stock market for investment in option B and C. Let the amount invested in options B and C be in the ratio x : 1. For rise in stock market, return = 5x – 2.5 For fall in stock market, return = 2 – 3x

∴

The maximum guaranteed return will be earned when 5x – 2.5 = 2 – 3x 8x = 4.5 or x =

∴ The maximum guaranteed return is when, the amounts invested are in the ratio 9 : 16 i.e., 36% and 64% respectively. Guaranteed return for this distribution

∴ Maximum guaranteed return = 0.20% 36. (c) Let us calculate the guaranteed return in each option (1) For rise in market: 0.3 × 0.1 + 0.32 × 5 – 0.38 × 2.5 = 0.68% Fall in market: 0.3 × 0.1 + 0.32 × (–3) + 0.38 × 2 = – 0.17% (2) It will give a return of 0.1% (3) Return = 0.2% (as calculated in above question) (4) Rise in market: 5 × 0.64 – 2.5 × 0.36 = 3.2 – 0.9 = 2.4% Fall in market: 2 × 0.36 – 3 × 0.64 = 0.72 –1.92 = –1.20 (loos) Similarly, the guaranteed return options [e] can be calculated. The guaranteed return cannot be calculated in case of options (a), (d) and (e) as it depends on the rise and fall of the market, whose probability cannot be predicted. So option (c) is correct as it gives a higher return (than option b) of 0.2%. Note: Return for, option 3 could be calculated as in this case the return for rise and fall of market is same. 37. (a) According to the given condition ⇒

⇒ ⇒ 1.8x + 3.3 = 1.95x + 3.25 ⇒ 0.05 = 0.15x ⇒ ⇒ 38. (a) Let the failed candidates be F and the total candidates be 100. So, F% students failedin examination. Then, (100 – F). x % + F . y % = z % (100). Solving the equation, we get x % – %Fx + %Fy = z; Hence % F = (z – x) / (y – x). 39. (b) Let the CP of the table be Rs.100x. SP of the table = Rs.115x According to the question, 90x × 1.25 = 115x – 21 ⇒ x = 8.4 So the answer = Rs.100x = Rs. 840. 40. (a) Let the total number of voters be x. Then, Votes polled = 90% of x. Valid votes = 90% of (90% of x). 54% of [90% of (90% of x)] – 46% of [90% of x)]= 1620 ⇒ 8% of [90% of (90% of x)] = 1620 ⇒

∴x=

× x = 1620 = 25000.

41. (c) Let the contractor had x trucks. According to question,

⇒ 3x – 24 = 2x + 16 ⇒ 3x – 2x = 16 + 24

⇒ x = 40 42. (c) List price of an article was increased by 10% and then decreases by 10%. ⇒

× initial list price = final list price

⇒ Initial list price = 43. (b)

By Allegation,

⇒1:2 Hence a : b = 1 : 2

⇒1:2 Hence, c : d = 1 : 2 Also,

Hence, x : y = 7 : 3 So, minimum weight of x (= 7 kg) and y (= 3 kg) we need (a + b) ≥ 7 and (c + d) ≥ 3. Hence, minimum a + b = 9 (as it has to be in the ratio of 1 : 2 it must be a multiple of 3) So, Minimum value of c + d = 3

∴ Minimum value of a + b + c + d + x + y = 9 + 3 + 7 + 3 = 22 kg. 44. (a) Let cost price of the item = ` 100 ⇒ Then, marked price = ` 105. On that day, 30% discount is offered on tripled the mark price ` 3 × 105 = ` 315 ×

= 220.50

Thus, new selling price = ` 220.50 ⇒ ∴ New profit percentage = = 120.50%. 45. (b) Let the container (without the handle) weight = 100x when it is completely filled with a liquid. ∴ The empty metal container (without its handle) weights 15x. After handle is added weight of fully filled container = 105x. ∴ Weight of handle = 5x. ∴ Weight of partly filled container =

= 35x.

∴ Weight of liquid in partly filled container = 35x – (15x + 5x) = 15x. Total capacity of container = 105x – (15x + 5x) = 85x. ∴ Fraction of container that is utilized = 46. (b)

Let percentage volume of milk in solution A, B and C vessels is a, ar and ar2 respectively. (Because geometric progression) According to question,

= =

...(i) ...(ii)

From (i) & (ii) we get a = 12 and r = 2. ∴ The percentage of milk in A = 12%. 47. (c) Let the number of female employees in factory A and the number of male employees in factory B be 2a and 5b respectively. Therefore, the number of male employees in factory A and that of female employees in factory B will be 3a and 3b respectively. ∴ 3b = 3a + 60 ⇒ b – a = 20 ...(i) Total number of male employees in the two factories A and B put together = 3a + 5b. = 3a + 5 × (20 + a) = 8a + 100. Among the given options only 8a + 100 = 320 will not give a positive integer value of ‘a’. So option (c) is correct answer. 48. (a) If the profit amount are in AP then the profit % ages are also in an A.P. If P4 = 13% and P7 = 10% then P5 = 12% and P6 = 11% Average of the middle terms will give the profit % on the whole i.e. (11 +12)/2 = 11.5 % 49. (b) Let the cost of pencil, eraser and sharpener (in rupees) be p, e, s respectively. 2p + 5e + 7s = 30 ...(1) 3p – 6e + 5s = 15 ...(2) We need the value of the following expression E = – 6p + 39e + s

We assume that by multiplying equation (1) by x and equation (2) by y and adding we get the equation E. By considering the coefficients of only p and e. we get 2x + 3y = – 6 and 5x – 6y = 39 This gives x = and ∴ y = –4 [Note : Observe that the coefficiens of s also combine in the same way to match the coefficient of s in E i.e., 3(7) – 4(5) = 1] ∴ E = 3(30) – 4(15) = 30 50. (c) According to questions,

To compare the profit percentages then we get ∴ It can be observed that the above fractions can be written as

(where a = x – 300, b = y) Now since no item sells at a loss, and given the identity that whenever

, and k is a +ve quantity, the

above ratios can be rearranged as

⇒ 51. (c) Let the number of friends initially be n and let the contribution of each be x. According to question, nx = (n – 2) (x + 1) ⇒ nx = nx – 2x + n – 2 ⇒ n = 2x + 2 ⇒ n = 2 (x + 1) Here, We take possible values of x, n and nx.

As 1000 < nx < 1100, (x, n) = (22, 46) i.e. n = 46. Hence, number of friends who actually contributed = n – 2 = (46 – 2) = 44. 52. (70,000) Let total monthly salary = ` x Now F.D = x/2 Stocks = 0.3 × Bank A/c =

– 0.3 × –

= 59500

x = 70, 000 53. (d) Let retail price be 100 Discount = 15 S.P = 85

C.P =

for make 2 % profit

C.P =

for making 20% profit

The seller must sell at the retail price. 54. (b) Let the price of each good mango be = x Price of medium quality mango = Total cost price = 80 x +

= 100x

Total selling price = 120 × 0.9x =108x over all profit = 8% 55. (d) Let the printed price be P If 40% discount is given, selling price = 0.6 × 60P = 36P In order to make a profit of 20% the selling price Total C.P =

= 30P

Ten toys are destroyed in the fire, the remaining toys are sold at a price such that the same amount of profit is made as in the conditional caseProfit make on remaining toys = 6P Total selling P of remaining toys = 36P Discount = 50P – 36P = 14P Discount = 28% 56. (d)

= 9 and

we get 4 cases a + 3 = 3b a + 3 = – 3b a – 1 = 2b – 2 a – 1 = 2b – 2

(i) (ii) (i) (ii)

a + 3 = – 3b a – 1 = – 2b + 2 a + 3 = – 3b a – 1 = – 2b + 2 Solved each case i.e. a = – 15 b=–6 ∴

(i) (ii) (i) (ii)

k1, k2, k3 are parallel lines. AD = 2 cm, BE = 8 cm and CF = 32 cm (1994)

Then I. (AB) × (EF) II. (BC) × (DE) (a) I > II (b) I < II (c) I = II (d) Nothing can be said 2. Which one of the following cannot be the ratio of angles in a right angled triangle? (1995) (a) 1 : 2 : 3 (b) 1 : 1 : 2 (c) 1 : 3 : 6 (d) None of these 3. In ∆ABC, And CE bisects the angle C. ∠A = 30º. What is ∠CED? (1995)

(a) (b) (c) (d) 4.

30° 60° 45° 65° In the given figure, AB is diameter of the circle and the points C and D are on the circumference such that ∠CAD = 30º and∠CBA 70º. What is the measure of ∠ACD? (1995)

(a) (b) (c) (d) 5.

40° 50° 30° 90° The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall the upper end of the ladder coincides with the tip of the wall. Then, the height of the wall is (1995) 12m. 15m. 18m. 11 m. In triangle ABC, angle B is a right angle. If (AC) is 6 cm, and D is the mid - point of side AC. The length of BD is (1996)

(a) (b) (c) (d) 6.

(a) 4 cm (b) (c) 3 cm (d) 3 . 5 cm 7. The points of intersection of three lines , (1996) (a) (b) (c) (d) 8.

form a triangle are on lines perpendicular to each other are on lines parallel to each other are coincident If ABCD is a square and BCE is an equilateral triangle, what is the measure of the angle DEC? (1996)

(a) 15° (b) 30° (c) 20° (d) 45° 9. AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral

ACBD 1997)

(

54 cm2 216 cm2 162 cm2 None of these In the given figure, EADF is a rectangle and ABC is a triangle whose vertices lie on the sides of EADF. (1997) AE = 22, BE = 6, CF = 16 and BF = 2 Find the length of the line joining the mid-points of the sides AB and BC. (a) (b) (c) (d) 10.

(a) (b) 5 (c) 3.5 (d) None of these 11. Three circles, each of radius 20 and centres at P, Q, R. further, AB = 5, CD = 10 and EF = 12. What is the perimeter of the triangle

PQR? (1998)

(a) (b) (c) (d) 12.

120 66 93 87 There is a circle of radius 1 cm. Each member of a sequence of regular polygons S1 (n), n = 4,5,6,....., where n is the number of sides of the polygon, is circumscribing the circle; and each member of the sequece of regular polygons where n is the number of sides of the polygon, is inscribed in the circle. Let L1 (n) and L2(n) denote the perimeters of the corresponding polygons of S1(n) and S2(n). Then

(a) (b) (c) (d) 13.

is (19 99) Greater than π/4 and less than 1 Greater than 1 and less than 2 Greater than 2 Less than π/4 The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at point B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?

(1999)

(a) (b) π (c) (d) 14. In the figure below, AB = BC = CD = DE = EF = FG = GA. Then, is approximately (2000)

(a) (b) (c) (d) 15.

15° 30° 20° 25° ABCD is a rhombus with diagonals AC and BD intersecting at the origin on the xy plane. If the equation of the line AD isx + y =

1 is

then

the

equation

line

(2000) (a) (b) (c) (d) None of these 16. There is a regular octagon A B C D E F G H, a frog is at the vertex A. It can jump on to any of the vertices except the exactly opposite vertex. The frog visits all the vertices exactly once and then reaches vertex E then how many times did it jump before reaching E? (2000) (a) (b) (c) (d) 17. (a) (b) (c) (d) 18. (a) (b) (c) (d) 19.

7 2n + 1 6 can’t be determined If the perimeter of a triangle is 14 and the sides are integers, then how many different triangles are possible? (2000) 6 5 4 3 a, b and c are sides of a triangle . If a2 + b2 +c2 = ab + bc + ac then the triangle will be (2000) equilateral isosceles right angled obtuse angle In triangle DEF shown below, points A, B, and C are taken on DE, DF and EF respectively such that EC = AC and CF = BC. If angle D = 40 degrees then what is angle ACB in degrees? (2001)

(a) (b) (c) (d) 20.

140 70 100 None of these Based on the figure below, what is the value of x, if y = 10 (2001)

(a) (b) (c) (d) 21.

10 11 12 None of these In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and , then the length of AD is (2002)

(a) (b)

(c) (d) 22. The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is (in cm) (2002) (a) 24 (b) 25 (c) 15 (d) 20 23. In the figure, ACB is a right angled triangle. CD is the altitude. Circles are inscribed within the triangles ACD, BAD. P and Q are the centres of the circles. The distance PQ is (2002)

(a) 5 (b) (c) 7 (d) 8 24. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is (2002) (a) 1/2

(b) (c) (d) 25.

(a) (b) (c) (d) 26.

(a) (b) (c) (d) 27.

2/3 1/4 3/4 Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be (2003C) 20 0 21 22 In a triangle ABC, AB =6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with centre B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP: QC is equal to (2003C) 1:1 3:2 4:1 3:8 In the diagram given below, the ratio of CD:PQ is (2003C)

(a) 1 : 0.69

(b) (c) (d) 28.

1 : 0.75 1 : 072 None of the above. In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle . What is the radius of the circle in cm ? (2003C)

(a) (b) (c) (d) 29.

10 cm 40 cm 50 cm None of the above. A vertical tower OP stands at the centre O of a square ABCD. Let h and b denote the length of OP and AB respectively. Suppose then the relationship between h and b can be expressed as (2003C)

(a) (b) (c) (d) 30. In the figure given below, AB is the chord of a circle with centre O. AB is extended to C such that BC=OB. The straight line CO is produced to meet the circle at D. If degrees and degrees such that x=ky, then the value of k is (2003C)

(a) (b) (c) (d) 31.

3 2 1 None of the above In the figure (not drawn to scale) given below, P is a point on AB such that AP : PB = 4 : 3. PQ is parallel to AC and QD is parallel to CP. In ARC, ARC = 90°, and in PQS, PSQ = 90°. The length of QS is 6 cms. What is ratio AP : PD? (2003)

(a) (b) (c) (d) 32.

10 : 3 2:1 7:3 8:3 In the figure (not drawn to scale) given below, if AD = CD = BC, and BCE = 96°, how much is DBC? (2003)

(a) (b) (c) (d) 33.

32° 84° 64° Cannot be determined. In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If ATC = 30° and ACT = 50°, then the angle BOA is (2003)

(a) (b) (c) (d)

100° 150° 80° not possible to determine

34. A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son’s head are incident at the same point on the ground. If the heights of the lamp post , the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in meters) is the son standing from his father? (2004) (a) 0.9 (b) 0.75 (c) 0.6 (d) 0.45 Directions for Questions 35 to 37 : Answer the questions on the basis of the information given below. In the adjoining figure, I and II are circles with centers P and Q respectively. The two circle touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the rartio 4 : 3. It is also known that the length of PO is 28 cm.

35. What QO?

the

ratio

the

(2004) (a) 1 : 4

length

that

(b) (d) (d) 36.

1:3 3:8 3:4 What II?

the

radius

the

circle

(2004) (a) (b) (c) (d) 37.

2 cm 3 cm 4 cm 5 cm The is

length

(2004) (a)

(b)

(c)

(d)

38. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If = 65°, then what is the value of ? (2004)

(a) 35°

(b) (c) (d) 39.

55° 45° 25° On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC? (2004)

(a) (b) (c) (d) 40.

7.5 7 7.75 None of the above If the length of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be (2004)

(a) equal to the side of the cube (b) times the side of the cube

(c)

times the side of the cube

(d) impossible to find from the given information 41. A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle? (2004)

(a) (b) (c) (d) 42. What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm? (2005) (a) 1 or 7 (b) 2 or 14 (c) 3 or 21 (d) 4 or 28 43. In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE : EB = 1 : 2, and DF is perpendicular to MN such that NL : LM = 1 : 2. The length of DH in cm is (2005)

(a) (b) (c) (d) 44. P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR? (2005) (a) (b) (c) (d) 45. Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and ∠BCD = ∠BAC. (2005)

What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC? (a) (b) (c) (d) 46. Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is (2005) (a) 780 (b) 800 (c) 820 (d) 741 47. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees? (2006) (a) 75 (b) 90

(a) (b) (c) (d) (e) 49.

(a) (b) (c) (d) (e) 50.

(a) (c) (d) (e)

120 135 150 Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees? (2007) Between 0 and 45 Between 0 and 90 Between 0 and 30 Between 0 and 60 Between 0 and 75 Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist? (2008) 5 21 10 15 14 In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangleABC? (2008) 17.05(b) 27.85 22.45 32.25 26.25

51. In the given figure ABCD is a quadrilateral with BC = 4 cm and AD = 2 cm. (2009)

What is the length of AB (in cm)? (a) (b) (c) (d) 52. ABCD is a parallelogram. E is a point on AB such that AE : BE = 2 : 3. A line EF is drawn parallel to AD and it meets CD at F. G is a point on BC such that GB : GC = 1 :4. What is the ratio of the area of ∆DEC to the area of ∆EFG? (2009) (a) 3 : 5 (b) 10 : 3 (c) 25 : 12 (d) None of these 53. A1, A2, A3, A4, A5, A6 are 6 points in clockwise order on the circumference of a circle of radius 4 cm.The length of the arc AiA i+1 is one-third the length of Ai+1Ai+2, for all i = 1 to 4. If the sum of the lengths of the 5 arcs is one-eighth the circumference of the circle, what is the angle (in radians) subtended by A2A3 at the center of the circle? (2009) (a)

(b) (c) (d) 54. In triangle ABC, the internal angle bisector of ∠A meets BC at point D. If AB = 8 cm, AD = 6 cm and∠ BAC =120º, then what is the length of AC? (2009) (a) 24 cm (b) 12 cm (c) (d) none of these 55. ABC is an equilateral triangle. Point D is on AC and point E is on BC, such that AD = 2CD and CE = EB. If we draw perpendiculars from D and E to other two sides and find the sum of the length of two perpendiculars for each set, that is, for D and E individually and denote them as per (D) and per (E) respectively, then which of the following option will be correct. (2009)

(a) (b) (c) (d)

per (D) > per (E) per (D) < per (E) per (D) = per (E) None of these

56. M is the centre of the circle. (QS) = 10 . (PR) = (RS) and PR || QS. Find the area of the shaded region. (use π = 3) (2009)

(a) (b) (c) (d) 57.

100 sq. units 114 sq. units 50 sq. units 200 sq. units Two circles, touching each other, are drawn inside a square of side 10 cm. Each circle also touches exactly two sides of the square. What is the maximum possible value (in cm) of the sum of their radii? (2010)

(a) (b) (c) (d) 10 58. The figure given below shows a circle with center O and radius 8 cm. BD is a chord of the circle and A is a point on the minor arc BD. C is a point on BD such that AC is perpendicular to BD. The length of AC is 4 cm and BC is 12 cm. What is the length (in cm) of CD? (2010)

(a) 2 (b) 4 (c) (d) 59. In a ∆ABC, AD is the bisector of ∠BAC, AB = 8 cm, BD = 6 cm and DC = 3 cm. Find AC. (2010)

(a) (b) (c) (d) 60.

4 cm 6 cm 3 cm 5 cm In the figure given below, AD = BC and BD = AC. Which of the following is not true? (2011)

(a) ∠ADB = ∠ACB (b) ∠ABD = ∠ACD (c) ∠ACD = ∠ BAC (d) ∠ADB = ∠CAD 61. Two vertical lamp-posts of equal height stand on either side of a road 50m wide. At a point P on the road between them, the elevation of the tops of the lamp-posts are 60º and 30º. Find the distance of P from the lamp post which makes angle of 60º. (2011) (a) (b) (c) (d) 62.

25 m 12.5 m 16.5 m 20.5 m The sum of the areas of two circles which touch each other externally is 153π. If the sum of their radii is 15, find the ratio of the larger to the smaller radius (2011) (a) 4 (b) 2 (c) 3 (d) None of these 63. ABCD is a rectangle. The points p and Q lie on AD and AB respectively. If the triangles PAQ, QBC and PCD all have the same areas and BQ = 2, then AQ = (2011)

(a) (b) (c) (d) 64. Two circles with centers A and B touch each other at C. The radii of the two circles are 3 m and 6 m respectively. Ramu and Shamu start simultaneously from C with speeds 6 m/s and 3 m/s and travel along the circles with centers A and B respectively. If Ramu gives Shamu a start of 2 seconds, what time (in seconds) after Ramu’s start would they be separated by a distance of 18 m? (2012)

(a) (b) (c) (d) 65.

7 10 125 Never From a point P, the tangents PQ and PT are drawn to a circle with centre O and radius 2 units. From the centre O, OA and OB are drawn parallel to PQ and PT respectively. The length of the chord TQ is 2 units. Find the measure of the ∠AOB. (2012)

(a) 30°

(b) (c) (d) 66.

90° 120° 45° In the figure given below, AB is a diameter of the circle. If AB ||CD, AC|| BE and BAE = 35o, then the absolute difference between ∠CDB and ∠ABD is (2013)

(a) (b) (c) (d)

90° 70° 55° 125°

67. E is a point on the side AB of a rectangle ABCD, the adjacent sides of which are in the ratio 2 : 1. If ∠AED = ∠DEC, then what is the measure of ∠AED? (2013) (a) (b) (c) (d) 68.

15° 45° 75° Either (a) or(c) AC is a chord of a circle whose centre is at O. If B is any point on the arc AC and ∠OCA = 20°, then the magnitude of ∠ABC is (2014 )

(a) (b) (c) (d) 69.

110° 70° 140° Either (a) or (b) ABCD is a rectangle with points E and F lying on sides AB and CD respectively. If the area of quadrilateral AEFD equals the area of quadrilateral CBEF, then which of the following statements is necessarily false with respect to the rectangle ABCD? (2014) (a) Length of AE is always equal to the length of CF. (b) If the length of BC is 4 units, then the smallest integral length of EF is 5 units. (c) Length of AE is equal to the length of DF. (d) ∠AEF = ∠EFC 70. Let S be an arbitrary point on the side PQ of an acute-angled PQR. Let T be the point of intersection of QR and the straight line PT drawn parallel to SR through P. Let U be the point of intersection of PR and the straight line QU drawn parallel to SR through Q. If PT = a units and QU = b units, then the length of SR is (2014) (a) (b) (c) (d) 71. The bisector of BAC of ∆ ABC cuts BC at D and the circumcircle of the triangle at E. If DE = 3 cm, AC = 4 cm and AD = 5 cm, then the length of AB is (2014) (a) 7 cm

(b) (c) (d) 72.

8 cm 9 cm 10 cm In the given figure, AB is the diameter of the circle with centre O. If ∠BOD = 15o, ∠EOA = 85o, then find the measure of ∠ECA. (2015)

(a) (b) (c) (d) 73.

20° 25° 35° Cannot be determined The line is the radius of the circle, it meets the circle centred at origin O at point M circle

shown,

(2015)

If PQ is the tangent to the find

the

length

the

PQ.

(a) (b) (c) (d) 74.

(a) (b) (c) (d) 75.

(a) (b) (c) (d)

An isosceles right angled triangle with length of its equal sides being 30 cm, is rotated 180° about its centroid to form a new triangle. Find the area of the region common to the original and the new triangles. (2015) 275 sq. cm 300 sq. cm 375 sq. cm 350 sq. cm ∆ ABC is a right angled triangle, with ∠B = 90o, AB = 20 cm and BC = 21cm. A circle with centre O is inscribed in triangle ABC. OD, OE and OF are perpendiculars drawn on the sides AB, BC and CA respectively. Find the ratio of the area of the quadrilateral FOEC to the area of the quadrilateral ADOF. (2015) 15 : 14 14 : 15 12 : 11 7:5 76.

In the figure, O and O’ are the centres of the bigger and smaller circles respectively and small circle touches the square ABCD at the mid point of side AD. The radius of the bigger circle is equal to 15 cm and the side of the square ABCD is 18 cm. Find the

radius circle.

the

smaller

(2015) (a) (b) (c) (d) 77.

4.25 cm 4.5 cm 4.75 cm 5 cm In the figure below, P, Q and R are points on a circle with centre O. The tangent to the circle at R intersects secant PQ at T. If ∠QRT = 55° and ∠QTR = 25°, find ∠POQ. (2016)

(a) (b) (c) (d) 78.

110° 100° 90° 50° In the figure below, BD = 8 cm and DC = 6 cm. AE : ED = 3 : 4. If AF =12 cm, find AC (in cm). (2016)

(a) 28 (b) 38 (c) 44

(d) 40 79. From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is (2017) (a) (b) (c) (d) 80. Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is (2017) (a) 9π – 18 (b) 18π (c) 9π (d) 9 81. Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is (2017) 82. Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K and O so as to form a triangle? (2017)

83. The shortest distance of the point 1| + |x + 1| is (a) 1 (b) 0 (c)

from the curve y = |x – (2017)

(d) 1.

⇒ (AB) × (EF) = (DE) × (BC) (c) Clearly option (a) shows the angles would be 30, 60 and 90. It can be the ratio of angle in a right angled triangle. Option (b) shows the angles would be 45, 45 and 90, then it can be the ratio of angle in a right angled triangle. But option (c) cannot form the ratio of angles of right angled triangle. (b) In

Again in (a)

(b)

Using Pythagoras theorem, ⇒ Height of wall = 12 + 3 =15 m 6.

(d) = This means the points of intersection are coincident

(a)

the

(d) Since AB is diameter = AB = 15cm

∴ = 90° [Angle subtended by diameter forms 90°] Hence, using Pythagorous theorem, BC = 9 ∴ AD = 12 Hence, area of ∆ ABC = ∆ ABD ∴ Area of quadrilateral

= 108 cm2

10. (b) Since EADF is a rectangle

(By Pythagorous theorem) Also since line joining mid-points of two sides is half the length of the third side.

Hence, required length 11.

(c) PR = PB + AR – 5 = 20 + 20 – 5 [ ] So, perimeter = PR + PQ + QR = 20 + (20 – 5) + 20 + (20 – 10) + 20 + (20 – 12) = 35 + 30 + 28 = 93

12. (c) The equation given, Where L1 is the perimeter of the polygon circumscribing the circle and L2 is the polygon inscribed in the circle and therefore we can definitely say that L1(13) > L2 (17) and at the same time circumference of the circle circumscribing the polygon will be always greater than the perimeter of the respective polygon. Therefore we can say that the value of the above equation has to be greater than 2. 13. (c) Let the diagonal of PQRS be 2r. Therefore, side = . Now, ABCD is a square. And side Perimeter of ABCD = 4r. Circumference of bigger circle =

= r. .

Therefore, required ratio = 14. (d) Let ∠EAD = α, then, ∠AFG = α and also ∠ACB = α Hence ∠CBD = 2α (exterior angle to ∆ABC). Since CB = CD, hence ∠CDB = 2α

∠FGC = 2α (exterior angle to ∆AFG). Since GF = EF, ∠FEG = 2α Now, Then, Since, Therefore, in ∆DCB, Further Then, If CD and EF meet at P, then Now in ∆PED, Therefore, in ∆EFD,

or approximately 25º

15. (b)

The slope of the equation y = – x + 1 is –1. Hence, equation of line BC, passing through (–1, 0) and parallel to x + y = 1 is (y – 0) = –1 (x + 1) y = –x – 1 x + y = –1 Equation of Equation of

16. (c)

A frog couldn’t jump on the vertices E. Therefore, there are 6 other vertices where it jumped. Thus, there are 6 jumps before reaching E. 17. (c) Thus 2(a + b) > 14, a + b > 7 So, the possible measures of sides are (2, 6, 6), (3, 5, 6), (6, 4, 4) & (5, 5, 4). Thus, there are four pairs possible. 18. (a) a2 + b2 + c2 = ab + bc + ac Put a = b = c = k we get 3k2 = 3k2, which satisfies the above equation. Thus the triangle is equilateral.

19. (c)

In ∆DEF, In ∆AEC, In ∆BCF, = 180

20. (b)

AB2 = Since solving this equation is very difficult. So, it is a better approach (Time saving) to put the values given in the options and try to find out a solution. Hence, trying out we get 11 as the value of x .

21. (b)

Let BC = x and AD = y Using the theorem of angle of bisector,

In ∆ABD, by sine rule, In ∆ABC, by sine rule; ⇒ [Putting value of sin B from (i)]

......(i)

22. (a)

Given AB = 25 cm, AN = 20 cm, BM = 15 cm Then,

⇒ ⇒ Let MO = x, ON = 10 – x, (since we know PQ ⊥ AB) ∴ In ∆AOP OP2 = (20)2 – (10 + x)2 .....(i) In ∆BOP,

= – x2 + 30x By (i) and (ii), we have ⇒ ⇒ ∴ MO = 6 hence, AO = 16 We know

.....(ii)

23. (b)

In right angled ∆BAC, BC2 = 152 + 202 ⇒ BC = 25 In right angled ∆ADB, AB2 = ⇒

152 =

In right angled ∆ADC, AC2 = DC2 + AD2 ⇒ 202 =

....(i)

....(ii) ....(iii)

Subtracting (i) from (ii), ⇒ ....(iv) Adding, (iii) and (iv), we get, Using x1, x2 in (ii), we get, In ∆ADB, using the formula for inradius

Where S is semi-perimeter

In ∆ADC,

In ∆PQR,

24. (d)

Let x and y be the longer and shorter side respectively of the rectangular field. According to the question,

Squaring both sides, we get,

25. (c) The number of convex corners is always less than concave corners by 4. Hence 25 – 4 = 21. 26. (d) From the question, we get the following diagram:

In ∆ABC and ∆BDC, ; is common; One side is common

27. (b) Using the quality of similar triangles,

28.

(c)

In the right angled ∆, = 2r2 – 60r + 500 Solving, we get, r = 50.

29. (b)

Given that Then, ∆ APB is an equilateral ∆ ∴ AP = AB = b. Now in right angled ∆ ΑΟP, AP2 = AO2 + PO2 ⇒ ⇒

⇒

30. (a)

In ∆ BOC, Then, In ∆ AOB,

[since BC = OB] [external angles] [isosceles triangle] [sum of angles = 180 ]

Then, Hence k = 3 31. (c) From figure

Given that, PQ | | AC,

Again, QD | | CP,

⇒

32. (c)

Let ∠CAD = ∠ACD = x At point C, x + (180° – 4x) + 96° = 180° ∴ x = 32° Hence, ∠DBC = 2 × 32 = 64º 33. (a)

In ∆ACT, ∠C = 50º and ∠T = 30º ∴ ∠A = 100º Applying tangent theorem

∠B = 50º ∠C = 50º ∴ ∠BOA = 100º 34. (a) We get the following diagram.

In the above diagram, AB is the lamp-post (6 metres), DE is father (1.8 metres), FG is the son (0.9 metres) and the shadows meet at C. We have to find DF. Using the porperties of similar triangles, we get,

Also Now we have, CD = 2CF and CD = 0.3 CB. Hence, 2CF = 0.3 CB. But CB = BD + DF + CF = 2.1 + 2CF (since CF = DF) = 2.1 + 0.3 CB ⇒ 0.7 CB = 2.1 ⇒ CB = 3 and CD = 3 – 2.1 = 0.9. [Since FD = 35-37.

CF, then DF =

= 0.45]

35. (b) In ∆SOQ and ∆ROP ∠O is common ∠S = ∠R = 90º (tangent at circle) ∴ ∆ SOQ ~ ∆ROP

or ⇒ PQ = 7 and OQ = 21 ∴ Required ratio 36. (b) PQ = r1 + r2 = 7 As the ratio of radii is 4 : 3. So, the only value which satisfies the radii ofcircle II = 3 37. (c) In ∆SOQ, ⇒ SO2 + SQ2 = OQ2 ⇒ SO2 = 212 – 32 = (21 – 3) (21 + 3) = 18 × 24 = 432

38. (d)

Let DEC = ∠ACE = x [Since AC || ED] Complete the ∆CAE ∠CBE = ∠CAE [angles in same segment] ∠AEC = 90º [angle subtended in semi circle] ∴ In ∆CAE, ∠CAE + ∠AEC + x = 180º or 65 + 90 + x = 180 ⇒ x = 25º ∴ ∠DEC = 25º

39. (b)

AO = BO = radius = 4 AE = 2 cos A ∴ BC = AD – AE – FD

( AE = FD)

40. (a) Let the side of the cube be 1. Then, diagonal

Now we have an equilateral triangle with side

and its altitude

will be 3/2. Circumradius = 2/3 × altitude = 2/3 × 3/2 = 1. Thus, the radius of the circle circumscribing that triangle will be equal to the side of the cube.

41. (d)

OABC is square with side = 2 Let r be the radius of smaller circle OB = 2 = OD + r + O'B = 2 + r + r ⇒ r(

+1) = 2(

–1)

42. (d) Remember that a perpendicular from the centre to a chord divides it into two equal parts.

In ∆ OBB', OB2 = BB'2 + OB'2 ⇒ 202 = 162 + OB'2 ⇒ Similarly in ∆ OAA', ∴ Distance between the two parallel chords = 16 – 12 = 4 cm or 16 + 12 = 28 cm

43. (b)

Given that,

⇒ EB = 2AE and LM = 2NL ⇒ EB + AE = 3 and LM + LN = 3 ⇒ AE = 1 & EB = 2 and LN = 1 & LM = 2 Now, OL = LM – OM = 2 – 1.5 = 0.5 And EO = EB – OB = 2 – 1.5 = 0.5

Hence, EOHL is a square of side 0.5 cm. In ∆ DOL, DO2 = DL2 + OL2 ⇒ (1.5)2 = (DH + 0.5)2 + 0.52 ⇒ (DH + 0.5)2 = (1.5 + 0.5) (1.5 – 0.5) = 2

44. (a)

As PQR is an equilateral triangle, hence PS will be perpendicular to QR and will divide it into 2 equal parts. ∠P & ∠S will be supplementary so ∠S = 120º and ∠QSA = ∠RSA = 60º. In ∆ OAQ, OA = OQ sin30º =

Now in ∆ PAQ, PA = PQ cos30º Hence, Similarly in ∆ AQS,

∴ Perimeter of PQSR = 2(PQ + QS) 45. (a) In ∆ABC and ∆BDC BC = BC (common) ∠BCD = ∠BAC (given) ∠DBC = ∠ABC (common)

and ∴

AD = 16 – 9 = 7

46. (a) The equation of the line becomes

The (x, y) co-ordinates (x and y ∈ I) satisfying this equation are (1, 40) (2, 39).......(40, 1) Total required points are : (1, 1) (1, 2)...............(1, 39) = 39 points (2, 1) (2, 2)..............(2, 38) = 38 points and so on. So total integral points = 39 + 38 + 37 +..............+ 1 which is an A.P.

Hence

47. (e)

= 90° – 60° = 30° Further in PB = AB = a Further

Similarly Again in right angled = 90° – 15° = 75° Similarly we can calculate that = 75° = 75° + 75° = 150° 48. (d) Since P and Q are outside the intersection of the two circles,

therefore r < PQ < 2r Where PQ r, then ∠AQP

60°

and when PQ 2r, ∠AQP 0° Hence, in both the cases, 0° ∠AQP ∠60° 49. (c) If ‘a’, ‘b’ and ‘c’ are the length of sides of a obtuse triangle and ‘a’ be the length of longest side. Then a2 > b2 + c2 Case (i) : If length of one longest side be 15 cm, then 225 > 64 + x2 ⇒ x2 < 161 ∴ x = 8, 9, 10, 11, 12 [Since, the value of x is less than 8, because sum of length of any two sides of a triangle is greater than the longest side. Case (ii) : If length of longest side be x cm, then 2 x > 225 + 64 ⇒ x2 > 289 ∴ x = 18, 19, 20, 21 and 22 [Since the value of x is less than 23] Therefore, total number of values of x is 10 and hence total number of triangles is 10.

50. (e)

Radius of circum circle of a trianlge,

Also

∴ R = 26.25. 51. (b) ∠BAD = 90º

Extend BA and CD to meet at E. ∆EBC becomes an equilateral triangle. So BE = 4 cm In ∆ADE,∠ADE = 30º tan 30º

52. (d)

Area of ∆DEC=Area of ∆DBC ……..( ∆’s between same parallel line and same base) Area of parallelogram ABCD

Area of ∆EFG

Area of parallelogram EBCF

Area of parallelogram ABCD

53. (b)

Arc length As the radius is fixed, the arc length is directly proportional to the angle subtended by the arc at the centre. So if the arc length is getting tripled the angle is also getting tripled. Therefore ⇒

⇒

Angle subtended by A2A3 at the centre is 3θ

54. (a)

Area of triangle ABC Area of triangle Area

AB × AC × sin ∠ BAC...(i)

× AB × AD × sin ∠BAD ...(ii)

triangle

ACD

CAD (iii) Also, ∠×BAD = CAD

sin

∠ ...

BAC = 60º and (i) = (ii) + (iii)

Hence

⇒ AC = 24cm 55. (c) Sum of length of all perpendiculars drawn on the sides of any equilateral triangle is constant. Perpendicular (D) = Perpendicular (E) 56. (c) ∠ PQS = ∠ PRS = 900. [Diameter subtends 900 at the centre] PR = RS and PR || QS Rectangle PQRS is a square. PS = × QS [Diagonal = × side] = × 10 = 20 Radius = 10

Area of circle = r2 = 3 × 10 × 10 = 3000 Area of square = (10 )2 = 200 Area of shaded region

57.

(Area of circle – Area of square)

× 100 = 50 sq. units.

(a)

From the above figure

⇒

58.

(c)

Given, AC = 4 and BC = 12. Let DC = 2x. Now, AC × CE = BC × CD or 4 × CE = 12 × 2x. Hence, CE = 6x. AE = AC + CE = 4 + 6x

BD = BC + CD = 12 + 2x and CF = OG

= 6 – x.

As OG is perpendicular to AE, in right triangle EGO: EG2 + OG2= EO2

Hence, CD = 2x =

59. (a)

Line AD bisects ∠CAB Then

60. (c)

In ∆ ADB and ∆BCA, we have

AD = BC, BD = AC, AB is the common side. By SSS congruency, ∆ADB ∆BCA ⇒ ∠ADB = ∠ACB ...(i) Also, ABCD is a cyclic quadrilateral. ⇒ ∠ABD = ∠ACD ...(ii) In ∆ACD and ∆BDC, we have AD = BC, BD = AC, CD is the common side. By SSS congruency, DACD ∆BDC ⇒ ∠ACD =∠BDC Since ∠BDC = ∠ BAC ∴ ∠ACD = ∠BAC. 61. (b) Let AB be the road between the lamp-posts AL and BM. AB = 50 m. From triangle LAP, From triangle MPB,

= tan 60º ⇒ AP = = tan 30º ⇒ PB = h

PA + PB = AB = 50 [Given] ⇒

∴ AP = 62. (a) Let the radii be r1 and r2

= 12.5m.

.....(i) ....(ii) ⇒ If r1 and r2 are roots of equation then,

63. (a) As areas of APQ, QBC and PDC one equal, so

Again, or

64. (d) 65. (c)

This is never possible, because data is not sufficient. Since, OQ = TQ = 2 units, therefore ∆OTQ is an equilateral.

∴ ∠TOQ = 60° Since, PQ is a tangent to the circle, therefore ∠OQP = 90°. Since, PQ is a parallel to OA therefore ∠AOQ = 90° For the same reason ∠BOT = 90°. ∴ ∠ΑΟΒ = 360° − (∠TOQ + ∠AOQ + ∠BOT) = 120°.

66. (b)

∠AEB = 90° (Angle in a semicircle) ∠BAE = 35° (Given) ∴ ∠ABE = 180 – (90 + 35) = 55° ∴ ∠BAC = 55° (Alternate interior angles) Now, ∠CDB = 180 – 55 = 125° (Sum of opposite angles of a cyclic quadrilateral is 180°.) ∴ ∠ABD = 180 – 125 = 55° (Sum of interior opposite angles is 180°). Hence required difference ∠CDB – ∠ABD = 125 – 55 = 70°. 67. (c) Let the two sides of the rectangle be x and 2x and ∠AED be θ. ∴ ∠DEC = θ

∴ ∠CEB = 180 – 2θ Also, ∠EDC = ∠AED = θ (AB is parallel to CD.) in ∆DEC, ∠DEC = ∠EDC ⇒ CD = EC = 2x In ∆BCE,

cosα =

⇒ α = 60°

Now, in ∆BCE 2θ = 90° + 60° (Exterior angle is equal to the sum of opposite interior angles.) ⇒ θ = 75° 68. (d) Here, Two cases are possible Case I : When B lies in greater arc AC. Then,

∠OAC = ∠OCA = 20° ⇒ ∠AOC = 140° ∴ ∠ABC =

∠ΑOC = 70°

Case II : When B lies in smaller arc AC.

Then,

Let D be a point O is the greater arc AC. ∠OAC = ∠OCA = 20° ⇒ ∠AOC = 140° ∴ ∠ADC =

∠AOC = 70°

ABCD is a cyclic quadrilateral ∴ ∠ABC = 180° – 70° = 110°. 69. (b) Option (a) – The length of AE is always equal to the length of CF because E and F is midpoint of side AB and CD. So, statement – I is always true. Option (b) : the Length of BC is equal to length of EF so statement II is always False. Option (c) : Length of AE is equal to the length of DF because of EF is parallel to BC Option (d) : ∠AEF = ∠EFC = 90° So statement III is also true.

70. (c)

Given that PT||SR|| QU PT = a units, QU = b units. ∆PTQ and ∆SRQ are similar. ∴ We have

...(i) ∆UQP and ∆RSP are similar. ∴ We have

...(ii)

Combining (i) and (ii)

[As SQ + PS = PQ] =

or SR =

71. (d)

The figure would be as shown above. Join EC. Let ∠BAD = x° and ∠ABD = y°. ⇒ ∠DAC = x° and ∠AEC = y°. In ∆ABD and ∆AEC, ∠ABD = ∠AEC ∠BAD = ∠EAC ∴ ∆ABD ~ ∠AEC ⇒ ⇒ AB = 72. (c)

Here, ∠EOQ = 85° and

= 10 cm.

∠BOD = 15° ∴ ∠EOD = 180° – (85° + 15°) = 80° ∴ In ∠OED OE = OD (radius), ∠OED = ∠ODE = θ° (let) ∴ θ + θ + 80° = 180 ⇒ 2θ° = 180 – 80 = 100° ∴θ=

= 50°

∴ ∠OED = ∠ODE = 50° In ∠EOC, ∠EOC = 80° + 15° = 95° and ∠OEC = 50° ∴ ∠ECA =180° – (95° + 50°) = 35° 73. (d)

PQ is perpendicular to line y = ∴ Slop of PQ =

Let equation of line PQ be y = At point M,when x = , y = 1. ∴c=4 ⇒y= ∴ Co-ordinates of point Q =

and

Co-ordinates of point P = (0, 4). Hence, PQ =

units.

74. (b)

Area of the shaded region = 300 sq. cm.

75. (a)

∴ AB = 20 BC = 21 ∴ AC = and (20 – r) + (21 – r) = 29 or, 2r = 41 – 29 ⇒ r = 6 cm ∆OEC ∆OFC (RHS) Area ( FOEC) = 2 × Area (∆OEC) =

= 90 cm2

Similarly, ∆AOD ∆AOF (RHS) AREA ( ADOF) = 2 × Area (∆AOD) =

= 84 cm2

= 29 cm

So, Required ratio =

76. (b)

Let the radius of the bigger circle be R and the smaller circle be r and the side of the square is 2a. ∴ OE = R – EF = R – [2R – (2r + 2a)] OE2 + EB2 = OB 2 i.e [2a +2r – R]2 +a2 = R2 a = 9 ( 2a = 18); R = 15 ∴ (18 + 2r – 15)2 + 92 =152 ∴ 2r + 3 = 12 ∴r=

= 4.5 cm

Radius of smaller circle = 4.5 cm.

77. (c)

In ∆QTR, ∠QTR + ∠QRT + ∠RQT = 180º ∠RQT = 180° – (55º + 25º) = 100º ∠ORT = 90° (TR is a tangent to the circle at R) ∠QRT + ∠ORQ = 90° ∠QRQ = 90º – 55º = 35° OQ = OR (Both are radius of circle) ∴ ∠OQR = ∠ORQ = 35º ∠RQT + ∠PQR = 180º (PQT is a straight line)

100° + 35° + ∠PQO = 180° ∴ ∠PQO = 45º In ∆OQP, OQ = OP (radius of circle) ∴ ∠OPQ = ∠PQO = 45º ∠POQ = 90º 78. (d) Let G be a point on AC such that DG is parallel to BF.

Here, BD = 8 cm DC = 6 cm and AE : ED = 3 : 4 AF = 12 cm AC = ? = ∴ AF : FG : GC = 3 : 4 : 3. ∴ AC = 79. (b) Area of GBC =

(area of ∆ABC)

Area of remaining part = = = =

× Area of ∆ABC

80. (b)

Enclosed Area = Area of semi circle BQC with centre O – Area of Arc BPC with O Now, Area of triangle ABC + BPCO (Arc) = Area of Quarter circle (ABPC)

Area of BPCO = 9π –18 Put the value in equation (i) Enclosed Area = = 18 sq cm 81. (24) In a 3, 4, 5 triangle the length of the altitude to the Hypotenuse =

= 2.4

therefore in a 15, 20, 25 triangle it is 1.2. This is the shortest distance from A to BC. At 60 km/hr i.e. 1 km/min It would be take 24 min to cover 24 km.

82. (160)

Total 11 point formed triangle = 11C3 – colinear point group = =

–5

–5 ⇒ 165 – 5 = 160

83. (a)

shortest distance according graph = 1 y = |x – 1| + | x + 1 | let x, – 1 ≤ x ≤ 1 y=–x+1+x+1⇒y=2

(a) (b) (c) (d) 2.

(a) (b) (c) (d) 3.

A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of cone and cylinder are equal to their diameters. Then their volumes are proportional, respectively, to (1994) 1:3:1 2:1:3 3:2:1 1:2:3 A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and frustum are in the ratio (1994) 1:3 8 : 19 1:4 1:7 In ∆ACD, AD = AC and . The distance between parallel lines AB and CD is h. (1994)

Then I. Area of parallelogram ABCD II. Area of ∆ ADE (a) I > II

(b) I < II (c) I = II (d) Nothing can be said 4. PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR=OS. Then, the ratio of area of the circle to the area of the square is (1995)

(a) (b) (c) (d) 5.

(a) (b) (c) (d) 6.

In the adjoining figure, AC + AB = 5 AD and AC – AD = 8. Then the area of the rectangle ABCD is (1995)

36 50 60 Cannot be answered ABCD is a square of area 4, which is divided into four non overlapping triangles as shown in the fig. Then the sum of the perimeters of the triangles

is (1995)

(a) (b) (c) (d) 7.

(a) (b) (c) (d) 8.

(a) (b) (c) (d) 9.

(a) (b)

The sides of a triangle are 5, 12 and 13 units respectively. A rectangle is constructed which is equal in area to the triangle and has a width of 10 units. Then the perimeter of the rectangle is (1995) 30 26 13 None of these From a circular sheet of paper with a radius 20 cm, four circles of radius 5cm each are cut out. What is the ratio of the uncut to the cut portion? (1996) 1:3 4:1 3:1 4:3 A closed wooden box of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is painted inside. The expenses of painting are Rs 70. What is the rate of painting in rupees per sq. cm.? (1996) 0.7 0.5

(c) 0.1 (d) 0.2 10. The figure shows a rectangle ABCD with a semi-circle and a circle inscribed inside it as shown. What is the ratio of the area of the circle to that of the semicircle? (1996)

(a)

(b) (c) (d) None of these 11. A cube of side 12 cm. is painted red on all the faces and then cut into smaller cubes, each of side 3cm. What is the total number of smaller cubes having none of their faces painted? (1996) (a) 16 (b) 8 (c) 12 (d) 24 12. The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ABC (1996)

(a) (b) (c) (d) 13.

60 sq. cm. 30 sq. cm. 40 sq. cm. 52 sq. cm. The adjoining figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh square, counting from the innermost square (199 7)

(a) (b) (c) (d) 14.

10.2 30 35.2 None of these In a triangle ABC, points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq. units, find the area of the triangle PQR (1997) 10 sq. units 5.3 sq. units 5 sq. units None of these In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side? (1997)

(a) (b) (c) (d) 15.

(a)

(b) (c) (d) 3 : 4 16. The sum of the areas of two circles which touch each other externally is 153π. If the sum of their radii is 15, find the ratio of the larger to the smaller radius (1997) (a) 4 (b) 2 (c) 3 (d) None of these 17. In the adjoining figure, points A, B, C and D lie on the circle. AD = 24 and BC = 12. What is the ratio of the area of the triangle CBE to that of the triangle ADE (1997)

(a) (b) (c) (d) 18.

1:4 1: 2 1:3 Insufficient data Four identical coins are placed in a square. ratio of area to circumference is same circumference to area. Then find the area of not covered by coins

For each coin the as the ratio of the square that is the (1998)

(a) 16(π–2) (b) 16(8–π) (c) 16(4–π) (d) 16(4–π/2) Directions for questions 19 & 20 : Read the information given below and answer the questions that follow : A cow is tethered at A by a rope. Neither the rope nor the cow is allowed to enter the triangle ABC.

19. (a) (b) (c) (d) 20. (a) (b) (c) (d) 21.

A = 30º (AB) = (AC) = 10 m. (BC) = 6 m. What is the area that can be grazed by the cow if the length of the rope is 8 m? (1998) 133 1/6 π sq. m. 121 π sq. m. 132 π sq. m. 176/3 π sq. m. What is the area that can be grazed by the cow if the length of the rope is 12 m? (1998) 133 1/6 π sq. m. 121 π sq. m. 132 π sq. m. 176/3 π sq. m. There is a square field of side 500 metres. From one corner of the field a triangular area has to be cordoned off with a straight fence of

(a) (b) (c) (d) 22.

(a) (b) (c) (d) 23.

length 100 metres, using the boundaries of the field as the other two sides. What is the maximum area that can be cordoned off (1999) 2500 1250 5000 2000 There are two tanks, one cylindrical and the other conical. The cylindrical tank contains 500 litres limca more than the conical tank. 200 litres is removed both from the cylindrical and conical tank. Now the cylindrical tank contains double the volume of liquid in the conical tank. What is the capacity of the cylindrical tank in litre? (2000) 1000 700 800 1200 Consider a circle with unit radius. There are seven adjacent sectors with area S1, S2, S3, ........., S7, in the circle such that their total area is

units. Further, the area of the jth sector is twice

that of the (j – 1)th sector i.e., Sj = 2S(j – 1) for j = 2, ......, 7 What is the angle, in radians, subtended by the arc of S1 at the centre of the circle ? (a) (b) (c) (d) 24. What is the area of the region bounded by

, (2000)

(a) (b) (c) (d) 25.

(a) (b) (c) (d) 26.

2 4 1 3 A rectangular pool 20 metres wide and 60 metres long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 square metres, how wide, in metres, is the walkway? (2001) 43 4.3 3 3.5 A square, whose side is 2 metres, has its corners cut a way so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres is (2001)

(a) (b) (c) (d) 27. A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, three kms north of the north gate, and it can just be seen from a point nine kms east of the south gate. What is the diameter of the wall that surrounds the city? (2001) (a) 6 km

(b) 9 km (c) 12 km (d) None of these 28. In the diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the area of the triangle CEF and that of the rectangle?(2001)

(a) (b) (c) (d) None of these 29. A ladder leans against a vertical wall. The top of the ladder is 8m above the ground. When the bottom of the ladder is moved 2m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder? (2001) (a) 10 m (b) 15 m (c) 20 m (d) 17 m 30. Two sides of a plot measure 32 metres and 24 metres and the angle between them is a perfect right angle. The other two sides measure 25 metres each and the other three angles are not right angles.

What plot?

the

area

the

(2001) (a) (b) (c) (d) 31.

768 534 696.5 684 Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side? (2001)

(a) (b) (c) (d) 32. Four horses are tethered at four corners of a square plot of side 14 metres so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. The area left ungrazed is (2002) 2 (a) 22 m (b) 42 m2 (c) 84 m2 (d) 168 m2 33. Neeraj has agreed to mow the front lawn, which is a 20 m by 40 m rectangle. The mower mows a 1 m wide strip. If Neeraj starts at one corner and mows around the lawn toward the centre,

(a) (b) (c) (d) 34.

about how many times would he go round before he has mowed half the lawn? (2002) 2.5 3.5 3.8 4.0 In the figure given below, ABCD is a rectangle. The area of the isosceles right traingle ABE = 7 cm2; EC = 3 (BE). The area of ABCD (in cm2) is (2002)

(a) (b) (c) (d) 35.

21 28 42 56 The area of the triangle whose vertices are (a, a), (a + 1, a + 1), (a + 2, a) is (2002) 3 (a) a (b) 1 (c) 2a (d)21/2 Directions for questions 36 & 37 : Read the information given below and answer the questions that follow : Answer these questions based on the following diagram. In the diagram below : and AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN

36. The

magnitude

(2002) (a) (b) (c) (d) 37. (a) (b) (c) (d) 38.

(a) (b) (c) (d) 39.

30° 45° 60° None of these The ratio of the areas of the two quadrangles ABCD and DEFG is (2002) 1:2 2:1 12 : 7 None of these Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be (2003C) 85.5 92.5 90.5 87.5 In the figure below , ABCDEF is a regular hexagon and is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? (2003C)

(a) (b) (c) (d) 40. Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with centre at O. The horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centres at P and R respectively, and S is the centre of the circle touching the two semi-circles with diameters AO and OB. The horses tied at P and R can graze within the respective semi–circles and the horse tied at S can graze within the circle centred at S. The percentage of the area of the semi circle with diameter AB that cannot be grazed by the horses is nearest to (2003C)

(a) (b) (c) (d)

20 28 36 40

41. There are two concentric circles such that the area of the outer circle is four times the area of the inner circle . Let A,B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters ) of the triangle ABC would be (2003C) (a) (b) (c) (d) 42. The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle , and square are c, t, and s, respectively. Then (2003) (a) s > t > c (b) c > t > s (c) c > s > t (d) s > c > t 43. Let be a square of side a. Another square is formed by joining the mid-points of the sides of . The same process is applied to to form yet another square and so on. If ............ be the areas and perimeters of

(b) 2(2 – (c) 2( 2 +

)/a )/a )/a

............... be the

.......... , respectively, then the ratio equals

(a) 2(1 +

(2003)

(d) 2(1 + 2 )/a 44. Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side a in the following steps : the original square of side a is divided into n smaller squares, not necessarily of the same size ; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is (2003) (a) 1 : 1 (b) :1 (c) (d) Directions for questions 45 to 47 : Read the information given below and answer the questions that follow : Consider a cylinder of height h cms and radius r =

cms as

shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns). 45. What is the vertical spacing in cms between two consecutive turns? (2003)

(a) h / n (b) h/ (c) h/ (d) Can’t be determined 46. The same string, when wound on the exterior four walls of a cube of side n cms, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale). The length of the string, in cms, is (2003)

(a)

(b)

47. In the setup of the previous two questions, how is h related to n? (2003) (a) h = n

(b) h =

48. A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle . If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle? (2003) (a) 16.665 (b) 16.565 (c) 15.465 (d) 14.365 49. A square tin sheet of side 12 inches is converted into a box with open top in the following steps: The sheet is placed horizontally; Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet; Finally, the four resulting sides are bent vertically upwards in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?(2003) (a) 3 (b) 4 (c) 1 (d) 2 50. Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF?(2003) (a) (b) (c)

(d) 51. In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with center at O. The length of side AB is greater than that of side BC. The ratio of the area of the circle to the area of the rectangle ABCD is : . The line segment DE intersects AB at E such that AE : AD?

ODC =

ADE. What is the ratio (2003)

(a) 1: (b) 1: (c) 1 : 2 (d) 1 : 2 52. A rectangular sheet of paper, when halved by folding it at midpoint of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle? (2004) (a) (b) (c) (d) None of the above

53. Let C be a circle with center P0 and AB be a diameter of C. Suppose P1 is the mid-point of the line segment P0B, P2 is the mid-point of the line segment P1B and so on. Let C1, C2, C3, ............. be circles with diameters P0P1, P1P2, P2P3, ............... respectively. Suppose the circles C1, C2, C3, ............. are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is (2004) (a) 8 : 9 (b) 9 : 10 (c) 10 : 11 (d) 11 : 12 54. Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is (2005) (a) (b) (c) (d) 55. A jogging park has two identical circular tracks touching each other and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jogs along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting

point? (2005) (a) (b) (c) (d) 56. (a) (b) (c) (d) 57.

(a) (b) (c) (d) 58.

(a) (b) (c) (d) 59.

3.88% 4.22% 4.44% 4.72% In the X-Y plane, the area of the region bounded by the graph |x + y| + |x – y| = 4 is (2005) 8 12 16 20 A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of the white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is : (2005) 10 12 14 16 Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD and the length of AB is 1 meter. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one meter of any insect repellent. The minimum distance in meters the ant must traverse to reach the sugar particle is (2005) 1+π 4π / 3 5 Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such

that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is (2005) (a) 4 (b) 5 (c) 6 (d) 7 60. The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will ( 2006) (a) remain the same (b) decrease by 13.64% (c) decrease by 15% (d) decrease by 18.75% (e) decrease by 30% Directions for Questions 61 & 62 : Answer the questions on the basis of the information given below. A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square.

61. The proportion of the sheet area that remains after punching is: (2006)

(a) (b) (c) (d) (e) 62. (a) (b) (c) (d) (e) 63.

(a) (b) (c) (d) (e) 64.

(a) (b) (c) (d) (e)

(π + 2) / 8 (6 – π) / 8 (4 – π) / 4 (π – 2) / 4 (π – 2) / 6 Find the area of the part of the circle (round punch) falling outside the square sheet. (2006) π/4 (π – 1) / 2 (π – 1) / 4 (π – 2) / 2 (π – 2) / 4 A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq.cm) will be: (2006) 32 50 40.5 81 undeterminable Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surfaces resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinder. (2008)

65. Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD? (2008) (a) (b) (c) (d) (e) 66. Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecting region? (2008) (a) (b) (c) (d) (e) 67. Find the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height. (2009)

(a) (b) (c) (d) 68.

(a) (b) (c) (d) 69.

(a) (b) (c) (d) 70. (a)

1:2:1 1:2:3 1:3:4 3 : 2 :1 The resistance of a wire is proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the same resistance and their radii are in the ratio 9 : 8. If the length of the first wire is 162 cms., find the length of the other. (2009) 64 cm. 120 cm. 128 cm. 132 cm. The area of a regular polygon of side ‘x’ units is ‘10x’ sq units and the length of its inradius is an integer. How many such polygons would be there? (2010) 6 4 3 2 The area of the circle circumscribing three circles of unit radius touching each other is (2010) (π/3)

(b) (c) (d) 71. A 20 litre vessel is filled with alcohol. Some of the alcohol is poured out into another vessel of an equal capacity, which is then completely filled by adding water. The mixture thus obtained is

then poured into the first vessel to capacity. Then 6

(a) (b) (c) (d) 72.

(a)

litres is

poured from the first vessel into the second. Both vessels now contain an equal amount of alcohol. How much alcohol was originally poured from the first vessel into the second ? (2010) 9 litres 10 litres 12 litres 12.5 litres A conical vessel, with a circular base, is filled with water to twothirds of its volume. The pointed end of the cone is snipped off and replaced with a lid. The lid is kept open for 10 hours every day during which some water evaporates. The volume of the water that evaporates on a day is directly proportional to the area of the water surface at the beginning of the day. The volume of the water left in the container after evaporation on the 1st day is half the volume of the original cone. If V is the volume of the original cone, then what is the volume of the water that evaporates on the 2nd day? (2011)

(b) (c) (d) 73.

(a) (b) (c) (d) 74.

A cube of edge 12 cm is cut into 64 equal cubes. All the cubes are now arranged on a table such that one face of each cube touches the table. The resulting figure is a solid cuboid whose length and breadth are in the ratio 4 : 1 respectively. What is the total surface area of the table occupied by the cuboid? (2011) 144 cm2 288 cm2 576 cm2 None of these ABDC is circle and circles are drawn with AO, CO, DO and OB as diameters. Areas E and F are shaded. E/F is equal to

(2011) (a) (b) (c) (d)

1 2/3 1/2 π/4

75. An unsharpened cylindrical pencil consists of a layer of wood surrounding a solid cylinder of graphite. The radius of a pencil is 7 mm, the radius of the graphite cylinder is 1 mm and the length of the pencil is 10 cm. Find the cost of the material used in a pencil, if the cost of wood is ` 0.70/cm3 and that of graphite is ` 2.10/cm3. (2011) (a) ` 9.84 (b) ` 10.80 (c) ` 11.22 (d) ` 12.44 76. Suresh, who runs a bakery, uses a conical shaped equipment to write decorative labels (e.g., Happy Birthday etc.) using cream. The height of this equipment is 7 cm and the diameter of the base is 5 mm. A full charge of the equipment will write 330 words on an average. How many words can be written using three fifth of a litre of cream? (2011) (a) 45090 (b) 45100 (c) 46000 (d) None of these 77. A pole has to be erected on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. The distance of the pole from one of the gates is: (2011) (a) 8 metres (b) 8.25 metres (c) 5 metres (d) None these 78. From a square piece of card-board measuring 2a on each side of a box with no top is to be formed by cutting out from each corner a square with sides b and bending up the flaps. The value of b for which the box has the greatest volume is (2011)

(a) (b) (c) (d) 79. A circle of radius 6.5 cm is circumscribed around a right-angled triangle with the sides a, b and c cm where a, b and c are natural numbers. What is the perimeter of the triangle? (2012) (a) 30 cm (b) 26 cm (c) 28 cm (d) 32 cm 80. In the regular hexagon shown below, what is the ratio of the area of the smaller circle to that of the bigger circle? (2012)

(a) (b) (c) (d) 81. A rectangle with perimeter 88 m is partitioned into 5 congruent rectangles, as shown in the diagram given below. The perimeter of each of the congruent rectangles is (2012)

(a) (b) (c) (d) 82.

20 m 32 m 48 m 40 m A trapezium DEFG is circumscribed about a circle that has centre at C. If DM = 1 cm, GN = 4 cm and the measure of then find the radius of the circle. (2012)

(a) (b) (c) (d) 83.

2 cm 2.5 cm 2.25 cm 4 cm How many triangles can be drawn by joining any three vertices of a pentagon? (2013) 8 9 11 10 A spherical ball of the maximum possible volume is placed inside a right-circular cone of height ‘h’ units. If the radius of the base of the cone is equal to units, then the ratio of the volume of the sphere to that of the cone is (2013) 4:9

(a) (b) (c) (d) 84.

(a)

(b) 5 : 9 (c) (d) 85. How many rectangles with integral sides are possible where the area of the rectangle equals the perimeter of the rectangle?(2014) (a) One (b) Three (c) Two (d) Infinitely many 86. The length of the hypotenuse of a right-angled triangle is 240 units. The perimeter of the given triangle is a perfect square. If the perimeter of the given triangle is greater than 550 units, then which of the following can be the length of a side of the given right-angled triangle? (2014) (a) (b) (c) (d) 87.

(a) (b) (c) (d) 88.

192 units 168 units 144 units Both (a) and (c) The top and bottom radii of a frustrum of a solid cone are 3 cm and 6 cm respectively. Its height is 8 cm. There is a conical cavity of height 3 cm and radius 6 cm at the bottom. The amount of material in the solid is (2014) 132 cm3 168 cm3 159 cm3 Data Insufficient The smallest possible circle touching two opposite sides of a rectangle is cut-out from a rectangle of area 60 sq. units. If the area of this circle is

times the area left out in the rectangle, find

the length of the smaller side of the rectangle. (2015) (a) (b) (c) (d) 89.

(a) (b) (c) (d) 90.

ABCD is an isosceles trapezium with BC = AD = 10 units, AB = 2 units and CD = 14 units. The mid-points of the sides of the trapezium are joined to form a quadrilateral PQRS. Find the ratio of the area of the circle inscribed in the quadrilateral PQRS to the area of trapezium ABCD. (2015)

Through point P, lines are drawn parallel to the sides of triangle ABC. The areas of the ∆PED, ∆PFG and ∆PHI are 9, 16 and 49 sq. cm respectively. Find the area (in sq. cm) of triangle ABC. (2015) 91. All reputed B-schools place their students. One-sixth of those Bschools that place their students are reputed and one-fourth of all B-schools that are recognised, place their students. There are exactly 6 reputed B-schools that are recognised too and there are 39 B-schools that are recognised but do not place their students. If there is a total of 78 B-schools that place their students, then how many of these B-schools are neither recognised nor reputed but place their students? (2015) 92. A field is in the form of a rectangle of dimension 24 m × 56 m. There is 2700 m of fencing that is available. The field has to be divided into many identical smaller square plots, having integral sides (in metres), each of which is to be fenced. Find the side of each of the square plots such that the fencing material that is left out is minimum. (2015) (a) 1 m (b) 2 m (c) 4 m (d) 8 m 93. A regular polygon has an even number of sides. If the product of the length of its side and the distance between two opposite sides is ¼ th of its area, find number of sides it has (2016) (a) 6 (b) 8 (c) 20 (d) 16 94. A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. The percentage by which the sum of the surface areas of these five cubes exceeds

(a) (b) (c) (d) 95.

the surface area of the original cube is nearest to (2017) 10 50 60 20 A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is (2017) (a) Let radius of cone, cylinder and hemisphere be r and the height of cone and cylinder, h = 2r Then, required proportion is = =

(b)

Volume of the original cone Height of the smaller cone = 2h / 3 and radius

(from similar ∆’s)

Volume of smaller cone

(c)

In ∆ ACD, (since AC = AD and ∠C = 60º) CAD = 180 – (60 + 60) = 60° ∆ ACD is equilateral. Let each side of ∆ ACD be x So, its area And area of parallelogram ABCD

In ∆ ADE, DAE = 150 – 60 = 90° and ADE = 180 – (90 + 30) = 60° Now, area of

Therefore, we see,

Area of parallelogram ABCD = area of ∆ ADE

(a)

In ∆ SOR, a2 + r2 = (2r)2 = 4r2 In ⇒

a2 = 3r2

∴

(c)

or AC + a = 5b or AC = b + 8

....(i) ....(ii)

Using (i) and (ii), ....(iii) Using Pythagorus theorem, ⇒ ⇒ ⇒ 166 + 64 = 16b2 + 64 – 64b ⇒

[From (iii)]

Putting b = 5 in (iii), we have a = 4b – 8 = 20 – 8 = 12 Area of rectangle = 12 × 5 = 60 Alternatively : AC + AB = 5AD (given) or AC + AB = 5BC ....(i) (ABCD being a rectangle) and AC – BC = 8 (given) or AC = BC + 8 ....(ii) From (i) AC + AB = 5BC BC + 8 + AB = 5BC (using ii) ⇒ AB = 4 (BC – 2) ....(iii) By the Pythagorus theorem, AB2 + BC2 = AC2 Expressing AB and AC in terms of BC, we get BC = 5 ∴ AB = 12 and AC = 13. So area of the rectangle = 5 × 12 = 60 sq. units. (b) Let each side of square be a Then, area = a2 = 4

Perimeters of four triangles

(b) ABC forms a right angled triangle Since (122 + 52 = 132)

∴ Area =

Let l be the length of rectangle Then, area of rectangle ∴ Perimeter = 2 (10 + 3) = 26 8.

(c) The total area painted for the closed box will be the total inside surface area. Hence, total inside area = sq. cm = 700 sq. cm. Therefore, the rate of painting per sq. cm. = Rs 0.1

10.

(d) Let the radius of the semi-circle be R.

Now join O to B OC = OD = R OB = The diameter of the smaller circle = OQ – OP And < OB – OP

Area of the semicircle Area of the circle Hence the ratio of the area of the smaller circle to that of the semicircle or but all the given options are greater then this ratio. Thus option (d) is the correct alternative. 11.

(b) Total No. of cubes

Total no. of smaller cubes having none of their faces painted will be just behind the shaded cubes = centre cubes = 8

12. (b) In the ∆ ABC, is 90° ( Angle subtended by diameter = 90°) AC = 5 and AB = 6.5 × 2 = 13. Using Pythagoras theorem,

Area of

sq. cm.

13. (b) Diagonal of innermost square = 2 Diagonal of 7th square = 14 then, diagonal of 8th square = 16 Required difference between the area of = 30 14. (c) ∆ABC will be an equilateral triangle. Because it consists of 4 such triangles with end-points on the mid-points of AB, BC and CA

Hence

area of ∆ABC = area of ∆PQR area of ∆PQR = 5 sq. units

15. (d)

Let ‘a’ be the shorter and ‘b’ be the longer sides of rectangle

then, Squaring both sides,

16. (a) Let the radii be r1 and r2

.....(i) ....(ii) ⇒ If r1 and r2 are roots of equation then,

17. (a) AD = 24, BC = 12 In ∆ CBE and ∆ ADE since (Angles by same arc) (Angles by same arc) (Opp. angles) are similar [From AAA]

with sides in the ratio 1 : 2 Hence, ratio of area = 1 : 4 (i.e. square of sides) 18. (c) Let ‘r’ be the radius of each circle. Then by given condition

[since r ≠ 0] ∴ Length of the side of the square = 8 The area of square which is not covered by the coins = 64 – 4 π(2)2 = 19. (d) Area grazed or Area =

sq. cm.

20. (c) If the length of the rope (radius) is 12 m Then, area grazed = r = 12

Then, we can consider B, C as centres and it will also graze some area without attending the triangle. Thus required area would be

21. (a) Let x and y be the sides of triangluar portion

x2 + y2 = 1002 ∴ Area of triangular portion By rule, given that the sum of two variables is constant, their product is maximum when they are equal.Thus x2 = y2. Therefore we have, . Hence, the maximum area is

22. (d) Let the capacity of cylindrical tank = a litres and that of conical tank = b litres Then, a = b + 500 ....(i) From the second given condition a – 200 = 2 (b – 200) ....(ii) After solving (i) & (ii) we get, a = 1200 litres 23. (a) We know the area of sectors is directly proportional to the angle subtended by the arc at the centre for a given radius. Hence, area S1, S2, ........... S7 are in the ratio of1 : 2 : 4 : 8 : 16 : 32 : 64 and the area of the sectors taken together is 127. So, the ratio of the areas are 1 : 127 and the angle subtended by the combined sector is

radians and

where q is

the angle subtended by the arc of combined sector and by solving this comes out to be

radians.

24. (d) Required area is shown as the shaded portion.

Required area =

25. (c)

Let width of the walkway be x metre Then,

∴ Width of walkway = 3 metres

26. (a)

Let side of octagon be x metre Since the resulting figure is a regular octagon then,

27. (b)

Using the fact, that it makes equal (in length) tangents to a circle from a point. Length of the total hypotenuse (AB) ....(i) From ∆ ABS AB

....(ii)

From (i) & (ii), =

On squaring,

= = 4r2 + 6r = 2r2 + 3r

again squaring and solving, we get, Hence diameter = 9 km

28. (a)

Let AB = x and BC = y Area Area of rectangle = xy ∴ Ratio 29. (d)

Let base be x metre ∴ Length of ladder = x + 2 (x + 2)2 = x2 + 64 4x = 60 ∴ x + 2 = 17 Hence the length of the ladder = 17 m

x = 15

30. (d) Drawing DN ⊥ BC

Area of ABND = AB × AD = 25 × 24 = 600 sq. units and Area of

Area of ABCDA = area of ABND + Area of ∆DNC = (600 + 84) sq. units = 684 sq. units Alternatively: In ∆ ABC AC2 = AB2 + BC2 = 242 + 322 = 576 + 1024 = 1600 ∴

AC = 40 m

area of area of ∆ACD

= 384 m2 = 300 m2

area of ABCD = 384 + 300 = 684 m2

31. (a)

Let attitude of ∆ADC be h and third side be x Then, area of triangle = 80 = So, using Pythagorous theorem =12

32. (a)

Shaded region of the above figure is ungrazed Area of grazed portion = Area of APS + Area of BPQ + Area of CRQ + Area of DRS

= 49 π ∴ Ungrazed area = = 22m2 33. (c) Area of lawn = 20 × 40 = 800 m2

∴ area of half lawn = 400 m2 Area left after mowing 2 rounds = 36 × 16 = 576 m2 Area left after mowing 3 rounds = 34 × 14 = 476 m2 Similarly, area left after moving 4 rounds = 32 × 12 = 384 m2 Thus, he has to make rounds slightly less than 4 in order to mow just less than half the area.

34. (d)

Area of In ∆ ABE, Area = ⇒

× BE × AB = 7

BE × AB = 14

In ∆AEC, Area =

× EC × AB = =

× 3 BE × AB × 3 × 14 = 21

Area of = 7 + 21 = 28 cm2 Area of rectangle, ABCD = 2 Area of ∆ABC (since diagonal of rectangle divides rectangle in two equal halves)

35. (b) Area

Applying C1 → C1–C3 & C2 → C2–C3 Expanding we get, Area = –1 But area is considered always +ve. ∴ Required area = 1 sq. unit

36. (d)

Let AB be x Then, according to the question BC = x (since AB = BC) CH = x / 2 = HK = LM = CD CLGD is a rectangle ∴ given that AB = EH = x

Since CHOD is a square

OTFE is also a square Then, As KLGT is a rectangle, Let ∠FGT = θ

Therefore, ‘None of these’ is correct option. 37. (c)

[since OTFE is a square ∴ EF = x/2]

∴ Required ratio = 12 : 7. 38. (d) Let the radius of A be ‘a’ and that of B be ‘b’. Since the surface area ‘a’ is 300% higher than that of ‘b’. Then Volume of As the volume of A is k% lower than B then difference

39. (a)

Area of Area of hexagon, ABCDEF = Area of rectangle ABDE = 2OF × AO + 2 AO × 2 OF = 6OF.AO [ ED = AB = 2 OF and AE = 2 AO] Required

40.

(b) Let PO = r Then area grazed by the horses P and R = πr2. Radius of circle with centre

(by theorem)

Area grazed by Total area grazed Percentage of area that cannot be grazed approx

41. (c)

sin . Hence ∆ABC is equilateral. The next step is to find side AB and OD =

Using Pythagorous theorem, we get, DB2 = OB2 – OD2

;

Hence, side AB Area of ∆ABC = 42. (c) Let r be the radius of circle, a and x be the side of triangle and square respectively.

Then, 2πr = 3a = 4x

So, Thus, c > s > t

43. (c)

Required ratio

44. (a) First Process : Consider a square of side a, which is divided into n squares of different sides. In each square there is a circle of maximum area cut out. The remaining area of square is scrap. For any square say side be b,

The ratio remains same for all the squares combined. Second Process : The above ratio is

Hence, the required ratio = 1 : 1 45. (a) Vertical spacing in cms = h/n because the total height h used divided equally in n parts. Also the strings’ length is the minimum required to wound n turns.

46. (b)

length As this string passes through the four faces of the cube. Hence, length of the string 47. (c) Straighten the wire on the cylinder and apply Phythogorous theorem

or h = n 48. (d) Let h and b be the height and breadth respectively of original triangle.

Then, area of original triangle =

= 34

Hence, area of smaller triangle

49. (d) Volume = (12 – 2x)2 × x For V to be maximum,

= (12 – 2x)[12 – 2x – 4x] = 0 ⇒ x = 2 or 6

50. (b)

Join all the vertices with the centre

Area (∆ ACE) = Area (∆ AOC) + Area (∆ OAE) + Area (∆ OEC) = Area (∆ ABC) + Area (∆ AFE) + Area (∆ EDC) Hence, required ratio =

51. (a)

Given that, ratio of area of the circle to area of the rectangle ABCD ∴ Area of rectangle =

sin 2θ sin ( 30°) = 1/2 AE = DE sin θ, AD = DE cos θ

52. (b) Let longer side of larger rectangle = a Initial ratio of larger to shorter side

Ratio of longer to shorter side in case of second rectangle

According to given conditions, ⇒ ∴ Area of smaller rectangle

53. (d)

Area of C = πr2 Area of C1

;

Area of C2 ∴ Area of shaded region

[Sum of infinity terms of G.P.

]

54. (b)

Area of each circle = π r2 = π sq cm Area of sector ACB = Area of sector AC’B Area of the square ACBC’ = 1 sq. cm. Common Area = Area of sector ACB + Area of sector AC’B – Area of Square =

–1

55. (d)

∴

Required percentage

56. (c) The four equations are : x+y+x–y=4 or x = 2 x + y – (x – y) = 4 or y = 2 –(x + y) + x – y = 4 or y = –2

...(i) ...(ii) ...(iii)

–(x + y) – (x – y) = 4 or x = –2 ...(iv) The area bounded by the given curve is shown below

Hence, area = 4 × 4 = 16 sq. units. 57. (b) Consider the tile is of unit length and let the dimensions of the rectangular floor be x and y. No. of tiles on the edges = 2x + 2(y – 2) No. of tiles in the interior = (x – 2) (y – 2) ∴ 2x + 2(y – 2) = (x – 2) (y – 2) ⇒ 2x = (y – 2) (x – 4) or Hence x > 4, at x = 5, y = 12. 58. (b) The ant would follow the path :

Hence it follows 2 quarter circles of radius 1 m and a distance of 1 m. ∴ Minimum distance covered = 59. (d) The tiles can be adjusted on the floor as shown below

So, maximum 7 tiles can be accomodated on the floor. Alternatively: Area of floor = 130 × 110 = 14300 cm2 Area of 1 tile = 70 × 30 = 2100 cm2 No. of tiles 60. (e) Total area of four walls of a room = Let the height of the room be x. The breadth = 2x and length = 3x Area (1) = Area (2) = ∴ Area of 4 walls decreases by 30%. For Qs. 61-62.

= 90° as it is an angle of a square.

Further EF will be the diameter of the circle as an angle subtended by a diameter on the circumference of a circle = 90°. So, EF will pass through the centre O. In and OF = OE (radius of circle) AO is common = (45°) So AF = AE Area of (Pythagorus theorem) or

Area of

Area of shaded region 2 =

Area of the white portion of circle = Area of shaded region Hence required proportion of the sheet = Alternatively

Complete the square AEGF. Note 2 diagonals of a square make angles of 90° with each other. The area of the shaded region 2 can also found by: 2(Area of sector AOE – Area of ) =

[AO = OE = radius = 1]

= Again, area of region 1 = Area of square ABCD – Area of square AEGF – Area of region 2. [Note : Area of region 2 = Area of region x + region y] Area (region 1) = [Note : Area of square AEGF = Further ⇒ Area (region 1) = Required proportion = 61. (b) 62. (e)

]

63. (b)

, using Pythagorus theorem

or 4R = 40

R = 10 cm

Area of semi-circle = =

64. (a)

Let height and radius of the cylinder are h and r cm respectively. Since ∆ABC ~ ∆ADE ,

Total surface area of the cylinder, S = 2πrh + 2πr2 ⇒ S=

⇒ S = 20πr – 6πr Now, But

Now, Hence, area of the cylinder is maximum when

and

Therefore, total surface area of the largest possible cylinder cm2.

65. (e)

Let AD = 2 units, then AH = 1 unit. In right ∆AHP, tan30° ⇒ ∴

Area of ∆APD

sq.units

Now, area of ABQCDP = Area of square ABCD – 2 (Area of ∆APD)

sq. units

Required ratio

66. (e)

AC = 1 cm CD = 2

In right ∆AEC, cos CAE ∆CAE = 60°, ∆CAD = 120° Area of intersecting region = 2 × (Area of minor segment BCDB of circle with centre A)

67. (b)

Let side of equilateral triangle = a Then height ⇒ Outer circle radius = ⇒ Outer circle diameter ⇒ Inner circle radius = ⇒ Inner circle diameter = Required ratio =

⇒1:2:3

68. (c) If R is the resistance, l is the length and r is the radius. Rα

∴

∴R=

(where k is a constant)

; But R1 = R2.

∴

=k×

∴

∴ = 128 cms. 69. (b) Area of any polygon = r × s (where r is the inradius and s is the semiperimeter) Hence, for any n sided regular polygon with inradius r and side x units,

Since the area is given as 10x sq units

⇒ n × r = 20 Here n must be more than or equal to 3. So the possible values of (n, r) are (4, 5), (5, 4), (10, 2), and (20, 1).

70. (a)

In this figure, the sides AB = CD = FE = distance between 2 radii = 2 cm ∠AOP = ∠BO′C = ∠EO′′D = 120º So perimeter of the bigger triangle = (2 + 2 + 2 + 2 × 3.14 × 1) (because 3 sectors of circles of 120º = 1 full circle of same radius) Let the radius of longer circle be = R Then 2 × π × R = 12.28 ⇒ R

Area = AR2 ⇒ 3.14 × 4 ⇒ 13 cm2 (approximately) Option (a) is closest to the answer. 71. (b) Vessel 1 Vessel 2 Operation 1 20 litres alcohol Empty Operation 2 (20 – x) alcohol (20 – x) litres, water and x litres alcohol Operation 3 (20 – x) litres (20 – x) alcohol +x litres litres mixture mixture i.e.,

Now

rd of C1 is poured into C2

Quantity of alcohol in C1 = C2 = 10 litres ⇒ In C1 ⇒

= 10

Solving we get, x = 10 litres ∴ 10 litres of alcohol was initially poured from C1 to C2. 72. (c) Let the base radius be r and the total height of the cone (without cut) be nr (where n is a constant).

Let the radius at the beginning of the 1st day be r1. So,

Area at the beginning of the 1st day

Volume lost to evaporation on the 1st day ⇒ It is also given that: constant K (say) Similarly, radius at the beginning of the 2nd day ⇒ Area at the beginning of the 2nd day Volume lost to evaporation on the 2nd day ⇒ 73.

Edge of each smaller cube = 3 cm Let the number of cubes along the length and the breadth of the cuboid be 4x and x respectively. 4x × x = 64 or x = 4 Length of the cuboid = 4x × 3 = 48 cm Breadth of the cuboid = x × 3 = 12 cm Required surface area = 48 × 12 = 576 cm2 74. (a) AO = CO = DO = OB = radius of bigger circle = r(let) Then area of (G + F) Area of 2 (G + F) = πr2. Also area of 2G + F + E = πr2 i.e. 2G + F + F = 2G + F + E ⇒ F = E So the ratio of areas E and F = 1 : 1

75.

(c) Volume of a cylinder = πr2h, where r = radius of the cylinder h = height of the cylinder Volume of the graphite cylinder

Volume of the layer of wood

Cost of the material in a pencil = `11.22 76. (d) Volume of Equipment = cm3

0.4579 cm3 can write 330 words ∴

1 cm3 can write =

words

Now, 1 litre = 1000 cm3 = 1000 ml ∴ ∴

litre =

= 600 cm3

600 cm3 can write = = 432408 words

77. (c)

words

In right ∆APB, x2 + (x + 7)2 = 132 x=5 ∴ x + 7 = 12. 78. (c) Since cubic shape will be the greatest volume(as volume = side3)

Hence, 3b = 2a ∴b= 79. (a)

Centre of the circle will be mid-point of the hypotenuse of the triangle. So, hypotenuse = 2 × 6.5 = 13 cm. According to Pythagorean triples. other sides are 5 cm and 12 cm because all sides are natural number. ∴ So perimeter = 5 + 12 + 13 = 30 cm

80. (d)

Let EF = s unit In ∆ DEF : DF = 2EF cos30° = Semi perimeter of ∆ DEF (in units) = S

= Area of ∆ DEF (in unit2 = ∆ =

(EF sin 30°) DF =

Inradius of ∆ DEF (in units) = r2

In radius of triangle DEF (in units) = r2 =

Ratio of area 81. (d) Let the lengths and breaths of each, Small rectangles be ‘x’ meter and ‘y’ meter respectively.

Perimeter = 88 m ∴ 5y + 4x = 88 and 3y = 2x ∴ 5y + 3y × 2 = 88 5y + 6y = 88 ⇒ 11y = 88 ∴y=

= 8 meter

∴ 5 × 8 + 4x = 88 4x = 88 – 40 = 48 ∴x=

= 12

∴ Perimeter of each small rectangle = 2 (x + y) = 2 (12 + 8) = 40 meter. 82. (a) Let, the radius of circle be ‘x’ cm.

∴ CM = CN = CR = x Given that GN = 4 cm ∴ GP = 4 cm Also, DP = DM = QN = 1 cm ∴ GD = 5 cm GQ = GN – QN = 4 – 1 = 3 cm In ∆DGQ : DQ = ⇒ 2x = 4 cm ∴ x = 2 cm ∴ radius or circle = 2 cm 83. (d)

= 4 cm (

DQ = MN)

Required number of traingles =

Here, n = number of items and k = number you are picking at time ∴ n = 5, k = 3 =

84. (a)

Let the semi vertical angle of the cone be θ. tan θ =

θ = 30°.

The vertical angle of the cone = 60° Therefore, the triangle ABC is an equilateral triangle. Therefore, the center (O) of the circle will coincide with the centroid of the triangleABC. In triangle ACM, OC is angle bisector of ∠ACM. ∴ ∠OCM = 30° In ∆OCM, tan30° = Hence, the ratio of the volume of the sphere to that of the cone =

∴ Required ratio = 4 : 9 85. (c) Let the length and breadths of rectangle be a units and b units.

According to question, ab = 2a + 2b a = 2b / (b – 2) Here, Two cases are possible (i) a = 4, b = 4 (ii) a = 3 and b = 6 Thus, two different rectangles are possible. 86. (d) Let the length of the other two sides of the triangle be ‘x’ and ‘y’ respectively. then, 2 x + y2 = (240)2 (hypotenuse of triangle = 240) Also, x + y + 240 must be perfect square (because perimeter of triangle is perfect square). When the two sides other than hypotenuse are equal length than perimeter of right angled triangle is maximized. Therefore, The maximum perimeter of right angled triangle = + 240 = 579 (approx) Also, The perimeter of triangle should be greater than twice the length of hypotenuse of triangle. Then, the perimeter of triangle should be greater than 480 and less than 579. according to question. Perimeter of triangle should be 484, 529 and 576 (because perimeter is perfect square) Again, according to question, Perimeter of triangle is greater than 550, So perimeter = 576. Here, perimeter of triangle = 576. According to pythogorean triples. The value of x and y will be 192 and 144 units.

87. (a)

Here, ABC represents cone; DEBC represents frustum which was made by cone and BRC represents conical cavity. So, Volume of material = cone ABC – (cone ADE + conical cavity of BRC). Now, ∆APE and ∆AQC are similary, ⇒ ⇒ So, AP = 8 cm. Volume of cone ABC = Volume of cone APE = Volume of conical cavity BRC = Required volume of solid = = 132π cm3.

88. (c)

Let length of smaller side of rectangle = a ∴ Radius = of circle According to question, ⇒ = 180

⇒ ⇒

= 36

a= So,

units. length

smaller

side

rectangle

units.

89. (d) PQRS is a rhombus, so the centre of the inscribed circle will be the center of the rhombus PQRS SQ =

= 8 units

OR = DU =

PR (CD – MU) =

(14 – AB) = 6

units PR = AU = = 8 units PR = SQ = 8 units ⇒ PQRS is a square ⇒ OT = units ∴ OT2 =

= 8 units

Area of trapezium =

(AB + CD) × PR =

(2 +

14) × 8 = 64 sq. unit.

Required ratio =

90. (196) Here, ∆PED is similar to ∆GFP Ratio of area = 9: 16 of ∆PED and ∆PFG ∴ ratio of sides =

=3:4

Hence, P divides GD in the ratio 3 : 4. ∴ ∆AGD =

= 49 sq. cm [∆AGD similar to ∆FGP]

So area of AEPF = 49 – [16 + 9] = 24 sq. cm Similarly area of BFI =

× 9 = 100 sq. cm

Therefore area of BHPG = 100 – (49 + 9) = 42 sq. cm Similarly area of PDCI =

× 49 – 49 – 16

= 56 sq.cm Area of triangle ABC = (9 +16 + 49 + 24 + 42 + 56) = 196 sq. cm 91. (58) There are a total of 78 B–schools that place their students ∴ No. of B–schools which are reputed and place their students =

= 13

Let No. of B–schools that are recognised = x According to question, ∴ No. of recognised B–schools that place their students =

∴ No. of recognised B–schools that do not place their students = ∴

= 39 ⇒ x = 52

Out of 13 reputed B–schools, 6 are recognised too ∴ Number of B–schools that are either recognised and place their students or reputed and place their students =13+13 – 6 = 20 ∴ Number of B–school that are neither reputed nor recognised but place their students = 78 – 20 = 58. 92. (b) Here, HCF of 24 and 56 = 8 then, the side of the identical square plots = factors of 8. The factors of 8 are 1, 2, 4 and 8 If side of the square plot is 1 m. the length of fencing material required is (25 × 56 + 57 × 24) = 2768 m But 2768 m > 2700 m. (So, It is not possible)

If side of the square plot is 2 m. the length of fencing material required is (29 × 24+13 × 56) =1464m < 2700 m ∴ minimum fencing material to be left the side of identical square plot = 2m. 93. (d) Let the number of sides be 2n. Let the length of the side of S and the length of the perpendicular from the centre to each side be P. Since the number of sides is even, the opposite sides will be parallel and the distance between any two opposite sides is equal to 2P. Also, area of the polygon (A) =

...(1)

According to question, S(2P) = A/4 or SP = A/8 ∴ (1) ⇒ A = n (A/8) ⇒ n = 8 or 2n = 16 ∴number of sides = 16. 94. (b) Volume ratio of 5 smaller and original cube = 1:1 : 8 : 27 : 27 : 64 Side ratio of 5 smaller and original cube =1:1:2:3:3:4 Surface area ratio of 5 smaller and original cube = 1 : 1 : 4 : 9 : 9 : 16 Sum of smaller cube (surface area) = 24 parts. Big cube = 16 parts. The sum is 50% greater. 95. (6) The height of cylinder (h) = 3 volume = 9π πr2h = 9π r =cm Radius of the ball (R) = 2. Hence, the ball will lie on top of the cylinder. Based on the pythagoras theorem, the other leg will be 1 cm. Thus, the height will be 3 + 1 + 2 = 6 cm.

(a) (b) (c) (d) 2.

(a) (b) (c) (d) 3.

(a)

Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of town A. Expenditure on transport is Rs. 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at (1994) 33 km from Town A 33 km from Town B Town A Town B One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs. 1113 at the end of the days work. What must be the daily wage of a child, if the wages are proportional to the amount of work done? (1994) Rs. 14 Rs. 5 Rs. 20 Rs. 7 A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together a full tank is emptied in 2 hours. If a bucket can hold 5 litres of water, what is the capacity of the tank? (1994) 120 litres

(b) 240 litres (c) 180 litres (d) 60 litres 4. Shyam went from Delhi to Simla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Simla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Simla. If the average speed for the entire journey was 49 kmph. What was the average speed from Chandigarh to Simla? (1994) (a) 39.2 kmph (b) 63 kmph (c) 42 kmph (d) None of these 5. It takes the pendulum of a clock 7 seconds to strike 4 o’clock. How much time will it take to strike 11 o’clock? (1994) (a) 18 seconds (b) 20 seconds (c) 19.25 seconds (d) 23.33 seconds 6. Four friends start from four towns, which are at the four corners of an imaginary rectangle. They meet at a point which falls inside the rectangle, after travelling distances of 40, 50, and 60 metres. The maximum distance that the fourth could have travelled is (approximately) (1994) (a) 67 metres (b) 52 metres (c) 22.5 metres (d) Can’t be determined 7. A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to

Z? (1994) (a) (b) (c) (d) 8.

(a) (b) (c) (d) 9.

(a) (b) (c) (d) 10.

(a) (b) (c) (d)

25 km 22.5 km 24 km 20 km There is leak in the bottom of a tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 litres per hour and the tank is now emptied in 12 hours. What is the capacity of the tank? (1994) 28.8 litres 36 litres 144 litres Can’t be determined The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to time taken by D? (1994) 5 : 16 5 : 17 9:8 8:9 In a race of 200 metres run, A beats S by 20 metres and N by 40 metres. If S and N are running a race of 100 metres with exactly same speed as before then, by how many metres will S beat N ? (1995) 11.11 metres 10 metres 12 metres 25 metres

Directions for questions 11 to 14 : Read the information given below and answer the questions that follow : A and B are running along a circular course of radius 7 km in opposite directions such that when they meet they reverse their directions and when they meet A will run at the speed of B and vice-versa. Initially, the speed of A is thrice the speed of B. Assume that they start from M0 and they first meet at M1, then at M2, next at M3, and finally at M4 11.

What M2?

the

shortest

distance

between

and

(1995) (a) 11km. (b) (c) 7 km (d) 14 km 12. What is the shortest distance between M1 and M3 along the course? (1995) (a) 22 km (b) (c) (d) 14 km 13. Which M0?

the

point

that

coincides

with

(1995) (a) (b) (c) (d) 14.

M1 M2 M3 M4 What is the distance travelled by A when they meet at M3 (1995)

(a) 77 km.

(b) (c) (d) 15.

66 km 99 km 88 km A man travels three-fifths of a distance AB at a speed of 3a, and the remaining at a speed of 2b. If he goes from B to A and back at a speed of 5c in the same time, then (1996) (a) 1/a +1/b = 1/c (b) a + b = c (c) 1/a +1/b = 2/c (d) None of these Directions for questions 16 to 20 : Read the information given below and answer the questions that follow :

16.

(a) (b) (c) (d) 17.

(a)

Persons X, Y and Z wish to go from place A to place B, which are separated by a distance of 70 km. All the three persons start off together from A, with X and Y going by Luna at a speed of 20 kmph. X drops Y somewhere along the way and returns to pick up Z, who has already started walking towards B at a speed of 5 kmph. Y, after being dropped by X, starts walking towards B at a speed of 5 kmph. In this manner, all three of them reach B at the same time. How much distance is covered by Z on foot? (1996) 25 km 10 km 20 km 15 km What is the total distance travelled by x? (1996) 130 km

(b) (c) (d) 18.

140 km 110 km 90 km How long B?

does

take

them

from

(1996) (a) (b) (c) (d) 19.

(a) (b) (c) (d) 20.

(a) (b) (c) (d) 21.

(a) (b) (c)

6.0 hours 6.5 hours 7.0 hours 14.0 hours After how much time is Y dropped on the way by X? (1996) 2.0 hours 3.0 hours 2.5 hours 1.5 hours For how long does X travel alone over the entire journey? (1996) 2.5 hours 1.0 hours 2.0 hours 1.5 hours A man travels from A to B at a speed of x kmph. He then rests at B for x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to 12 km, the time for which he rested at B could be (1996) 3 hours 6 hours 2 hours

(d) 4 hours 22. In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hrs., 18 min., 15 seconds of watch time. What is the time gained or lost by this watch in one day? (1996) (a) 14 min. 10 seconds lost (b) 13 min. 50 seconds lost (c) 13min. 20 seconds gained (d) 14 min. 40 seconds gained 23. In a mile race, Akshay can be given a start of 128 metres by Bhairav. If Bhairav can give Chinmay a start of 4 metres in a 100 metres race, then who out of Akshay and Chinmay will win a race of one and a half mile, and what will be the final lead given by the winner to the loser? (one mile is 1600 metres) (1996) (a) Akshay, 1/12 miles (b) Chinmay, 1/32 miles (c) Akshay, 1/ 24 miles (d) Chinmay, 1/16 miles 24. An express train travelling at 80 kmph overtakes a goods train, twice as long and going at 40 kmph on a parallel track, in 54 seconds. How long will the express train take to cross a station 400 m long? (1997) (a) 36 sec (b) 45 sec (c) 27 sec (d) None of these Directions for questions 25 to 27 : Read the information given below and answer the questions that follow : Boston is 4 hours ahead of Frankfurt and two hours behind India. X leaves Frankfurt at 06:00 pm on Friday and reaches

Boston the next day. After waiting there for two hours, he leaves exactly at noon and reaches India at 01:00 am. On his return journey, he takes the same route as before, but halts at Boston for one hour less than his previous halt there. He then proceeds to Frankfurt. 25. If his journey, including stoppages, was covered at an average speed of 180 miles per hour, what was the distance between Frankfurt and India? (1997) (a) 3600 miles (b) 4500 miles (c) 5580 miles (d) Insufficient data 26. If X had started his return journey from India at 02:55 am on the same day that he reached there, after how much time would he reach Frankfurt? (1997) (a) 24 hrs (b) 25 hrs (c) 26 hrs (d) Insufficient data 27. What was X’s average speed for the entire journey? (1997) (a) 170 mph (b) 180 mph (c) 165 mph (d) Insufficient data Directions for questions 28 & 29 : Read the information given below and answer the questions that follow : A thief, after committing the burglary, started fleeing at 12:00 noon, at the speed of 60 kmph. He was then chased by a

28.

(a) (b) (c) (d) 29.

(a) (b) (c) (d) 30.

(a) (b) (c) (d) 31.

policeman X. X started the chase 15 minutes after the thief had started, at a speed of 65 kmph. At what time did X catch the thief? (1997) 3:30 pm. 3:00 pm 3:15 pm None of these If another policeman had started the same chase along with X, but at a speed of 60 kmph, then how far behind was he when X caught the thief? (1997) 18.75 km 15 km 21 km 37.5 km A company has a job to prepare certain no. of cans and there are three machines A, B & C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will take to complete job if all the machines are used simultaneously? (1998) 4 days 4/3 days 3 days 12 days Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph. While the other man travelled with varying speeds as follows : In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on.

When other?

will

they

meet

each

(1998) (a) (b) (c) (d) 32.

7 hours 10 hours 35 km from A midway between A & B I started climbing up the hill at 6 am and reached the temple at the top at 6 pm Next day I started coming down at 6 am and reached the foothill at 6 pm. I walked on the same road. The road is so short that only one person can walk on it. Although I varied my pace on my way, I never stopped on my way. Then which of the following must be true (1998) (a) My average speed downhill was greater than that uphill (b) At noon, I was at the same spot on both the days. (c) There must be a point where I reached at the same time on both the days. (d) There cannot be a spot where I reached at the same time on both the days. Directions for questions 33 & 34 : Read the information given below and answer the questions that follow : Rajiv travels to B from A in 4 hrs. travelling at 35 kmph for two hrs and at 45 kmph for the next two hrs. Aditi travels on the same route at speeds of 30, 40 and 50 kmph, covering equal distances at each of these speeds. The relation between fuel consuption and speed is given in the following graph.

33. How Aditi

many

litres

fuel

consumed

(1999) (a) (b) (c) (d) 34.

(a) (b) (c) (d) 35.

7 9 10 15 Zorin would like to drive Aditi’s car over the same route form A to B. minimize the petrol consumption for the trip. The amount of petrol required by him is (1999) 6.67 litres 7 litres 6.33 litres 6.0 litres Navjeeven exp., which goes form Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at a constant speed of 50 kmph towards Baroda, which is 100 kms away. At 7:00, the How -Ambd exp. leaves for Ahmedabad from Baroda at a

(a) (b) (c) (d) 36.

(a) (b) (c) (d)

constant speed of 40 kmph. At 7:30 Mr. Shah, the control officer, realises that both the trains are on the same track. How much time does Mr. Shah have to avert the accident? (1999) 30 min 20 min 25 min 15 min A railway engine moves with the speed of 42 kmph. The reduction in speed varies as the square root of the number of compartments attached to it. The speed is 24 kmph when 9 compartments are attached. What is the maximum number of compartments that the engine can pull? (1999) 47 48 49 42

Directions for questions 37 to 39 : Read the information given below and answer the questions that follow : There is a network of routes as shown in the figure given below. D is the mid point of AC, AB is perpendicular to BC andAB = 100km. The persons, X & Y, go from A to C, starting at the same time and reaching at the same time. X follows the pathA-B-C with an average speed of 61.875 kmph, and Y follows the straight path A-C, covering part AD at 45 kmph and part DC at 55 Kmph.

37. What

the

average

speed

between

A-C

(1999) (a) (b) (c) (d) 38.

52 kmph 50 kmph 49.5 kmph 48 kmph What C?

the

distance

B-

the

distance

A-

(1999) (a) (b) (c) (d) 39.

30.55 km 37.5 km 62.5 km Indeterminable What is C (1999)

(a) (b) (c) (d) 40.

105 km 112.5 km 135.5 km Indeterminable A and B are two cities 10 km apart. A load of 80 kg has to be transported form A to B. The courier service charges @ 10Rs per hour. The optimal speed that one can go without load is 10 km/hr, the speed reduces to 5 km/hr with a weight of 10 Kg. Further with 20 kg (which is the maximum weight that can be

carried), the speed is 2 km/hr. what is the minimum cost? (2000) (a) 200 (b) 180 (c) 160 (d) 140 Directions for questions 41 & 42 : Read the information given below and answer the questions that follow : There are five machines A, B, C, D and E – situated on a straight line at distances of 10 m, 20 m, 30 m, 40 m and 50 m respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw materials are located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot-station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message(s) is/are received. 41. Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the 1st second, C has sent a message at the beginning of the 5th second, B at the beginning of the 6th second and E at the beginning of the 10th second. How much distance has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 m/s. (2000) (a) 140 m

(b) (c) (d) 42.

(a) (b) (c) (d) 43.

(a) (b) (c) (d) 44.

(a) (b) (c) (d)

80 m 340 m 360 m Suppose there is a second station with raw material for the robot at the other extreme of the line which is 60 m from the origin, i.e., 10 m from E. After finishing the services in a trip, the robot returns to the nearest station. If both stations are equidistant, it chooses the origin as the station to return to. Assuming that both stations receive the message sent by the machines and that all the other data remains the same, what would be the answer to the above question? 120 140 340 70 The vehicle of Mr. Ghosh needs 30% more fuel at the speed of 75 kmph than it needs at the speed of 50 kmph. At a speed of 50 kmph, Mr. Ghosh can go to a distance of 195 kms. At the speed of 75 kmph, he will able to travel a distance of (2000) 120 kms 150 kms 160 kms 140 kms A can complete a piece of work in 4 days. B takes double the times taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two- third the time needed by the second pair to complete the work. Which is the first pair? (2001) A, B A, C B, C A, D

45. If 09/12/2001 happens to be Sunday, then 09/12/1971 would have been (2001) (a) Wednesday (b) Tuesday (c) Saturday (d) Thursday 46. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour? (2001) (a) (b) (c) (d) 47. Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up? (2001) (a) 40 (b) 50 (c) 60 (d) 80 48. There’s a lot of work in preparing a birthday dinner. Even after the turkey is in the oven, there’s still the potatoes and gravy,

yams, salad, and cranberries, not to mention setting the table. Three friends, Asit, Arnold, and Afzal, work together to get all of these chores done. The time it takes them to do the work together is six hours less than Asit would have taken working alone, one hour less than Arnold would have taken alone, and half the time Afzal would have taken working alone. How long did it take them to do these chores working together? (2001) (a) 20 minutes (b) 30 minutes (c) 40 minutes (d) 50 minutes 49. A train X departs from station A at 11.00 am for station B, which is 180 km away. Another train Y departs from station B at 11.00 am for station A. Train X travels at an average speed of 70 kms/hr and does not stop any where until it arrives at station B. Train Y travels at an average speed of 50 kms/hr, but has to stop for 15 minutes at station C, which is 60 kms away from station B enroute to station A. Ignoring the lengths the train , what is the distance , to the nearest km, from station A to the point where the trains cross each other? (2001) (a) 112 (b) 118 (c) 120 (d) None of these 50. Three runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of C. Each runner travels the entire distance at constant speed. What was the length of the race? (2001) (a) 36 metres

(b) 48 metres (c) 60 metres (d) 72 metres Directions for questions 51 & 52 : Read the information given below and answer the questions that follow : The petrol consumption rate of a new model car ‘Palto’ depends on its speed and may be described by the graph below.

51. Manasa makes the 200 km trip from Mumbai at a steady speed of 60 km per hour. What is the amount of petrol consumed for the journey? (2001) (a) 12.5 litres (b) 13.33 litres (c) 16 litres (d) 19.75 litres 52. Manasa would like to minimize the fuel consumption for the trip by driving at the appropriate speed. How should she change the speed? (2001) (a) Increase the speed (b) Decrease the speed

(c) Maintain the speed at 60 km/hour (d) Cannot be determined 53. 6 technicians take total 10 hours to build a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11:00 am, and one technician per hour is added beginning at 5:00 pm, at what time will the server be complete? (2002) (a) 6:40 pm (b) 7:00 pm (c) 7:20 pm (d) 8 pm 54. 3 small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3rd the rate of the large pump. If all 4 pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone? (2002) (a) 4/7 (b) 1/3 (c) 2/3 (d) 3/4 55. On a straight road XY, 100 metres long, five heavy stones are placed two metres apart beginning at the end X. A worker, starting at X, has to transport all the stones to Y, by carrying only one stone at a time. The minimum distance he has to travel (in metres) is (2002) (a) (b) (c) (d)

472 422 744 860

56. Only a single rail track exists between station A and B on a railway line. One hour after the north bound super fast train N leaves station A for station B, a south bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day N leaves for station B from Station A, 20 minutes behind the normal schedule. In order to maintain the schedule both N and S increased their speed. If the super fast train doubles its speed, what should be the ratio (approximately) of the speed of passenger train to that of the super fast train so that passenger train S reaches exactly at the scheduled time at station A on that day (2002) (a) 1 : 3 (b) 1 : 4 (c) 1 : 5 (d) 1 : 6 57. On a 20 km tunnel connecting two cities A and B there are three gutters. The distance between gutter 1 and 2 is half the distance between gutter 2 and 3. The distance from City A to its nearest gutter, gutter 1 is equal to the distance of city B from gutter 3. On a particular day the hospital in city A receives information that an accident has happened at the third gutter. The victim can be saved only if an operation is started within 40 minutes. An ambulance started from city A at 30 km/hr and crossed the first gutter after 5 minutes. If the driver had doubled the speed after that, what is the maximum amount of time the doctor would get to attend the patient at the hospital? Assume 1 minute is elapsed for taking the patient into and out of the ambulance (2002) (a) 4 minutes (b) 2.5 minutes (c) 1.5 minutes (d) Patient died before reaching the hospital

58. A car rental agency has following terms. If a car is rented for 5 hours or less the charge is Rs 60 per hour or Rs 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hours, the charge is Rs 50 per hour or Rs 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 kilometers and ended up paying Rs 300. For how many hours did he rented the Car? (2002) (a) 4 (b) 5 (c) 6 (d) None of these 59. A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the entrance of the tunnel, A, the train catches the cat exactly at the entrance. If the cat moves to the exit, B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order? (2002) (a) 3 : 1 (b) 4 : 1 (c) 5 : 1 (d) None of these 60. In a 4000 metre race around a circular stadium having a circumference of 1000 metres, the fastest runner and the slowest runner reach the same point at the end of the 5th minute for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race? (2003C)

(a) 20 min (b) 15 min (c) 10 min (d) 5 min Directions for questions 61 to 63 : Read the information given below and answer the questions that follow : A city has two perfectly circular concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR) . These are also four (straight line) chord roads form E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR, from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road and km/hr on all the chord 61.

(a) (b) (c) (d) 62.

(a) (b) (c)

roads. Amit wants to reach E2 from N1 using first the chord N1-W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question (2003C) 60 45 90 105 Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1-E1 on OR, and then on the chord road E1-N2. What is the radius of the outer ring road in kms? (2003C) 60 40 30

(d) 20 63. The ratio of the sum of the lengths of all chord roads to the length of the outer ring road is (2003C) (a) (b) (c) (d) None of the above. 64. A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower? (2003) (a) 5(

+ 1)

(b) 6(

(d) 8(

– 2)

) (c)7(

– 1)

Directions for questions 65 to 67 : Read the information given below and answer the questions that follow : Consider three circular parks of equal size with centers at A1, A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3 and C1C2C3 as shown. Three sprinters A, B and C begin running from points A1, B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.

65. Let the radius of each circular park be r, and the distances to be traversed by the sprinters A, B and C be a,b and c, respectively. Which of the following is true? (2003) (a) b – a = c – b = 3 (b) b – a = c – b = (c) b =

r r

= 2(1 +

(d) c = 2b – a = (2 +

66. Sprinter A traverses distances , and at average speeds of 20, 30 and 15, respectively. B traverses her entire path at a uniform speed of (10 + 20). C traverses distances + 1 ),

, (

and

at average speedsof

(

+ 1) and 120, respectively. All speeds are in

the same unit. Where would B and C be respectively when A

finishes sprint?

her (2003)

(a)

(b)

(c)

, (d)

, somewhere between

67. Sprinters A, B and C traverse their respective paths at uniform speeds of u, v and w respectively. It is known that : : is equal to Area A : Area B : Area C, where Area A, Area B and Area C are the areas of triangles , andC1 C2 C3, respectively. Where would A and C be when B reaches point B3? (2003) (a) A2, C3 (b) A3, C3 (c) A3, C2 (d) Somewhere between A2 & A3, somewhere between C3 & C1 68. Two straight roads R1 and R2 diverge from a point A at an angle of 120°. Ram starts walking from point A along R1 at a uniform speed of 3 km/hr. Shyam starts walking at the same time from A along R2 at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach points B and C on R1 and R2, respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram’s and shyam’s return to the point A is (2003)

(a) (b) (c) (d) 69. Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race? (2004) (a) Karan and Arjun reach the following line simultaneously (b) Arjun beats Karan by 1 metre (c) Arjun beats Karan by 11 metre (d) Karan beats Arjun by 1 metre 70. If a man cycles at 10 km/hr, then he arrives at a certain place at 1 pm. If he cycles at 15 km/hr, he will arrive at the same place at 11 am. At what speed must he cycle to get there at noon? (2004) (a) 11 km/hr (b) 12 km/hr (c) 13 km/hr (d) 14 km/hr 71. Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance 20 kms from each other. How far apart are they (in kms) one minute before they collide? (2004)

(a) (b) (c) (d) 72. In nuts and bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts? (2004) (a) 130 minutes (b) 135 minutes (c) 170 minutes (d) 180 minutes 73. A chemical plant has four tanks (A, B, C and D) each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows : (2005) From A to B @ 20 litres/minute From C to A @ 90 litres/minute From A to D @ 10 litres/minute From C to D @ 50 litres/minute From B to C @ 100 litres/minute From D to B @ 110 litres/minute Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts? (a) A, 16.66

(b) C, 20 (c) D, 20 (d) D, 25 Directions for questions 74 & 75 : Answer the questions on the basis of the information given below

74. (a) (b) (c) (d) 75. (a) (b) (c) (d) 76.

(a) (b) (c) (d)

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed. At what time do Ram and Shyam first meet each other? (2005) 10 a.m. 10:10 a.m. 10:20 a.m. 10:30 a.m. At what time does Shyam overtake Ram? (2005) 10:20 a.m. 10:30 a.m. 10:40 a.m. 10:50 a.m. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start? (2006) 3 3.5 4 4.5

(e) 5 Directions for Questions 77 & 78 : Cities A and B are in different time zones. A is located 3000 km east of B. The table below describes the schedule of an airline operating non–stop flights between A and B. All the times indicated are local and on the same day.

Assume that planes cruise at the same speed in both directions. However, the effective speed is influenced by a steady wind blowing from east to west at 50 km per hour. 77. What is the time difference between A and B? (2007) (a) 1 hour (b) 1 hour and 30 minutes (c) 2 hours (d) 2 hours and 30 minutes (e) Cannot be determined 78. What is the plane’s cruising speed in km per hour? (2007) (a) 500 (b) 700 (c) 550 (d) 600 (e) Cannot be determined. 79. Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train

(a) (b) (c) (d) (e) 80.

(a) (b) (c) (d)

leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and north-west of B, with BC at 60° to AB. Also, C is located between south and south-west of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to (2008) 6:15 am 6:30 am 6:45 am 7:00 am 7:15 am Ten workers started a job and worked on it for 10 days. Eleventh day onwards, a new worker joined them every day till the job was finished. It took exactly 20 days to finish the entire job. The same job has to be done starting with the minimum possible number of workers when it is known that a worker will quit the job every day after the first day. How many days will it take to finish the job in such a manner? (2009) 23 22 19 17

81. Two friends – Tarun and Sumit – started running simultaneously from a point P in the same direction along a straight running track. The ratio of the speeds of Tarun and Sumit was 2 : 5 respectively. Two hours later, Sumit turned back and started running backwards at one-fifth of his original speed. He met Tarun at a distance of 10 km from the point P. What was Tarun’s running speed? (2009) (a) 1.25 km/hr

(b) (c) (d) 82.

2.5 km/hr 3.75 km/hr 6.25 km/hr Ravi and Rahul started running from the same point in opposite directions on a circular track of length 120 m. Their speeds are 20 m/s and 40 m/s respectively. After every second, Ravi increases his speed by 2 m/s whereas Rahul decreases his speed by 2 m/s. How many times would they have met on the track by the time Rahul comes to rest? (2010) (a) 2 (b) 5 (c) 10 (d) None of these 83. A computer program was tested 300 times before its release. The testing was done in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only? (2010) (a) 10 (b) 13 (c) 15 (d) 17 84. A watch, which gains time uniformly, was 5 minutes behind the correct time when it showed 11:55 AM on Monday. It was 10 minutes ahead of the correct time when it showed 06:10 PM on the next day. When did the watch show the correct time? (2010) (a) 6 AM, Tuesday

(b) 6 PM, Monday (c) 2 PM, Tuesday (d) 10 PM, Monday 85. It takes 6 technicians a total of 10 hours to build a new server from direct computer, with each working at the same rate. If six technicians start to build the server at 11 : 00 am, and one technician per hour is added beginning at 5 :00 pm, at what time will the server be completed ? (2010) (a) 6 : 40 pm (b) 7 : 00 pm (c) 7 : 20 pm (d) 8 : 00 pm 86. A ship 55 kms. from the shore springs a leak which admits 2 tones of water in 6 min ; 80 tones would suffer to sink her, but the pumps can throw out 12 tones an hour. Find the average rate of sailing that she may just reach the shore as she begins to sink. (2011) (a) (b) (c) (d) 87.

5.5 km/h 6.5 km/h 7.5 km/h 8.5 km/h In a 400 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the

fastest race? (a) 20 mins (b) 15 mins

runner

finish (2011)

the

(c) 10 mins (d) 5 mins 88. A train crosses a platform 100 metres long in 60 seconds at a speed of 45 km per hour. The time taken by the train to cross an electric pole, is (2011) (a) 8 seconds (b) 1 minute (c) 52 seconds (d) Data inadequate 89. The radius of the cross-sections of pipes P1 and P2 are 7 m and 14 m respectively. Water flows through P1 at a constant rate of 10 m/s and it can alone fill a tank in 2 hours. If P1 is used as the inlet pipe and P2 as the outlet pipe then together they fill the tank in 4 hours. What is the rate of water flow (in m/s) through P2? (2012) (a) 1.00 (b) 1.25 (c) 1.50 (d) 2.00 90. During his trip to England, Mr. Clockilal, a horologist, decided to visit ‘The Cuckooland Museum’ dedicated to the exhibition of cuckoo clocks. He entered the museum between 12 noon and 1 p.m. The moment he entered the museum, he observed that the angle between the minute hand and the hour hand of one of the

clocks was 20°. While leaving the museum, he observed that the angle between the minute hand and the hour hand of the same clock was 220°. If he spent more than 3 hours and less than 4 hours in the museum, then how much time did he exactly spend in the museum? (2013) (a) 3 hours (b) 3 hours (c) 3 hours

minutes minutes minutes

(d) Either (a) or (c) 91. Anushka and Anirudh working together can complete a piece of work in 20 days. They started the work together, but Anushka left after x days and Anirudh finished the remaining work in the next x/2 days. Had Anushka left after 3x/4 days, Anirudh would have taken x days to finish the remaining work. Find the ratio of the efficiency of Anushka to that of Anirudh. (2013) (a) 2 : 3 (b) 3 : 2 (c) 2 : 1 (d) 1 : 1 92. Once upon a time, the king of a jungle planned a 2-kilometre race between a rabbit and a tortoise. Soon after the start of the race, the rabbit took a huge lead. On realizing that even after taking a nap of ‘t’ min, he would beat the tortoise by 13 min, he stooped under a tree and went to sleep. Meanwhile the tortoise kept walking. When the rabbit woke up, he realized that he had slept for (14 + t) min, and immediately started running towards the target at a speed

times his original speed. The race

eventually ended in a dead heat. If the ratio of the original speed of the rabbit to that of the tortoise was 6 : 1 and the rabbit

overstretched his nap by

t min, then how long did the tortoise

take to complete the race? (2013) (a) 24 min (b) 30 min (c) 28 min (d) 36 min 93. P, Q and R start walking from the same point. P and Q start at 1 PM and R starts at 3 PM. R takes over P at 5 PM and then doubles his speed and takes over Q after another hour. What is the ratio of speed of A and speed of B? (2014) (a) 8 : 5 (b) 3 : 4 (c) 4 : 3 (d) 5 : 8 94. There is a string of length 100 m running from east to west. 1000 ants are dropped onto the string. Assume that each ant lands on the string facing either the east or the west direction. As soon as they land, each ant starts moving in the direction which is being faced by it at 50 m/ min till it falls off the string. But if an ant collides with another ant coming from the opposite direction, both of them reverse their directions and proceed to move now in the opposite directions. Ants fall only at either of the ends of the string. What is the minimum time by which the string is definitely free of ants? (2015) (a) 1 min (b) 2 min (c) 200 min (d) Infinite time

95.

In a rowing competition, first boat rows over the course at an average speed of 4 yards/second. Second boat rows over the first half of the course at the rate of the remaining half at

yards /second and over

yards/second, thereby reaching the

winning post 15 seconds after the first boat. Find the time taken (in minutes) by the second boat to cover the entire course. (2015) 96. There are three cities A, B and C, not on the same straight road. Two buses P and Q start simultaneously from A and B respectively towards C. By the time Q reaches C, P is exactly halfway to C. Immediately after Q reaches C, it starts travelling towards A and it crosses P at a point 165 km from A. The ratio of the speeds of P and Q is 3 : 5 Assume that the roads joining A to C, B to C and B to A are all straight roads. If B is twice as far from A as it is from C and P would take to cover the distance from A to B, how much time would Q take to cover the distance from C to A? (2016) (a) (b) 3 hours (c) (d) 4 hours 97. A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job? (2017)

98. A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train’s departure. The distance (in km) from his home to the railway station is (2017) 99. A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is (2017) (a) (b) (c) (d) 3 : 2

(d) Let school be at a distance of x km from town B. Cost of transport for 130 students = 30 (100 – x) × 1.20 + 100 x × 1.20 = (3000 + 70 x) × 1.20 For cost to be minimum, x = 0, Hence, expenditure is least when school is built at town B. (d) One day work of man = 1 One day work of woman One day work of child

One day work ratio =

or 6 : 3 : 1

Ratio of men, women and children = 6 : 5 : 2 Their wages ratio = 6 : 3 : 1 Let wage per child = x Then, wage per woman = 3x And wage per man = 6x Let y = number of children There are 39 pairs of hands Therefore, or Hence, man = 18, woman = 15 and children = 6 Amount paid,

∴ x=`7 (b) Tap A fills 4 buckets (4 × 5 = 20 litres) in 24 min. In 1 hour tap A fills In 1 hour tap B fills = In 1 hour tap C fills If they open together they would fill litres in one hour but full tank is emptied in 2 hours So, tank capacity would be 120 × 2 = 240 litres.

Time taken from Chandigarh to Shimla Total time Also total time ∴ Total time would be same 5.

⇒ V = 42 km/h. (d) There are three intervals between four strikes

In one interval it will take

There would be 10 intervals between eleven strikes Pendulum will take 6.

= 23.33 sec.

(a) Suppose A travelled distance a, B travelled distance b, C travelled distance c, and D travelled distance d They meet at a point o which at a distance x from AD, y from BC, p from AB and q from CD.

we get,

Therefore, we see

for d to be maximum

4500 = d2

or ∴ 7.

d = 67 m (approx.)

(b) Time taken by A from X to Z would be same as time taken by B from X to Y and Y to Z. Let XZ = x. So, time taken by A

and

time taken by B

∴ (c) Let the capacity of tank be x litres In one hour tank empties =

of x

litre

In one hour, tap admits 6 litres after opening tap tank is emptied in 12 hours. So in one hour tank empties by Therefore equation becomes

∴ x = 144 litres

of x =

litres.

10. (a) In a 200 m race, A beats S by 20 m and A beats Nby 40 m Then, when S runs 180m, N runs 160 m only Hence, when S runs 100 m, N runs

∴ S beats N by 100 – 88.88 = 11.11 m For Qs. 11-14. The points are clearly shown in the figure

Circumference 11.

(b) Hence, shortest distance between M1 and M2 =

12. (a) Shortest distance between M1 and M3 along = 22 km

13. (d) M4 is the point that coincides with M0. 14. (a) Distance travelled by A = 33 + 11 + 33 = 77 km 15. (c)

Speed

......(i) ......(ii)

......(iii)

For Qs. 16-20.

Time taken by

......(i)

Time taken by

......(ii)

Equating (i) & (ii), ⇒ time taken by ......(iii) Equating (1) & (3), Using

we get

16. (c) Distance

and covered by

foot

17. (a) Total distance travelled by

18. (b) Time taken to reach from A to B

19. (c) Time when Y was dropped by

20. (d) X covers the distance s1 – s2 alone, i.e. 30 km at speed of 20 kmph in hours

=1.5

21. (a) Let total time taken by the man to reach D

Hence, he rested for 3 hours at B 22. (b) When watch, runs correct the minute hand should cross the hour hand once in every

minutes.

So, they should ideally cross 3 times once in minutes = 196.36 minutes. But in the watch under consideration, they meet after every 3 hour, 18 minutes and 15 seconds, i.e., minutes In 24 hours a watch has 1440 minutes. Thus, our watch is actually losing time (as it is slower than the normal watch). Hence, when our watch elapsed = 1426.27 minutes. Hence, the amount of time lost by our watch in one day i.e., 13 minutes and 50 seconds (approx). 23. (d) When Bhairav covers 1600m, Akshay covers (1600 – 128) m.

So, when Bhairav covers (1600/16) = 100m, Akshay covers (128/16) m = 8 m less. When Bhairav covers 100m. Chinmay covers (100 – 4) = 96 m. Thus, the ratio in which Akshay and Chinmay cover distances is 92 : 96. In 96 m, Chinmay gains (96 – 92) = 4m over Akshay. So in 1.5 miles, Chinmay gains 100 m = (1/16) miles over Akshay. 24. (a) Let express train be l km and goods train be 2l km long. Then, relative speed of both trains = 80 – 40 = 40 kmph km = 200 m Hence, time taken to cross a station = 25. (b) Total time for journey = 12 + 2 + 11 = 25 hrs. Average speed ∴ Total Distance = 180 × 25 = 4500 miles 26. (a) Since he will halt at Boston for one hour less than his previous halt there. Hence, Total time = 12 + 1 + 11 = 24 hrs. 27. (b) Average speed of = 28. (c) Let after t seconds X catches thief, hence, distance travelled by thief = distance travelled by policeman

hrs = 3 hrs 15 minutes. ∴ At 3 : 15pm, x will catch thief. 29. (b) Since other policemen started 15 minutes later then the thief with speed of 60 kmph.

So, distance he lagged behind the thief = distance behind policeman when he caught the thief = 30. (b) Let work done by A in one day be a, similarly, for B, b and for C, c So, 3a = 1, 4b = 1, 6c = 1 [Total work be 1 unit] So, Total work done by the 3 Machines in one day = Therefore, time taken to complete the work is days. 31. (d)

Speed of man B is in Arithmetic Progression. Let they meet when A has covered x km Then, time taken by A for covering x km Distance covered by B = (72 – x) km Also, Distance covered by B no. of terms i.e.,

Put the options in above equation we get x = 36 km. Hence, they meet midway between A & B

32. (c) 1st day he climbing up at 6.00 a.m. and reached at 6.00 p.m. 2nd day he coming down at 6.00 a.m. and reached the foothill 6.00 p.m. Hence, average speed of both path is same. At noon it is not necessary that he was at same spot. There must be a point where he reached at the same time on both the days. 33. (b) Total distance travelled by Rajeev = 35 × 2 + 45 × 2 = 160. Aditi travels equal distances with speeds 30, 40, 50. Thus, she covers a stretch of 160 / 3 km by every speed. From graph we can say that fuel consumed is given by litres 34. (a) In order to minimize the petrol consumption mileage has to be maximum from the graph given in the question. Maximum mileage is 24 kms/ltr and the distance to be travelled is 160 kms so the minimum petrol consumption = distance / mileage = 160 / 24 = 6.66 ltrs. 35. (b) At 7 : 00 am; Navjeevan Express travels for Hence, distance covered = 50 ×

hr.

= 25 km.

Now, the relative speed between the two trains is50 + 40 = 90 kmph Relative distance = 75 km. So, the time for collision= 75 / 90 = 50 min from 7 : 00 am. Thus, after 7 : 30 when Mr. Shah notices it, 20 minutes are left. 36. (b) Let r = reduction in speed and w = number of wagons Given that r = 42 – 24 = 18 and w = 9

Now let us find out how many wagons will be required so that the train stops. For that let’s take the speed as 0. For this to happen the reduction has to be 42.

With 49 wagons the train will stop. So, we subtract one wagon so that the train will just move. Hence, the answer is 48. 37. (c) Let AD = DC = x. Time taken by Y to cover AC = Average speed of Y between A – C, =

kmph

38. (a) X and Y each reaches C at the same time

Using Pythagorous theorem in ABC,

39. (a) From above solution

40. (c) Total cost for 10 kg, = Total

cost

for

kg,

Hence, minimum cost = Rs 160. 41. (a) The installation and functioning of all the five machines will be as per the following figure. The robot begins to give material to machine A and then to D, thus it covers 40 m in that time span and takes 4 seconds.

Also it returns to the origin at the same time and takes4 seconds covering 40 metres again. When it arrives at the origin the messages of B and C are already present there. Hence it starts to deliver the material to them taking in all 6 seconds in doing so and covers 30 + 30 = 60 metres. Hence the distance travelled by the robot will be 40m + 40m + 60m = 140m. 42. (a) Once the robot has delivered the material to machines A and D, it shall reach the origin 2 (nearest) taking 6 sec. and covering 60 m. Then it immediately moves to deliver material to machines C and B covering a distance of 40 m and finally back to origin (nearest). Thus it covers a distance of 60 m. Hence, it covers a total distance of 120 metres. 43. (b) The only thing which matters in this problem is mileage or kms per litre of the fuel. At 50 kmph 195 kms can be covered. According to condition 1.3 times the fuel will be required at 75kmph. Therefore, distance travelled will be 195/1.3 = 150 kms. 44. (d) A’s 1 day work

; B’s

; C’s

Consider pairs A, B and C, D For A, B combined, 1 day work

per day

; D’s

For C, D combined, 1 day work

per day

For A, C combined, 1 day work

per day

For B, D combined, 1 day work

per day

For B, C combined, 1 day work

per day

For A, D combined, 1 day work

per day

Hence, we see that A, D is first pair B,C is second 45. (d) We know every year has 1 odd days and leap year has 2 odd days Total number of years = 30 Here, no. of normal years = 22 And no. of leap years = 8 So, total no. of odd days between 9/ 12/ 71 and 9/ 12/ 2001 = 22 + 16 = 38 i.e., 3 odd days (remainder when 38 is divided by 7,i.e., 3) Hence, it was a Thursday 46. (d) Time taken in downstream = Time taken in upstream – 6 hr. Let his speed be x in normal water and speed of current be y Then,

.....(i) ......(ii)

[from (i)] [from (ii)]

Subtracting, 3x2 = 20y or Putting x2 in 4y = x2 – y2 or 47. (b) If Shyama takes 1 minutes for every 3 steps, then she takes 1/3 minutes for every step. For 25 steps, he takes 25/3 minutes = 8.33 minutes. So, Vyom takes

minutes for every step.

For 20 steps, he takes 10 minutes. Difference between their times = 1.66 minutes Escalator takes 5 steps in 1.66 minutes. Speed of escalator is 1 step for 0.33 minutes = 3 steps per minutes. If escalator is moving, then Shyam takes 25 steps and escalator also takes 25 steps. Hence, total number of steps = 50. 48. (c) Let the time taken by Asit, Arnold and Afzal to do the work alone be x, y and z hrs respectively. Therefore, time taken to do the work together is

In one hour, they can together do of the work. Therefore,

total

work

can

completed

them

Now, put y = x – 5 and z = 2 (x – 6) in the above equation and solve for x. We get x = 20/3 hrs.

Hence, time taken by them to complete the work when working together = 49. (a) ← 11.00 am Y X 11.00 a.m. → Time taken by Y for distance cover from B to C with stoppages

Say they cross each other at x distance from A

∴

= 112.29

112 km

50. (b) Let L be length in metres of the race which A finishes in t seconds. Speed of A =

m/s; speed of B =

m/s and

speed of C = Time taken by B to finish the race =

seconds

In this time, C covers (L – 8) m.

51. (b) We have been given a graph of fuel consumption versus speed At 60 km / hr time taken

and fuel consumption is 4 litres / hr.

from graph. Petrol consumed

= 13.33 litres

52. (b) For consumption to be less say at 40 km/ hr, time= 5 hrs. So, consumption = 2.5 × 5 = 12.5 litres at 80 km/hr, time = 2.5 hr, consumption = 7.4 × 2.5 which is high So for consuming lesser petrol she should decrease the speed. 53. (d) 6 technicians take 10 hours to complete the work 1 technician take 60 hours to complete work 1 hour work of 1 technicians complete

part of work

6 hours (11:00 to 5:00) work of 1 technician complete part of work 6 hours (11:00 to 5:00) work of 6 technicians

part of work

6 technicians work together 6 hours (11:00 to 5:00), therefore, they have completed Remaining work after 5:00 pm

part of work part of work

Now, one technician per hour is added beginning at 5:00 pm. Therefore, 7 technicians.

Work between 5:00 pm to 6:00 pm 8 technicians work between 6:00 to 7:00 pm complete part of work Total work after 5:00 pm ∴

technicians

work

part of work between

7:00

8:00

Total work up to 8:00 pm Hence, remaining work after 5:00 pm that is

part is

completed up to 8:00 pm 54. (b) Suppose large pump takes t hours to fill a tank ∴ 1 hour work of large pump fills

part

1 hour work of each small pump fills 1 hour work of all 4 pumps fill Therefore, ∴

Whole

part is filled by all 4 pumps in 1 hour tank

would

filled

this is 1/3 of the

time taken by large pump i.e., t hour

55. (d) To transport first stone S1 to Y, worker travel a distance = 100 m, now he returns at S2 To transport S2 worker travels a distance = 2 × 98 m To transport S3 worker travels a distance = 2 × 96 m To transport S4 worker travels a distance = 2 × 94 m To transport S5 worker travels a distance = 2 × 92 m Total distance covered = 100 + 2(98 + 96 + 94 + 92) = 100 +2(380) = 100 + 760 = 860 56. (d) Let speed of normal express train be e then speed of passenger train will be e/2 and speed of super fast train will be 2e According to question

on a particular day speed of super fast train = 4e on a particular day speed of passenger train

Required ratio

or 1 : 6 ( approx ) [if ratio be 1 : 5 then train will not reach]

57. (c)

Time to reach Time from A to G1 = 5 minutes Time from Time elapsed at G3 = 1 minutes Total time from A to G3 & G3 to A = 5 + 15 + 1 + 17.5 = 38.5 minutes The time for doctor = 40 – 38.5 = 1.5 minutes 58. (c) He drove 30 km and paid 300 rupees according to the rate Rs 12 per km rent be 12 × 30 = Rs 360 but he paid Rs 300 So, he rented the car according to second condition i.e. Rs 50 per hour Rent hours 59. (b) Let speed of cat be s and speed of train be t. If train catch the cat then, distances would be travelled in the same time If train catches the cat at A then, If train catches the cat at B then,

or or or 60. (c) Since the speed is double, the fastest runner will complete 200 m and the slowest runner will complete 100 m. Let x m/minute be the speed of the slowest runner.

Time taken

or x

= 200. Speed of the fastest runner = 2 × 200 = 400 m/min ∴ Time taken by the fastest runner = 4000/400 m = 10 min Alternatively : This question can be solved verbally. The first line clearly says that the fastest runner is one round ahead after 5 min. Further he runs at twice the speed, which again means that they have met at the starting point only after 5 min. i.e. the fastest runner runs 2000 m in 5min hence he would run 4000 m in10 min. 61. (d) Let length of each chord be x Radius of I R = r. So, radius of OR = 2r In ∆N2OE1,

∴ length of chords = He travels one chord and one semi-circle. ∴ Time =

Minutes

62. (c) Amit travel one quarter circle of OR and one chord. Dividing by speed, we get,

Solving, we get r = 15 and 2r = 30 kms

63. (c) Required ratio =

64. (a) Let, CD be the tower of length and A and B, the two points Let velocity be v, and required time be x Then,

65. (a) Let the sprinters run distances of a, b, c which are nothing but the perimeter of their respective triangles. A1 A2 = 2r; B1 B2 = 2r + r√3; C1 C2 = 2r + 2r√3

⇒ b – a =3√3r .....(i) ⇒ c – a = 6√3r .....(ii) Subtracting (i) from (ii) we get, c – b = 3√3r

66.

= B1 B2 + B2B3 + B3B1 Therefore, B will be at B1 Now time taken by C for each distance are

≡ i.e., or We can observe that time taken for C1 C2 and C2 C3 combined is

Which is same as time taken by A Therefore, C will be at C3. 67. (b) In similar triangles, ratio of Area = Ratio of squares of corresponding sides. Hence, A and C reach A3 and C3 respectively. 68. (b) Time difference = = 69. (d) When Karan runs 100m, Arjun runs only 90m So, in the new situation,

Karan has to run 110 m Hence, distance covered by Arjun when Karan covers

Therefore, Karan beats Arjun by 1m 70. (b) Let distance be d and time taken to cover this distance at speed of 10 km/h be x. Then,

or d = 10x

....(i)

Similarly, or From (i) and (ii) : 10x = 15x – 30

d = 15x – 30

....(ii)

5x = 30 x = 6 hrs and d = 60 km

To reach at noon (i.e. 12 pm), he should cycle for 5 hrs. So, required speed 71. (c) Relative speed of the boats = 15 km/ hour km/min i.e., they cover minute before collision. 72. (c) Machine I : Time to produce 9000 nuts

Machine II : Time to produce 9000 bolts

km in the last one

So minimum time required for the production of 9000 nuts and bolts = 170 minutes. 73. (c) Water entering (positive sign) or leaving (negative sign) representation : Tank A = (90 – 20 – 10) = 60 litres/min. Tank B = (110 – 100 + 20) = 30 litres/min. Tank C = (100 – 90 – 50) = –40 litres/min. Tank D = (10 + 50 – 110) = –50 litres/min. Hence, Tank D gets emptied first. Time taken by tank D to get empty = 74. (b) Ram starts at 9:00 a.m. from A and reaches B in 1 hr.(@ 5 km/hr.) i.e., 10:00 a.m. At 10:00 a.m., Shyam covers ∴ Time required for Ram and Shyam to meet =

Hence, they first meet at 10:00 a.m. + 10 min = 10:10 a.m. 75. (b) Ram reaches at B at 10.00 a.m. and Shyam reaches at B at 10:15 a.m. For Ram to overtake Shyam, time required (taking 10:00 a.m. as base)

Hence, Shyam overtakes Ram at 10:00 am + 30 min. = 10:30 am

76. (c) Barun starts 2 hours after Arun in which Arun covers 30 × 2 = 60 km Barun catches up with Arun in

hours, i.e. after 8 hours

from Arun’s start. Now, distance traveled by Arun = 8 × 30 = 240 hours Further Kiranmala will cover this 240 km in

hours.

So, she shall start 4 hours after Arun starts. 77. (a) Let the speed of the plane = x km/hr And time difference between A and B = y hr [This means that when 4.00 p.m. at A then (4 + y).00 p.m. at B] According to the question, ...(i) and

...(ii)

On solving equation (i) and (ii) for y, we get y = 1 78. (c) From,

and

...(i)

...(ii)

On solving equation (i) and (ii) for x, we get x = 550

79. (b) ∆ABC is right angled at C. sin60°

km,

cos60°

∴ BC = 250 km

Time taken by the train to reach C from B So, the train reach the C at 1 p.m. Time taken by Rahim to reach C from A

= 6 hr 11 min.

So, to reach C before atleast 15 min. before 1 p.m. i.e., 12.45 pm, Rahim should start at 6.30 a.m. 80. (d) Let’s assume that each worker completes W units of the job in a day. The number of units completed by 10 workers in 10 days = 10 × 10 = 100W. If one more worker joins them, then the number of units completed on the 11th day will be 11W. As it took exactly 20 days to finish the job, it can be concluded that the job consisted of (100W + 11W + 12W + .... + 20W) = 255W units of work. In the second situation, let the number of workers who started the job be n. Hence, nW + (n – 1)W + (n – 2)W + ... + W ≥ 255W or The minimum possible value of n which satisfies the above inequality is 23. However, it must be noticed that 23 + 22 + 21 + … + 7 = 255. Hence, the work will get completed in exactly 23 – 6 = 17 days.

81. (b)

Let the speeds of Tarun and Sumit be 2x and 5x respectively. Let’s assume that Sumit turned back from point Q as shown in the figure given below, ran at a speed of x after turning back and met Tarun at point R, ‘t’ hours after they started running.

From the given conditions, 2x × t = 10 = 5x × 2 – x × (t – 2) ⇒t=4 So the running speed of Tarun

82.

(c) Rahul will come to rest after 20 seconds. The combined distance covered by them every second is 60 m. Since the track length is 120 m, they will meet after every 2 seconds. So they would have met 10 times by the time Rahul comes to rest. 83. (b) Assume that the software fails a, b, and c times in a single stage, in two stage, and in all stages respectively. ∴ b + 3c = 6+ 7 + 4 = 17 but c = 4, hence b = 5 Similarly, we have a + 2b + 3c = 15 + 12 + 8 = 35 a = 35 – 12 – 10 = 35 – 22 = 13 84. (d) The watch gains (5 + 10) = 15 min in 30 hours (12 Noon to 6 PM next day). This means that it will show the correct time when it gains 5 min in 10 hours or at 10 PM on Monday. 85. (d) Total time taken to build the server = 60 man hours. 6 of them starts at 11 : 00 am and works till 5 pm They will complete 6 × 6 = 36 man hours of work. At 5 pm they will have 24 more man hours of work to complete. Between 5 pm and 6 pm they will complete 7 man hours.

Between 6 pm and 7 pm they will complete 8 man hours. Between 7 pm and 8 pm they will complete 9 man hours. So, totally they will complete 36 + 7 + 8 + 9 = 60 man hours by 8 pm. 86. (a) Rate of admission of water =

tonnes / min. =

tonnes/ min

Rate of pumping out of water =

tonnes/min. =

tonnes/ min.

Rate of accumulation =

tonnes / min.

Time to accumulate 80 tonnes of water =

= 600 min.

= 10 hours Average sailing rate so as avoid sinking =

km/ h = 5.5 km/h

87. (c) Let the slowest runner covers a distance of x ms. from the starting point. Then the fastest runner will cover a distance of 1000 + x from the starting point. Let the speed of the slowest runner be y. Then, speed of the fastest runner will be 2y. Slowest Fastest S:y 2y D:x 1000 + x

But time taken for both is same . Hence, ∴ Fastest runner completes a distance of 2000m in 5 mins. ∴ Fastest runner can complete a distance of 4000m in 10 min. 88. (c) Let the length of train = x metres Speed =

m/sec =

m/sec

Distance covered in crossing the platform = (x + 100) m ∴ (x + 100) ×

= 60

or 2x + 200 = 1500 or x = 650 Now, time taken to cross the pole = 89. (b)

Area of cross section for P1 pipe

= A1 =

= 154 m2

Volume of water flowing through P1 in one second = 154 × 10 = 1540 m3 Volume of tank = V = 1540 × 2 × 3600 = 11088 × 103 m3 Area of cross section for P2 pipe = A2 =

= 616 m2

Let the rate of water flowing through P2 = s m/s

Volume of water flowing through P2 in one second = 616s m3 Volume of water flow in the tank when P1 is used as inlet and P2 is used as outlet pipe: (1540 – 616s) Time taken to fill = 4 hours = 4 × 3600 seconds So, (1540 – 616s) × 4 × 3600 = V ⇒ (1540 – 616s) × 4 × 3600 = 11088 × 103 or 1540 – 616s= 770 or s = 1.25 m/s ∴ Rate of water flow through P2 = 1.25 m/s 90. (d)

Let the time at which Mr. Clockilal entered the museum be ‘m’ minutes past 12 noon. ∴

= 20 ⇒ m =

As he spent more than 3 hours and less than 4 hours in the museum, and the angle between the minute and hour hands at the time of leaving was 220°, he must have left the museum between 3 :

p.m. and 4 p.m.

Let the time at which he left the museum be ‘n’ minutes past 3 pm. ∴

= 220 ⇒ n = 56

or 41

Hence, the time spent by Mr. Clcckilal in the museum was either 3 hours 91.

minutes or 3 hours

minutes.

(d)

Let the efficiencies of Anirudh and Anushka be ‘a’ and ‘b’ units/day respectively. according to question, ∴ (a + b) x + a × So, the required ratio is 1 : 1.

= (a + b)

92. (b)

The rabbit overstretched his sleeping time by

min.

= 14 + t ⇒ t = 12

∴

Let the speed (in km/min) of the rabbit and tortoise be 6x and x respectively. Had the rabbit not overstretched his hap, he would have beaten the tortoise by 13 min. ∴

⇒x=

Hence the time taken by the tortoise to complete the race = = 30 min. 93.

(d)

The distance covered by R in 2 hours (3 PM to 5 PM) is same as the distance covered by P in 4 hours (1 PM to 5 PM). Ratio of speeds of P and R = 1 : 2. Now, R takes over Q in another hour by doubling his speed, so R has covered a total distance in 3 hours (3 PM to 6 PM) which he would have covered in 4 hours without changing his speed. To cover the same distance, a takes 5 hours (1 PM to 6 PM) Ratio of speed of Q and R = 4: 5 ⇒ Ratio of speed of P and Q = 5: 8.

94. (b) Let’s take there are two ants. Considering worst possible case we can see easily the required time is same as the time taken by an ant to reach one extreme point to another extreme point. Which will be same when there are 1000 ants. i.e.maximum time =

min. = 2 min.

95. (16) Let the distance be x According to question, ∴ 15 +

x = 3780 Total time taken by the second boat =

= 960 sec = 16 min.

96. (a) Let BC = 5 k Given, by the time Q reaches C, P was halfway to C, i.e., AC/2 = 3k and AC = 6k. As Q met P, 165 km away from A, the distance to the meeting point from A is 3k i.e., Given,

⇒ k = 40

∴ Distance between A and C is 240 km and that between B and C is 200 km. From the data, as distance between A and B is twice that between B and C, it is 400 km. ∴ Speed of P = ⇒ Speed of ∴

Time

kmph = 100 kmph

taken

reach

C hr.

97. (15) Work

from

⇒ [1 + 2 + 3 + ... n] = 1

⇒

⇒ ∑n = 120

⇒

= 120

⇒ n = 15 98. (20)

⇒

⇒ T=

D = S×(T + 1/6) D = 12

= 20 km

99. (b) Let the speed of the boat in still water and the speed of the river be u and v respectively u=x v=y According to question,

or u : v = : 2

1. II. (a) (b) (c) (d) 2.

(a) (b) (c) (d) 3.

(a) (b) (c) (d) 4.

I. The probability of encountering 54 Sundays in a leap year (1994) The probability of encountering 53 Sundays in a non-leap year I > II I < II I = II Nothing can be said A,B,C and D are four towns any three of which are non-colinear. Then the number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is (1995) 7 8 9 More than 9 Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects? (1995) 8 10 15 22 A man has nine friends – four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the

invitees? (1996) (a) 320 (b) 160 (c) 80 (d) 200 5. In how many ways can the eight directors, the vice-chairman and the chairman of a firm be seated at a round-table, if the chairman has to sit between the vice-chairman and the director? (1997) (a) 9! × 2 (b) 2 × 8! (c) 2 × 7! (d) None of these 6. ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B? (1997) (a) 9 (b) 7 (c) 4 (d) 2 7. How many numbers can be formed from 1,2,3,4 and 5 (without repetition), when the digit at the units place must be greater than that in the tenth place? (1998) (a) 54 (b) 60 (c)

(d) 2 × 4! 8. How many five digit numbers can be formed using 2,3,8,7,5 exactly once such that the number is divisible by 125? (1998) (a) 0 (b) 1 (c) 4 (d) 3 9. A, B, C, D, ..................X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 points. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, the ranking list is published which is in accordance with the alphabetical order. Then (1998) (a) M wins over N (b) N wins over M (c) M does not play with N (d) None of these 10. Five persons A, B, C, D and E along with their wives are seated around a round table such that no two men are adjacent to each other. The wives are three places away from their husbands. Mrs. C is on the left of Mr. A, Mrs. E is two places to the right of Mrs. B. Then, who is on the right hand side of Mr. A? (1999) (a) Mrs.B (b) Mrs.D (c) Mrs. E (d) Either Mrs B or Mrs D 11. There are 10 points on a line and 11 points on another line, which are parallel to each other. How many triangles can be drawn taking the vertices on any of the

line? (1999) (a) (b) (c) (d) 12.

(a) (b) (c) (d) 13.

(a) (b) (c) (d) 14.

(a) (b) (c)

1,050 2,550 150 1,045 There are three boxes with 2 red, 2 white and one red and one white ball. All of them are mislabelled. You have to correct all the labels by picking only one ball from any one of the boxes. Which is the box that you would like to open (1999) White Red Red & White None of these Out of 2n+1 students, n students have to be given the scholarships. The number of ways in which at least one student can be given the scholarship is 63. What is the number of students receiving the scholarship? (1999) 5 7 3 9 Sameer has to make a telephone call to his friend Harish Unfortunately he does not remember the 7- digit phone number. But he remembers that the first 3 digits are 635 or 674, the number is odd and there is exactly one 9 in the number. The minimum number of trials that Sameer has to make to be successful is (2000) 10, 000 3,402 3,200

(d) 5,000 15. There are three books on table A which has to be moved to table B. The order of the book on Table A was 1, 2, 3, with book 1 at the bottom. The order of the book on table B should be with book 2 on top and book 1 on bottom. Note that you can pick up the books in the order they have been arranged. You can’t remove the books from the middle of the stack. In how many minimum steps can we place the books on table B in the required order? (2000) (a) 1 (b) 2 (c) 3 (d) 4 16. X is an odd integer such that 100 < x < 200 and x is divisible by 3 but not 7. The possible number of values of x is (2000) (a) 16 (b) 15 (c) 14 (d) 13 17. One red, three white and two blue flags are to be arranged in such a way that no two flags of the same colour are adjacent and the flags at the two ends are of different colours. The number of ways in which this can be done is (2000) (a) 6 (b) 8 (c) 4 (d) 12 Directions for questions 18 to 21 : Read the information given below and answer the questions that follow : The tournament for ABC Cup is arranged as per the following rules: in the beginning 16 teams are entered and divided in 2

18.

(a) (b) (c) (d) 19. (a) (b) (c) (d) 20. (a) (b) (c) (d) 21. (a) (b) (c) (d)

groups of 8 teams each where the team in any group plays exactly once with all the teams in the same group. At the end of this round top four teams from each group advance to the next round in which two teams play each other and the losing team goes out of the tournament. The rules of the tournament are such that every match can result only in a win or a loss and not in a tie. The winner in the first round takes one point from the win and the loser gets zero. In case of tie on a position the rules are very complex and include a series of deciding measures. What is the total number of matches played in the tournament? (2000) 63 56 64 55 The maximum number of matches that a team going out of the tournament in the first round itself can win is (2000) 1 2 3 4 The minimum number of matches that a team must win in order to qualify for the second round is (2000) 4 5 6 7 Which of the following statements about a team which has already qualified for the second round is true? (2000) To win the cup it has to win exactly 14 matches To win the cup it has to win exactly 3 matches To win the cup it has to win exactly 4 matches To win the cup it has to win exactly 5 matches

22. There are five boxes each of a different weight and none weighing more than 100. Arun weights two boxes at a time and obtains the following readings in grams : 110, 112, 113, 114, 116, 117, 118, 119, 120, 121. What is the weight of the heaviest box? (2000) (a) 60 (b) 61 (c) 64 (d) can’t be determined 23. A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the time, how many times do they flash together in each hour? (2001) (a) 30 (b) 24 (c) 20 (d) 60 24. Ashish is given Rs. 158 in one rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required? (2001) (a) 11 (b) 12 (c) 13 (d) None of these 25. The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F? (2001)

(a) (b) (c) (d) 26.

9 10 11 None of these Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5, and 6, no digit being repeated in the numbers. What is the value of n? (2001) (a) 144 (b) 168 (c) 192 (d) None of these 27. 10 straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is (2002) (a) 56 (b) 255 (c) 1024 (d) not unique Directions for questions 28 & 29 : Read the information given below and answer the questions that follow : Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters.

28. How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)? (2002) (a) 7920 (b) 330 (c) 14640 (d) 419430 29. How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? (2002) (a) 990 (b) 2730 (c) 12870 (d) 15600 30. In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lie in the same row or column? (2002) (a) 56 (b) 896 (c) 60 (d) 768 31. How many numbers greater than 0 and less than a million can be formed with the digits of 0, 7 and 8? (2002) (a) 486 (b) 1086 (c) 728 (d) None of these 32. If there are 10 positive real numbers n1 < n2 < n3 ... < n10. How many triplets of these numbers (n1, n2, n3), (n2, n3, n4), ... can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number? (2002)

(a) (b) (c) (d) 33.

34.

(a) (b) (c) (d) 35.

(a) (b) (c) (d) 36.

45 90 120 180 An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group? (2002) Twenty-seven persons attend a party. Which one of the following statements can never be true? (2003C) There is a person in the party who is acquainted with all the twenty-six others Each person in the party has a different number of acquaintances There is a person in the party who has an odd number of acquaintances In the party, there is no set of three mutual acquaintances How many three digit positive integers, with digits x, y and z in the hundred’s, ten’s and unit’s place respectively, exist such that and ? (2003C) 245 285 240 320 There are 6 boxes numbered 1,2,.........6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is (2003C)

(a) (b) (c) (d) 37.

5 21 33 60 A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any other point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition (2003C) (a) (b) (c) (d) Directions for questions 38 & 39 : Read the information given below and answer the questions that follow : A string of three English letters is formed as per the following rules : (a) The first letter is any vowel. (b) The second letter is m, n or p (c) If the second letter is m then the third letter is any vowel which is different from the first letter (d) If the second letter is n then the third letter is e or u. (e) If second letter is p then the third letter is the same as the first letter. 38. How many strings of letters can possibly be formed using the above rules? (2003) (a) 40 (b) 45 (c) 30 (d) 35 39. How many strings of letters can possibly be formed using the above rules such that the third letter of the string is e? (2003)

(a) (b) (c) (d) 40.

(a) (b) (c) (d) 41.

(a) (b) (c) (d) 42.

(a) (b) (c)

8 9 10 11 There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? (2003) 72 90 96 144 An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, ............ , 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion when read upside down –– for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise? (2003) 80 78 71 69 N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N? (2004) 5 7 9

(d) None of the above 43. Suppose n is an integer such that the sum of the digits of n is 2, and 1010 < n < 1011. The number of different values for n is (2004) (a) (b) (c) (d) 44.

(a) (b) (c) (d) 45.

11 10 9 8 Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is (2004) 4 5 2 3 In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A? (2004)

(a) 15 (b) 56

(c) 120 (d) 336 46. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour out is (2004) (a) 12 × 81 (b) 16 × 125 (c) 20 × 125 (d) 24 × 216 47. In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is (200 5) (a) 200 (b) 216 (c) 235 (d) 256 48. Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose? (2005) (a) 5 (b) 10 (c) 9

(d) 15 49. Let S be the set of five-digit numbers formed by the digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd positions are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S? (2005) (a) 228 (b) 216 (c) 294 (d) 192 50. Let n! = 1 × 2 × 3 × ..... × n for integer If p = 1! + (2 × 2!) + (3 × 3!) + ..... + (10 × 10!), then p + 2 when divided by 11! leaves a remainder of (2005 - 2 marks) (a) 10 (b) 0 (c) 7 (d) 1 51. Let S be a set of positive integers such that every element n of S satisfies the conditions 1. 2. every digit of n is odd Then how many elements of S are divisible by 3? (2005 2 marks) (a) 9 (b) 10 (c) 11 (d) 12 52. There are 6 tasks and 6 persons. Task I cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done? (2006)

(a) (a) (c) (d) (e)

144 180 192 360 716 Directions for Questions 53 & 54 : Let S be the set of all pairs (i, j) where and . Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies. 53. For general n, how many enemies will each member of S have? (2007) (a) (b) n – 3 (c) (d) 2n – 7 (e) 54. For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members? (2007) (a) (b) (c) 2n – 6

(d) (e) n – 2 55. In a tournament, there are n teams T1, T2, ..., Tn, with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common: T1 & T2, T2 & T3,..., Tn–1 & Tn, and Tn & T1. No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together? (2007) (a) (n – 1)(k – 1) (b) n(k – 1) (c) k(n – 1) (d) n(k – 2) (e) k(n – 2) 56. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos? (2007) (a) 19 (b) 17 (c) 16 (d) 18 (e) 15 Directions for Questions 57 & 58 : The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

57. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is (2008) (a) 60 (b) 75 (c) 45 (d) 90 (e) 72 58. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is (2008) (a) 1170 (b) 630 (c) 792 (d) 1200 (e) 936 59. A man, while driving to his office, finds three traffic signals on his way. The probability that the traffic light is red when he reaches the first, second and third traffic signal is respectively. What is the probability that he finds at least one traffic light on his way which is not red? (2009)

(a) (b) (c) (d) 60. A and B throw with one dice for a stake of Rs. 11 which is to be won by the player who first throws 6. If A has the first throw, what are their respective expectations (2009) (a) Rs 7, Rs 4 (b) Rs 6, Rs 5 (c) Rs 4, Rs 7 (d) Rs 5 , Rs 6 61. In how many ways can 6 letters A, B, C, D, E and F be arranged in a row such that D is always somewhere between A and B? (201 0) (a) 324 (b) 240 (c) 60 (d) 48 62. A cube is painted with red colour and then cut into 64 small identical cubes. If two cubes are picked randomly from the heap of 64 cubes, what is the probability that both of them have exactly two faces painted red? (2010) (a) (b)

(c) (d) 63. A box contains five yellow and five green balls. A ball is picked from the box and is replaced by a ball of the other colour. For instance, if a green ball is picked then it is replaced by a yellow ball and vice-versa. The process is repeated ten times and then a ball is picked from the box. What is the probability that this ball is yellow? (2011) (a) (b) (c) (d) None of these 64. What is the probability that the product of two integers chosen at random has the same unit digit as the two integers? (2012) (a) (b) (c) (d) 65. In how many ways can 18 identical candies be distributed among 8 children such that the number of candies received by each child is a prime number? (2013)

(a) 4

(b) 8 (c) 28 (d) 12 66. There are exactly sixty chairs around a circular table. There are some people sitting on these chairs in such a way that the next person to be seated around the table will have to sit next to someone. What is the least possible number of people sitting around the table currently? (2014) (a) (b) (c) (d) 67.

10 20 30 40 If p is the probability of head turning up in the toss of a coin (not necessarily fair) and q is the probability of a tail turning up. Find the

(a) (b) (c) (d) 68.

(a) (b) (c) (d) 69.

minimum

possible

value

. (2014) 4.25 2 2 None of these Amar, Akbar and Antony are three students in a class of 9 students. A class photo is taken. The number of ways in which it can be taken such that no two of Amar, Akbar and Antony are sitting together is: (2014) 151200 120960 181440 241920 Three persons - A, B and C - are playing the game of death. 3 bullets are placed randomly in a revolver having 6 chambers. Each one has to shoot himself by pulling the trigger once after which the revolver passes to the next person. This process

continues till two of them are dead and the survivor of the game becomes the winner. What is the probability that B is the winner if A starts the game and A, B and C take turns in that order.

(a)

(2015) 0.33

(b) 0.3 (c) 0.25 (d) None of these 70. If we arrange the letters of the word ‘KAKA’ in all possible ways, what is the probability that vowels will not be together in an arrangement? (2015) (a) (b) (c) (d) 71. The first n natural numbers, 1 to n, have to be arranged in a row from left to right. The n numbers are arranged such that there are an odd number of numbers between any two even numbers as well as between any two odd numbers. If the number of ways in which this can be done is 72, then find the value of n. (2016) (a) 6 (b) 7 (c) 8 (d) More than 8 1.

(b) There are 5 weeks and 2 days in a leap year. Therefore, 53 Sundays can occur if 1st of Jan is either a Saturday or a Sunday, but 54 Sundays cannot be their in a

leap year. (d) To construct 2 roads, three towns can be selected out of 4 in 4 ×3×2 = 24 ways. Now if the third road goes from the third town to the first town, a triangle is formed, and if it goes to the fourth town, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding a triangle. (d) Each box can be filled in 2 ways. Hence, total no. of ways = 25 = 32 Blue balls cannot be filled in adjacent boxes Total no. of such cases in which blue ball is filled in 2 adjacent boxes is 2 blue + 3 blue + 4 blue + 5 blue = 4 ways ( 12, 23, 34, 45) + 3 ways ( 123, 234, 345) + 2 ways (1234, 2345) + 1 way = 10 ways Hence, total cases in which blue balls can not be filled in adjacent boxes = 32 – 10 = 22 (b) Out of five girls, he has to invite exactly 3. This can be done in 5C3 ways. Out of 4 boys he may invite either one or two or three or four or none of them. This may be done in = (1 + 1)4 = 24) ways. Hence, the total number of ways in which he can invite his friends are

(b) Let the vice-chairman and the chairman from 1 unit along with the eight directors, we now have to arrange 9 different units in a circle. This can be done in 8! ways. At the same time, the vice-Chairman & the chairman can be arranged in two different ways. Therefore, the total number of ways = 2 × 8!.

(c) Seeing the options. Since 7! = 5040 and 9! = 362880 are four and 6 digit numbers respectively, hence, B can’t be 7 or 9. 3 digits number will be of the form 100 A + 10 B + C. ∴ 100A + 10B + C = A! + B! + C! Now by hit & trial method i.e., with B = 2 and B = 4 find which one is better. Hence, B = 4, A = 1 , C = 5 7. (b) The numbers should be formed from 1, 2, 3, 4 and 5 (without repetition), such that the digit at the units place must be greater than in the tenth place. Tenth place has five options. If 5 is at the tenth place then the digit at the unit’s place cannot be filled by the digit greater than that at the tenth place. If 4 is at the tenth place, then the unit’s place has only option of 5, while the three places can be filled up in 3! Ways. If 3 is at the tenth place, then the units’ place can be filled up by 4 or 5, i.e. in 2 ways. While other three places can filled up in 3! ways. If 2 is at the tenth place, then the unit’s place can be filled up by 3, 4 or 5 i.e. in 3 ways. While other three places can be filled up in 3! Ways. If 1 is at the tenth place, then any other four places can be filled up in 4! Ways. Thus the total number of numbers satisfying the given conditions is 0 + 3! + 2(3!) + 3(3!) + 4! = 60. 8. (c) Only those numbers which last 3 digits are divisible by 125 are divisible by 125. So, those contain 375 & 875 at the end and the remaining two digits at the unit and tenth places can be arranged in two different ways. Therefore, 4 such number can be formed. 9. (a) Each one of the 26 players played 25 matches and none of the matches ended in a draw.

Hence, all the scores must be even. Also each one of them scored different from the other. The maximum score possible is 50 and minimum score is 0. There are exactly 26 possible scores, 50, 48, 46 .....0. The ranking is in a alphabetical order means A scored 50, B – 48, Z – 0. This is possible if A wins all the matches B loses only to A win against all others etc. In final rank, every player win only with all players who are below in final ranking . Since M > N hence M wins over N.

10. (d)

Since no two men are adjacent to each other, therefore no male is on the right of Mr. A. Since wives are three places away from their husbands, therefore Mrs. A cannot be on the right of Mr. A. Mrs. E cannot be on the right of Mr. A, since Mrs. B cannot be on left of Mr. A. Hence, either Mrs. B or Mrs. D can be on the right of Mr. A. 11. (d) For a triangle, two points on one line and one on the other has to be chosen. No. of ways = . 12. (c) Since all are mislabeled open red / white. Now, if red comes out then both are red in the box. And now change the label, make the box as all red. Now change all white in red / white and all red into all white. Labels are now correct.

If white comes out then both are white in the box. And now change the label, make the box as all white. Now change all red in red / white and all white into all red. Labels are now correct. 13. (c) No. of ways in which at least one student can be given the scholarship = 63

[Since coefficients of binomial expansion equidistant from begining and end are equal]

14. (b) There are two ways of selecting 635 or 674. If last digit is 9 , then there are 9 ways of filling each of the remaining 3 digits. Thus total no. of this type of numbers = 2 × 93 = 1,458. When last digit is not 9, total no. of this type of numbers = 2 × 3 × 4 × 92 = 1944. [9 can be selected at any of the 4th, 5th or 6th place in 3 ways. Also at the unit place 4 odd nos. except 9 can be used.] Thus required no. = 1,944 + 1,458 = 3,402 15. (d) First step — take book 3 to the table B and, second step — put the book 2 on top of 3. Third step — Transfer the arrangement and keep it over book 1 on table A. The last

16.

17.

18.

19.

20. 21. 22.

step is transfer the whole arrangement to the table B which is the fourth step to take. Thus total 4 steps are required. (d) Between 100 and 200 no.of multiple of 3 are 102 , 105........,198 these when are counted We find 33 such numbers And out of these 16 are odd. But 105, 126, 147, 168, 189 are multiple of 21. And three of these are odd. Thus required no. = 16 – 3 = 13 (a) There are three white flags and ends having different colours, the only possibility at the ends are red and white or white and blue. W___W___W___ the empty spaces can be filled in 3 ways by one red and two blue flags. ___W___W___W again the empty spaces can be filled in 3 ways so, the total number of ways will be 6. (a) In the first round, total no of matches = 2 × (7 + 6 + 5+ 4 + 3 + 2 + 1) = 56. In the second round total no. of matches = 4 Therefore are 2 semifinals & one final. Thus total no. of matches played in the tournament= 63 (c) Each team will play 7 matches and so any team can win any no. of matches between 0 to 7 (i.e. 0, 1, 2, 3, 4, 5, 6, 7). Four teams will be selected (Who win either 7, 6, 5, or 4 matches). Thus team which wins maximum 3 matches will be out of the first round (a) From the above question minimum number of matches that a team must win in order to qualify for second round is 4. (b) In second round; it has to win three matches, one in quater final, one in semifinal and one in final. (b) We will get 10 values because 5C2 = 10. Let A, B, C , D and E be the boxes in ascending order of their weights. Then the largest value of 10 weights is 121and D + E = 121 Similarly, we have C + E = 120, A + B =110 and A + C = 112

...(i) We know that 4 (A + B + C + D + E) = 1160 ⇒ A + B + C + D + E = 290 ∴ From (i), But A+ C = 112 23. (a) Red light flashes 3 times / min. i.e after every20 seconds. Green light flashes 5 times in 2 min. i.e. after every24 seconds. So, they flash together after every 2 minutes = 120 seconds (L.C.M. of 20 & 24 = 120) Hence, in 1 hour they flash together 60/2 = 30 times 24. (d) Minimum number of bags we have to allocate them in such a way that we get all the numbers i.e., 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 Hence, minimum no. of bags required is 8; having number of coins 25. (b) Paths from A to F are ABCF, ADEF, ABEF, ADCF, ABDEF, ABDCF, ABDCEF, ABCEF, ADCEF and ABF Hence, 10 possible distinct roots. 26. (c) For a number to be divisible by 4, its last two digits should be divisible by 4. i.e., the last two digits should be 12, 16, 24, 32, 36, 52, 56 or 64. No. of numbers end with 12 = = 24 Similarly number of numbers end with 16, 24, 32, 36, 52, 56 or 64 each = 24. Thus, value of n = 24 × 8 = 192 27. (a) For 2 such lines, no. of regions formed are 4 For 3 lines no. of regions formed are 7 (= 4 + 3) For 4 lines, no. of regions formed are 11 (= 7 + 4) For 5 lines no. of regions formed are 16 (= 11 + 5)

Similarly for 6, 7, 8, 9 and 10 lines, no. of regions are 16 + 6 = 22 22 + 7 = 29 29 + 8 = 37 37 + 9 = 46 46 + 10 = 56 ∴ For 10 lines no. of regions = 10C2 + 10 + 1 = 45 + 11 =56 28 (a) Four letter passwords have four places of which 1st place can be filled in 11 ways 2nd place can be filled in 10 ways 3rd place can be filled in 9 ways 4th place can be filled in 8 ways Total passwords formed = 11× 10 × 9 × 8 = 7920 29. (c) Total three-letter computer passwords from any of the 26 letters = 26 × 25 × 24 Again, three letter passwords from asymmetric letters= 15 × 14 × 13 ∴ Passwords with atleast one symmetric letter = 26 × 25 × 24 – 15 × 14 × 13 = 12870 30. (d) There are 32 black and 32 white squares on a chess board. Then no. of ways in choosing one white and one black square on the chess = There are 8 rows and 8 columns on a chess board. In each row or column, there are 4 white and 4 black squares. Therefore number of ways to choose a white and a black square from the same row = = 128 No. of ways to choose a white and a black square from the same column Total ways in which a white and a black squares lie on the same row or same column = 128 + 128 = 256 Hence, required no. of ways = 1024 – 256 = 768

31. (c) No. of 1 digit numbers = 2 No. of 2 digit numbers = 3 × 2 = 6 No. of 3 digit numbers = 3 × 3 × 2 =18 No. of 4 digit numbers = 33 × 2 = 54 No. of 5 digit numbers = 34 × 2 = 162 No. of 6 digit numbers (less than a million) = 35 × 2 = 486 ∴ Required numbers = 486 + 162 + 54 + 18 + 6 + 2 = 728 32. (c) If n1 at the first place and n2 at the second place in one triplet, then the number at the third place may ben3, n4, n5, n6, n7, n8, n9 or n10 (any one number out of the remaining 8 numbers i.e. 8 ways) We can represent it as (n1, n2)8. In the similar way we can find that : (n1, n3)7, (n1, n4)6, (n1, n5)5, (n1, n6)4, (n1, n7)3, (n1, n8)2, (n1, n9)1. Thus when n1 is at the first place, then number of triplets = 8 + 7 +6+5+4+3+2+1 In the same way we can find that, when n2 at the first place, then total number of triplets = 7 + 6 + 5 + 4 + 3 + 2 + 1 and so on. Hence, total number of triplets = (8 + 7 + ......... + 2 + 1) + (7 + 6 + ........ + 2 + 1) + (6 + 5 + ......... + 2 + 1) +.........+ (2 + 1) + 1 =8×1+7×2+6×3+5×4+4×5+3×6+2×7+1×8 = 8 + 14 + 18 + 20 + 20 + 18 + 14 + 8 = 120 33. (11) According to question, the maximum weight limit is 630. The lightest person’s weight is 53 kg and the heaviest person’s weight is 57 kg. In order to have maximum people in the lift, all the remaining people should be of the lightest weight possible, which is 53kg. Let there be ‘x’ people. 53 + x (53) + 57 = 630 53 x = 630 – 53 – 57 ⇒ x = 9.8 Hence, 9 people are possible.

34.

35.

36. 37.

Therefore, a total of 9 + 2 = 11 people can use the elevator. (b) It can be clearly established that the choices (a), (c) and (d) may or may not be true. Statement (b) can never be true because every person cannot have a different number of acquaintances. (c) Consider the number : x y z where x < y, z < y and . If y = 9, x can be between 1 to 8 and z can be between0 to 8. Total combinations = 9 × 8 = 72 If y = 8 , x can be between 1 to 7 and z can be between0 to 7. combinations = 7 × 8 = 56 Similarly, we add all combinations 8 × 9 + 7 × 8 + 6 × 7 + 5 × 6 + 4 × 5 + 3 × 4 + 2 × 3 + 1 × 2 = 240 ways. (b) As the boxes containing the green balls are consecutively numbered total number of ways will be 6 + 5 + 4 + 3 + 2 + 1 = 21 ways (a) There are 12 points. Since they can be reached from any other point, the edges will be = 66. Also the minimum

number of edges will be 11. 38. (d) 5 vowels = a, e, i, o and u If second letter is m then no. of strings = 5 × 4 = 20 If second letter is n then no. of strings = 5 × 2 = 10 If second letter is P then no. of strings = 5 × 1 = 5 ∴ Total string of letters can be formed = 20 + 10 + 5 = 35 39. (c) Taking the 3 cases as above no. of strings = 4 + 5 + 1 = 10 40. (b) Consider zone 1 No. of lines for internal connections in each zone = 9 Total number of lines for internal connections infour zones = 9 × 4 = 36

No. of lines for external connections between anytwo zones = 3 ×3=9 (as shown in figure) ∴ Total no. of lines required for connecting towns of different zones = ∴ Total no. of lines in all = 54 + 36 = 90 41. (c) 1 6 8 9 are the digits which cause confusion, when read upside down, since 0 cannot be first digit Number of pairs causing problem = (2 digits selected from 4 digits) Out of these numbers, 69 & 96 are the numbers which do not cause any confusion as they remain same when read upside down. ∴ No. of pairs causing problem = 12 – 2 = 10 Number of two digit codes = 9 × 9 = 81 Required no. of codes = 81– 10 = 71 42. (b) There are 28 minutes, hence total no. of songs are 14. Since each pair sings one song. Hence, total number of pairs is 14. Since, in each possible pair persons are not standing next to each other. Hence, total number of people = 7. 43. (a) As 1010 < n < 1011 , it means that n has 11 digits. Further sum of digits of n = 2, it means that either there are 2 one’s or a ‘two’ in the whole digit, 2 one’s can be obtained by fixing the first digit as 1 and the remaining 10 digits can be organised in 10 ways. In case of one ‘2’ there can be only 1 possibility with 2 as the 1st digit. ∴ Hence, total no. of different values for n = 10 + 1 = 11. 44. (d) Given that A > B > G > F. Satisfying this condition, ifF = 2, then, G = 3, B = 4, A = 5.

But this violates the condition that adults per family should be atmost 2. Hence, we take the next option : F = 3, then G = 4, B = 5, A = 6. Here all conditions are satisfied. Hence, the answer is (d). 45. (b) The car requires 3 steps north and 5 steps west so as to reach B. Hence, total no. of ways 46. (a) There are 6 stripes. The first stripe can be coloured in 4 ways, 2nd in 3, 3rd in 3, and so on. Thus total no. of ways = 4 × 3 × 3 × 3 × 3 × 3 = 12 × 81. 47. (a) Let number of girls = x and the number of boys = y 45 games in which both the players were girls

⇒ 190 games, where both the players were boys. y C2 = 190 ⇒ y(y – 1) = 380 ∴ y = 20 Hence, the total number of games in which one player was a boy and the other was a girl = 10 × 20 = 200 48. (c) Let E1, E2, E3 are three Englishman and F1, F2, F3 are three Frenchmen. Also suppose E1 is the only Englishman who knows the French and no Frenchman knows the English. For minimum number of phone calls; (i) E2 and E3 both call E1 and give secret information to E1. (ii) Any two Frenchmen (let F2 and F3) call the third Frenchman F1 and give secret information to F1. (iii) Englishman E1 and Frenchman F1 communicate all the secrets each other. (iv) E1 communicates E2 and E3 all the secrets received from others. (v) F1 communicats F2 and F3 all the secrets received from others.

Hence minimum number of phone calls = 2 + 2 + 1 + 2 + 2 = 9. 49. (b) There can be 2 possibilities – last digit is odd or even. Case I : Last digit is odd. Fixing one out of 1, 3 & 5 in the last position. Then only one odd number can occupy odd position which can be chosen in 2C1 ways = 2. One of the two odd digits can be selected for this position in again, 2C1 ways = 2. The other odd number can be put in either of the two even places in 2 ways. Finally the two even numbers can be arranged in 2! ways. Hence sum of last digit of these nos. = (2 × 2 × 2 × 2)(1 + 3 + 5) = 144 ways Case II : Last digit is even. Then 2 odd nos. out of 3 can be arranged in 3P2 = 3! ways. Again the even nos. can be arranged in 2! ways ∴ Sum = (3! × 2) (2 + 4) = 72 ways. Total ways = 144 + 72 = 216. 50. (d) p + 2 = 1! + (2 × 2!) + (3 × 3!) +.........+ (10 × 10!) + 2 = (1! + 2) + (2 × 2!) +.........+ (10 × 10!) = 1 + 2! + (2 × 2!) +.........+ (10 × 10!) = 1 + 2! (1 + 2) + (3 × 3!) +.........+ (10 × 10!) = 1 + 3! + (3 × 3!) +.........+ (10 × 10!) = 1 + 10! + (10 × 10!) = 1 + 11! Hence, p + 2 leaves 1 as remainder when divided by 11! 51. (a) For a number to be divisible by 3, the sum of its digits has to be divisible by 3. Given : ...(1) Again, for every digit of n to be odd, the four digits can be selected from 1, 3, 5, 7 and 9. Again with (1), the first two digits of n can be 1 & 1 only. So the sum of the remaining two digits has to be divisible by 3. Thus the possible digits can be 19, 73, 79, 13 and 55. These can be organised in 2 + 2 + 2 + 2 + 1 = 9 ways.

Hence, 9 elements of S are divisible by 3. 52. (a) Task 2 can be assigned to 3 or 4 So, there are only 2 options for task 2. Now, task 1 can not be assigned to 1 or 2 i.e. there are 3 options. So required no. of ways = (2 options for task 2) × (3 options for task 1) × (4 options for task 3) × (3 options for task 4) × (2 options for task 5) × (1 option for task 6). = 2 × 3 × 4 × 3 × 2 × 1 = 144. 53. (e) A member, say (a, b) will have an enemy of the form say (c, d) where c, d, a, b are all distinct. ∴ Enemies can be chosen in n – 2C2 ways, as for a general set of n elements, there will be n – 2 elements which will form the pairs of enemies. Therefore number of enemies = 54. (e) Consider friends (a, b) and (a, c). Their common friend can be either (b, c), only one of its kind, or a member of the form (a, d) or (d, a) where d is different from a, b, c. Now, d can be chosen in (n – 3) ways. Therefore number of common friends = (n – 3) + 1 = n – 2 55. (b) Since there are k players in each of the n terms, therefore, total number of players in the tournament will be nk. Since, one player is common in the pair of teams T1 and T2, T2 and T3, ..., Tn–1 and Tn and Tn and T1 Hence, there are n common players Therefore, total number of players, who are participating in the tournament = nk – n = n(k – 1) 56. (d) Case (I): When number of 50 misos is 0, The No. of 10 misos No. of 1 misos 10 7 9 17 8 27

1 97 0 107 Number of ways to pay the bill = 11 Case (II): When number of 50 misos is 1, then No. of 10 misos No. of 1 misos 5 7 4 17 3 27 2 37 1 47 0 57 Number of ways to pay the bill = 6 Case (III) : When number of 50 misos is 2, then No. of 10 misos No. of 1 misos 0 7 Number of ways to pay the bill = 1. Hence, from all the three cases, we got total numbers of ways to pay a bill of 107 misos = 11 + 6 + 1 = 18

57. (d)

To reach B from A through the shortest possible path, Neelam has to first reach the point E, then cover EF and then reach B from F. There are 6 different shortest paths to reach F from A. They are (A, 2, 5, 7, E, F), (A, 2, 4, 7, E, F), (A, 2, 4, 6, E, F), (A, 1, 4, 7, E, F), (A, 1, 4, 6, E, F) and (A, 1, 3, 6, E, F). Also there are 15 different shortest paths to reach B from F which are

(F, 9, 12, 15, 18, 20, B), (F, 9, 12, 15, 17, 20, B), (F, 9, 12, 15, 17, 19, B), (F, 9, 12, 14, 17, 20, B), (F, 9, 12, 14, 17, 19, B), (F, 9, 12, 14, 16, 19, B), (F, 9, 11, 14, 17,20, B), (F, 9, 11, 14, 17, 19, B), (F, 9, 11, 14, 16, 19, B), (F, 9, 11, 13, 16, 19, B), (F, 8, 11, 14, 17, 20, B), (F, 8, 11, 14, 19, B), (F, 8, 11, 14, 16, 19, B), (F, 8, 11, 13, 16, 19, B) and (F, 8, 10, 13, 16, 19, B) Hence, number of different shortest paths to reach B from A = 6 × 15 = 90 58. (a) From the solution of above question, we get the number of different shortest paths to reach B from A = 90

There are 13 different shortest paths to reach C from B, which are (B, 1, 3, 5, 7, 9, 11, 13, C), (B, 1, 3, 5, 7, 9, 12, 13, C), (B, 1, 3, 5, 7, 9, 12, 14, C), (B, 1, 3, 5, 7, 10, 12, 13, C), (B, 1, 3, 5, 7, 10, 12, 14, C), (B, 1, 3, 5, 8, 10, 12, 13, C), (B, 1, 3, 5, 8, 10, 12, 14, C), (B, 1, 3, 6, 8, 10, 12, 13, C), (B, 13, 6, 8, 10, 12, 14, C), (B, 1, 4, 6, 8, 10, 12, 13, C), (B, 1, 4, 6, 8, 10, 12, 14, C), (B, 1, 2, 4, 6, 8, 10, 12, 13, C) and (B, 1, 2, 4, 6, 8, 10, 12, 14, C) Hence, number of different shortest paths to reach C from A via B = (No. of different shortest paths to reach B from A) × (No. of different shortest paths to reach C from B) = 90 × 13 = 1170

59.

(b)

Probability that the man finds all three traffic lights red

Probability that he finds at least one light which is not red 60. (b) In his first throw A’s chance is 1/6, in his second throw it is , because each player must have failed once before A can have a second throw, in his third throw his chance =

because each player must have failed

twice, and so on. Thus A’s chance is the sum of the infinite series =

Similarly, B’s chance is the sum of the infinite series = ∴ A’s chance is to B’s as 6 is to 5. Their respective chances are therefore 6/11 and 5/11, and their expectations are Rs. 6 and Rs. 5 respectively. 61. (b) Total number of arrangements are 6! = 720. A, B, D can be arranged in 6 ways out of which D would be somewhere between A and B in exactly two cases. Hence the answer is 62. (a) The number of ways of picking two small cubes = 64C2 =

The number of small cubes with exactly two faces painted red = 2 × 12 = 24 (Since two such cubes will be obtained from each edge of the large cube.) The number of ways of picking two such cubes 24

C2 =

So the required probability 63.

(d) The number of yellow balls initially in the box is the same as the number of green balls. None of the ten operations involved after this favour any particular colour between the two. So the probability of the final ball picked being yellow (p(Y)) must be the same as that of being green (p(G)). Thus, p(Y) = p(G) and the ball picked should be either yellow or green, which means that p(Y) + p(G) = 1. Hence, p(Y) = p(G) =

64. (b) An integer can end with any of ten digits = (0, 1, 2, ......9) but (0, 1, 5, 6) has same unit of ten product of two integers. So, the probability of an integer ending with 0 or 1 or 5 or 6. = and the probability of 2nd integer = ∴ Required probability = 65.

(c)

Since the number of candies received by each child must get at least 2 candies. Once each child has received 2 candies, the remaining 2 candies should be distributed in such a maniner that the number of candies with any child after the distribution remains a prime number.

The remaining 2 candies are given to exactly two children in such a way that both the children receive one candy each. Hence, the number of ways of distribution = 8C2 = 28. 66. (b) If there are 60 chairs around a circular table, consider a scenario wherein there ae two chairs vacant between every two consecutive people. Thus, there will be exactly 20 people sitting and exactly 40 vacant seats between them and in such a scenario, next person coming to sit will have to sit next to someone. 67. (a) p + q = 1, i.e. q = 1 – p (0 = p, q = 1) Now when the sum of two variables is a constant then their multiplication is the maximum when they are equal. So, pq will be maximum and

the minimum when p = q =

. Thus, the minimum value of X = 0.25 + 4 = 4.25. 68. (a) First let the 6 other students be seated in 6 chairs. The number of spaces between the 6 students = 7. ∴ Amar, Akbar and Anthony can be seated in the 7 places in 7C3 ways. Thus, the number of ways in the class photo can be taken such that no two of Amar, Akbar and Anthony are sitting together is 7 = C3 × 3! × 6! = 151200. 69. (b) Total number of the cases = 6C3 = 20. The favourable cases for B surviving are: (B : Bullet; N : No Bullet) B N B B N N or B NBNBN or BNBNNB or BNNNBB or NNBBNB or NNBBBN. Required probability = 70. (c)

= 0.3.

Letters of the word ‘KAKA’ can be arranged in

= 6 ways If we will take all vowels are together, then arrangements are = 3 arrangements. So, (6 – 3) = 3 arrangements, where vowels are not together. So, required probability=

71. (a) If n is even, i.e., say n = 2 m then the number of ways is 2 × m! × m!, i.e., m odd numbers in alternate places and m even numbers in alternate places. If n is odd, i.e., say n = 2m + 1, then the number of ways = m!(m + 1)! Hence, either 2(m!)2 = 72 or m! (m + 1)! = 72 If 2(m!)2 = 72 ⇒ m! = 6 ⇒ m = 3 for m!(m + 1)! = 72, there is no solution. Hence m = 3, and n = 2m = 6.

Directions for Questions 1 to 5 : These questions are based on the graph given below. Solubility-Temperature relationships for various salts [The Y-axis denotes solubility (kg / litre of water)]

Which of solubility?

the

following

salts

has

greatest

(1994) (a) Potassium Chlorate at 80°C (b) Potassium Chloride at 35°C (c) Potassium Nitrate at 39°C (d) Sodium Chloride at 85°C 2.

Approximately, how many kg of Potassium Nitrate can be dissolved in 10 litres of water at 30°C? (1994)

(a) 0.04 (b) 0.4

By what % is the solubility of Potassium Chlorate in water increased as the water is heated from 30°C to 80°C? (1994) (a) 100 (b) 200 (c) 250 (d) 300 4.

If 1 mole of Potassium Chloride weighs 0.07456 kg, approximately. How many moles of Potassium Chloride can be dissolved in 100 litres of water at 36°C? (1994) (a) 700 (b) 650 (c) 480 (d) 540 5.

Which of the salts has greatest change in solubility in kg / litre of water between 15°C and 25°C? (1994)

(a) Potassium Chlorate (b) Potassium Nitrate (c) Sodium Chlorate (d) Sodium Nitrate Directions Questions 6 to 9 : These questions are based on the graph given below.

6. (a) (b) (c) (d) 7.

What was the total number of engineering students in 198990? (1994) 28500 4400 4200 42000 The growth rate in students of Govt. Engg. Colleges compared to that of Private Engg. Colleges between 1988-89 and 1989-90 is (1994)

(a) (b) (c) (d) 8. (a) (b) (c) (d) 9.

more less almost equal 3/2 The total number of Engg. Students in 1991-92, assuming a 10% reduction in the number over the previous year, is (1994) 5700 57000 44800 None of these In 1990-91, what percent of Engg. Students were studying at IIT’s? (1994)

(a) 16 (b) 15 (c) 14 (d) 12 Directions for Questions 10 to 14 : These questions are based on the graph given below. FOREIGN TRADE (In billion dollars)

10. In ?

which

year

was

the

trade

deficit

greatest

(1995) (a) (b) (c) (d) 11. (a) (b) (c) (d)

87-88 88-89 89-90 90-91 Export earning in 90-91 is how many percent of imports in 91-92 ? (1995) 82 85 92 15

12. In how many years was the trade deficit less than the trade deficit in the succeeding year ? (1995) (a) 1 (b) 2 (c) 3 (d) 4 13. In the last three years the total export earnings have accounted for how many percent of the value of the imports (1995) (a) 80 (b) 83 (c) 95 (d) 89 14. Which of the following statements can be inferred from the graph? (1995) I. In all the years shown in graph, the trade deficit is less than the export earning II. export earnings increased in every year between 89-90 and 91-92. III. In all the years shown in the graph, the earning by exports is less than the expenditure on imports in the preceding year. (a) I only (b) II only (c) III only (d) I and III only Directions for Questions 15 to 19 : These questions are based on the graph given below. Revenue obtained by a publishing house by selling books, magazines and journals ( in rupees lakh)

15. Which year shows the least change in revenue obtained from journals? (1995) (a) ‘89 (b) ’90 (c) ‘91 (d) ‘92 16. The is

growth

total

revenue

from

‘89

‘92

(1995) (a) 21% (b) 28% (c) 15% (d) 11% 17. In’92 what percent of the total revenue came from books ? (1995) (a) 45% (b) 55% (c) 35% (d) 25%

18. If ‘93 were to show the same growth as ‘92 over ‘91 the revenue in ‘93 must be (1995) (a) 194.5 (b) 186.6 (c) 172.4 (d) 176.7 19. The number of years in which there was an increase in revenue from at least two categories is (1995) (a) 1 (b) 2 (c) 3 (d) 4 Directions for Questions 20 to 24 : These questions are based on the graph given below.

(All figures in rupees lakhs)

20. Which year showed the greatest percentage increase in profit as compared to the previous year? (1996) (a) 1993 (b) 1994 (c) 1990 (d) 1992 21. The average revenue collected in the given seven years is approximately (1996) (a) Rs. 164 lakh (b) Rs. 168 lakh (c) Rs. 171 lakh (d) Rs. 175 lakh 22. In which year was the growth in expenditure greatest as compared to the previous year? (1996) (a) 1993 (b) 1995 (c) 1991 (d) 1992 23. The expenditures for the seven years together form what percent of the revenues during the same period? (1996) (a) 75% (b) 67% (c) 62% (d) 83% 24. If the profit in 1996 shows the same annual rate of growth as it had shown in 1995 over the previous year, then what approximately will be the profit in 1996 (1996) (a) Rs. 72 lakh (b) Rs. 86 lakh (c) Rs. 93 lakh (d) Rs. 78 lakh Directions for Questions 25 to 29 : These questions are based on the graph given below.

25. Which month has the highest profit per employee? (1996) (a) September (b) July (c) January (d) March 26. Which month records the highest profit? (1996) (a) September (b) July (c) March (d) May 27. In which month is the percentage increase in Sales over the Sales two months before, the highest? (1996) (a) March (b) September (c) July (d) May 28. In which month is the total increase in the Cost, highest as compared to the Cost two months ago? (1996) (a) March (b) September (c) July (d) May 29. Assuming that no employee left the job, how many more people did the company take on in the given period? (1996)

(a) 4,600 (b) 5,100 (c) 5,800 (d) 6,400 Directions for Questions 30 to 35 : These questions are based on the graph given below.

30. When least?

was

the

per

capita

production

milk

the

(1997) (a) (b) (c) (d) 31. (a) (b) (c) (d) 32. (a) (b) (c) (d)

1990 1992 1994 1996 When was the per capita production of foodgrains the most? (1997) 1992 1993 1994 1995 In which year was the difference between the increase in the production of foodgrains and milk the maximum? (1997) 1993 1994 1995 1996

33. If milk contains 320 calories and foodgrains contain 160 calories, in which year was the per capita consumption of calories the highest? (1997) (a) 1993 (b) 1994 (c) 1995 (d) 1996 34. If one gallon of milk contains 120 gm of a particular nutrient and one ton of foodgrains contain 80 gm of the same nutrient, in which year was the availability of this nutrient the maximum? (1997) (a) 1993 (b) 1994 (c) 1995 (d) 1996 35. Referring to the above question, in which year was the per capita consumption of this nutrient the highest? (1997) (a) 1993 (b) 1994 (c) 1995 (d) 1996 Directions for Questions 36 to 41 : These questions are based on the graph given below.

36. In which year was the increase in raw material the maximum? (1997) (a) 1992 (b) 1993 (c) 1994 (d) 1995 37. In which two successive years was the change in profit the maximum? (1997) (a) 1991-92 (b) 1992-93 (c) 1993-94 (d) 1994-95 38. Which component of the cost of production has remained more or less constant over the period? (1997) (a) Interest (b) Overheads (c) Wages (d) Raw material 39. In which year were the overheads, as a percentage of the raw material, the maximum? (1997) (a) 1995 (b) 1994 (c) 1992 (d) 1993 40. Over the period, the profits formed what percent of the costs? (1997) (a) 3% (b) 5% (c) 8% (d) 11% 41. If the interest component is not included in the total cost calculation, which year would show the maximum profit per unit cost? (1997) (a) 1991

(b) 1992 (c) 1993 (d) 1995 Directions for Questions 42 to 45 : These questions are based on the information and graph given below. The following bar chart gives the percentage growth in households in the middle, upper middle and high income categories in the four regions for the period between 87-88 to 94-95.

42. Which region showed the highest growth in number of households in all the income categories for the period? (1997) (a) North (b) South (c) West (d) None 43. What was the total household income in Northern Region for upper middle class? (1997) (a) 50 lakhs (b) 500 million (c) 300 million (d) Cannot be determined 44. What is the percentage increase in total number of households for the Northern Region (upper middle) over the given period? (1997) (a) 100 (b) 200 (c) 240

(d) Cannot be determined 45. What is the average income of the high-income group in 8788? (1997) (a) 75000 (b) 25000 (c) 225000 (d) Cannot be determined ADDITIONAL Directions for Questions 46 & 47 : If the same data as above can be used, with the additional information that the numbers of households in each category were equally distributed in all the regions then 46. If the numbers of households in each category were equally distributed in all the regions then. The ratio of total income for the high-income category to the upper middle class increased by how much percentage in the given period? (1997) (a) 20 (b) 38 (c) 25 (d) Cannot be determined 47. If the numbers of households in each category were equally distributed in all the regions then. (1997) The average income for the northern region in 87-88, was (a) 37727 (b) 37277 (c) 35000 (d) Cannot be determined Directions for Questions 48 to 52 : These questions are based on the information and graph given below. Ghosh Babu has a manufacturing unit. The following graph gives the cost for various number of units. Given the Profit = Revenue - Variable Cost - Fixed Cost. The fixed cost remains constant upto 34 units after which additional investment is to be done in fixed assets. In any case production can not exceed 50 units.

48. (a) (b) (c) (d) 49. (a) (b) (c) (d) 50.

What is the minimum number of units that need to be produced to make sure that there was no loss? (1998) 5 10 20 indeterminable How many units should be manufactured such that profit was atleast Rs. 50? (1998) 20 34 45 30 If at the most 40 units can be manufactured then what is the number of units that can be manufactured to maximize profit? (1998)

(a) (b) (c) (d) 51.

40 34 35 25 If the production can not exceed 45 units then what is the number of units that can maximise profit per unit? (1998) (a) 40 (b) 34

(c) 415 (d) 35 52. If the fixed cost of production goes up by Rs 40 then what is the minimum number of units that need to be manufactured to make sure that there is no loss (1998) (a) 10 (b) 19 (c) 15 (d) 20 Directions for Questions 53 to 58 : These questions are based on the information and chart given below. In the following chart, the price of logs shown is per cubic meter and that of plywood and saw timber is per ton. Given that 1 cubic meter of Plywood and Saw Timber = 800 kg. (1 ton = 1000 kg )

53. What is the maximum percentage increase in price per cubic meter or per tonne over the previous year? (1998) (a) 33.33% (b) 85% (c) 50% (d) Can not be determined 54. Which product shows maximum percentage increase in price over the period? (1998) (a) Saw Timber

(b) (c) (d) 55. (a) (b) (c) (d) 56.

Plywood Logs Can not be determined If 1 cubic meter = 750 kg for saw timber, find in which year was the difference in prices of logs and saw timber the least?(1998) 1989 1990 1991 1992 If 1 cubic meter = 700 kg for Plywood and 800 kg for Saw timbre find in which year was the difference in prices of plywood and saw timber the least? (1998)

(a) (b) (c) (d) 57.

(a) (b) (c) (d) 58.

(a) (b) (c)

1989 1990 1991 1992 If the volume of sales of Plywood, saw timber and Logs were 40%, 30% and 30% respectively then what was the average realisation in 1993 per cubic meter of sales? (One cubic metre of saw timber and plywood both = 800 kg) (1998) 18 15 16 13 If in 1994 prices increased by 5%, 1% and 10% while the volume of sales breakup was 40%, 30% and 30% for plywood, Saw Timber and Logs respectively then what was the average realisation per cubic meter of sales? (1998) 18.95 16.45 13.15

(d) 10.25 Directions for Questions 59 to 62 : Answer the questions based on the following information. The figure below represents sales and net profit in ` crore of IVP Ltd. for five years from 1994-95 to 1998-99. During this period the sales increased from ` 100 crore to ` 680 crore. Correspondingly, the net profit increased from ` 2.5 crore to ` 12 crore. Net profit is defined as the excess of sales over total costs.

59. (a) (b) (c) (d) 60. (a) (b) (c) (d)

The highest percentage of growth in sales, relative to the previous year, occurred in (1999) 1995-96 1996-97 1997-98 1998-99 The highest percentage growth in net profit, relative to the previous year, was achieved in (1999) 1998-99 1997-98 1996-97 1995-96

61. Defining profitability as the ratio of net profit to sales, IVP Ltd., recorded the highest profitability in (1999) (a) 1998-99 (b) 1997-98 (c) 1994-95 (d) 1996-97 62. With profitability as defined in question 61, it can be concluded that (1999) (a) profitability is non-decreasing during the five years from 1994-95 to 1998-99. (b) profitability is non-increasing during the five years from 1994-95 to 1998-99. (c) profitability remained constant during the five years from 1994-95 to 1998-99. (d) None of the above Directions for Questions 63 to 66 : These questions are based on the information and graph given below. These questions are based on the price fluctuations of four commodities - arhar, pepper, sugar, and gold during February - july 1999 as described in the figures below :

63. Price change of a commodity is defined as the absolute difference in ending and beginning prices expressed as a percentage of the beginning. What is the commodity with the highest price changes (1999) (a) Arhar (b) Pepper (c) Sugar (d) Gold 64. Price volatility (PV) of a commodity is defined as follows (1999) PV = (highest price during the period- lowest price during the period)/ average price during the period and

What is volatility?

the

commodity

with

the

lowest

price

(1999) (a) (b) (c) (d) 65.

(a) (b) (c) (d) 66. (a) (b) (c) (d)

Arhar Pepper Sugar Gold Mr. X, a fund manager with an investment company invested 25% of his funds in each of the four commodities at the beginning of the period. He sold the commodities at the end of the period. His investments in the commodities resulted in (1999) 17% profit 5.5% loss no profit, no loss 5.4% profit The price volatility of the commodity with the highest PV during the February - July period is approximately equal to (1999) 3% 40% 20% 42% Directions for Questions 67 to 71 : Answer these questions based on the data provided in the figure below.

FEI for a country in a year, is the ratio (expressed as a percentage) of its foreign equity inflows to its GDP. The following figure displays the FEIs for select Asian countries for the years 1997 and 1998.

67.

The country with the largest change in FEI in 1998 relative to its FEI in 1997, is (2000) (a) India (b) China (c) Malaysia (d) Thailand 68. Based on the data provided, it can be concluded that (20 00) (a) absolute value of foreign equity inflows in 1998 was higher than that in 1997 for both Thailand and South Korea. (b) absolute value of foreign equity inflows was higher in 1998 for Thailand and lower for Chaina than the corresponding values in 1997. (c) absolute value of foreign equity inflows was lower in 1998 for both India and China than the corresponding value in 1997. (d) none of the above can be inferred. 69. It is known that China’s GDP in 1998 was 7% higher than its value in 1997, while India’s GDP grew by 2% during the same period. The GDP of South Korea, on the other hand, fell by 5%. Which of the following statements is/are true? (2000) I. Foreign equity inflows to China were higher in 1998 than in 1997. II. Foreign equity inflows to China were lower in 1998 than in 1997. III. Foreign equity inflows to India were higher in 1998 than in 1997. IV. Foreign equity inflows to South Korea decreased in 1998 relative to 1997. V. Foreign equity inflows to South Korea increased in 1998 relative to 1997. (a) I, III & IV (b) II, III & IV (c) I, III & V (d) II & V 70. China’s foreign equity inflows in 1998 were 10 times that into India. It can be concluded that (2000) (a) China’s GDP in 1998 was 40% higher than that of India. (b) China’s GDP in 1998 was 70% higher than that of India. (c) China’s GDP in 1998 was 50% higher than that of India. (d) No inference can be drawn about relative magnitudes of China’s and India’s GDPs. 71. Which of the following is true ?

(a) (b) (c) (d)

(2000) China’s GDP is more than India China’s GDP is less than India India’s GDP is less than Malaysia Nothing can be deduced

Directions for Questions 72 to 77 : These questions are based on the information and graph given below. The following graph gives the data of four of the commodities produced by a company. Manufacturing constitutes 20% Mining 15%, Electricity 10% and Chemicals 15% of its production. The graph gives the percentage change in production over the previous years’s production and 1989 production values have been assigned an index of 100 for each of the four commodities.

72. Which is the sector with the highest growth during the period 1989 to 1998? (2000) (a) Manufacturing (b) Mining and quarrying (c) Electricity (d) Chemicals 73. The overall growth rate in 1991 of the four sectors together is approximately : (2000) (a) 10% (b) 1% (c) 2.5% (d) 1.5%

74. When was the highest level of production in the manufacturing sector achieved during the 9-year 1990-98? (2000) (a) 1998 (b) 1995 (c) 1990 (d) cannot be determined 75. When was the lowest level of production of the mining and quarrying sector achieved during the 9-year period 1990-98? (2000) (a) 1996 (b) 1993 (c) 1990 (d) can’t be determined 76. The percentage of increase of production in the four sectors, namely, manufacturing, mining and quarrying, electricity and chemicals, taken together in 1994, relative to 1989 is approximately : (2000) (a) 25 (b) 20 (c) 50 (d) 40 77. It is known that the index of total industrial production in 1994 was 50% more than in 1989. Then, the percentage increase in production between 1989 and 1994 in sectors other than the four listed above is : (2000) (a) 57.5 (b) 87.5 (c) 127.5 (d) 47.5 Directions for Questions 78 to 83 : These questions are based on the information and two graphs given below. Figure 1 shows the amount of work distribution , in man - hours for a software company between offshore and onsite activities. Figure 2 shows the estimated and actual work effort involved in the different offshore activities in the same company during the same period. [Note : onsite refers to work performed at the customer’s premise and offshore refers to work performed at the developer’s premise.]

78. Which of the work requires as many man- hours as that spent in coding? (2001) (a) Offshore, design and coding (b) Offshore coding. (c) Testing (d) Offshore, testing and coding. 79. Roughly what percentage of the total work is carried out onsite? (2001) (a) 40 percent (b) 20 percent (c) 30 percent (d) 50 percent 80. The total effort in man- hours spent onsite is nearest to which of the following? (2001) (a) The sum of the estimated and actual effort for offshore design (b) The estimated man-hours of offshore coding (c) The actual man-hours of offshore testing (d) Half of the man-hours of estimated offshore coding

81. If the total working hours were 100 which of the following tasks will account for approximately 50 hours? (2001) (a) Coding (b) Design (c) Offshore testing (d) Offshore testing plus design 82. If 50 percent of the offshore work were to be carried out onsite, with the distribution of effort between the tasks remaining the same, the proportion of testing carried out offshore would be (2001) (a) 40 Percent (b) 30 Percent (c) 50 Percent (d) 70 Percent 83. If 50 percent of the offshore work were to be carried out onsite, with the distribution of effort between the tasks remaining the same, which of the following is true of all work carried out onsite? (2001) (a) The amount of coding done is greater than that of testing. (b) The amount of coding done onsite is less than that of design done onsite (c) The amount of design carried out onsite is greater than that of testing (d) The amount of testing carried out offshore is greater than that of total design Directions for Questions 84 to 86 : These questions are based on the information and graph given below. There are six companies, 1 through 6. All of these companies use six operations, A through F. The following graph shows the distribution of efforts put in by each company in these six operations.

84. Suppose effort allocations is inter-changed between operations B and C, then C and D, and then D and E. If companies are then ranked in ascending order of effort in E, what will be then rank of company 3? (2001) (a) 2 (b) 3 (c) 4 (d) 5 85. A new technology is introduced in company 4 such that the total effort for operations B through F get evenly distributed among these . What is the change in the percentage of effort in operation E? (2001) (a) Reduction of 12.3 (b) Increase of 12.3 (c) Reduction of 5.6 (d) Increase of 5.6 86. Suppose the companies find that they can remove operations B,C and D re-distribute the effort released equally among the remaining operations. Then, which operation will show the maximum across all companies and all operations? (2001) (a) Operation E in company 1 (b) Operation E in company 4 (c) Operation F in company 5 (d) Operation E in company 5

Directions for Questions 87 to 92 : These questions are based on the graph given below. Graph indicates the annual sales tax revenue collections (in Rupees in crores) of seven states from 1996 to 2001. The values given at the top of each bar represents the total collections in that year.

87. If for each year, the states are ranked in terms of the descending order of sales tax collections, how many states don’t change the ranking more than once over the five years (2002) (a) 1 (b) 5 (c) 3 (d) 4 88. Which of the following states has changed its relative ranking most number of times when you rank the states in terms sof the descending volume of sales tax collections each year? (2002) (a) Andhra Pradesh (b) Uttar Pradesh (c) Karnataka (d) Tamil Nadu

89. The percentage share of sales tax revenue of which state has increased from 1997 to 2001? (2002) (a) Tamil Nadu (b) Karnataka (c) Gujarat (d) Andhra Pradesh 90. Which pair of successive years shows the maximum growth rate of tax revenue in Maharashtra? (2002) (a) 1997 to 1998 (b) 1998 to 1999 (c) 1999 to 2000 (d) 2000 to 2001 91. Identify the state whose tax revenue increased exactly by the same amount in two successive pair of years? (2002) (a) Karnataka (b) West Bengal (c) Uttar Pradesh (d) Tamil Nadu 92. Which state below has been maintaining a constant rank over the years in terms of its contribution to total tax collections? (2002) (a) Andhra Pradesh (b) Karnataka (c) Tamil Nadu (d) Uttar Pradesh Directions for Questions 93 to 95 : These questions are based on the information and graph given below. Each point in the graph below shows the profit and turnover data of a company. Each company belongs to one of the three industries: textile, cement and steel.

93.

(a) (b) (c) (d) 94. (a) (b) (c) (d) 95. (a) (b) (c) (d)

Turnover An investor wants to buy stock of only steel or cement companies with a turnover more than 1000 and profit exceeding 10% of turnover. How many choices are available to the investor? (2003C) 6 7 8 9 For how many steel companies with a turnover of more than 2000 is the profit less than 300? (2003C) 0 1 2 7 For how many companies does the profit exceed 10% of turnover? (2003C) 8 7 6 5

Directions for Questions 96 to 99 : These questions are based on the information and graph given below. The length of an infant is one of the measures of his/her development in the early stages of his /her life. The figure below shows the growth

chart of four infants in the five months of life.

96. Among the four infants, who grew the least in the first five months of life? (2003C) (a) Geeta (b) Seeta (c) Ram (d) Shyam 97. The rate of growth during the third month was the lowest for (2003C) (a) Geeta (b) Seeta (c) Ram (d) Shyam 98. Who grew at the fastest rate in the first two months of life ? (2003C) (a) Geeta (b) Seeta (c) Ram (d) Shyam 99. After which month did Seeta’s rate of growth start to decline? (2003C) (a) Second month (b) Third month (c) Fourth month

(d) Never Directions for Questions 100 to 102 : These questions are based on the charts given below.

100. In which year during the period 1996-1999 was Chaidesh’s export of tea, as a proportion of tea produced, the highest? (2003) (a) 1996 (b) 1997 (c) 1998 (d) 1999 101. In which of the following years was the population of Chaidesh the lowest? (2003) (a) 1995 (b) 1996 (c) 1997 (d) 1999 102. The area under tea cultivation continuously decreased in all four years from 1996 to 1999, by 10%, 7%, 4% and 1%, respectively. In

which year was tea productivity (production per unit of area ) the highest? (2003) (a) 1999 (b) 1998 (c) 1997 (d) 1996 Directions for Questions 103 to 106 : These questions are based on the information and charts given below. The profitability of a company is defined as the ratio of its operating profit to its operating income, typically expressed in percentage. The following two charts show the operating income as well as the profitability of six companies in the Financial Years (F. Y.s) 2001-02 and 2002-03.

The operating profits of four of these companies are plotted against their respective operating income figures for the F. Y. 2002-03, in the third chart given below.

103. What is the approximate average operating profit, in F.Y. 2001 - 2002, of the two companies excluded from the third chart? (2003) (a) – 7.5 crore (b) 3.5 crore (c) 25 crore (d) Cannot be determined. 104. Which company recorded the highest operating profit in F. Y. 200203? (2003) (a) A (b) C (c) E (d) F 105. Which of the following statements is NOT true? (2003) (a) The company with the third lowest profitability in F.Y. 2001-02 has the lowest operating income in F. Y 2002-03 (b) The company with the highest operating income in the two financial years combined has the lowest operating profit in F. Y. 2002-03 (c) Companies with a higher operating income in F. Y. 2001-02 than in F.Y. 2002-03 have higher profitability in F. Y. 2002-03 than in F. Y. 2001-02 (d) Companies with profitability between 10% and 20% in F. Y. 2001-02 also have operating incomes between 150 crore and 250 crore in F. Y. 2002-03

106. The average operating profit in F. Y. 2002-03, of companies with profitability exceeding 10% in F. Y. 2002-03, is approximately (2003) (a) 17.5 crore (b) 25 crore (c) 27.5 crore (d) 35 crore Directions for Questions 107 & 108 : These questions are based on the figure given below. Rainfall at selected locations in certain Months

107. Which of the following statements is correct? (2003)(a) November rainfall exceeds 100 cm. in each location (b) September rainfall exceeds 50 cm. in each location (c) March rainfall is lower than September rainfall in each location (d) None of the above 108. Locations 6 and 7 differ from all the rest because only in these two location, (2003) (a) April rainfall exceeds March rainfall (b) Peak rainfall occurs in April. (c) November rainfall is lower than March rainfall

(d) April rainfall is less than 200 cm. Directions for Questions 109 to 111 : These questions are based on the figure given below. Mid-year Prices of Essential Commodities 109. During 1996-2002, the number of commodities that exhibited a net overall increase and a net overall decrease, respectively, were

(2003) (a) 3 and 3 (b) 2 and 4 (c) 4 and 2 (d) 5 and 1 110. The number of commodities that experienced a price decline for two or more consecutive years is (2003) (a) 2 (b) 3 (c) 4 (d) 5 111. For which commodities did a price increase immediately follow a price decline only once in this period? (2003) (a) Rice, Edible oil & Dal (b) Egg and Dal (c) Onion only (d) Egg and Onion Directions for Questions 112 to 115 : Answer the questions on the basis of the information given below. The data points in the below represent monthly income and expenditure data of individual members of the Ahuja family (), the Bose family (), the Coomar family ( ), and the Dubey family (

For these questions, saving is defined as

112. Which family expenditure?

has

the

highest

average

(2004) (a) Ahuja (b) Bose (c) Coomar (d) Dubey 113. Which income?

family

has

the

lowest

average

(2004) (a) Ahuja (b) Bose (c) Coomar (d) Dubey 114. Which highest amount of saving accrues to a member of which family? (2004) (a) Ahuja (b) Bose (c) Coomar (d) Dubey 115. Which family has the lowest average saving? (2004) (a) Ahuja (b) Bose (c) Coomar (d) Dubey Directions for Questions 116 to 119 : Answer the questions on the basis of the information given below. Purana and Naya are two brands of kitchen mixer- grinders available in the local market. Purana is an old brand that was introduced in 1990, while Naya was introduced in 1997. For both these brands, 20% of the mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that 10 Purana mixer-grinders were disposed off in 1997. The following figures show the number of Purana and Naya mixer-grinders in operation from 1995 to 2000, as at the end of the year.

116. How many Naya mixer-grinders were disposed off by the end of 2000? (2004) (a) 10 (b) 16 (c) 22 (d) Cannot be determined from the data 117. How many Naya mixer-grinders were purhsed in 1999? (2004) (a) 44 (b) 50 (c) 55 (d) 64 118. How many Purana mixer-grinders were purchased in 1999? (2004) (a) 20 (b) 23 (c) 50 (d) Cannot be determined from the data

119. How many Purana mixer-grinders 2000? (2004) (a) 0 (b) 5 (c) 6 (d) Cannot be determined from the data

were

disposed

off

Directions for Question 120 to 123 : Answer the question on the basis of the information given below. A management institute was established on January I, 2000 with 3, 4, 5, and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member in each of the four areas. All these new faculty members, who joined the institute subsequently over the years, were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The following diagram gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002 and 2003.

120. In which year did the new faculty member join the Finance area? (2005) (a) 2000 (b) 2001 (c) 2002 (d) 2003 121. What was the age of the new faculty member, who joined the OM area, as on April 1, 2003? (2005) (a) 25 (b) 26 (c) 27 (d) 28 122. From which area did the faculty member retire? (2005) (a) Finance

(b) Marketing (c) OB (d) OM 123. Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the Institute since its inception, share a birthday, which falls on 20th November. One was, born in 1947 and the other one in 1950. On April 1, 2005, what was the age of the third faculty member, who has been in the same area since inception? (2005) (a) 47 (b) 50 (c) 51 (d) 52 Directions for Questions 124 to 126 : Answer the following questions based on the information given below : Telecom operators get revenue from transfer of data and voice. Average revenue received from transfer of each unit of data is known as ARDT. In the diagram below, the revenue received from data transfer as percentage of total revenue received and the ARDT in US Dollars (USD) are given for various countries.

124. It is expected that by 2010, revenue from data transfer as a percentage of total revenue will triple for India and double for Sweden. Assume that in 2010, the total revenue in India is twice that of Sweden and that the volume of data transfer is the same in both the countries. What is the percentage increase of ARDT in India if there is no change in ARDT in Sweden? (2008) (a) 400 % (b) 550 % (c) 800 % (d) 950 % (e) cannot be determined 125. It was found that the volume of data transfer in India is the same as that of Singapore. Then which of the following statements is true? (2008) (a) Total revenue is the same in both countries (b) Total revenue in India is about 2 times that of Singapore (c) Total revenue in India is about 4 times that of Singapore (d) Total revenue in Singapore is about 2 times that of India (e) Total revenue in Singapore is about 4 times that of India 126. If the total revenue received is the same for the pairs of countries listed in the choices below, choose the pair that has approximately the same volume of data transfer. (2008) (a) Philippines and Austria (b) Canada and Poland (c) Germany and USA (d) UK and Spain (e) Denmark and Mexico

Directions for Questions 127 to 130 : Answer the following questions based on the information given below: The bar chart below shows the revenue received, in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The bar chart also shows the estimated revenues from subscription to this service for the period 2008 to 2010.

127. Consider the annual percent change in the gap between subscription revenues in the US and Europe. what is the year in which the absolute value of this change is the highest? (2008) (a) 03-04 (b) 05-06 (c) 06-07 (d) 08-09 (e) 09-10 128. While the subscription in Europe has been growing steadily towards that of the US, the growth rate in Europe seems to be declining. Which of the following is closest to the percent change in growth rate of 2007 (over 2006) relative to the growth rate of 2005 (over 2004)? (2008) (a) 17 (b) 20 (c) 35 (d) 60

(e) 100 129. The difference between the estimated subscription in Europe in 2008 and what it would have been if it were computed using the percentage growth rate of 2007 (over 2006), is closest to: (2008) (a) 50 (b) 80 (c) 20 (d) 10 (e) 0 130. In 2003, sixty percent of subscribers in Europe were men. Given that women subscribers increase at the rate of 10 percent per annum and men at the rate of 5 percent per annum, what is the approximate percentage growth of subscribers between 2003 and 2010 in Europe? The subscription prices are volatile and may change each year. (2008) (a) 62 (b) 15 (c) 78 (d) 84 (e) 50 DIRECTIONS (Qs. 1-2) : Answer the questions on the basis of the information given below. In a country called XYZ, the number of patients changes every year. The graph given below shows the percentage change in the number of patients w.r.t. the previous year. The table given below shows the number of hospitals available in XYZ. The number of patients in 1999 were 2,00,000.

The Unhealthiness Index of XYZ for a year is defined as the number of patients per hospital in the country. (2009) 1. Find the year for which the Unhealthiness Index of XYZ was the maximum. (a) 2000 (b) 2003 (c) 2004 (d) 2006 2. In 2006, WHO launched a massive health improvement program in XYZ. As a result there was 30% reduction in the number of patients per year for the next two years and the number of hospitals in the country was also increased by 10% per year during the same period. Find the Unhealthiness Index of XYZ for the year 2008. (a) 15.4 (b) 19.8 (c) 13.9 (d) 21.3 3. The Government of XYZ targets an Unhealthiness Index of 15 for the year 2007. By approximately what percent should the number of hospitals be increased in 2007 over the previous year if the number

(a) (b) (c) (d)

of patients in 2007 is expected to decrease by 40% over the previous year? 27% 34% 47% 37%

DIRECTIONS (Qs. 4 & 5) : The following network gives details about the various activities carried out in a bottling firm for their latest project and the time required for each activity. The average cost incurred in each activity is 5 times the square of the duration of the activity. If the organisation wants to reduce the duration of any particular activity, in addition to the average cost, it will have to incur an amount equal to 15 times the cube of the new duration of the activity.

4. (a) (b) (c) (d) 5. (a) (b) (c)

(2011) The completion of one cycle of the network results in one bottle ready to be sold in the market. The project involves a total of 800 bottles. What is the average cost of the entire project? Rs. 74400 Rs. 372000 Rs. 15000 Rs. 18500 If profit is defined as the difference between the selling price and the average cost, and each bottle is sold for Rs. 510, what is the approximate percent profit earned by the firm? 5% 10% 15%

(d) 17.5% DIRECTIONS for Questions 6 to 8: Answer the questions on the basis of the information given below. The bar charts given below shows the details of the “Budgeted I-Tax” collections and the “Actual I-Tax” collections of India in each of the years from 2004-05 to 2008-09. Bar Chart-I shows the details of the Total I-Tax collections and bar chart-II shows the details of the Corporate I-Tax collections. There are only two categories of taxpayers in India “Individual Taxpayers” and “Corporate Taxpayers”. All the figures are in Rs. crores. (2012) Total I-Tax collections Corporate I-Tax collections

For how many of the given years the Efficacy Ratio of at least two out of “Total I-Tax” collections, “Corporate I-Tax” collections and “Individual I-Tax” collections is greater than 1? (a) 0 (b) 1 (c) 2 (d) Data Insufficient

In which of the following years, for either of the Corporate I-Tax collections or the Total I-Tax collections, the percentage growth of ITax over the previous year for both the Budgeted and the Actual is approximately the same? (a) 2005-06 (b) 2006-07 (c) 200708 (d) Both 2006-07 and 2007-08 8. Which of the following statements (is/are) true? I. Percentage contribution of the corporate I-Tax (Actual) collections to the total I-Tax (Actual) collections has decreased in the year 2008-09 in comparison to the year 2005-06. II. Simple Annual growth rate of Actual I-Tax paid by the individual taxpayers for the period 2004-05 to 2008-09 is more than 90 percent III. Efficacy ratio for the “Corporate I-Tax” collections is the highest in the year 2008-09. (a) I (b) II (c) III (d) I, II and III DIRECTIONS (Qs. 9 - 11) : Answer the questions on the basis of the information given below. The bar graphs given below show the gender-wise deaths (in ‘000) due to NCDs (Non Communicable Diseases) in five countries for the years 2008 and 2009. (20 13)

9. (a) 10. (a) 11. (a)

In how many countries was the number of deaths due to NCDs in 2009 less than that in 2008? 1 (b) 2 (c) 3 (d) 4 By what percent was the total number of female deaths due to NCDs in the five countries put together in 2009 more/less than that in 2008? 7.10 (b) 6.40 (c) 8.60 (d) 7.90 What was the absolute difference between the total number of male deaths due to NCDs in the five countries put together in 2008 and 2009? 22500 (b) 23000 (c) 24000 (d) None of these

DIRECTION for questions 12 to 15: Answer the questions on the basis of the information given below. The graphs given below show the revenues and profits of four IT education companies. (2014) Profitability = (Profit/Revenue) Total cost = Revenue – Profit Revenues

Profits In 1999, how many companies have a profitability less than the average of the profitabilities of the four companies?

12. (a) (b) (c) (d) 13.

(a) (b) (c) (d)

1 2 3 0 In 2002, if the cost in each company increased by 10% over 2001 and the revenue for each company decreased by 10% over 2001, what is the approximate profitability of all the companies taken together in 2002? 10.25% –10.25% –9.25% 8.75%

14.

Arrange the companies in increasing order of their profitability in 2001. (a) NIIT, Tata Infotech, Aptech, SSI (b) NIIT, Tata Infotech, SSI, Aptech (c) NIIT, Aptech, Tata Infotech, SSI (d) SSI, Aptech, Tata Infotech, NIIT 15. Which company has the highest profitability in 2000? (a) NIIT (b) Aptech (c) SSI (d) Tata Infotech DIRECTIONS for questions 16 to 18: Answer the questions on the basis of the information given below. The average annual salary figures of five leading B-schools have been shown below. Average Annual Salary (` in lakh)

The percentage of students getting PPOs (Pre-Placement offers) and their average annual salary in lakhs is shown below:

The number of students, the number of companies visiting the campus and total offers made (including PPO’s) have been shown below for these five leading B-schools. (2014)

16. (a) (b) (c) (d) 17. (a) (b) (c) (d) 18.

Which school has the highest total number of offers per student? IMT Narsee Monjee IMI FMS The ratio of number of offers to the number of companies visiting the campus is highest for: IMT K.J. Somaiya IMI FMS At FMS, what is the average salary of students, who did not get a PPO?

(a) ` 6.5 lakh (b) ` 4.5 lakh (c) ` 8 lakh (d) ` 6 lakh DIRECTIONS for questions 19 to 21: Answer the questions on the basis of the information given below. There are ten real numbers A, B, C, D, E, F, G, H, I. Differences between any two of them are given in the diagram below. (2014)

19.

If the value of A is known then how many distinct values are possible for J? (a) 512 (b) 256 (c) 128 (d) None of these 20. If all the 10 numbers from A to J are positive integers then at least how many of them are even? (a) 3 (b) 4 (c) 5 (d) 6 21. If all the 10 numbers from A to J are positive integers and A is equal to 1 then at a time at most how many of them can be perfect squares? (a) 7 (b) 9 (c) 8 (d) 6

DIRECTIONS (Qs. 22-25) : Answer the questions on the basis of the information given below. The following pie chart gives the distribution of the total loans disbursed by ADB in 2012 among eleven Asian countries. Total amount of loans disbursed = Rs. 7200 cr

The following line graph gives the percentage contribution of loan from ADB in the total investment made in different sectors in the same year by India and China.

For both China and India, the loan received from ADB was utilized in the given sectors only. (2015) 22. If the total investment in Education sector in China was 60% higher than that in India, then what is the ratio of A and B, where

A : The percentage of loan from ADB invested in Education sector by China B : The percentage of loan from ADB invested in Education sector by India (a) 256 : 135 (b) 256 : 189 (c) 256 : 225 (d) Cannot be determined 23. The amount of loan invested in Transport sector by China was equal to 60% of the total loan given by ADB to Malaysia. The amount of loan invested in Transport sector by India was equal to 60% of the total loan given by ADB to North Korea. The total investment made in Transport sector by India was approximately what percent of that made by china? (a) 75.76 (b) 91.67 (c) 80.80 (d) 81.81 24. If the total investments made in Education, Health and Agriculture sectors in India in 2012 was Rs. 150 cr., Rs. 120 cr and Rs. 400 cr. respectively, then the amount of ADB loan invested by India in these three sectors constitute what percentage of the total loan granted to India by ADB? (a) 15.05% (b) 18.85% (c) 12.33% (d) 16.66% 25. The total loan invested in Power, Transport and Education sectors by India was 500 cr. What was the maximum possible investment (in Rs. crore) in these three sectors made by India? [The loan amount invested in all of these three sectors is a multiple of 30 cr] (a) 2000 (b) 2100 (c) 2360 (d) 2400 DIRECTIONS for questions 26 and 27: Answer the questions on the basis of the information given below.

Each point in the graph below shows the sales and expenses of a company. Each company belongs to one of the three sectors among manufacturing, automobiles, and software. (2016) 26. For how many of the companies, is the profit more than 40% of the sales (Profit = Sales Expenses)? (a) 4 (b) 5 (c) 6 (d) 7 27. For how many software companies are the sales more than Rs.2500 crore but the expenses less than Rs. 2100 crore? (a) 2 (b) 3 (c) 4 (d) 6

ANSWERS WITH SOLUTIONS 1. 2.

(c) At 39°C solubility of potassium nitrate = 0.48 kg/litre of water In other cases solubility is less than or equal to 0.4 kg/litre of water (c) Solubility of potassium nitrate at 30°C = 0.38 kg /litre so in 10 litres of water it can be dissolved (d) Solubility of potassium chlorate at 30°C = 0.1 Solubility of potassium chlorate at 80°C = 0.4 % increase

(d) Solubility of Potassium chloride at 36°C = 0.4 kg/litre it means in 1 litre it can be dissolved = 0.4 kg In 100 litre it can be dissolved = 100 × 0.4 = 40 kg 0.07456 kg weighs 1 mole ∴ 40 kg weighs

5. 6.

= 300%

(approx)

(c) It is clear from graph that greatest change in solubility between 15° and 25°C is of salt sodium chlorate and this change = 1.1 – 0.95 = 0.15 kg/litre (d) Total no. of students in 1989 – 90 = (185 + 120 + 70 + 45) 100 = 42000

(c) Growth rate of students of govt. college = (since students in 1988-89 = 80 and in 1989 – 90 = 120) growth rate of students of private engg. college from 1988-89 to 198990

Hence growth rate is equal (d) Total no of students in 1990 – 91 = 57000 reduction = 10% of 57000 = 5700 Hence total no. of students in 1991 - 92 = 57000 – 5700 = 51300 (c) Total no. of students in 1990-91 = 57000 (as calculated above) % students of IIT’s

approx.

approx

10. (b) Trade deficit in 87-88=17.5 – 11.75 = 5.75 Trade deficit in 88-89=19.5 – 13.25 = 6.25 (greatest) Trade deficit in 89-90 = 21 – 16.5 = 4.5 Trade deficit in 90-91=24.5 – 18.5 = 6 11.

(c)

12. (d) Clearly it is seen that the trade deficit is lower in 87-88, 89-90, 91-92, 93-94 13. (d) = 14. (a) (i) is clearly true (ii) is false as it remained same in 1991- 92 (iii) is false as export earning is more than expenditure on imports in the preceding year in 94-95. 15. (b) Change in revenue from journals: Hence least change is in 1990

Note : Here change is asked so we have to consider both, increase and decrease. 16. (c) Total revenue growth

17. (a) Revenue of books from total in 1992

18. (d) Growth in 92, over 91 = 2.5% Revenue in 93 = 172.4 × 1.025 = 176.7 19. (c) Increase in revenue from atleast 2 categories was in 1990, 1991, 1992 For Qs. 20-24. Corresponding values according to the graph are

20. (d) Percentage Increase = [final value - initial value] using this formula, we can find about % age increase for all the years, the maximum being for year 1992

21. (b) Average revenue

22. (d) From the above table, it can be seen that the growth in expenditure was maximum in 1992. 23. (a) Total Revenue = 1174. Total expenditure = 877 % formed by the revenue = 877 / 1174 = 74.7% 75% 24. (b) % growth in profit in 1995 = ( 72 – 60) / 60 = 1/5 = 20 % As per the given conditions % age profit in 1996 = 20%

∴ profit in 1996 25. (b) Profit per employee is highest in the month of July 26. (b) P = (S – C) which is maximum in July. From the graph only 26is near to July in profit. 27. (d) The graph clearly shows that highest growth in sales is in May. So, all other months following May have less growth in Sales. But for percentage increase in sales we need to consider March also. % increase in March = % increase in May = 28. (d) Increase in cost is maximum for May i.e. 34 – 30 = 4 on this line graph. 29. (b) No. of persons employed = No. of employees in Nov. – No. of employees in Jan. = 15800 – 10800 = 5000 (approx.) Closest answer is 5100 and so (b) is correct answer. 30. (a) Per capita production of milk Looking at the graph it is clear that per capita production of milk was least in 1990

Increase in milk production is much higher as compared to population. 31. (d) Food grains per capita production was maximum in 1995 i.e 30. It is clear from the graph. 32. (c) Clearly from the graph, the increase in the production of food grain is far more than production of milk in 1995. Note the drastic increase in production of food grains and fall in production of milk. 33. (c) Milk 320 Calories Food grain 160 Calories Let X = Required consumption

Hence it is found to be maximum in 1995 34. (c) X = (Food grain × 80 + Milk × 120) gm X 1993 2760 1994 3600 1995 3440 1996 2920 35. (c) This is similar to the above question no. 33 36. (b) In 1992, there was a decrease. Increase in raw material for the years 1993, 1994 and 1995 can be calculated as 30%, 15.38% and 0.66% respectively so the increase is the maximum in 1993. We can also see the length of the bars and can compare. 37. (c) The change in profit in 1991-92 is The change in profit in 1992-93 is The change in profit in 1993-94 is The change in profit in 1994-95 is Therefore, the change in profit is maximum in 1993-94. 38. (a) Comparing the lengths of the graphs we can include that the interest has remained more or less constant over the given period. 39. (c) The over heads, as a percentage of the raw material, in the years 1992, 1993, 1994 and 1995 can be calculated as 36%, 23.07%, 30.66% and 26.25% respectively. This was maximum in 1992 40. (b) The total profit over period Total cost So profit

41. (b) If interest is not part of the total cost, the total costs for the year 1991, 1992, 1993 and 1995 are 115, 123, 140 and 166 respectively. The profits per unit cost in these years are 0.1304, 0.2032, 0.1428, 0,0903. Hence the maximum profit per unit cost is in 1992. 42. (b) From the bar graph we could see that southern region had shown the highest growth for all the income categories for all the region. 43. (d) The no. of households have not been given regionwise so it cannot be determined. 44. (b) % increase for northern region, upper middle class for the given period is 200% [from the bar graph] 45. (a) Again, from the given data, average income of the high income group in 87-88 was 75000. 46. (b) Ratio of total incomes for high income category to that of uppermiddle category in 87-88 = 0.75 During this period , the income of higher-income category increased by 90% and that for the upper middle category increase by 60% No. of households in high-income in 94-95 = No. of households in upper middle-income in 94-95 = So ratio of incomes at the end of period

Percentage increase 47. (a) Number of households are equally distributed in all the regions. Hence in Northern region households in

Hence total number of households = 13750 Total income

So, average income

48-52. Profit = Revenue – variable cost – fixed cost Fixed cost remains constant upto 34 units after which additional investment is to be done in fixed assets. Maximum production = 50 units. 48. (b) For no loss Revenue = variable cost + Fixed cost and we can see from the graph that when production is equal to 10 units. Revenue = variable cost + Fixed cost and before this point there are losses and after this point, there are profits. Hence minimum number of units that must be produced to make sure that there are no losses is 10. At 10 units, Profit = 200 – 130 – 70 = 0. 49. (d) For 20 units, Profit = 400 – 280 – 70 = 50 Below 20 units the profit will be less than 50. So a minimum of 20 units is to be manufactured. 50. (b) Units Revenue Variable Fixed Profit Profit Cost Cost / Unit 25500 350 70 80 3.8 34680 475 70 135 3.97 35700 490 100 110 3.14 40800 560 100 140 3.5 So, 34 units shall be manufactured to maximise profit/unit. 51. (b) Units Revenue Variable Fixed Profit Profit Cost Cost /Unit 45900 630 100 170 3.77 So, from previous question it is clear that 34 units shall be manufactured. 52. (b) As per the question, Fixed Cost = 70 + 40 = 110 till 34 units. We know previously that there is no profit/loss at 10 units. Units Revenue Variable Fixed Profit Cost Cost 15300 210 110 –20

19390 275 110 5 20400 280 110 10 Hence, for no loss 19 units need to be manufactured. 53. (c) From the figure it is clear that the highest increase in price is shown by Saw timber in 1992-93, 1990-91, by Logs in 1990-91 and by Plywood in 1991-92. Logs

1990-91

Plywood

1991-92

Saw timber

1992-93

Saw timber

1990-91

54. (b) Increase in price of Plywood = 7 – 3 = 4 or Increase in price of Saw Timber = 19 – 10.5 = 8.5 or Increase in price of Log = 20 – 15 = 5 or 55. (b) Year Saw Timber Saw Timber Logs in Rs/tonne in Rs/m3 in Rs/m3 1989 12 9 18 9 1990 10.5 7.875 15 7.125 1991 13.5 10.125 18 7.875 1992 15 11.25 19 7.75 Use 1 ton =

Difference

56. (d) Year Saw Saw Plywood Plywood Difference Timber Timber in Rs in Rs 3 in Rs in Rs /m /m3 /tonne /m3 1989 12 9.6 4 2.8 6.8

1990 10.5 1991 13.5 1992 15 Use 1 ton = 57. (d)

8.4 10.8 12

5 4 6

3.5 2.8 4.2

4.9 8 7.8

for Plywood and 1 ton = Logs

Saw Timber

for Saw Timber. Plywood

Price/m3 in 1993 20 Average realisation/m3 of sales = 58. (c) The change for price increase

= ` 13.15 59. (a) Sales growth in 1995-96 = = 150% In 1996-97= In 1997-98= In 1998-99= Therefore, sales growth is highest in 1995-96. 60. (d) Net profit growth in 1995-96 = In 1996-97= In 1997-98= In 1998-99= It is maximum in the year 1995-96.

61. (b) Profitability in 1994-95 = 0.025, In 1995-96 = 0.018, In 1996-97 = 0.02, In 1997-98 = 0.029, In 1998-99 = 0.017 It is clear that profitability is maximum in the year 1997-98. 62. (d) None of the option is true. 63. (a) Price change of each commodity is as follows : Arhar = Pepper = Sugar = Gold = 64. (c) Price Volatility is defined in the question PV = H.P. L.P. A.P. PV Arhar 2300 1500 1912.50 0.42 Pepper 19500 17400 18622.50 0.112 Sugar 1500 1410 1446.25 0.06 Gold 4300 3800 4045 0.124 So the lowest price volatility is for sugar. 65. (d) Price change which we have calculated previously is nothing but profit percent or loss percent depending upon the sign. In the first two we have profit percentage which is 26.5 + 4% = 29.5% and the loss percentage is 0.3 + 9.4 = 9.7% then net profit % comes out to be 20.8% and then the average of which gives i.e. answer is (d).

so the closest

66. (b) From the table in earlier question the highest price volatility is 0.42 which in terms of % is 42%. 67. (a) The country with the largest change in FEI is India. 68. (d) Absolute value is not given, hence nothing can be inferred. 69. (d) Let GDP of China in 1997 be x, then GDP in 1998 = 1.07x FEI of China in 1997 = x × 5.96 FEI in 1998 = 1.07 × 4.8x = 5.136x ∴ FEI of China in 1998 < FEI in 1997 Likewise FEI of India in 1997 = 1.71y FEI in 1998 = 1.02 × 0.72y = 0.73y ∴ FEI of India in 1998 < FEI in 1997 and FEI of South Korea in 1998 > FEI in 1997. 70. (c) Let the equity inflow of India in 1998 be x, then equity inflow of China would be 10x. FEI of India in 1998 = 0.72 = ∴

GDP of India in 1998 =

GDP of China in 1998 = It is clear that GDP of China is 50% more than that of India. 71. (d) Nothing can be said about the GDP as all the values are given in a ratio of FEI & GDP. 72. (c) It is clear from the given graph. 73. (d) First find out the growth in 1990 of the all four sectors. Manufacturing 9% of 20 = 1.8. Hence, 20 + 1.8 = 21.8. Similarly, for mining and quarrying it is 15.6. For electrical, it is 10.81 and for chemical it is 16.1. Now in 1991, there is 1% negative growth in manufacturing. So 1% of 21.8 becomes 0.218. Thus, 21.8 – 0.218 = 21.582. Similarly, for mining and quarrying it is 15.75. For electrical it is 11.77 and for chemical it is 16.26. ∴ Total growth 21.582 + 15.75 + 11.77 + 16.26 = 65.36.

Now, 74. (b) Clear from the graph. 75. (b) Year Production 1990 4% of 15 = 0.6 ∴ Production = 15.6 1991 15.76 1992 16.1 1993 15.46 1994 16.69 Hence, it can be seen that the lowest level of production was in 1993. 76. (a) Sectors Production in 1994 Manufacturing 25.68 Mining & Quarrying 16.69 Electrical 14.41 Chemical 18.79 Total 75.57 Total production in 1989 = 60

77. (b) Since the index of total industrial production in 1994 is 50 percent more than in 1989, it becomes 150. Total weightage for manufacturing, mining and quarrying, electrical and chemical in 1994 is approximately 75.57. So Production of other sectors = 150 – 75.57 = 74.43. In 1989, it was 100 – 60 = 40.

78. (a) Man hours spent in coding = 430 + 100 = 530 Man hours spent in offshore design and coding = 100 + 430 = 530. Man hours spent in Testing = 290 + 180 = 570. 79. (c) Total work onsite

Total work done = 350 +100 + 430 + 290 = 1170. Hence approximately 30% of the work is carried out onsite. ∴ % work =

80. (c) Man hours spent onsite = 350. Sum of estimated and actual effort for offshore design = 100 + 80 = 180. Estimated man-hours of offshore coding = 430 Actual man hours of offshore testing = 290. Half of estimated offshore coding = So, (c) is correct. 81. (a) Total hours spent = 1170 (as calculated in Q. 27) Hours in coding = 430 + 100 = 530 = 45.3% House in Design = 190 = 16.2% House in Offshore testing = 290 = 24.8% House in Offshore testing + Design = 290 + 190 = 480 = 41%. Hence (a) is the closest option. 82. (b) Total offshore work = 100 + 430 + 290 = 820 man hours. 50% of offshore work is carried out on-site = 410. Distribution of effort is in ratio, 180 : 530 : 430 = 18 : 53 : 43. Effort distributed to testing will be man-hours. Offshore testing work is ∴

Proportion

. of

testing

carried .

83. (a) Offshore

Design 50

Coding 215

Testing 145

out

offshore

On-site = 80 + 65 = 145= 100 + 191 = 291 = 140 + 154 = 294 Amount of coding done = 215 + 291 = 506. Amount of testing done = 145 + 291 = 436. Hence (a) is true. 84. (b) Effort allocation of , , Hence we can say that new valves of E are older values of B So, rank of company 3, in order of effort of E is 3. 85. (a) In company 4, total effort for equations through B to F get evenly distributed. So each gets the value of Initial percentage of E = 28.6 New percentage = 16.3 i.e Reduction of 12.3 86. (d) So B, C & D efforts will be removed & redistributed equally among any A, E and F. It is clearly seen from the chart that E will show the maximum distribution of effort as E already shows the maximum distribution.

87. (b)

We see from table the required states are five MA, TN, AP, KA, WB

88. (b)

From above table we see that GU & UP are the states who change their relative rank two times but GU is not given in the options hence U.P will be the required state 89. (d) For Tamil Nadu, For Karnataka, For Gujarat, % share of A.P from 1997 - 2001 increased by

which is most among TN, KA, GU 90. (c) Growth rate in 1999-2000 = 27.5% approx. which is maximum in comparision to other pair of years 91. (a) In KA revenue increased from 1998 to 2000 = 4839 – 4265 = 574 & revenue increase from 2000 to 2001 = 5413 – 4839 = 574

92. (c)

From the table we see TN’s rank is constant (MA and WB are not in options). Therefore its contribution to total tax collections will also have constant rank 93. (d) Visual question. Simply count the circles and squares above the line for profit 100 crores and right of turnover = 1000 crores. 94. (d) Visual question. Simply count the number of circles between the line for turnover 2000 (right of this line) and profit 300 (below this line). 95. (b) Draw the line y = 10% of x. The number of points above this line are the required companies (7). 96. (d) Find the range for each person. We see that for Shyam the range is the lowest. 97. (a) Geeta’s graph is flat in the second to third month. 98. (a) Visual question. Geeta starts at the lowest but is at the maximum at month 2. 99. (b) Seeta grows maximum in 2-3 month but grows at a slower rate after 3rd month. 100. (b) Chaidesh’s export of tea, as a proportion of tea produced is given below : Year Required Proportion 1996 189/561 1997 209/587 1998 215/645 1999 1/3 Hence it would be highest in 1997.

101. (a) Chaidesh’s population for different years is calculated as follows : population

∴ For 1995, For 1997, For 1996, For 1999, Hence it would be lowest in 1995. 102. (a) Productivity is rising continuously and area under cultivation is decreasing throughout. Hence productivity also increases continuosly. So highest in 1999. 103. (a) Comparing the operating income for 2002-03 in the 1st and the 3rd graph we can find that companies B and D are excluded from the graph 3. As both B and D make loss in 2001-02, so the only possible answer is (a). 104. (c) This can be found out from the third chart at it gives the ratio of operating profit to operating income for the companies A, C, E and F. Clearly the highest point is the answer. On comparing the operating income from chart 1 we find it to be E. 105. (d) Option (a) talks about C (from chart 2) whose operating income is not lowest in 2002-03 (from chart 1) Option (b) talks about D Option (c) talks about B Option (d) talks about A, C, E and F. Their operating incomes lies between 150 to 250 crore in 2002-03.

106. (d) Companies exceeding 10% profitability in 2002-03 one C and E. The operating profits (from chart 3) of C and E are 38 and 32. Hence, the average operating profit = 35 crores. 107. (c) (a) November rainfall < 100 cm in location 7 (b) September rainfall < 50 cm in location 1 (c) True 108. (b) April rainfall exceeds March rainfall at all locations so (a) is not true. Peak rainfall is in April in both the location is true. November rainfall excceds March in location 6. 109. (c) The graph shows that Rice, Onion, Egg and Chillies increase and Dal & Edible Oil decrease. 110. (d) Commodities showing price decline for 2 or more years consecutively – Rice, Dal, Chillies, Egg, Onion. 111. (d) The graph shows that only for Egg & onion, the price decline is followed by an increase in price, only once in the entire period. 112. (d) In this question we have to see the relative position of the markers with respect to the X-axis (expenditure). We find that the Dubeys are on the extreme right. 113. (c) To find the lowest average income, we have to see the relative position of the markers with respect to Y-axis. We find that the circles representing Coomars are the lowest on the vertical scale. 114. (a) Highest saving will be of a person who is highest on Y-axis and lowest on X-axis. This is represented by a black square representing Ahuja. 115. (d) The family having lowest saving will be the one who lies on the line indicating income = expenditure. The closest is black circle, or Dubey. 116. (b) No. of Naya mixer grinders disposed off in 1999 = 0.2 × 30 = 6 No. of Naya mixer grinders disposed off in 2000 = 0.2 × (80 – 30) = 10 ∴ Total naya mixer grinders disposed = 6 + 10 = 16 117. (b) Naya mixer grinders purchased in 1999 = 124 – 80 + 6

= 50 Note 6 were disposed in 1994. 118. (a) Purana mixer grinders purchased in 1999 = 236 – 222 + purana mixers disposed in 1999 = 14 + 20% of purana mixers introduced in 1997 = 14 + 0.2 × (182 – 162 + 10) = 14 + 6 = 20 119. (d) Purana mixer grinders disposed off in 2000 can not be calculated as we do not know the grinders disposed off in 1996, and 1998. 120. (c) Looking carefully at the four bars in finance, we clearly understand that a faculty retired in 2001. CHECK : Again the dip in average age clearly shows that the new faculty joined in 2002. CHECK : 121. (c) Clearly the dip in 2001 shows that the faculty joined onApril 1, 2001. So age on April 1, 2003 is 25 + 2 = 27 years 122. (a) From Q. 64, we clearly see that the faculty member retired from Finance. NOTE : The area (from which a faculty retires) will show two drops in the average ages. 123. (d) As in 2000, Age of the faculty born in 1947 = 52 yrs Age of the faculty born in 1950 = 49 yres Average age on April 1, 2000 = 49.33 ∴ Age of the 3rd faculty = 49 .33 × 3 – (52 + 49) = 47 yrs So his age in 2005 is 47 + 5 = 52 yrs 124. (c)

Let revenue from data transfer and total revenue of India are R1 and T1 respectively. Also suppose that revenue from data transfer

and total revenue of Sweden are R2 and T2 respectively. Volume of data transfer in India is the same as that of Sweden. Let it be V. In 2010, ,

, ∴ R2 = 6V

Now, T1 = 2T2,

∴

Now,

, ,

∴

Hence, required percentage increase

Since ARDT for India is less than 1, hence required percentage increase will be more than 658%. 125. (e) Let revenue from data transfer and total revenue of India are R1 and T1 respectively. Also suppose that revenue from data transfer and total revenue of Singapore are R2 and T2 respectively. Volume of data transfer in India is the same as that of Singapore. Let it be V. Then,

and

(approx.) Hence, total revenue of Singapore is 4 times that of India. 126. (d) For option (a),

Let revenue from data transfer and volume of data transfer for Philippines are R1 and V1 respectively. Also suppose that revenue from data transfer and volume of data transfer for Austria are R2 and V2 respectively. Total revenue of Philippines is the same as that of Austria. Let it be T. Now, and

And,

∴ V1 ≠ V2 For option (b),

∴ V1 ≠ V2 For option (c),

∴ V1 ≠ V2 For option (d),

∴ V1 ≈ V2 Similarly, we can check the option (e) which will not be true. 127. (d) Absolute value of the annual percent change in the following years ;

Year 03 - 04

Year 05- 06

Year 06-07

Year 08-09

Year 09-10

128. (c) Growth rate in Europe in 2007 (over 2006)

Growth rate in Europe in 2005 (over 2004)

Therefore, required percentage change in growth (approx.) 129. (a) Estimated subscription in Europe in 2008 = 605 million USD. The percentage growth of 2007 in subscription in Europe (over 2006)

Estimated subscription in Europe if it would have been computed using the percentage growth rate of 2007 (over 2006) = 657.5 million USD (approx.)

Hence, required difference = 657.5 – 605 = 52.5 million USD (approx.) 130. (a) Let total number of subscribers in 2003 in Europe = 100 Hence, number of men subcribers in 2003 = 60 And number of women subscribers in 2003 = 40 No. of men subscribers in 2010

No. of women subscribers in 2010

Hence, total number of subscribers in 2010 = 84.40 + 77.94 = 162.34 Therefore, required percentage growth = 162.34 – 100 = 62% (approx.). (b) The Unhealthiness Index is maximum for the year 2003 and the value is

(c) The number of patients in 2008 = The number of patients in 2006 × (0.7)2 which comes out to be 95,596. The number of hospitals in 2008 will be = 5700 × (1.1)2 = 6897 Therefore, Unhealthiness Index

(d) As per the given data (using graph information), the number of patients in 2006 = 1,95,093. The number of patients in 2007 will be 1,95,093 × 0.6 = 1,17,056. To have an Unhealthiness Index of 15, the number of hospitals needed will be

= 7804.

Therefore the percentage increase needed in the number of hospitals will be

(b)

Average cost of each bottle

Average cost of the project 5.

(b) Profit % = 9.67 For the year (2005–06 to 2008–09) Efficacy Ratio

(c)

So only two years (2005 – 2006) and (2008 – 2009) efficacy ratio is greater than 1. (a) For the year 2005 – 06 in the Corporate I – Tax collectios the percentage growth of I–Tax over the previous year for both the Budgeted and the actual is approximately same.

(d)

I. Percentage contribution of Corporate I -Tax to the Total I-Tax in the year 2005-06

= 91.6%

In the year 2008–09 =

= 70%

II. Simple Annual Growth Rate =

= 94.4%

III. This is also true as evident from the table provided in solution 16. So, all statements are true. Solution (9–11) : Gender wise deaths due to NCDs in five countries for 2008 and 2009.

(c)

Indonesia, India and USA, were the number of deaths due to NCDs in 2009 was less than that in 2008. 10. (a) Total number of female death due to NCDs in five countries in 2008 = 8800 Total number of Female death due to NCDs in five countries in 2009 = 8175 ∴

Required percentage =

= 7.10% (decrease) 11. (b) Total number of male death due to NCDs in five countries in 2008 = 9753 Total number of male death due to NCDs in five countries in 2009 = 9730 ∴ Required difference = (9753 – 9730) × 1000 = 23000.

12. (b)

Profitability =

Profitability of NIIT in 1999 =

= 0.2204

Profitability of Aptech in 1999 = Profitability of SSI in 1999 =

= 0.1594 = 0.4

Profitability of Tata Infotech in 1999 =

= 0.0143

∴ Average of the profitabilities of the four companies in 1999 = = 0.1985. ∴ Only two companies Tata Infotech and Aptech have a profitability less than the average of the profitabilities in 1999. 13. (b) Total revenues of four companies in 2001 = 509 + 285 + 231 + 523 = 1548 crore Total profit of four companies in 2001 = 20 + 54 + 51 + 27 = 152 crore Total cost = Revenue – Profit ∴ Total cost = (1548 – 152) = 1396 crore In 2002, total revenue ≈ (1548 – 155) crore After decrease by 10% = 1393 crore. Total cost = (1396 + 140) = 1536 crore After increasing by 10% Hence, net profit= (1393 – 1536) = – 143 crore ∴ Profitability = 14. (a)

= – 10.25%

The profitability of NIIT, Aptech, SSI and Tata lnfotech in 2001 is ,

respectively. Thus, the increasing order is NIIT, Tata Infotech, Aptech and SSI.

and

0.051

15. (c)

The profitability of NIIT in 2000 =

The profitability of Aptech in 2000 = The profitability of SSI in 2000 =

= 0.2208 = 0.2029

= 0.3740

The profitability of Tata Infotech in 2000 = = 0.012 So SSI company has the highest profitability in 2000. Solution (16 to 18) :

16. (a) 17. (c)

IMT has the highest number of offers per student. According to above table, IMT has the highest ratio of offers per company. 18. (d) Total salary for FMS = 100 × 7 = ` 700 lakh Total salary of PPO holders = (25% of 100) × 10 = 250 lakh Total salary of people not getting PPOs = 700 – 250 = 450 Average annual salary of people not getting PPOs =

= 6 lakhs.

Solution (19 to 21): The table below gives all the possible values of B, C, D, E, F, G, H, l and J if the value of A is assumed to be ‘x’.

19. (d)

Clearly, if the value of A is known then 19 distinct values are possible for J. 20. (b) If, ‘x’ is even thenA D. G and J are even. If ‘x’ is odd then B, C E F, H and I are even. So, four numbers A, D, G and J are even. 21. (a) If x = 1, then a possibility is that B = 2, C = 4, D = 1, E= 2, F = 4, G = 1, H = 2, I = 4 and J = 1 in which case 7 values are perfect squares. This is the maximum number of perfect squares which can occur at the same time i.e. in a single case. 22. (a) Let the total investment in education sector by India = x Then, Total investment in education sector by China = 1.6x According to question, For china. 32% of 1.6x was from ADB loans A= For India, 20% of x was from ADB loans. B= Required ratio A : B = 256 : 135 23. (b) 24. (a) Loan amount invested in education = 20% of 150 = ` 30 r

Loan amount invested in Health = 22% of 120 = ` 26.4 cr Loan amount invested in Agriculture = 16% of 400 = Rs 64 cr ∴ Total loan amount invested in India = The required percentage = = 25.

= 15.05%

(c)

Total investment will be maximum when maximum loan amount is invested in education i.e. ` 440 cr. And `30 cr each is invested in power and transport sectors. ∴ Total investment in the 3 sectors =

= ` 2360 cr. 26. (c) Companies for which the expenses are less than 60% of the sales, will have a profit more than 40% of the sales. There are six such companies. 27. (b) According to graph, Only three software companies are the sales, more than Rs. 2500 crore and expenses are less than rs. 2100 crore.

Directions for Questions 1 to 4 : Refer to the pie-chart given below and answer the questions that follow :

1. (a) (b) (c) (d) 2. (a) (b) (c) (d) 3.

(a) (b)

What fraction of Ghoshbabu’s weight consists of muscular and skin proteins? (1994) 1/13 1/30 1/20 Can’t be determined Ratio of distribution of protein in muscle to the distribution of protein in skin is (1994) 3:1 3 : 10 1:3 3½ : 1 What percent of Ghoshbabu’s body weight is made up of skin? (1994) 0.15 10

(c) 1.2 (d) Can’t be determined 4. In terms of total body weight, the portion of material other than water and protein is closest to (1994) (a) 3/20 (b) 1/15 (c) 85/100 (d) 1/20 Directions for Questions 5 to 9 : Refer to the pie-chart given below and answer the questions that follow : Operating Profit 160 lakh.

(a) (b) (c) (d) 6. (a)

Operating Profit 130 lakh.

1991-92 1990-91 The operating profit in 1991-92 increased over that in 1990-91 by (19 95) 23% 22% 25% 24% The Interest burden in 1991-92 was higher than that in 1990-91 by (1995) 50%

(b) 25 lakh (c) 90% (d) 41 lakh 7. If, on an average, 20% rate of interest was charged on borrowed funds, then the total borrowed funds used by this company in the given two years amounted to .... (1995) (a) 221 lakh (b) 195 lakh (c) 368 lakh (d) 515 lakh 8. The retained profit in 1991-92, as compared to that in 1990-91 was (1995) (a) higher by 2.5% (b) higher by 1.5% (c) lower by 2.5% (d) lower by 1.5% 9. The equity base of these companies remained unchanged. Then the total dividend earning (in lakh rupees) by the share holders in 1991-92 is (1995) (a) 10.4 lakh (b) 9 lakh (c) 12.8 lakh (d) 15.6 lakh Directions for Questions 10 to 13 : Refer to the information and pie-charts given below and answer the questions that follow : Consider the information provided in the figure below relating to India’s foreign trade in 1997-98 and the first eight months of 1998-99. Total trade with a region is defined as the sum of

exports to and imports from that region. Trade deficit is defined as the excess of imports over exports. Trade deficit may be negative. A : U.S.A B: Germany C: Other E.U. D: U.K. E: Japan F: Russia G: Other East Europe H : OPEC I: Asia J: Other L.D. Cs K: Others SOURCES OF IMPORTS 1997-98; Imports into India : $ 40779 millon 1998-99; Imports into India (April-November) : $ 28126 million

DESTINATION OF EXPORTS 1997-98; Exports from India : $ 33979 million 1998-99; Exports from India (April-November) : $21436 million

10. What is the region with which India had the highest total trade in 1997-98? (1999) (a) USA (b) Other E.U (c) OPEC (d) Other 11.

In 1997-98, the amount of Indian exports, in million US $, to the region with which India had the lowest total trade, is

approximately

(1999) (a) 750 (b) 340 (c) 220 (d) 440 12. In 1997-98, the trade deficit with respect to India, in billion US $, for the region with the highest trade deficit with respect to India, is approximately equal to (1999) (a) 6.0 (b) 3.0 (c) 4.5 (d) 7.5 13. India had maximum trade surplus vis-a-vis which region in 199798 (1999) (a) USA (b) Asia (c) Others (d) Other E.U. ADDITIONAL Directions for Questions 14 & 15 : Refer to the information given below and answer the questions that follow : Assume that the average monthly exports from India and imports to India during the remaining four months of 1998-99 would be the same as that for the first eight months of the year.

14. What is the region to which Indian exports registered the highest percentage growth between 1997-98 and 199899 (1999) (a) Ohter East Europe (b) USA (c) Asia (d) exports have declined, no growth 15. What is the percentage growth rate in India’s total trade deficit between 1997-98 and 1998-99? (1999) (a) 43 (b) 47 (c) 50 (d) 40 Directions for Questions 16 to 18 : Refer to the pie-charts given below and answer the questions that follow : Chart 1 shows distribution of twelve million tonnes of crude oil transported through different modes over a specific period of time. Chart 2 shows the distribution of the cost of transporting this crude oil. The total cost was Rs. 30 million.

16. The cost in rupees per tonne of oil moved by rail and road happens to be roughly (2001) (a) 3 (b) 1.5 (c) 4.5 (d) 8 17. From the charts given, it appears that the cheapest mode of transport is (2001) (a) Road

(b) Rail (c) Pipeline (d) Ship 18. If the costs per tonne of transport by ship, air and road are represented by P, Q and R respectively, which of the following is true? (2001) (a) R > Q > P (b) P > R > Q (c) P > Q > R (d) R > P > Q Directions for Questions 19 & 20 : Refer to the pie-charts given below and answer the questions that follow :

Chart 1 shows the distribution by value of top 6 suppliers of MFA Textiles in 1995. Chart 2 shows the distribution by quantity of top 6 suppliers of MFA Textiles in 1995. The total value is 5760 million Euro (European currency). The total quantity is 1.055 million tonnes. 19. The country, is 002) (a) USA (b) Switzerland

which

has

the

highest

average

price, (2

price

Euro/Kg

for

Turkey

(2002) (a) (b) (c) (d)

6.20 5.60 4.20 4.80

(a) Ratio of protein in muscles to protein in skin

(d) We have only protein % in skin, therefore we would have weight of protein in skin but we can not determine the total weight of skin (a) In terms of body weight, other dry material = 15%

that is 5.

(a) Increase in operating profit

(b) Interest burden increase

(d) Borrowed funds in 1990-91 Borrowed funds in 1991-92 Total

(d) Retained Profit in 1990 - 91= Retained Profit in 1991 - 92= .2 × 160 = 32 Reduction

= 1.5%

9. (c) Dividend earning in 1991-92= 0.08 × 160= 12.8 10. (c) Total trade is export + import by options we see U.S.A. Import 9% of 40779 + Export 19% of 33979 = 3670.11 + 6456.01 = 10126.12 Other E.U. Import 12% of 40779 + Export 14% of 33979 = 4893.8 + 4757.06 = 9650.86 OPEC Import 23% of 40779 + Export 10% of 33979 = 9379.17 + 3397.9 = 12777.07 OTHERS Import 1% of 40779 + Export 1% of 33979 = 407.79 + 339.79 = 747.58 Note : This question can also be answered by observing the two pie-charts of 1997-98 for the four countries. USA = 9% + 19% ; Other EU = 12% + 14% OPEC = 23% + 10% ; Others = 1% + 1% As the first percentage is from a higher total ($40779 million) it is clear that OPEC is the right answer. 11. (b) Lowest total trade is in the region K and the export is 1% of 33979 = 339.79. 12. (a) Trade deficit is excess of imports over exports. From the pie-charts it is clear that H (23% imports and only 10% exports) has the highest trade deficit. Deficit = 23% of 40779 – 10% of 33979 = 9379.17 – 3397.9 = 5981.27 million USD = 5.98 billion USD 13. (a) Maximum trade surplus means lowest trade deficit. From the charts it is clear that USA (9% imports and 19% exports) is the right choice. 14. (b) In 1998-99 the total export and import for the whole year is 3/2 times of trade given Total export in 1998-99 will be 1.5 × 21436 = 32154

Total import in 1998-99 will be 1.5 × 28126 = 42189 Highest % growth in the exports can be interpreted from the graph either in the region A (19% to 23%) or in the region G (10% to 12%). Region A :

Region B :

So, Region A or USA is the answer. 15. (b) Trade deficit in 1997-98 = 40779 – 33979 = 6800 Trade deficit in 1998-99 = 42189 – 32154 = 10035 % growth in trade deficit = 16. (b) Total cost = Rs 30 million Total volume = 12 million ton Vol. transported by Rail & Road = 31% of 12 = 3.72 mT Cost by Rail & Road = 18% of 30 = 5.4 million Cost per tonne 17. (a) Since cost of transportation through road is minimum with a significant volume transported. Hence it is the cheapest mode of transport 18. (c) Cost per tonne ,

; hence

19. (b) Distribution (value) for USA (qty.) for USA

; Distribution = .1583

Distribution (value) Switzerland

;

Distribution (qty.) Switzerland Distribution (value) for Turkey

; Distribution

(qty.) for Turkey Distribution (value) for India = 1152; Distribution (qty.) for India Per Kg price in USA

;

Switzerland Turkey

; ;

India Highest price in Switzerland ALTERNATIVELY : Average price is So on carefully observing the pie-charts, we can find the highest average price for which the value is maximum and quantity

is minimum. Among the given options, Switzerland (20% value and 11% quantity) is the correct choice. 20. (b) Average price in Euro/ kg for turkey

(roughly) [Note : 1.055 m ton = 1055 m kg]

Directions for Questions 1 to 4 : These questions are based on the table and information given below. 1.

In 1984-85 value of exports of manufactured articles exceeds over the value of exports of raw materials by 100%. 2. In 1985-86 the ratio of % of exports of raw material to that of exports of manufactured articles is 3 : 4. 3. Exports of food in 1985-86 exceeds the 1984-85 figure by Rs. 1006 crore. Item 1984-85 1985-86 Food 23% Manufactured Articles Raw Material Total Value of Exports in Crore of Rs. 22400 25800 1. In 1984-85 what percentage of total values of exports accounts for items related to food (1994) (a) 23% (b) 29.2% (c) 32% (d) 22% 2. During 1984-85, how much more raw material than food was exported? (1994) (a) Rs.2580 crore (b) Rs. 896 crore (c) Rs. 1986 crore (d) Rs. 1852 crore 3. Value of exports of raw material during 84-85 was how much percent less than that for 85-86? (1994) (a) 39 (b) 42.5 (c) 7 (d) 31.6 4. The change in value of exports of manufactured articles from 1984-85 to 198586 is (1994) (a) 296 crore (b) 629 crore

(c) 2064 crore (d) 1792 crore Directions for Questions 5 to 8 : These questions are based on the table given below. The following table gives the sales details for text books and reference books at Primary / Secondary / Higher Secondary / Graduate levels Year Primary Secondary Higher Secondary Graduate Level 1975 42137 8820 65303 25343 1976 53568 10285 71602 27930 1977 58770 16437 73667 28687 1978 56872 15475 71668 30057 1979 66213 17500 78697 33682 1980

5. (a) (b) (c) (d) 6. (a) (b) (c) (d) 7. (a) (b) (c) (d)

68718 20177 82175 36697 What is the growth rate of sales of books at primary school level from 1975 to 1980? (1994) 29% 51% 63% 163% Which of the categories shows the lowest growth rate from 1975 to 1980? (1994) Primary Secondary Higher Secondary Graduate level Which category had the highest growth rate in the period? (1994) Primary Secondary Higher Secondary Graduate level

8. (a) (b) (c) (d)

Which of the categories had either a consistent growth or a consistent decline in the period shown? (1994) Primary Secondary Higher Secondary Graduate level

Directions for Questions 9 to 13 : These questions are based on the table and information given below. Ghosh Babu surveyed his companies and obtained the following data. Income tax is paid from Profit BeforeTax and the remaining amount is apportioned to Dividend and Retained Earnings. The Retained earnings were accumulated into Reserves. The reserves at the beginning of 1991 were Rs. 80 lakh.

In ?

which

year

was

the

sales

per

rupee

of share (1995)

capital

highest

In which year was the tax per rupee of profit before tax lowest ? (1995)

the

reserves

(in

Rs.

Lakh)

the

end of (1995)

1994

(a) 935 (b) 915 (c) 230 (d) None of these Directions for Questions 14 to 18 : These questions are based on the table given below. Market Shares in four Metropolitan Cities

14. The market of which products did not decrease between 1993-94 in any city? (1995) (a) HD (b) CO (c) BN (d) None of these 15. The number of products which doubled their market shares in one or more cities is (1995) (a) 0 (b) 1 (c) 2 (d) 3 16. The is (a) 60%

largest

percentage

drop

market shares (1995)

(b) 50% (c) 53.3 % (d) 20 % 17. The number of products which had 100% market share in four metropolitan cities is (1995) (a) 0 (b) 1 (c) 2 (d) 3 18. The city in which the minimum number of products increased their market shares in 1993-94 was (1995) (a) Bombay (b) Delhi (c) Calcutta (d) Madras Directions for Questions 19 to 23 : These questions are based on the table and information given below. A company produces five types of shirts - A,B, C, D, E, - using cloth of three qualities High, Medium and Low -, using dyes of three qualities - High, Medium, and Low, The following tables give, respectively : 1. The number of shirts (of each category ) produced, in thousands. 2. The percentage distribution of cloth quality in each type of shirt, and 3. The percentage distribution of dye quality in each type of shirt. Note: Each shirt requires 1.5 metres of cloth.

19. What cloth? (1995) (a) 150,000 m (b) 200,000 m (c) 225,000 m (d) 250, 000 m

the

total

requirement

20. How many metres of high quality cloth is consumed by Ashirts? (1995) (a) 8,000 m (b) 112,000 m (c) 24,000 m (d) 30, 000 m 21. What is the ratio of low quality type dye used for C-shirts to that used for Dshirts? (1995) (a) 3 : 2 (b) 2 : 1 (c) 1 : 2 (d) 2 : 3 22. How many metres of lowquality cloth is consumed? (1995) (a) 22,500 (b) 46,500 (c) 60,000 (d) 40, 000 23. What is the ratio of the three qualities of dyes in high- quality cloth? (1995) (a) 2 : 3 : 5 (b) 1 : 2 : 5 (c) 7 : 9 : 10 (d) Cannot be determined Directions for Questions 24 to 28 : These questions are based on the table given below. Data about certain coffee producers in India

24. What is the maximum production capacity (in ‘000 tonnes ) of Lipton for coffee? (1996) (a) 2.53 (b) 2.85 (c) 2.24 (d) 2.07 25. The highest price of coffee per kg is for (1996)

(a) (b) (c) (d) 26.

Nestle MAC Lipton Insufficient data What percent of the total market share (by Sales value) is controlled by “others”? (1996) (a) 60% (b) 32% (c) 67% (d) Insufficient data 27. What approximately is the total production capacity (in tonnes) for coffee in India? (1996) (a) 18 (b) 20 (c) 18.9 (d) Insufficient data 28. Which company out of the four companes mentioned above has the maximum unutilized capcity (in ‘000 tonnes)? (1996) (a) Lipton (b) Nestle (c) Brooke Bond (d) MAC Directions for Questions 29 to 33 : These questions are based on the tables and information given below. Mulayam Software Co., before selling a package to its clients, follows the given schedule :

The number of people employed in each month is:

29. Due to overrun in “Design”, the Design stage took 3 months, i.e. months 3, 4 and 5 . The number of people working on Design in the fifth month was 5. Calculate the percentage change in the cost incurred in the fifth month.(Due to improvement in “Coding” technique, this stage was completed in months 6 - 8 only ) (1996)

(a) (b) (c) (d) 30.

225% 150% 275% 240% With reference to the above question, what is the cost incurred in the new “coding” stage ? (Under the new technique, 4 people work in the sixth month and 5 in the eighth) (1996) (a) Rs. 1,40,000 (b) Rs. 1,50,000 (c) Rs. 1,60,000 (d) Rs. 1, 80,000 31. Under the new technique, which stage of Software development is most expensive for Mulayam Software company? (1996) (a) Testing (b) Specification (c) Coding (d) Design 32. Which five consecutive months have the lowest average cost per man-month under the new technique? (1996) (a) 1- 5 (b) 9 - 13 (c) 11 - 15 (d) None of these 33. What is the difference in the cost between the old and the new techniques? (1996) (a) Rs.30,000 (b) Rs.60,000 (c) Rs.70,000 (d) Rs.40,000 Directions for Questions 34 to 38 : These questions are based on the table and information given below. The amount of money invested (in rupees crore ) in the core infrastructure areas of two districts, Chittoor and Khammam, in Andhra Pradesh, is as follows :

34. (a) (b) (c) (d) 35. (a) (b) (c) (d) 36.

(a) (b) (c) (d) 37.

(a) (b) (c) (d) 38.

By what percent was the total investment in the two districts more in 1996 as compared to that in 1995? (1996) 14% 21% 24% 18% Approximately how many times the total investment in Chittoor was the total investment in Khammam? (1996) 2.8 2.0 2.4 1.7 The investment in Electricity and Thermal Energy in 1995 in these two districts formed what percent of the total investment made in that year ? (1996) 41% 47% 52% 55% In Khammam district, the investment in which area in 1996 showed the highest percent increase over the investment made in that area in 1995? (1996) Electricity Chemical Solar Nuclear If the total investment in Khammam shows the same rate of increase in 1997, as it had shown from 1995 to 1996, what approximately would be the total investment in Khammam in 1997 (in Rs. crore?) (1996)

(a) 9, 850 (b) 10, 020 (c) 9, 170 (d) 8, 540 Directions for Questions 39 to 43 : These questions are based on the table and information given below. The first table gives the percentage of students in the class of M.B.A who sought employment in the areas of Finance, Marketing and Software. The second table gives the average starting salaries of the students per month, in these areas.

39. The number of students who got jobs in finance is less than the number of students getting marketing jobs, in the five years, by (1996) (a) 826 (b) 650 (c) 750 (d) 548 40. In 1994, students seeking jobs in finance earned Rs...................more than those opting for sofware (in lakhs) (1996) (a) 43 (b) 33.8 (c) 28.4 (d) 38.8 41. What is the percent increase in the average salary of Finance from 1992 to 1996? (1996) (a) 60 (b) 32 (c) 96 (d) 80 42. What is the average monthly salary offered to a management graduate in the year 1993? (1996) (a) 6403 (b) 6330 (c) 6333 (d) Can’t be determined 43. The average annual rate at which the initial salary offered in Software, increases (1996) (a) 21% (b) 33% (c) 16.3%

(d) 65% Directions for Questions 44 & 45 : These questions are based on the table given below. HOTELS IN MUMBAI

44. Which room?

the

following

had

the

least

cost (1997)

per

(a) Lokhandwala (b) Raheja (c) IHCL (d) ITC 45. Which of the following has the maximum number of rooms per crore of rupees? (1997) (a) IHCL (b) Raheja (c) Lokhandwala (d) ITC ADDITIONAL Directions for Questions 46 to 48 : For these questions, assume that the cost of the project is incurred in the year of completion. Interest is charged @10% per annum. 46. What is the cost incurred (in Rs. crore) for projects completed in 1998? (1997) (a) 475 (b) 500 (c) 522.5 (d) 502.5 47. What is the cost incurred (in Rs. crore) for projects completed in 1999? (1997) (a) 1282.6

(b) 1270.0 (c) 1805.1 (d) 1535.0 48. What approximately is the cost incurred (in Rs. crore) for projects completed by 2000? (1997) (a) 1785 (b) 2140 (c) 2320 (d) None of these Directions for Questions 49 & 50 : These questions are based on the table and information given below. The following table gives the tariff (in paise per kilo-watt-hour) levied by the UPSEB in 1994-95, in the four sectors and the regions within them. The table also gives the percentage change in the tariff as compared to 199192.

49. If the amount of power consumed by the various Regions in Sector 1 is the same, then, as compared to 1991-92, the net tariff in 1994-95 ... (1997) (a) increases by 6.5% (b) decreases by 3.5% (c) increases by 10.2% (d) decreases by 7.3% 50. What 92?

approximately

was

the

average

tariff in Region (1997)

1991-

(a) 407 (b) 420 (c) 429 (d) None of these ADDITIONAL Directions for Questions 51 to 53 : The UPSEB supplies power under four categories, Urban (25%), Domestic (20%), Industrial (40%) and Rural (15%). In 1994-95, the total power produced by the UPSEB was 7875 Mega-watts.

51. If in 1994-95, there was a 10% decrease in the Domestic consumption of power as compared to that in 1991-92, what was the consumption of power in the rural sector in 1991-92? (1997) (a) 1312 (b) 1422 (c) 1750 (d) None of these 52. In the given two years, what is the total tariff paid by the Urban sector (in Rs. lakh)? (1997) (a) 22.4 (b) 21.6 (c) 27.2 (d) Can’t be determined 53. Which of the following is true? (1997) (a) The average tariff in Region 4 is 437.5 p/kwh. (b) The average tariff in Region 2 is greater than the average tariff in Region 5 (c) In 1991-92, the industrial sector contributed to about 42% of the total revenue from power (d) None of these Directions for Questions 54 to 59 : These questions are based on the table given below :

54. In 1974, the Agricultural loans formed what percent of the Total loans? (1997) (a) 85% (b) 71% (c) 77% (d) Can’t be determined 55. From the given data, the number of rural loans upto 1980 formed approximately what percent of those in 1983? (1997) (a) 112%

(b) (c) (d) 56.

80% 97% Can’t be determined Which of the following pairs of years showed the maximum increase in the number of loans? (1997) (a) 1971-72 (b) 1974-75 (c) 1970-71 (d) 1980-81 57. What is the value (in Rs. mm) of the Agricultural loans in 1983 at 1970 prices? (1997) (a) 326 (b) 264 (c) 305 (d) None of these 58. In which year was the number of loans per rural bank the least? (1997) (a) 1974 (b) 1971 (c) 1970 (d) 1975 59. What is the simple annual rate of increase in the number of Agricultural loans from 1970 to 1983? (1997) (a) 132% (b) 81% (c) 75% (d) 1056% ADDITIONAL Directions for Questions 60 & 61 : The Consumer Price Index for 1970 is to be taken as 105 and the Indices for the subsequent years are to be corrected accordingly. 60. By roughly how many points do the Indices for the years 1983 and 1975 differ? (1997) (a) 174 (b) 180 (c) 188 (d) 195 61. What is the value of loans in 1980 at 1983 prices? (1997) (a) 570

(b) 675 (c) 525 (d) 440 Directions for Questions 62 to 67 : These questions are based on the table and information given below. The following table gives the quantity of Apples (in tons) arriving in the New Delhi market from various states in a particular year. The month in which demand was more than supply, the additional demand was met by the stock from cold storage.

62. What was the maximum percentage of Apples supplied by any state in any of the months? (1998) (a) 99% (b) 95% (c) 88% (d) 100% 63. Who Apples?

supplied

the

maximum

(1998) (a) UP (b) HP (c) J&K (d) Cold Storage 64. Which state supplied the highest percentage of Apples from the total Apples supplied ? (1998) (a) HP (b) UP

periods

supply

was (1998)

greater

than

the

(a) Aug-Mar (b) June-Oct (c) May-Sep (d) Nov-April 66. If the yield per tree was 40 kg then from how many trees were the apples supplied to Delhi (in million )? (1998) (a) 11.5 (b) 12.36 (c) 13.5 (d) Can not be determined 67. Using data in previous question, if there were 250 trees per hectare then how many hectare of land was used? (1998) (a) 9400 (b) 49900 (c) 50000 (d) 49453 Directions for Questions 68 & 69 : These questions are based on the table given below. RELATIVES SWEETNESS OF DIFFERENT SUBSTANCES

68. How many grams of sucrose must be added to one gram of saccharin to make a mixture hundred times as sweet as glucose (1999) (a) 7 (b) 8 (c) 9 (d) 23

69. How many times sweeter than sucrose is a mixture of glucose, sucrose and fructose in the ratio 1:2:3 (1999) (a) 0.6 (b) 1.0 (c) 1.3 (d) 2.3 Directions for Questions 70 to 74 : Answer the questions based on the following information. The table below presents data on percentage population covered by drinking water and sanitation facilities in selected Asian countries. Population covered by drinking water and sanitation facilities Percentage coverage

(Source: World Resources 1998-99, p. 251, UNDP, UNEP and World Bank.) Country A is said to dominate B or A > B if A has higher percentage in total coverage for both drinking water and sanitation facilities, and, B is said to be dominated by A, or B < A. A country is said to be on the coverage frontier if no other country dominates it. Similarly, a country is not on the coverage frontier if it is dominated by at least one other country. 70. Which countries are the countries on the coverage frontier? (a) India and China (b) Sri Lanka and Indonesia (c) Philippines and Bangladesh (d) Nepal and Pakistan 71. Which of the following statements are true? A. India > Pakistan and India > Indonesia B. India > China and India > Nepal C. Sri Lanka > China D. China > Nepal (a) A and C (b) B and D (c) A, B and C (d) B, C and D

72.

Using only the data presented under ‘sanitation facilities’ columns, it can be concluded that rural population in India, as a percentage of its total population is approximately (a) 76 (b) 70 (c) 73 (d) Cannot be determined 73. Again, using only the data presented under ‘sanitation facilities’ columns, sequence China, Indonesia and Philippines in ascending order of rural population as a percentage of their respective total population. The correct order is (a) Philippines, Indonesia, China (b) Indonesia, China, Philippines (c) Indonesia, Philippines, China (d) China, Indonesia, Philippines 74. India is not on the coverage frontier because A. it is lower than Bangladesh in terms of coverage of drinking water facilities. B. it is lower than Sri Lanka in terms of coverage of sanitation facilities. C. it is lower than Pakistan in terms of coverage of sanitation facilities. D. it is dominated by Indonesia. (a) A and B (b) A and C (c) D (d) None of these Directions for Questions 75 to 79 : Answer the following questions based on the information given below. Information Technology Industry in India (Figure are in million US dollars)

75. The total annual exports lay between 35 and 40 percent of the total annual business of the IT industry, in years (a) 1997-98 & 1994-95

(b) (c) (d) 76. (a) (b) (c) (d) 77.

1996-97 & 1997-98 1996-97 & 1998-99 1996-97 & 1994-95 The highest percentage growth in the total IT business, relative to the previous year was achieved in 1995-96 1996-97 1997-98 1998-99 Which one of the following statements is correct?

(a) The annual software exports steadily increased but annual hardware exports steadily declined during 1994-1999. (b) The annual peripheral exports steadily increased during 1994-1999. (c) The total IT business in training during 1994-1999 was higher than the total IT business in maintenance during the same period. (d) None of the above statements is true. 78. In which of the following years the total hardware revenue is more than 50% of the software revenue in the same year? (a) 1994-95 (b) 1995-96 and 1996-97 (c) 1997-98 and 1994-95 (d) None of the above 79. In how many years the total revenue of training and maintence is less than ten percent of the total revenue? (a) 2 (b) 3 (c) 4 (d) all Directions for Questions 80 & 81 : Answer the following questions based on the information given below. For any activity, A, year X dominates year Y if IT business in activity A, in the year is greater than the IT business, in activity A, in the year Y. For any two business activities, A & B, year X dominates year Y if i. the IT business in activity A, in the year X, is greater than or equal to the business, in activity A in the year Y, ii. the IT business in activity B, in the year X, is greater than or equal to the business in activity B in the year Y and iii. there should be strict inequality in the case of at least one activity. 80. For the IT hardware business activity, which one of the following is not true? (2000) (1) 1997-98 dominates 1996-97 (b) 1997-98 dominates 1995-96

X, IT IT IT

(c) 1995-96 dominates 1998-99 (d) 1998-99 dominates 1996-97 81. For the two IT business activities, hardware and peripherals, which one of the following is true? (2000) (a) 1996-97 dominates 1995-96 (b) 1998-99 dominates 1995-96 (c) 1997-98 dominates 1998-99 (d) None of these Directions for Questions 82 to 87 : Answer the following questions based on the information given below. Factory Sector by Type of Ownership. All figures in the table are in percent of the total for the corresponding column

82.

(a) (b) (c) (d) 83. (a) (b) (c) (d) 84.

(a) (b) (c) (d)

Suppose the average employment level is 60 per factory. The average employment in “wholly private” factories is approximately (2000) 43 47 50 54 Among the firms in different sectors, value added per employee is highest in (2000) Central government Central and State/local governments Joint sector Wholly private Capital productivity is defined as the gross output value per rupee of fixed capital. The three sectors with the higher capital productivity, arranged in descending order are (2000) Joint, wholly private, central and state/local Wholly private, joint, central and state/local Wholly private, central and state/local, joint Joint, wholly private, central

85.

A sector is considered “pareto efficient” if its value added per employee and its value added per rupee of fixed capital is higher than those of all other sectors. Based on the table data, the pareto efficient sector is

(a) (b) (c) (d) 86.

Wholly private Joint Central and state/local Others The total value added in all sectors is estimated at ` 140,000 crores. Suppose that the number of firms in the joint sector is 2700. The average value added per factory, in ` crores, in the central government is

(a) (b) (c) (d) 87.

141 14.1 131 13.1 Which of the following statement is true. The no. of govt. employees are more than the no. of joint sector. The no. of employees in the public sector is same as fixed capital of joint sector. Both (a) and (b) Cannot say

(a) (b) (c) (d)

Directions for Questions 88 to 91 : These questions are based on the table and information given below. The following is a table describing garments manufactured based upon the colour and size for each lay. There are four sizes : M-Medium, L-Large, XL-Extra Large and XXL-Extra-Extra Large. There are three colours: Yellow, Red and White.

88. How many lays are used to produce yellow coloured fabrics? (2001) (a) 10 (b) 11 (c) 12 (d) 14 89. How many lays are used to produce ExtraExtra Large fabrics? (2001) (a) 15 (b) 16 (c) 17 (d) 18 90. How many lays are used to produce Extra-Extra Large Yellow or Extra-Extra Large White fabrics? (2001) (a) 8 (b) 9 (c) 10 (d) 15 91. How many varieties of fabrics, which exceed the order, have been produced? (2001)

(a) (b) (c) (d)

3 4 5 6

Directions for Questions 92 to 95 : These questions are based on the table and information given below. THE BUSIEST TWENTY INTERNATIONAL AIRPORTS IN THE WORLD

92. How many international airports of type ‘A’ account for more than 40 million passengers? (2001) (a) 4 (b) 5 (c) 6 (d) 7 93. What percentage of top ten busiest airports is in the United States of America? (2001) (a) 60 (b) 80 (c) 70 (d) 90 94. Of the five busiest airports, roughly what percentage of passengers is handled by Heathrow airport? (2001) (a) 30 (b) 40 (c) 20

(d) 50 95. How many international airports not located in the USA handle more than 30 million passengers? (2001) (a) 5 (b) 6 (c) 10 (b) 14 Directions for Questions 96 to 98 : These questions are based on the table and information given below. The following table provides data on the different countries and location of their capitals. (the data may not match the actual Latitude, Longitudes) Answer the following questions on the basis of the table. Sl. No. Country

Capital

Latitude

Longitude

Argentina

Buenes Aires

34.30 S

58.20 E

Australia

Canberra

35.15 S

149.08 E

Austria

Vienna

48.12 N

16.22 E

Bulgaria

Sofia

42.45 N

23.20 E

Brazil

Brasilia

15.47 S

47.55 E

Canada

Cambodia

Ottawa Phnom Penh

Equador Quito Sl. No. Country Capital

45.27 N 11.33 N

75.42 E 104.55 E

0.15 S Latitude

78.35 E Longitude

Accra

5.35 N

0.6 E

Ghana

10.

Iran

Teheran

35.44 N

51.30 E

11.

Ireland

Dublin

53.20 N

6.18 E

12.

Libya

Tripoli

32.49 N

13.07 E

13.

Malaysia

14.

Peru

15.

Poland

Kuala Lampur Lima Warsaw

3.9 N 12.05 S

101.41 E 77.0 E

52.13 N

21.0 E

16.

New Zealand Wellington

41.17 S

174.47 E

17.

Saudi Arabia

Riyadh

24.41 N

46.42 E

18.

Spain

Madrid

40.25 N

3.45 W

19.

Sri Lanka

Colomba

6.56 N

79.58 E

20.

Zambia

Lusaka

15.28 S

28.16 E

96. What percentage of cities located within 10°E and 40°E (10-degree East and 40 degree East) lie in the Southern Hemisphere? (2002) (a) 15% (b) 20% (c) 25% (d) 30% 97. The number of cities whose names begin with a consonant and are in the Northern Hemisphere in the table (2002) (a) exceeds the number of cities whose names begin with a consonant and are in the southern hemisphere by 1 (b) exceeds the number of cities whose names begin with a consonant and are in the southern hemisphere by 2 (c) is less than the number of cities whose names begin with a consonant and are in the meridian by 1 (d) is less than the number of countries whose name begins with a consonant and are in the meridian by 3 98. The ratio of the number of countries whose name starts with vowels and located in the southern hemisphere, to the number of countries, the name of whose capital cities starts with a vowel in the table above is (2002) (a) 3:2 (b) 3:3 (c) 3:1 (d) 4:3 Directions for Questions 99 to 102 : These questions are based on the table and information given below. The following table gives details regarding the total earnings of 15 employees and the number of days they have worked on complex, medium and simple operations in the month of June 2002. Even though the employees might have worked on an operation, they would be eligible for earnings only if they have minimum level of efficiency. Total Earnings Total Days Emp. No. Complex Medium Simple Total Complex Mediu m Simple Total 2001147 82.98 636.53 719.51 3.00 0.00 23.00 26.00

2001148 2001149 2001150 2001151 2001156 2001158 2001164 2001170 2001171 2001172 2001173 2001174 2001179

51.53 16.00 171.71 8.50 100.47 7.33 594.43 0.00 89.70 1.00 472.31 0.00 402.25 0.67 576.57 0.00 286.48 0.38 512.10 3.50 1303.88 0.50 1017.94 0.00

461.73

513.26

3.33

1.67

79.10

250.81

5.50

4.00

497.47

597.95

6.00

4.67

754.06

9.67

13.33

21.00 18.00 18.00 159.64 23.00

89.70 9.00 109.73 11.00 735.22 213.67 18.00

582.04 1351.14

8.00 1.39 5.27

0.00 9.61 12.07

576.57

21.00

0.00

6.10

292.57

8.38

4.25

13.00 117.46 22.00

629.56

10.00

8.50

1303.88

25.50

0.00

1017.94

26.00

0.00

21.00

26.00 26.00

46.56 776.19 822.75 2.00 19.00 0.00 21.00 2001180 116.40 1262.79 1379.19 5.00 19.00 0.00 24.00 99. The number of employees who have earned more than 50 rupees per day in complex operations is (2002) (a) 4 (b) 3 (c) 5 (d) 6 100. The number of employees who have earned more than 600 rupees and having more than 80% attendance (there are 25 regular working days in June 2002; some might be coming on overtime too) is (2002) (a) 4 (b) 5

(c) 6 (d) 7 101. The employee number of the person who has earned the maximum earnings per day in medium operation is (2002) (a) 2001180 (b) 2001164 (c) 2001172 (d) 2001179 102. Among the employees who were engaged in complex and medium operations, the number of employees whose average earning per day in complex operations is more than average earning per day in medium operations is (2002) (a) 2 (b) 3 (c) 5 (d) 7 Directions for Questions 103 to 110 : These questions are based on the table and information given below. The following table shows the revenue and expenses in millions of Euros (European currency) associated with REPSOL YPF company’s oil and gas producing activities in operations in different parts of the world for the years 1998-2000. REPSOL YPF’S Operations of Oil and Gas Producing Activities

103. How many operations (Spain, North Africa and Middle East, ....) of the company accounted for less than 5% of the total revenue earned in the year 1999? (2002) (a) 2 (b) 3

(c) 4 (d) None of these 104. How many operations (Spain, North Africa and Middle East, ....) of the company witnessed more than 200% increase in revenue from the year 1999 to 2000? (2002) (a) 1 (b) 2 (c) 3 (d) None of these 105. How many operations registered a sustained yearly increase in income before taxes and charges from 1998 to 2000? (2002) (a) 3 (b) 4 (c) 5 (d) None of these 106. Ignoring the loss making operations of the company in 1998, for how many operations was the percentage increase in net income before taxes and charges higher than the average from 1998 to 1999? (2002) (a) 0 (b) 1 (c) 2 (d) None of these 107. If profitability is defined as the ratio of net income after taxes and charges to expenses, which of the following statements is true? (2002) (a) The Far East operations witnessed its highest profitability in 1998 (b) The North Sea operations increased its profitability from 1998 to 1999 (c) The operations in Argentina witnessed a decrease in profitability from 1998 to 1999 (d) Both (b) and (c) are true 108. In the year 2000, which among the following countries had the best profitability? (2002) (a) North Africa & Middle East (b) Spain (c) Rest of Latin America (c) Far East 109. If Efficiency is defined as the ratio of revenue to expenses, which operation was the least efficient in the year 2000? (2002) (a) Spain (b) Argentina

(c) Far East (d) None of these 110. Of the following statements, which one is not true? (2002) (a) The operations in Spain had the best efficiency in 2000 (b) The Far East operations witnessed an efficiency improvement from 1999 to 2000 (c) The North Sea operations witnessed an efficiency improvement from 1998 to 1999 (d) In the year 1998, the operations in Rest of Latin America were the least efficient. Directions for Questions 111 to 116 : These questions are based on the table and information given below. There are 6 refineries, 7 depots and 9 districts. The refineries are BB, BC, BD, BE, BF and BG. The depots are AA, AB, AC, AD, AE, AF and AG. The districts are AAA, AAB, AAC, AAD, AAE, AAF, AAG, AAH ad AAI. Table A gives the cost of transporting one unit from refinery to depot. Table B gives the cost of transporting one unit from depot to a district.

111. What is the least cost of sending one unit from any refinery to any district? (2002) (a) 95.2 (b) 0

(c) 205.7 (d) 284.5 112. What is the least cost of sending one unit from any refinery to the district AAB? (2002) (a) 0 (b) 284.5 (c) 95.2 (d) None of these 113. What is the least cost of sending one unit from refinery BB to any district? (2002) (a) 284.5 (b) 311.1 (c) 451.1 (d) None of these 114. What is the least cost of sending petrol from refinery BB to district AAA? (2002) (a) 765.6 (b) 1137.3 (c) 1154.3 (d) None of these 115. How many possible ways are there for sending petrol from any refinery to any district? (2002) (a) 63 (b) 42 (c) 54 (d) 378 116. The largest cost of sending petrol from any refinery to any district is (2002) (a) 2172.6 (b) 2193.0 (c) 2091.0 (d) None of these Directions for Questions 117 to 119 : These questions are based on the table and information given below. The table below gives information about four different crops, their different quality categories and the regions where they are cultivated. Based on the information given in the table answer the questions below.

117. How many regions produce medium qualities of Crop-1 or Crop-2 and also produce low quality of Crop-3 or Crop 4 (2002) (a) Zero (b) One (c) Two (d) Three 118. Which true?

the

following

statements

is (2002)

(a) All Medium quality Crop-2 producing regions are also high quality Crop-3 producing regions (b) All High quality Crop-1 producing regions are also medium and low Crop-4 producing regions (c) There are exactly four Crop-3 producing regions, which also produce Crop-4 but not Crop-2 (d) Some Crop-3 producing regions produce Crop-1, but not high quality Crop-2 119. How many low quality Crop-1 producing regions are either high quality Crop-4 producing regions or medium quality Crop-3 producing regions? (2002) (a) One (b) Two (c) Three (d) Zero Directions for Questions 120 to 122 : These questions are based on the table and information given below.

One of the functions of the Reserve Bank of India is to mobilize funds for the Government of India by issuing securities. The following table shows details of funds mobilized during the period July 2002 - July 2003. Notice that on each date there were two rounds of issues, each with a different maturity.

120. Which true?

the

following

statements

is not (2003C)

(a) Competitive bids received always exceed non–competitive bids received. (b) The number of competitive bids accepted does not always exceed the number of non-competitive bids accepted. (c) The value of competitive bids accepted on any particular date is never higher for higher maturity. (d) The value of non-competitive bids accepted in the first round is always greater than that in the second round. 121. Which true?

the

following

(2003C) (a) The second round issues have a higher maturity than the first round for all dates. (b) The second round issue of any date has a lower maturity only when the first round notified amount exceeds that of the second round. (c) On at least one occasion, the second round issue having lower maturity received a higher number of competitive bids. (d) None of the above three statements is true.

122. How many times was the issue of securities subscribed, i.e., how often did the total amount mobilized fall short of the amount notified? (2003C) (a) 0 (b) 1 (c) 2 (d) 3 Directions for Questions 123 to 125 : These questions are based on the table and information given below. In each question, there are two statements : A and B, either of which can be true or false on the basis of the information given below. A research agency collected the following data regarding the admission process of a reputed management school in India. Year Gender Number bought Number appeared Number called Number selected application forms for written test for interviews for the course 2002 Male 61205 59981 684 171 Female 19236 15389 138 48 2003 Male 63298 60133 637 115 Female 45292 40763 399 84 Choose (a) if only A is true Choose (b) if only B is true Choose (c) if both A and B are true Choose (d) if neither A nor B is true 123. Statement A: The percentage of absentees in the written test among females decreased from 2002 to 2003 (2003C) Statement B: The percentage of absentees in the written test among males was larger than among females in 2003. 124. Statement A : In 2002 the number of females selected for the course as a proportion of the number of females who bought application forms, was higher than the corresponding proportion for males (2003C) Statement B: In 2002 among those called for interview, males had a greater success rate than females.

125. Statement A : The success rate of moving from written test to interview stage for males was worse than for females in 2003(2003C) Statement B: The success rate of moving from written test to interview stage for females was better in 2002 than in 2003 Directions for Questions 126 to 128 : These questions are based on the table and information given below. Table A below provides data about ages of children in a school. For the age given in the first column, the second column gives the number of children not exceeding that age. For example, first entry indicates that there are 9 children aged 4 years or less. Tables B and C provide data on the heights and weights respectively of the same group of children in a similar format. Assuming that an older child is always taller and weighs more than a younger child, answer the following questions.

126. Among the children older than 6 years but not exceeding 12 years, how many weigh more than 38 kg? (2003C) (a) 34 (b) 52 (c) 44 (d) Cannot be determined 127. How many children of age more than 10 years are taller than 150 cm. and do not weigh more than 48 kg? (2003C) (a) 16 (b) 40 (c) 9 (d) Cannot be determined 128. What is the number of children of age 9 years or less whose height does not exceed 135 cm? (2003C) (a) 48 (b) 45 (c) 3

(d) Cannot be determined Directions for Questions 129 & 130 : These questions are based on the table and information given below. An industry comprises four firms ( A, B, C, and D). Financial details of these firms and of the industry as a whole for a particular year are given below. Profitability of a firm is defined as profit as a percentage of sales .

129. Which profitability (2003C)

firm

has

the

highest

(a) A (b) B (c) C (d) D 130. If Firm A acquires Firm B, approximately what percentage of the total market (total sales ) will they corner together (2003C) (a) 55% (b) 45% (c) 35% (d) 50% Directions for Questions 131 to 133 : These questions are based on the table and information given below. Details of the top 20 MBA schools in the US as ranked by US News and World Report, 1997

131. How many university in the list above have single digit rankings on at least 3 of the 4 parameters (overall ranking, ranking by academics, ranking by recruiters and ranking by placement) (2003C) (a) 10 (b) 5 (c) 7 (d) 8 132. In terms of starting salary and tution fee, how many schools are uniformly better (higher median starting salary AND lower annual tution fee) than Dartmouth College? (2003C) (a) 1 (b) 2 (c) 3 (d) 4 133. Madhu has received admission in all university listed above. She wishes to select the highest overll ranked university whose a) annual tution fee does not exceed $ 23, 000 and b) median starting salary is at least $ 70, 000. Which school will she select? (2003C) (a) University of Virginia (b) Univeristy of Pennsylvania (c) Northwestern University (d) University of California -Berkeley. Directions for Questions 134 to 136 : These questions are based on the table and information given below.

The table below provides certain demographic details of 30 respondents who were part of a survey. The demographic characteristics are : gender, number of children and age of respondents. The first number in each cell is the number of repondents in that group. The minimum and maxinum age of respondents in each group is given in brackets. For example, there are five female respondents with no children and among these five, the youngest is 34 years old, while the oldest is 49.

134. The percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least (2003C) (a) 6.67% (b) 10% (c) 13.33% (d) 26.67% 135. Given the information above, the percentage of respondents older than 35 can be at most (2003C) (a) 30% (b) 83.33% (c) 76.67% (d) 90% 136. The percentage of respondents aged less than 40 years is at least (2003C) (a) 10% (b) 16.67% (c) 20.0% (d) 30% Directions for Questions 137 to 139 : These questions are based on the table and information given below. Spam that enters our electronic mailboxes can be classified under several spam heads. The following table shows the distribution of such spam worldwide over time. The total number of spam emails received during December 2002 was larger than the number received in June 2003. The Figures in the table represent the perecentage of all spam emails received during that period, falling into respective categories

137. In the financial category, the number of spam emails received in September 2002 as compared to March (2003C) (a) was larger (b) was smaller (c) was equal (d) Can not be determined 138. In the health category, the number of spam emails received in December 2002 as compared to June 2003 (2003C) (a) was larger (b) was smaller (c) was equal (d) Cannot be determined 139. In which category was the percentage of spam emails increasing but at a decreasing rate? (2003C) (a) Financial (b) Scams (c) Products (d) None of the above Directions for Questions 140 to 143 : These questions are based on the table and information given below. Below is a table that lists countries region - wise. Each region - wise list is sorted, first by birth rate and then alphabetically by name of country. We now wish to merge the region - wise list into one consolidated list and provide overall rankings to each country based first on birth rate and then on death rate. Thus, if some countries have the same birth rate, then the country with a lower death rate will be ranked higher. Further, countries having identical birth and death rates will get the same rank. For example, if two countries are tied for the third position, then both will be given rank 3, while the next country (in the ordered list) will be ranked 5.

140. In the consolidated list, what would be the overall rank of the Philippines? (2003) (a) 32 (b) 33 (c) 34 (d) 35 141. In the consolidated list, how many countries would rank below Spain and above Taiwan? (2003) (a) 9 (b) 8 (c) 7 (d) 6

142. In the consolidated list, which country ranks 37th? (2003) (a) South Africa (b) Brazil (c) Turkey (d) Venezuela 143. In the consolidated list, how many countries in Asia will rank lower then every country in South America, but higher than at least one country in Africa? (2003) (a) 8 (b) 7 (c) 6 (d) 5 Directions for Questions 144 to 146 : These questions are based on the table and information given below. In a Decathlon, the events are 100m, 400m, 100m hurdles, 1500m, High jump, Polevault, Long jump, Discus, Shot Put and Javelin. The performance in the first four of these events is consolidated into Score-1, the next three into Score-2, and the last three into Score-3. Each such consolidation is obtained by giving appropriate positive weights to individual events. The final score is simply the total of these three scores. The athletes with the highest, second highest and the third highest final scores receive the gold, silver and bronze medals, respectively. The table below gives the scores and performances of nineteen top athletes in this event.

144. The athletes from FRG and USA decided to run a 4 × 100 m relay race for their respective countries with the country having three athletes borrowing the athlete from CZE. Assume that all the athletes ran their stretch of the relay race at the same speed as in Decathlon event. How much more time did the FRG relay team take as compared to the USA team? (2003) (a) 0.18

(b) 0.28 (c) 0.78 (d) 0.00 145. What is the least Daley Thompson must get in Score-2 that ensures him a bronze medal? (2003) (a) 5309 (b) 5296 (c) 5271 (d) 5270 146. At least how many competitors (excluding Daley Thompson) must Michael Smith have out-jumped in the long jump event? (2003) (a) 1 (b) 2 (c) 3 (d) 4 Directions for Questions 147 to 150 : These questions are based on the table and information given below. The following is the wholesale price index (WPI) of a select list of items with the base year of 1993-94. In other words, all the item prices are made 100 in that year (1993-94). Prices in all other years for an item are measured with respect to its price in the base year. For instance, the price of cement went up by 1% in 199495 as compared to 1993-94. Similarly, the price of power went up by 3% in 199697 as compared to 1993-94.

147. Let us suppose that one bag of cement (50 kgs) consumes 100 kgs of limestone and 10 units of power. The only other cost item in producing cement is in the form of wages. During 1993-94, limestone, power and wages contributed, respectively, 20%, 25%, and 15% to the cement price per bag. The average operating profit (% of price per cement bag) earned by a cement manufacturer during 2002-03 is closest to

(2003) (a) 40% (b) 39.5% (c) 38.5% (d) 37.5% 148. Steel manufacturing requires the use of iron ore, power and manpower. The cost of iron ore has followed the All Items index. During 1993-94 power accounted for 30% of the selling price of steel, iron ore for 25%, and wages for 10% of the selling price of steel. Assuming the cost and price data for cement as given in the previous question, the operating profit (% of selling price) of an average steel manufacturer in 200203 (2003) (a) is more than that of a cement manufacturer (b) is less than that of a cement manufacturer (c) is the same as that of a cement manufacturer (d) cannot be determined 149. Which item experienced continuous price rise during the ten-year period? (2003) (a) power (b) Cement (c) Wages (d) Limestone 150. Which item(s) experienced only one decline in price during the ten-year period? (2003) (a) Steel and Limestone (b) Steel and Timber (c) Timber (d) Timber and Wages Directions for Questions 151 to 153 : These questions are based on the table and information given below. Sex Ratio (Number of females per 1000 males) of Selected States in India : 19012001

151. Each of the following statements pertains to the number of states with females outnumbering males in a given census year. Which of these statements in NOT correct? (2003) (a) This number never exceeded 5 in any census year. (b) This number registered its sharpest decline in the year 1971. (c) The number of consecutive censuses in which this number remained unchanged never exceeded 3. (d) Prior to the 1971 census, this number was never less than 4. 152. The two states which achieved the largest increases in sex ratio over the period 1901-2001 are (2003) (a) (b) (c) (d)

Punjab and HP HP and Kerala Assam and J & K Kerala and J & K

153. Among the states which have a sex ratio exceeding 1000 in 1901, the sharpest decline over the period 1901-2001 was registered in the state of (2003) (a) Goa (b) TN (c) Bihar (d) Orissa

Directions for Question 154 to 157 : These questions are based on the table and information given below. Answer the Question on the basis of the information given below. Prof. Singh has been tracking the number of visitors to his homepage. His service provider has provided him with the following data on the country of origin of the visitors and the university they belong to :

154. University to

can

belong

(2004) (a) UK (b) Canada (c) Netherlands (d) USA 155. To which country does University 5 belong? (2004) (a) India or Netherlands but not USA (b) Netherlands or USA but not India (c) India or USA but not Netherlands (d) India or USA but not UK 156. Visitors from how many universities from UK visited Prof. Singh’s homepage in the three days? (2004) (a) 1 (b) 2 (c) 3 (d) 4 157. Which among the listed countries can possibly host three of the eight listed universities? (2004)

(a) (b) (c) (d)

None Only UK Only India Both India and UK Directions for Question 158 to 161 : Answer the question on the basis of the information given below.

A study was conducted to ascertain the relative importance that employees in five different countries assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country.

158. Three of the following four pairs of countries have identical levels of dissimilarity. Which pair is the odd one out? (2004) (a) Malaysia & China (b) China & Thailand (c) Thailand & Japan (d) Japan & Malaysia 159. Which amongst the following countries is most dissimilar to India? (2004) (a) China (b) Japan (c) Malaysia (d) Thailand 160. Which of the following countries is least dissimilar to India? (2004) (a) China (b) Japan (c) Malaysia (d) Thailand

161. Which of the dissimilar? (a) China & Japan (b) India & China (c) Malaysia & Japan (d) Thailand & Japan

following

pairs

countries are (2004)

most

Directions for Question 162 to 165 : Answer the question on the basis of the information given below. The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves that space blank. The scanner output reads as follows :

In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2 and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects. For example Nisha’s GPA is (6 + 2 + 4 + 6 + 0) / 5 = 3.6. Some additional facts are also known about the students’ grades. These are (a) Vipul obtained the same grade in marketing as Aparna obtained in Finance and Strategy. (b) Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.

Operation,

Tara

could

have

received

the same (2004)

grade

(a) Ismet (b) Hari (c) Jagdeep (d) Manab 163. What Statistics? (2004)

grade

did

Preeti

obtain

Utkarsh

obtain

(a) A (b) B (c) C (d) D 164. What Finance? (2004)

grade

did

(a) B (b) C (c) D (d) F 165. In by

Strategy,

Gowri’s

grade

point

was

higher than (2004)

that

obtain

(a) Fazal (b) Hari (c) Nisha (d) Rahul Directions for Question 166 to 168 : Answer the question on the basis of the information given below. The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (BO), Communication Skills (CS), and E-Governance (EG).

M=Male, F= Female; Exe=Executive, Mgr=Manager, Dir=Director; Y=Young, I=Inbetween, O=Old For each workshop, exactly (our employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he/she is not interested in. An employee cannot attend the workshop on • Communication Skills, if he/she is committed to internal projects in the month of January; • Business Opportunities, if he/she is committed to internal projects in the month of February; • E-governance, if he/she is committed to internal projects in the month of March. 166. Assuming that Parul and Hari are attending the workshop on Communication Skills (CS), then which of the following employees can possibly attend the CS workshop? (2005) (a) Rahul and Yamini (b) Dinesh and Lavanya (c) Anshul and Yamini (d) Fatima and Zeena 167. How many Executives (Exe) cannot attend more than one workshop? (2005)

(a) 2 (b) 3 (c) 15 (d) 16 168. Which set workshops?

employees

cannot

attend

any of (2005)

the

(a) Anshul, Charu, Eashwaran and Lavanya (b) Anshul, Bushkant, Gayatri and Urvashi (c) Charu, Urvashi, Bushkant and Mandeep (d) Anshul, Gayatri, Eashwaran and Mandeep Directions for Question 169 to 171 : Answer the question on the basis of the information given below. The table below reports annual statistics to rice production in select states of India for a particular year.

169. How many states have a per capita production of rice (defined as total rice production divided by its population) greater than Gujarat? (2005) (a) 3 (b) 4 (c) 5 (d) 6 170. An intensive rice producing state is defined as one whose annual rice production per million of I population is at least 400,000 tons. How many states are intensive

rice producing (2005)

states?

(a) 5 (b) 6 (c) 7 (d) 8 171. Which two states account for the highest productivity of rice (tons produced per hectare of rice ,cultivation)? (2005) (a) Haryana and Punjab (b) Punjab and Andhra Pradesh (c) Andhra Pradesh and Haryana Haryana

(d) Uttar Pradesh and

Directions for Question 172 to 176 : Answer the question on the basis of the information given below. In a Class X Board examination, ten papers are distributed over five Groups - PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan’s score in English Paper II has been intentionally removed in the table.)

Note : B or G against the name of a student respectively indicates whether the student is a boy or a girl. 172. How much did Dipan get in English Paper II? (2006) (a) 94 (b) 96.5 (c) 97 (d) 98 (d) 99

173. Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, then their standing in decreasing order of final score would be: (2006) (a) Pritam, Joseph, Tirna, Agni (b) Joseph, Tirna, Agni, Pritam (c) Pritam, Agni, Tirna, Joseph (d) Joseph, Tirna, Pritam, Agni (e) Pritam, Tirna, Agni, Joseph 174. Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was: (2006) (a) Ram (b) Agni (c) Pritam (d) Ayesha (e) Dipan 175. Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups? (2006) (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 176. Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to : (2006) (a) Shreya (b) Ram (c) Ayesha (d) Dipan (e) no one from the top ten Directions for Question 177 to 180 : Answer the question on the basis of the information given below.

The following table shows the break–up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product:

The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures for the year 2007, answer the following questions : 177. What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007? (2007) (a) 104 (b) 107 (c) 110 (d) 115 (e) 116 178. What is the minimum number of units that the company needs to produce and sell to avoid any loss? (2007) (a) 313 (b) 350 (c) 384 (d) 747 (e) 928 179. Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs.5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that the company can earn? (2007) (a) 25,400 (b) 24,400 (c) 31,400 (d) 32,900 (e) 32,000 180. If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units the company should produce to maximize its

profit? (2007) (a) (b) (c) (d) (e)

1400 1600 1800 1900 2000

Directions for Question 181 to 184 : Answer the question on the basis of the information given below. The Table shows the comparative costs, in US’Dollars, of major surgeries in USA and a select few Asian countries.

The equivalent of one US Dollar in the local currencies is given below : 1 US Dollar equivalent India

40.928

Rupees

Malaysia

3.51

Ringits

Thailand

32.89

Bahts

Singapore

1.53

S Dollars

A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below: Comparative Costs in USA and some Asian countries Procedure (in US Dollars) USA India Thailand Singapore a Heart Bypass

Malaysi

4 Heart Replacement

Valve 0

5 Angioplasty

6 Hip Replacement

8 Hysterectomy

4 Knee Replacement 4 Spinal Fusion

6 181. The rupee value increases to Rs. 35 for a US Dollar, and all other things including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account? (2007) (a) 700 (b) 2500 (c) 4500 (d) 8000 (e) No difference 182. Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her native country, taking into account the cost of poor quality? It costs 7500 Bahts for one–way travel between Thailand and India. (2007) (a) 23500 (b) 40500 (c) 57500 (d) 67500 (e) 75000 183. A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?

(2007) (a) India (b) Thailand (c) Malaysia (d) Singapore (e) USA 184. Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement? (2007) (a) India (b) Thailand (c) Malaysia (d) Singapore (e) India and Singapore Directions for Question 185 to 189 : Answer the question on the basis of the information given below. A low–cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports. Sector No. Airport of Airport of Distance Departure Arrival between the Airports (km)

Price (Rs.)

560

670

790

1350

850

1250

1245

1600

1345

1700

1350

2450

1950

1850

1650

2000

1750

1900

2100

2450

2300

2275

460

450

410

430

910

1100

540

590

625

700

640

750

950

1250

1650

2450

1250

1700

970

1150

850

875

900

1050

875

950

970

1150

510

550

830

890

790

970

400

425

460

540

185. What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J? (2007) (a) 2275 (b) 2850 (c) 2890 (d) 2930 (e) 3340 186. The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight if it is priced 5% below the minimum price that they pay at present. What should the company charge approximately, in rupees, for this direct flight? (2007)

(a) 1991 (b) 2161 (c) 2707 (d) 2745 (e) 2783 187. If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J? (2007) (a) 2275 (b) 2615 (c) 2850 (d) 2945 (e) 3190 188. If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometer that the company incurs in flying from A to J? (2007) (a) 0.77 (b) 0.88 (c) 0.99 (d) 1.06 (e) 1.08 189. If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company? (2007) (a) 2170 (b) 2180 (c) 2315 (d) 2350 (e) 2390 Directions for Questions 190 to 192 : Answer the questions on the basis of the information given below. There are 100 employees in an organization across five departments. The following table gives the department-wise distribution of average age, average basic pay and

allowances. The gross pay of an employee is the sum of his/her basic pay and allowances.

There are limited numbers of employees considered for transfer/promotion across departments. Whenever a person is transferred/promoted from a department of lower average age to a department of higher average age, he/she will get an additional allowance of 10% of basic pay over and above his/her current allowance. There will not be any change in pay structure if a person is transferred/promoted from a department with higher average age to a department with lower average age. Questions below are independent of each other. 190. What is the approximate percentage change in the average gross pay of the HR department due to transfer of a 40-year old person with basic pay of Rs. 8000 from the Marketing department? (2008) (a) 9% (b) 11% (c) 13% (d) 15% (e) 17% 191. There was a mutual transfer of an employee between Marketing and Finance departments and transfer of one employee from Marketing to HR. As a result, the average age of Finance department increased by one year and that of Marketing department remained the same. What is the new average age of HR department? (2008) (a) 30 (b) 35 (c) 40 (d) 45 (e) cannot be determined 192. If two employees (each with a basic pay of Rs. 6000) are transferred from Maintenance department to HR department and one person (with a basic pay of Rs. 8000) was transferred from Marketing department to HR department, what

(a) (b) (c) (d) (e)

will be the department? (2008) 10.5% 12.5% 15% 30% 40%

percentage

change

average

basic

pay

ANSWERS WITH SOLUTIONS 1.

(d) Since exports of food in 1985 - 86 exceeds the 1984 - 85 figure by Rs. 1006 crore Exports of food in 1984 - 85 = Exports of food in 1985 - 86 – 1006 = 23% of 25800 – 1006 = % food exports in 1984 – 85 =

(b) From table we have (Exports of food) + (Exports of manufactured articles)+ (Raw materials exports) = 22400 ......(i) From previous question, we have food exports = 4928, Also we have, Exports of manufactured articles = 2 (exports of raw materials) = 2x (say x) Therefore by (i) we get

Difference of export of raw material and food export = 5824 – 4928 = 896 crore (d) In 1985 - 86 manufactured articles % and raw materials % = 100- 23 = 77% In 1985 - 86, raw materials % In 1985 - 86 raw materials manufactured

Value of raw material in 1985 – 86 = 33% of 25800 = 8514 Difference of exp. of raw materials = 8514 – 5824 = 2690 = 31.6% approx 4.

(a) Value of exports of manufactured articles in 1984 – 85 = 2 (exports of raw materials in 1984 – 85)

crores Value of exports of manufactured articles in 1985 - 86 crore Required difference = 11648 – 11352 = 296 crores 5.

= 11352

approx.

(using approximations) At higher secondary level, G.R.

approx.

At graduate level, G.R. 7. 8. 9.

growth rate % is least at higher secondary level. (b) Growth rate % is highest at secondary level (126% approx) (from Q. 6) (d) It is obvious from the table that at graduate level there is consistent growth as indicated by the figures in ascending order. (a) Sales per rupee of share capital is highest for 1991 For

; For

10. (a) Reserves at the start of 1991 = 80 lakh %addition to reserves in 1991 %addition to reserves in 1992 %addition to reserves in 1993 %addition to reserves in 1994

Clearly % addition in 1991 is highest. 11. (d) Tax = Profit before Tax – Dividends – Retained Earnings Tax per rupee of PBT, 1991 Tax per rupee of PBT,

1992 Tax per rupee of PBT, 1993 Tax per rupee of PBT, 1994

(Lowest)

12. (d)

(Highest) 13. (a) Reserves after 1994 = 80 + 140 + 70 + 245+ 400 = 935 lakhs 14. (d) It is clearly seen that all the products decrease in one city or the other in 1993 - 94 15. (b) MT doubles its share in Calcutta. Only one product 16. (b) The largest % age drop in market share is in CO In Calcutta (30 - 15) 17. 18. 19. 20.

(a) (b) (a) (c)

None of the products have 100% market share Delhi, where none of the products increased their market share Cloth required High quality of cloth consumed by A shirts

21. (b) Reqd. Ratio 22. (b) Low Quality cloth = 23. (d) Can not be determined There is no relationship between cloth type and dye quality. 24. (a) Lipton production is 1.64 ( in ‘000 tonnes) which corresponds to 64.8% capacity. Maximum capacity will be 100%. For 64.8% it is 1.64. ∴ For 100% it will be

(in 000 tonnes)

25. (d) Data insufficient, because different varieties of coffee of the same brand may have different prices. We can not assume that there will be only one variety of coffee of each brand. 26. (b) Total sales of the 4 brands = ( 31.15 + 26.75 + 15.25 + 17.45) = Rs 90.6 corers. Total sales value of others = 132.8 – 90.6 = Rs. 42.2 crore

27. (c) Total production capacity (in tonnes)

28. (d)

Hence , we find that the maximum unutilized capacity is for MAC, viz. 1050 tonnes. 29. (b) As per the plan, number of men working in 5th month was 4 and these 4 men were supposed to do coding. Cost per man- month for coding = Rs 10, 000. Total cost in 5th month . Number of people actually th working in 5 month is 5 & these 5 men are doing the design part of the project. Cost per man - month for design = Rs,20,000 Total cost in 5th month , % change 30. (a) Total man months required for coding Cost per man month coding = Rs. 10,000 Total cost incurred in new coding stage 31. (d) Total cost in a stage = ( No. of man months) × ( cost per man month in that stage ) Total cost in specification = (2 + 3)40,000 = Rs 2,00,000 Total cost in design Total cost in coding = Rs 1,40,000 (from previous Q.) Total cost in testing = Hence design is the most expensive stage.

32. (c) Average cost /man month Average cost per man month will be minimum for 11-15 month = Rs 10, 000. 33. (b) The difference is in the 5th, 6th and the 8th month Cost under old technique in these months = (4 + 5 + 4) × 10,000 = 1,30,000/Cost under new tehnique = 5 × 20,000 + (4 + 5) × 10,000 = Rs 1,90,000/Hence the difference = 1,90,000 – 1,30,000 = Rs 60,000/34. (d) Total investment in 1995 = 2923.1 + 7081.6 = 10004.7 Total investment in 1996 = 3489.5 + 8352.0 = 11,841.5 ∴ % increase

= 18.36 %

35. (c) Total investment in Chittor = 6412.6 Total investment in Khammam = 15433.6

36.

(b) Investment in electricity & thermal energy in 1995 in two districts = 4746.1 % in terms of total investment = 47.43%

37. (b) % increase in Khammam district in the area of Electricity Chemical Solar Nuclear Hence highest increase is in the area of chemical 38. (a) % increase in investment from 1995 to 1996

∴ Total investment in 1997 = 1.1793 × 8352 = Rs 9850 crores

39. (c) Difference in the number of students employed from finance and marketing = (36 – 22) % × 800 + (48 – 17)% × 650 + (43 – 23)% × 1100 + (37 – 19)% × 1200 + (32 – 32)% × 1000 = 749.5 = 750 40. (b) In 1994 , students seeking jobs in finance earned in one month = 7550 × 0.23 × 1100 = Rs. 1,910, 150 In 1994, students seeking jobs in software earned in one month = 7050 × 0.2% × 11100 = Rs. 1,628, 550 ∴ in the whole year, the difference between the two is = Rs ( 1910150 - 1628550) × 12 41. (d) % increase in the average salary of finance from 1992 to 1996

42. (a) Average monthly salary offered to a management graduate in 1993 = 43. (c) Average annual rate at which the initial salary offered in software, increases

44. (a) Cost per room Lokhandwala = Rs Raheja = Rs

;

= 0.5; IHCL = Rs

ITC Hence Lokhandwala has minimum cost per room. 45. (c) This is another way of asking the previous question. Hence Lokhandwala has maximum number of rooms per crore of rupees. 46. (c) Cost incurred in projects completed in 1998 = Rs 225 + Rs 250 = Rs 475 crore Total cost including interest = Rs 475 + Rs 47.5 = Rs 522.5 47. (a) For projects completed in 1999 cost incurred = Rs 275 + Rs 235 + Rs. 250 + Rs 300 = Rs 1060 Total cost including interest = Rs 1060 × = Rs 1282. 6 crores (Because, interest is for 1998 and 1999) 48. (b) For projects completed in 2000, cost = Rs 250 crore Total cost (with tax) = Rs 250 × (1.1)3 = Rs 332.75

Total cost incurred for projects completed by 2000 = Rs 522.5 + Rs 1282.6 + Rs 332.75 = Rs 2140 crores 49. (a) Let the power consumed by each sector be 1 kwh

Hence % age increase

50. (b)

Hence average tariff 51. (a) Power consumption in 1994-95 Domestic (20%) = 1575 MW Urban (25%) = 1968.75 MW Industrial (40%) = 3150 MW Rural (15%) = 1181.25 MW Domestic Consumption in 94 - 95 is 1575 MW so domestic consumption 91-92 so consumption of the power in Rural sector in 91 - 92 = 1312.5 MW 52. (d) Since for 91-92 and 94-95, we do not know the consumption of power by the various region sectors. Hence total tariff cannot be determined using the given data. 53. (b) Total tariff for 1K wh of power in, total tariff 4 sectors in region 4 is 1730. So avg = 432.5. For region 2 total tariff is 1888 so avg = 472. For Region 5 total

= 1752 so avg is 438. Hence, average tariff in Region 2 is greater than the average tariff in region 5 54. (a) Agriculture loans = Rs 34.54 million Loans from Rural Banks = 260 × 98 × 243 = Rs 6.19 millions Total = 34.54 + 6.19 = Rs 40.73 million ∴ Agricultural loans formed 55. (b) Total number of rural loans = (Avg No. of loans) × (Number of Banks) ∴ Total loans upto 1980 = 90 × 28 +115 × 39 + 130 × 52 + 260 × 98 + 318 × 121 + 605 × 288 = 2520 + 4485 + 6760 + 25480 + 38478 + 174 240 = 251963. Total in 1983 = 840 × 380 = 319200 ∴ Loans upto 1980 56. (d) This question can be answered by carefully observing the data in the table. Among the given years the maximum increase in number of loans is for 1980-81. Note that Agriculutral loans showed maximum increase from 1980 to 1981 (i.e., 152800 – 135700) Further for rural loans, both the increase in no. of rural banks (665 – 605 = 60) and average loans (312 – 288 = 24) are highest for 1980-81. 57. (b) CPI in 1983 = 149 Agricultural loans in 1983 = 915.7 mn CPI in 1970 = 43 ∴ The value of the agricultural loans in 1983 at 1970 prices was = 915.7 264.26 58. (b) 1970

231.3

1971

216.4

1974

256.5

1975

121

282.6

Hence least for 1971. 59. (b) From 1970 - 1983,

Agricultural loans increased from 18300 to 211600, i..e., an increase of 211600 – 18300 = 193300 Annul rate of increase 60.

= 81.25 %

(a) Change in CPI from 1975 to 1983, (when CPI for 1970 = 43) = 149 – 78 = 71 ∴ Required difference (with CPI for 1970 = 105)

61. (b) Value of the loans in 1980 = (605 × 288 × 567) + 498 × 106 = 5.98 × 108 Loans in 1980 at 1983 prices = 679.2 × 108

million

Note : This value remains same irrespective of the change in CPI. 62. (a) To see the maximum percentage by any states in any month, we should see such a month, such that apples stored in cold storage and apples supplied by other two states in that month are relatively very small (i.e., one state is dominant). Hence we could see that in the month of Feb Percentage supplied 63. (c) We can see from the table that J & K supplied very high number of apples as compared to UP & HP. 64. (c) This is similar as the above question. Again J& K had the highest contribution to percentage of apples supplied. 65. (c) We can see from the data, that in the period of May- September, the cold storage had zero contribution. Hence we can say that in this period supply was greater than the demand 66. (b) Yield per tree = 40 kg total apples supplied = 494.525 million [from the sum of total column] Hence time reqd. = 67. (d) From the data above. No. of trees Trees per hectare = 250 so land used 68. (b) Mean mixture is required to be 100 times as sweet as glucose. So the mean rate of sweetness per unit of the mixture must be 100 × 0.74 or 74. Then using alligation.

So, we can say, we have to mix glucose and lactose in the ratio of 601 : 73 or for every 1 gram of saccharine, sucrose to be added will be

69. (c) Sweetness per unit of the mixture of Glucose, Sucrose & Fructose in the ratio of 1 : 2 : 3 is equal to the ratio of total sweetness (sum of the sweetness of one unit of Glucose, two units of Sucrose and three units of Fructose) and total number of units. So sweetness per unit of mixture = Sweetness of sucrose is 1.0 per unit so sweetness per unit of mixture is

1.3 times then that of sucrose. 70. (c) Also Bangladesh > Philippines (97 > 86) for drinking water. And Philippines > any other countries for sanitation facilities. Thus, these three countries are on the coverage frontier for two facilities. 71. (b) Statement A > Statement B only if statement A has higher percentage in total coverage for both drinking water and sanitation facilities taken independently and not as a total of the two facilities. Thus, only statement B and statement D are India > China (81 > 67 and 29 > 24) India > Nepal (81 > 63 and 29 > 18) Also China > Nepal (67 > 63 and 24 > 18) 72. (c) Let the urban population be x and rural population be y. From the sanitation column, we have 0.7x + 0.14y = 0.29 (x + y) 0.41x = 0.15y x= Percentage of rural population =

= = = 73.2% 73. (a) In the same way as the previous questions, we can find percentage of rural population for Philippines, Indonesia and China.

74. (i) (ii) 75.

Thus, P < I < C (d) India is not on coverage frontier because it is below Bangladesh and Philippines for drinking water. for sanitation facilities it is below Philippines, Sri Lanka, Indonesia and Pakistan. (b) Total exports = Software export + Hardware export + Peripherals export Hence, total export as a percentage of IT business for 1994-95 = For 1995-96 = For 1996-97 = For 1997-98 = For 1998-99 =

76. (a) Percentage growth for 1995-96 = 41%, 1996-97 = 32%, 1997-98 = 32%, 1998-99 = 20%. 77. (b) (a) and (b) can be easily eliminated from the given table. 78. (c) 79. (b) 80. (d) Total IT business in hardware (Export + Import) shows a continuous increase from 1994-95 to 1997-98 and then declines in 1998-99. 81. (d) In this question there are two activities–hardware and peripherals, hence for year X to dominate year Y, at least one activity in year X has to be greater than that in year Y and the other activity in year X cannot be in year Y. In (a),

(b) and (c) while hardware dominates in one year, the peripherals dominate in the other. 82. ( ) If the total number of factories is 100, then the total number of employees = 60 × 100 = 6000 of which 64.6% = 3876 work in wholly private factories. Since the number of wholly private factories = 90.3, the answer = Short cut : 83. ( )

Value added per employee =

84. ( )

Compound productivity =

Hence, compound productivity for various sectors is : Public sector = 0.6, Central Government = 0.725, States/Local = 0.47. Central/States/Local = 1.07, Joint sector = 1.23 and wholly private = 1.36. Hence, the order should be : Wholly private, Joint, Central/State/Local, Central Government, Public sector and State/Local government. 85. ( ) Calculate the ratios : Value added/employment and value added/fixed capital for the sectors mentioned in the choices. The respective values are : Wholly private 0.9 and 1.25; Joint sector 1.59 and 1.19; Central/State/Local 1.8, 1.28; others 0.92 and 0.75. 86. ( ) The number of factories in joint sector is 1.8% = 2700, thus the number of factories in Central Government = 1% of (2700 × 100/1.8) = 1500. Value added by Central Government = 14.1% of 1,40,000 crore Hence, answer = 87. (a) 88. (d) Since we have to find number of lays which produced yellow colored fabrics, we can easily count the number of lays which have not produced any size of yellow garments i.e. counting lays with production 0,0,0,0 for all sizes than we get, 13 such numbers. Hence lays used to produce yellow fabrics = 27 – 13 = 14 89. (b) Similarly, as done in last question, we will find the number of lays which have not produced any X X L size of garments (of any colour). Hence we found lays with no XXL fabrics = 11. Hence lays used to produce extraextra large fabrics = 27 – 11 = 16

90.

91.

92. 93. 94.

(d) Again, we will just have to first find lays which don’t produce XXL yellow and X XL white fabrics i.e with count 0 & 0 in XXL yellow and XXL white. So counting such lays we get 12 number of lays. Hence lays used to produce XXL yellow or XXL white fabrics = 27 – 12 = 15 (b) Easily seen from the given table, number of fabrics which exceeded production is 4. They’re Yellow (M & XL one each), white (L & XXL one each). (b) Counting number of ‘A’ type airports with more than 40 million passengers there are 5 such airports (a) We can see that of the top 10 airports. i.e top in the order of passengers, 6 are from USA. Hence 60% of top ten busiest airports are from U.S.A (c) For the five busiest airports : Total passengers = 77939536 + 72568076 +....+60000125 = 336648008 Heathrow airport passenger = 62263710

95. (b) We can easily find the number of international airports that are not located in USA and handle more than 30 million passenger is 6. Note : All airports mentioned in the table handle more than 30 million passengers. 96. (b) The cities located between 10° & 40° E are Austria, Bulgaria, Libya, Poland and Zambia. Out of these only Zambia is in Southern hemisphere. ∴ Required percentage 97. (d) The cities whose name begins with a consonant and are in Northern Hemisphere are Sri Lanka, Spain, Saudi Arabia, Poland, Malayasia, Libya, Ghana, Cambodia, Canada, Bulgaria, i.e. 10. No. of countries whose name begins with consonant and are in east of meridian = 13 98. (a) Countries whose name start with vowels and are located in southern hemisphere = 3 (Argentina, Australia, Equador) Countries whose capital cities starts with a vowel = 2 (Ottawa & Accra) Hence required ratio

99. (c) For Emp. no. For Emp no. For Emp no. For Emp no. For Emp no. Therefore there are five such employees 100. (d) 80% of 25 or 80% attendance = 20 days Employees with total earnings more than 600 and having attendance more than 20 days, are : Emp No. 2001147, 2001151, 2001172, 201173, 2001174, 2001179, 2001180. Hence, there are seven employees.

101. (a)

From above it is obvious that emp. No. 2001180 has max. Earning per day in medium operation. 102. (c) In all there are 7 employees who are engaged in both complex and medium operations. Among them, average earnings per day is more for complex operations in case of 2001151, 2001158, 2001164, 2001171 and 2001172. Hence 5. 103. (c)

5% of 3374

= 168.7

Spain = 55 < 168.7 North Africa & Middle east = 666 > 168.7 Argentina =2006 > 168.7 Rest of Latin America = 115 < 168.7 Far East = 301 > 168.7 North Sea = 140 < 168.7 Rest of world = 91 < 168.7 Therefore operations less than 168.7 are 4 104. (b) Change in revenue from 1999-2000

Spain : 55 to 394 = more than 200%; Rest of Latin America : 115 to 482 more than 200% Hence, there are two operations.

105. (b)

Hence four operations show sustained increase in income. 106. (b) % increase in net income (average) from 1998 - 99

Only Argentina is here for which,

Hence only 1 operation. 107. (b) In 1998, profitability of North sea In 1999, profitability of North sea , hence the profitability of North Sea increases. 108. (b) Profitability of North Africa & middle east in 2000 Profitability of Spain in 2000 Profitability of Rest of Latin America in 2000 Profitability of Far East in 2000 These ratios clearly show that Spain has highest profitability. 109. (d) Efficiency of Spain Efficiency of Argentina Efficiency of Far east

Efficiency of Rest of world Rest of world is least. 110. (d) In 2000, Efficiency of Spain which is higher than 1998 & 1999. Efficiency of N. Sea in 1998 Efficiency of N Sea in 1999 Hence efficiency increases from 1998 to 1999. (c) is true Efficiency of Rest of Latin in 1998 the world

; which was more efficient than Rest of

. Hence it is not true.

Efficiency of Far East in 2000 efficieny in 1999 which was

which shows an improvement from ; hence (b) is true.

111. (b) The least cost of sending one unit is 0 as it is obvious from table A & B that or 112. (c) From table A & table B , Cost = 0 which is minimum & , Cost = 284.5 , Cost = 0 + 284.5 = 284.5 also we have , Cost = 0 which is minimum , Cost = 95.2 which is least , Cost = 0 + 95.2 = 95.2 Hence least cost from any refinery to AAB = 95.2 113. (b) Cost from which is least Cost from which is also least so least cost from 114. (a) Least cost from BB to AAA would be on the route BB → AC → AAA = 451.1 + 314.5 = 765.6 115. (d) There are 6 refineries, 7 depot, 9 districts. So total ways from refinery to district = 6 × 7 × 9 = 378 116. (b) Largest cost from table A (AE → AAH) = 1157.7

(BE → AE or BF → AE) Largest cost from table B = 1035.3 Largest cost from refinery to any district = 1157.7 + 1035.3 = 2193 .0 117. (b) Medium quality R6, R7, R8, R9, R13 Low quality R1, R4, R5, R9 Here R9 is the common region 118. (d) Crop - 3 regions R2, R6, R7, R13, R3, R9, R11, R1, R4 Crop -1 regions R1, R2, R3, R3, R4, R5, R6, R7, R8, R9, R10, R11 Common regions R2, R3, R6, R7, R9, R10, R11 None of these regions produce high quality crop - 2 ( R5, R8, R12) 119. (c) Low quality Crop -1 regions - R9, R10, R11 high quality Crop -4 regions - R3, R10, R11 medium quality Crop -3 regions - R3, R9, R11 Therefore we see that the required regions are three. 120. (d) Check the figures for 5 May 03. The value of non-comprehensive bids accepted in the 2 rounds is 0.31 and 0.41. Further 7 Nov. 2002 and 2 July 2003 also show similar figures. Hence statement (d) is not true . 121. (c) Check the figures for 4 June 03. We find maturity in second round is 9 while the bids are more = 378. 122. (b) Compare the columns of Notified amount with total amount realised. Only on 17 july 02 notified amount is 40 crore while amount mobilised is 16 crore. 123. (a) Statement A : Female absentees in 2002 = ( 19236 – 15389) = 3847 Percentage = Figure for 2003 : =

Hence (a) is correct

Statement B: Absentees among males in 2003 . Hence (b) is not true. 124. (d) Statement A : Females Selected

Males selected

Hence false.

Statement B : Success rate of Males

Success rate of Females

Hence statement B is false. 125. (d) Statement A : Success rate for males in 2003 . Success rate for females in 2003 = less than 1% Sucess rate for males was more. Hence A is false. Statement B : Success rate of females in 2002 Success rate of females in 2003

Hence B is false. 126. (c) Children between age 6-12 years = 77 – 22 = 55. Children older than 12 years = 100 – 77 = 23. Children with weight more than 38 kg = 100 – 33 = 67. Children satisfying given condition = 67 – 23 = 44. 127. (a) Children with age higher than 10 years = 100 – 60 = 40 Children taller than 150 cm = 100 – 75 = 25 Children more than 48 kg = 100 – 91 = 9 To find children not more than 48 kg, we get 25 - 9 = 16. 128. (b) Table A gives children of age 9 or less as 48. Table B give children of height 135 cm or less as 45. Hence 45 children satisfy both conditions. 129. (d) For D, profitability 130. (a)

which is the highest. approx.

131. (d) Simple digit rankings in 3 of 4 parameters are for universities with overall ranking as 1 to 7 and 9 or 8 universities in all. 132. (b) Universities with salary higher than $770,000 and fees less than $23,700 are Stanford and New York University.

133. (d) Only University of California, Berkeley has median starting salary of $70, 000 with fees of $ 18,788 (less than $ 23,000). 134. (c) Male in 35-40 category = 1 + 0 + 0 + 0 =1. Females = 0 + 1 + 1 + 1 = 3. Required percentage Note : The figure in bracket (age limits - upper & lower) shows that a male or female of the upper limit age and the other of the lower limit age are part of the survey. But nothing can be said about the age of the other respondents between these age limits. 135. (b) Male = 1+ 0 + 7 + 0 = 8. Female = 4 + 7 + 5 + 1 = 17, total 25. Required percentage 136. (d) Number of respondents less than 40 years can be : Male 1+ 1 + 1 + 2 = 5 Female 1 + 1 + 1 + 1 = 4; Total = 5 + 4 = 9. Required percentage 137. (d) Since we do not know the total spam emails for the period, it is not possible to say which figure is greater. 138. (a) December 2002 = 19%, June 2003 = 18%. It is also given that December 2002 has higher spam mails than June 2003. Hence first figure is greater than second. 139. (c) Only for products is the percentage of spam increasing at a decreasing rate. In other categories it is either declining or increasing at a faster rate. Scams declined on 3rd June. 140. (b) Countries from the various continents which would rank above Philippines are: Africa = 0, Europe = 20, Asia = 6, N America = 3, Pacific = 1, S America = 2 Note : Countries with same birth & death rate get the same rank. Hence Philippines is ranked 33. 141. (a) Spain — 18, 8; Taiwan — 26, 5 Countries featuring between Spain & Taiwan would be country No. 15 to 20 from Europe, i.e. 6 in number, Cuba, Argentina, Chile i.e., 9 in all. Note : Sri Lanka and Korea (ROK) have higher death rate than Taiwan. 142. (d) Philippines (34, 10) ranks 33 (from above question) Colombia, Thailand are at the same position Turkey would rank 36 and Venezuela would rank above S. Africa & Brazil because of lower death rate. So Venezuela is 37th rank.

143. (a) Countries below Burma would rank lower than every country in S. America, i.e., 9 countires. Out of these, Afghanistan would not rank higher than any country in Africa ∴ Required countries = 9 – 1 = 8 144. (a) Time taken by the US athletes = 10.78 + 10.75 + 10.94 + 10.36 = 42.83 Time taken by the FRG + 1 CZE athelete = 10.95 + 10.85 + 10.58 + 10.63 = 43.01 ∴ Excess time taken by the FRG relay team = 43.01– 42.83 = 0.18 sec. 145. (b) From the final score it is clear that Frank Busemann got the Gold and Dan O’Brien got the Silver medal. The third highest score is of Trosten Voss, 8880. Hence for a bronze, Daley Thompson must have a final score of 8881 ∴ He must score, 8881 – 582 – 3003 = 5296 146. (d) From score-2, it is clear that Michael Smith is ranked 12th in a mix of three events, viz. High Jump, Pole-vault and Long jump (Daley Thompson is excluded). So in all, there are 6 atheletes (18 – 12 = 6) below Smith. Let us have a look at their scores. Score-2 HJ PV Smith 5274 2.0 4.9 take base Tomas 5169 1.9 4.7 lower Torsten 5234 2.1 5.1 higher Jurgen 5223 2.0 4.9 equal Siegfried 5250 2.1 4.8 ? Grigory 5196 2.1 4.9 higher Steve 5163 2.0 5.0 higher So from the above table we can clearly say that Smith, to maintain his position, has to at-least out-perform (ones with a equal or higher scores) Torsten Voss, Jurgen Hingsen, Grigory Degtyarov and Steve Fritz. Note : He need not defeat Siegfried as the weightage of pole-vault might be high (where his score is higher) and inspite of scoring less in long jump his final score-2 might out class Siegfried’s. As the question asks atleast so we can exclude Siegfried. 147. (c) New price of materials = 20 × 1.05 + 25 × 1.08 + 15 × 1.053 = Rs 63.79 New selling price = Rs 104 Profit 148. (b) Steel = 100 Rs; Power = 30 Rs; Iron-ore = 25 Rs wages = 10 Rs

Costprice in 2002-03 = 30 × 1.08 + 25 × 1.06 + 10 × 1.053 = 32.4 + 26.5 + 10.53 = 69.43 New selling price = Rs. 105.5 Operating profit

=34.2%

Which is lesser than cement. 149. (a) The table clearly shows that the price of power increases continuously 150. (d) The table clearly shows that the price of timber & wages decline only once in 1998-99 and 1999-00 respectively. 151. (c) Statement (c) is false, as this number remain same from 1971 to 2001, i.e. 4 years. 152. (b) HP & Kerela shows largest increase in sex ratio of 86 & 54 respectively. 153. (c) The five states which exceeded the sex ratio of 1000 in 1901 are Bihar, Goa, Kerala, Orissa and TN. Among them Bihar registered the sharpest decline of 140. 154-157. From the tables given, following information can be directly inferred : University 8 is from India University 7 is from UK/ Canada University 6 is from USA University 5 can be from India / Netherland University 4 is from UK University 3 is from Netherland University 2 is from Canada / UK University 1 is from Netherland / India 154. (c) 155. (a) 156. (b) 157. (a) 158. (d) Clearly the level of dissimilarity between Malaysia and China is 4 (for N or V) Level of dissimilarity for China and Thailand is 4 (for V) Level of dissimilarity for Thailand and Japan is 4 (for D) But level of dissimilarity for Japan and Malaysia is 3 (for V or N) 159. (b) Dissimilarity of India with China = 2 (for N) Dissimilarity of India with Japan = 4 (for D) Dissimilarity of India with Malaysia = 3 (C, N or D) Dissimilarity of India with Thailand = 3 (V) 160. (a) From above least dissimilar is China 161. (d) China - Japan = 3, Malaysia - Japan = 3 India - China = 2, Thailand - Japan = 4

162. (d) or sum of rest 4 courses = 12 – 4 = 8 As Tara received same grades in exactly 3 courses ∴ Tara received 3 B’s and 2 F’s Ismet’s grade in operations = A Hari’s grade in operations = D Jagdeep’s grade in operations = C Manab’s grade in operations = B The only grade which matches is B. 163. (a) For Preeti, or x + y = 16 – 4 = 12 This can only happen when she gets A in both the subjects. 164. (b) From (b) statement, in question For Fazal, or x = 12 – 8 = 4 or B in strategy Hence Utkarsh gets B in Marketing For Utkarsh x + 4 + 0 + 3 + 6 = 3 × 5 = 15 or x = 2 i.e., a C in finance. 165. (b) For Gowri, 3 + 3 + 6 + x + 4 = 3.8 × 5 = 19 or x = 19 – 16 = 13 or C grade Fazal gets B in strategy (from Q 15) For Hari, x + 4 + 6 + y + 2 = 2.8 × 5 = 14 or x + y = 2 i.e., maximum Hari can get a D in Strategy. Nisha get a A. For Rahul, 6 + 3 + 6 + x + 0 = 4.2 × 5 = 21 or x = 6 or A in strategy. Hence Gowri’s grade is higher than Hari. 166. (a) Parul (F, Y) and Hari (M, I) are attending the CS workshop. So atleast one female has to be present. Further there should be no commitment in January. Dinesh, Anshul and Zeena have a project is Jan, so option (b), (c) and (d) are ruled out.

167. (b) Three executives Gayatri, Zeena and Urvashi can not attend more than one workshop. Gayatri and Urvashi can not attend even one workshop because of their project commitments. Zeena can attend only BO. 168. (b) Anshul can not attend any workshop because of projects in Jan (CS) and March (EG). Similarly, Charu, Eashwarn, Bushkant, Gayatri and Urvashi cannot attend any of the workshops. Lavanya can attend 2, CS & EG, Mandeep can attend only BO. 169. (b) See the following table :

So clearly 4 states –– Haryana, Punjab, Maharastra and Andhra Pradesh –– have higher per capita production as compared to Gujarat (0.47) 170. (d) The per capita production in the table is given in million tons/million 400,000 tons 0.4 million tons So intensive producing state are 8 in number, who have higher than this production. 171. (a) The productivities can be seen from the given table. So Haryana and Punjab have the highest productivity. 172. (c) Dipan’s score = 96 = 98 + 95 + 95.5 + 95 + y = 96 × 5 = 480 Here y = y = 480 – 383.5 = 96.5 96 + x = 2 × 96.5 or x = 97. 173. (a) Old SS New SS Score Addn.

New

Score

J 95.5

100

95.9

A95.5

100

94.3

95.2

P 89

100

93.9

96.1

T89.5

100

93.7

95.8

So the order is P > J > T >A. 174. (d) Score Inc. Imp. Old New Imp. in Score Score Score R Maths 3 3/5 = 0.6 96.1 96.7 Ag Ver. 18/2 = 9 9/5 = 1.8 94.3 96.1 P SS 17/2 = 8.5 8.5/5 = 1.7 93.9 95.6 Ay Geo. 7/2 = 3.5 3.5/5 = 0.7 96.2 96.9 D Maths 5 5/5 = 1 96.0 96.6 Note : The score is improved in a subject which maximises the final score. Remember the scores of individual groups are averaged. So the topper is Ayesha. 175. (a) From the table, among the boys (7 in the table marked by B), its only Dipan who has scored atleast 95 in at least one paper from each of the groups. Ram, Sanjiv, Joseph, Agni, Pritam could not do so in Vernacular group. Sagnik could not do so in English group. 176. (d) As per the given condition, the students eligible for the prize is only Dipan; Rest of the nine student fail to quality the cut-off of 95 in one or the other group.

177. (b)

Cost per unit = 149370/ 1400 = Rs 106.7

178. (c)

From the table it is clear that the company needs to produce 384 for break even.

179. (a)

180. (e)

The profit increases with the number of units initially, then decreases and finally it increases again. 181. (b) New cost of spinal fusion in India = = $ 6431.5

∴ Difference in cost between India and Singapore = 9000 – 6431.5 = $ 2568.5 ≈ $ 2500 [Note cost of poor quality is same in both the countries] 182. (d) Cost of hysterectomy in Thailand (considering poor quality) = 4500 + 6000 = $ 10500 = 10500 × 32.89 Bahts Cost of hysterectomy in India = Surgery cost + travel cost + poor quality cost = $ 3000 + $ 5000 + (7500 × 2) Bahts = 8000 × 32.89 + 15000 Bahts Difference = (10500 – 8000) 32.89 – 15000 = 82225 – 15000 = 67225 183. (c) Cost of Angioplasty, his replacement and knee replacement in different countries: USA = 57000 + 43000 + 40000 = $ 1,40,000 India = (11000 + 5000) + (9000 + 7000) + 17500 = $ 49,500/ Thailand = (13000 + 5000) + (12000 + 5000) + 16000 = $ 51,000/Singapore = (13000 + 4000) + (12000 + 5000) + 17000 = $ 51,000/Malaysia = (11000 + 6000) + (10000 + 8000) + 12000 = $ 47,000/184. (a) Cost of knee replacement in various countries: India = 8500 + 9000 = $ 17,500/Thailand = 10000 + 6000 = $ 16,000/Singapore = 13000 + 4000 = $ 17,000/Malaysia = 8000 + 4000 = $ 12,000/185. (d) Route Distance Price ABJ 2860 2945 ADJ 2500 3700 AFJ 2315 2850 AGJ 2180 3340 AHJ 2350 2275 ACFJ 2170 2930 186. (b) From above question the route with the lowest price is AHJ. The lowest price = Rs. 2275/So, the company shall charge = 0.95 × 2275 = Rs. 2161. 187. (c) Route ABJ AFJ AGJ Price 2945 2850 3340 So, AFJ is the best route and the best price is Rs. 2850. 188. (b) The minimum cost = Rs. 2275 Remaining the margin, the net price = Cost/kilometre =

189. (d) From above it is clear that the price : distance ratio is less than 1 only in case of AHJ route. In rest of the cases, it is above 1. So, in all the cases the cost/km is going to be minimum for AHJ route (even after considering 15% margin). So the distance covered = Rs. 2350/190. (c) Initial gross average salary of HR department

When the person from the marketing department transfer to HR department, then new average salary of HR department

Hence, approximate percentage change in the average gross pay of the HR department

. 191. (c) Let the age of the person who goes from marketing to finance be x years. The age of the person who goes from finance to marketing be y years. And the age of the persons who goes from marketing to HR be z years. New avg. age of marketing dept. = ⇒ y – x – z = – 35

...(i)

New avg. age of finance department = ⇒ y – x = – 20 .... (ii) From equation (i) and (ii), z = 15 New average age of HR

192. (b) New average basic pay of HR department = Rs. 5625 Percentage change in avg.

Directions for Questions 1 to 10 : These questions are based on the information given below. Each item has a question followed by two statements, Mark ‘a’, if the question can be answered with the help of I alone, Mark ‘b’, if the question can be answered with the help of II alone, Mark ‘c’, if the question can be answered with the help of both, I and II, Mark ‘d’, if the question cannot be answered even with the help of both statements. 1. Is the distance from the office to home less than the distance from the cinema hall to home? (1994) I. The time taken to travel from home to office is as much as the time taken from home to the cinema hall, both distances being covered without stopping. II. The road from the cinema hall to home is bad and speed reduces, as compared to that on the road from home to the office. 2. A and B work at digging a ditch alternately for a day each. If A can dig a ditch in ‘a’ days, and B can dig it in ‘b’ days, will work get done faster if A begins the work? (1994) I.

n is a positive integer such that

II. 3.

b>a If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boy gets three sweets, what is the number of boys and girls? (1994) The number of girls is not more than five. If each girl gets 3 sweets and each boy gets 2 sweets, the number of sweets required for the children will still be the same If the selling price were to be increased by 10%, the sales would reduce by 10%. In what ratio would profits change? (1994) The cost price remains constant The cost price increased by 10% What is the average weight of the 3 new team members who are recently included in the team? (1994) The average weight of the team increases by 20 kg. The 3 new men substitute 3 earlier members whose weights are 64 kg, 75 kg and 66 kg

I. II. 4. I. II. 5. I. II.

Is segment PQ greater than segment RS? (1994) I. PB > RE, BQ = ES II. B is a point on PQ, E is a point on RS. 7. Three boys had a few Coffee Bite toffees with them. The number of toffees with the second were four more than those with the first and the number of toffees with the third were four more than those with the second. How many toffees were there in all? (1994) I. The number of toffees with each of them is a multiple of 2 II. The first boy ate up four toffees from what he had and the second boy ate up six toffees from what he had and the third boy gave them two toffees each from what he had and the number of toffees remaining with each of them formed a geometric progression. 8. Little Beau Peep she lost her sheep, she couldn’t remember how many were there, (1994) She knew she would have 400 more next year, than the number of sheep she had last year. How many sheep were there? I. The number of sheep last year was 20% more than the year before that and this simple rate of increase continues to be the same for the next 10 years. II. The increase is compounded annually. 9. What will be the total cost of creating a 1-foot border of tiles along the inside edges of a room? (1994) I. The room is 48 feet in length and 50 feet in breadth. II. Every tile costs Rs. 10. 10. Ten boys go to a neighbouring orchard. Each boy steals a few mangoes. What is the total number of mangoes they steal? (1994) I. The first boy steals 4 mangoes and the fourth boy steals 16 mangoes and the eighth boy 32 mangoes and the tenth boy steals 40 mangoes. II. The first boy stole the minimum number of mangoes and the tenth boy stole the maximum number of mangoes. Directions for Questions 11 to 19 : These questions are based on the information given below. Each item has a question followed by two statements, Mark (a) If the question can be answered with the help of both the statements but not with the help of either statement itself. (b) If the question can not be answered even with the help of both the statements.

(c) If the question can be answered with the help of statement II alone (d) If the question can be answered with the help of statement I alone 11. What is the number x if (1995) I. The LCM of x and 18 is 36 II. The HCF of x and 18 is 2 12. If x, y and z are real numbers. Is z-x even or odd? (1995) I. xyz is odd II. xy + yz + zx is even 13. What is value of x, if x and y are consecutive positive even integers? (1995) I. II. 14. What percent? I. II. 15.

I. II. 16. I. II. 17. I. II. 18.

I. II. 19.

the

profit

(1995) The cost price is 80% of the selling price The profit is Rs 50 What is the length of the rectangle ABCD? (1995) Area of the rectangle is 48 square units Length of the diagonal is 10 units What is the price of bananas? (1995) With Rs. 84 I can buy 14 bananas and 35 oranges If price of bananas by 50% then we can buy 48 bananas in Rs 12 What is the first term of an arithmetic progression of positive integers? (1995) Sum of the squares of the first and second term is 116 The fifth term is divisible by 7. Is x + y z + t even? (1995) x + y +t is even tz is odd What is the area of the triangle?

(1995) I. Two sides are 41 cm. each II. The altitude to the third side is 9 cm. long Directions for Questions 20 to 29 : These questions are based on the information given below. In each question, you are given certain data followed by two statements. For answering the questions , Mark (a), if even both the statements together are insufficient to answer the question. Mark (b), if any one of the two statements is sufficient to answer the question. Mark (c), if each statement alone is sufficient to answer the question. Mark (d), if both the statements together are sufficient to answer the question, but neither statement alone is sufficient. 20. What is the Cost Price of the article? (1996) (i) After selling the article, a loss of 25% on Cost Price is incurred (ii) The Selling price is three- fourths of the Cost Price 21. If a, b, c are integers, is ? (1996) (i) b is negative (ii) c is positive 22. What is the Selling Price of the article? (1996) (i) The profit on Sales is 20% (ii) The profit on each unit is 25% and the Cost Price is Rs. 250 23. A tractor travelled a distance of 5m. What is the radius of the rear wheel? (1996) (i) The front wheel rotates “N” times more than the rear wheel over this distance (ii) The circumference of the rear wheel is “t” times that of the front wheel 24. What is the ratio of the two liquids A and B in the mixture finally, if these two liquids kept in three vessels are mixed together? (The containers are of equal volume.) (1996) (i) The ratio of liquid A to liquid B in the first and second vessel is, respectively, 3 : 5, 2:3 (ii) The ratio of liquid A to liquid B in vessel 3 is 4 : 3

25. If α, β are the roots of the equation ?

then what is the value of (1996)

(i) (ii) 26. What is the number of type-2 widgets produced, if the total number of widgets produced is 20, 000? (1996) (i) If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same (ii) The ratio in which type-1 and type-2 widgets are produced is 2 : 1 27. How old is Sachin in 1997? (1996) (i) Sachin is 11 years younger than Anil whose age will be a prime number in 1998 (ii) Anil’s age was a prime number in 1996 28. What is the total worth of Lakhiram’s assets? (1996) (i) A Compound interest at 10% on his assets, followed by a tax of 4% on the interest, fetches him Rs. 1500 this year. (ii) The interest is compounded once every four months 29. How many different triangles can be formed? (1996) (i) There are 16 coplanar, straight lines in all (ii) No two lines are parallel Directions for Questions 30 to 39 : These questions are based on the information given below. Mark (a), if the question can be answered with the help of statement 1 alone, Mark (b), if the question can be answered with the help of any one statement independently, Mark (c), if the question can be answered with the help of both statements together, Mark (d), if the question cannot be answered even with the hlep of both statements together. 30. What is the value of a3 + 3 b? (1997) I. a2 + b2 = 22 II. ab = 3 31. Is the number completely divisible by 99? (1997)

I. The number is divisible by 9 and 11 simultaneously II. If the digits of the number are reversed, the number is divisible by 9 and 11 32. A person is walking from Mali to Pali, which lies to its North-East. What is the distance between Mali and Pali? (1997) I. When the person has covered 1/3rd the distance, he is 3 km East and 1 km North of Mali II. When the person has covered 2/3rd the distance, he is 6 km East and 2 km North of Mali 33. What are the values of x and y? (1997) I. 3x + 2y = 45 II. 10.5x + 7y = 157.5 34. Three friends, P, Q and R are wearing hats, either black or white. Each person can see the hats of the other two persons. What is the colour of P’s hat? (1997) I. P says that he can see one black hat and one white hat II. Q says that he can see one white hat and one black hat 35. What is the speed of the car? (1997) I. The speed of the car is 10 more than that of a motor-cycle II. The motor-cycle takes 2 hours more than the car to cover 100 kms 36. What is the ratio of the volume of the given right circular cone to the one obtained from it? (1997) I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1 : 2 II. The height and the base of the new cone are one-third those of the original cone 37. What is the area bounded by the two lines and the co-ordinate axes in the first quadrant? (1997) I. The lines intersect at a point which also lies on the lines 3x – 4y = 1 and 7x – 8y =5 II. The lines are perpendicular, and one of them intersects the y-axis at an intercept of 4 38. What is the cost price of the chair? (1997) I. The chair and the table are sold, respectively, at profits of 15% and 20% II. If the cost price of the chair is increased by 10% and that of the table is increased by 20%, the profit reduces by Rs. 20 39. After what time will the two persons, Tez and Gati, meet while moving around the circular track? Both of them start from the same point and at the same

time. (1997) I. Tez moves at a constant speed of 5 m/s, while Gati starts at a speed of 2 m/s and increases his speed by 0.5 m/s at the end of every second thereafter. II. Gati can complete one entire lap in exactly 10 seconds. Directions for Questions 40 to 51 : These questions are based on the information given below. (a) (b) (c) (d) 40.

Read the following directions carefully and answer the questions. You should tick If any one of the statements alone is sufficient to answer the question If both statements individually are sufficient to answer the question If both statements together are required to answer the question If both statements are not sufficient to answer the question Find the length of AB? If (1998)

(i) Radius of the Arc is given (ii) OA = 5 41. Is odd?

n (1998)

(i) n is divisible by 3, 5, 7 and 9 (ii) 0 < n < 400 42. Find 2 3 , where 2 3 need not be equal to 3 2 (1998) (i) 1 2 = 3 (ii) a b = (a+b)/a, where a and b are positive 43. Radha and Rani appeared in an examination,. What was the toal number of questions? (1998) (i) Radha & Rani together solved 20% of the paper (ii) Radha alone solved 3/5 th of the paper solved by Rani. 44. What is the price of tea? (1998) (i) Price of coffee is Rs.5 more than that of tea

(ii) Price of coffee was Rs 5 less than the price of a cold drink which cost three times the price of tea 45. What is value of a? (1998) (i) Ratio of a & b is 3:5 where b is positive (ii) Ratio of 2a and b is 12/10 where a is positive 46. In a group of 150 students, find the number of girls? (1998) (i) Each girl was given 50 paise, while each boy was given 25 paisa to purchase goods totalling Rs 49 (ii) Girls and boys were given 30 paisa each to buy goods totaling Rs 45 47. There are four envelopes E1, E2, E3, E4 in which one was supposed to put letters L1, L2, L3, L4 meant for persons C1, C2, C3, C4, respectively but by mistake the letters got jumbled up and went in wrong envelopes. Now if C2 is allowed to open an envelope at random, then how will he identify the envelope containing the letter for him? (1998) (i) L2 has been put in E1 (ii) The letter belonging to C3 has gone in the correct envelope 48. There are four racks numbered 1,2,3,4 and four books numbered 1,2,3,4. If an even rack has to contain an odd numbered book and an odd rack contains an even numbered book then what is the position of book 4? (1998) (i) Second book has been put in third rack (ii) Third book has been put in second rack 49. Find the value of X in terms of a? (1998) (i) Arithmetic mean of X and Y is ‘a’ while the geometric mean is also ‘a’ (ii) X/Y = R;X -Y = D 50. Two concentric circles C1 and C2 with radii r1 and r2. The circles are such that C1 fully encloses C2, then what is the radius of C1?

(i) (ii) 51. (i) (ii)

(1998) The difference of their circumference is k cm The difference of their areas is m sq. cm A circle circumscribes a square. What is the area of the square? (1998) Radius of the circle is given Length of the tangent from a point 5-cm away from the center of the circle is given

Directions for Questions 52 to 61 : These questions are based on the information given below. In each question, you are given certain data followed by two statements, for answering the question Mark (a) , if the question can be ansered with the help of one of the statements, but not with the help of the other statement. Mark (b), if the question can be answered with the help of either of the statements alone. Mark (c), if the question can be answered only with the help of both the statements Mark (d), if the question can not be answered even with the help of both the statements together. 52. Mr Mendel grew one hundred flowering plants form black seeds and white seeds, each seed giving rise to one plant. A plant gives flowers of only one colour. From a black seed comes a plant giving red or blue flowers. From a white seed comes a plant giving red or white flowers. How many black seeds were used by Mr. Mendel (1999) I. The number of plants with white flowers was 10 II. The number of plants with red flowers was 70 53. What is the volume of the spherical tank? (1999) I. The tickness of the wall is 1 cm II. When immersed in water it displaces 20 litres of it. 54. 3 person were given certain calculations to perform. The calculations were 1 + 1, 1 +1+2, and 1 +2. Their respective answers were 3,3 and 2. How many of them are mathematicians (1999) I. Mathematicians can never add two numbers correctly, but they add three numbers correctly II. Whenever the mathematicians add two numbers there is a mistake of +1 or -1 55. What is the value of x (1999) I. II. 56. Mr. X starts walking northwards along the boundary of a field from point A on the boundary. After walking for 150 metres, he reaches B and then walks westwards, again along the boundary, for another 100 metres when he reaches C. What is the maximum distance between any pair of points on the boundary of the field ? (1999) I. The field is rectangular in shape. II. The field is a polygon, with C as one of its vertices and A the mid point of a side

57. A circle has radius r and origin as its centre. Two tangents are drawn from an external point D, d distance away from the origin. what are the angles made by the tangents with the positive Xaxis (1999) I. The co-ordinates of the point D are given II. The X-axis bisects one of the tangents 58. A line graph on a graph sheet shows the revenue for each year from 1990 through 1998 by points and joins the successive points by straight line segments. The point for revenue of 1990 is labelled A, that for 1991 as B, and that for 1992 as C. What is the ratio of growth in revenue between 91-92 and 9091? (1999) I. The angle between AB and X-axis when measured with a protactor is 40 degrees, and the angle between CB and X-axis is 80 degrees II. The scale of Y-axis is cm = 1000 Rs. 59. What is the number of students in the class if the average weight of the students is 50 kg (1999) I. The heaviest & lightest students in the class weigh 60 & 40 kg respectively II. If the heaviest & the lightest students are taken away from the group the average weight remains the same 60. How many sets of positive integers (x,y) satisfy the following equations ax + by = c; dx + ey = f where a, b, c, d, e, f are non- zero (1999) I. II. 61. A, B, C, D, are four students. How many of them have passed? (1999) I. Following statement is true: A & B have passed II. Following statement is false : at least one of C & D has passed Directions for Questions 62 to 71 : These questions are based on the information given below. Mark, (a) If one of the statement is sufficient to answer the question and another is not. (b) If both the statements can answer the question independently. (c) Both statements are required to answer the question. (d) Question cannot be answered. 62. In a triangle PQR, in which angle PQR is 90°. What PQ+RQ? (2000) (I) The diameter of in circle is 10 cm (II) The diameter of circumcircle is 18 cm 63. X, Y, Z are real numbers, is smallest?

(I) (II) 64.

(I) (II) 65.

(I) (II) 66. (I) (II) 67. (a) (b) 68. (a) (b) 69. (a) (b) 70.

(a) (b)

(2000) X is greater than at least one of the Y to Z Y is greater than at least one of the X or Z Today a person purchases some share and the next day he sells them. In both the transactions, he paid a brokerage of 1% per share. What is the profit per rupee invested? (2000) The selling price of a share is 1.05 times cost price The no of share he sells is 100 Is modulus of x always less than 3? (2000) x (x +3) < 0 x (x -3) > 0 A line cuts 2 concentric circles in points a, e and b, d. Is ac/ ce = 1 ? Point c lies on line are (2000) bc = cd If a third circle cuts in same points b and d, points c lies on line joining the centres of circle. If x and y are positive integer in the function f (x, y), find (0,1). (2000) f (a, b) = f (b, a) f (a, b) = 0 if b = 0 In a group, 100 people drink coffee only, how many drink tea only? (2000) 100 drink both tea and coffee Number of people having tea or coffee or both is 1500 The equation of two lines are ax + by = c and dx +ey = f, are lines intersecting? (2000) a, b, c, d, e, f are distinct real no’s c and f are non zero’s no’s A person leaves for No man Island in North America from Mumbai at 5.00 pm. Local time and flies non stop. At what time he reaches No man Island (local time)? ( 2000) He flies with an average speed of 150 kmph The distance between Mumbai and No man Island is 1500 km

71. Ghosh Babu wanted to cordon off a triangular piece from a corner of his square piece of land of perimeter 400 meters. What was the length of the longest side of the cordoned off area? (2000) (a) The cordoned off area is an isosceles triangle (b) Each of the smaller sides of the triangle is 20 m Directions for Questions 72 to 78 : These questions are based on the information given below. Each item is followed by two statements, A and B. Answer each questions using the following instructions. Choose (a) if the question can be answered by one of the statements alone and not by the other. Choose (b) if the questions can be answered by using either statement alone. Choose (c) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone. Choose (d) if the question cannot be answered even by using both statements together. 72. What are the values of m and n? (2001) A. n is an even integer, m is an odd integer, and m is greater than n B. Product of m and n is 30 73. Is Country X’s GDP higher than country Y’s GDP? (2001) A. GDPs of the countries X and Y have grown over the past five years at compounded annual rate of 5% and 6% respectively B. Five years ago , GDP of country X was higher than that of country Y 74. What is the value of X? (2001) A. X and Y are unequal even integers, less than 10, and X/Y is an odd integer B. X and Y are even integers, each less than 10, and product of X and Y is 12 75. On a given day a boat ferried 1500 passengers across the river in twelve hours. How many round trips did it make? (2001) A. The boat can carry two hundred passengers at any time B. It takes 40 minutes each way and 20 minutes of waiting time at each terminal 76. What will be the time for downloading software? (2001) A. Transfer rate is 6 Kilobytes per second

B. The size of the software is 4.5 megabytes 77. A square is inscribed in a circle. What is the difference between the area of the circle and that of the square? (2001) A. The diameter of the circle is cm B. The side of the square is 25 cm 78. Two friends, Ram and Gopal, bought apples from a wholesale dealer. How many apples did they buy? (2001) A. Ram bought one half the number of apples that Gopal bought B. The wholesale dealer had a stock of 500 apples Directions for Questions 79 to 86 : These questions are based on the information given below. Each item is followed by two statements, A and B. Answer each questions using the following instructions. Choose (a), if the question can be answered by one of the statements alone but not by the other. Choose (b), if the question can be answered by using either statement alone. Choose (c), if the question can be answered by using both the statements together, but cannot be answered by using either statement alone. Choose (d), if the question cannot be answered by either of the statements. 79. In a hockey match, the Indian team was behind by 2 goals with 5 minutes remaining. Did they win the match? (2002) A : Deepak Thakur, the Indian striker, scored 3 goals in the last five minutes of the match B : Korea scored a total of 3 goals in the match 80. Four students were added to a dance class. Would the teacher be able to divide her students evenly into a dance team (or teams) of 8? (2002) A : If 12 students were added, the teacher could put everyone in teams of 8 without any leftovers. B : The number of students in the class is currently not divisible by 8. 81. Is x = y? (2002) A: B:

82. A dress was initially listed at a price that would have given the store a profit of 20 percent of the wholesale cost. What was the wholesale cost of the dress? (2002) A : After reducing the listed price by 10 percent, the dress sold for a net profit of 10 dollars B : The dress sold for 50 dollars 83. Is 500 the average (arithmetic mean) score on the GMAT? (2002) A : Half of the people who take the GMAT, score above 500 and half of the people score below 500. B : The highest GMAT score is 800 and the lowest score is 200 84. Is | x – 2 | < 1? (2002) A : |x| < 1 B : |x – 1| < 2 85. People in a club either speak French or Russian or both. Find the number of people in a club who speak only French (2002) A : There are 300 people in the club and the number of people who speak both French and Russian is 196 B : The number of people who speak only Russian is 58 86. A sum of Rs. 38,500 was divided among Jagdish, Punit and Girish. Who received the minimum amount? (2002) A : Jagdish received 2/9 of what Punit and Girish together received B : Punit received 3/11 of what Jagdish and Girish together received Directions for Questions 87 to 91 : These questions are based on the information given below. Each question is followed by two statements I and II. Answer each question using the following instructions. Choose (a) if the question can be answered by one of the statements alone but not by the other. Choose (b) if the question can be answered by using either statement alone. Choose (c) if the question can be answered by using both the statements together but cannot be answered be answered by using either statement alone. Choose (d) if the question can not be answered even by using both the statements together. 87. Is a44 < b11, given that a = 2 and b is an integer (2 003C) I. b is even

II.

b is greater than 16

88. What are the unique values of b and c in the equation the roots of the equation is

if one of

(2003C)

I. The second root is 1/2 II. The ratio of c and b is 1 89. AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle? (2003C) I. AB is not a diameter of the circle II. The distance between AB and the tangent at E is 5 cm 90. (2003 C) I. II.

One of the roots of the equation

is a

91. D, E, F are the mid points of the side AB, BC and CA of triangle ABC respectively. What is the area of DEF in square centimeters

I. II.

(2003C) AD= 1 cm, DF= 1 cm and perimeter of DEF = 3cm Perimeter of ABC = 6 cm, AB = 2 cm, and AC = 2 cm

Directions for Questions 92 to 95 : These questions are based on the information given below. In each question there are two statements A and B Choose (a) if the question can be answered by one of the statements alone but not by other Choose (b) if the question can be answered by using either statement alone. Choose (c) if the question can be answered by using both the statements together but cannot be answered using either statement alone Choose (d) if the question cannot be answered even by using both the statements A and B. 92. F and M are father and mother of S, respectively. S has four uncles and three aunts. F has two siblings. The siblings of F and M are unmarried. How many brothers does M have. (2003C) A. F has two brothers B. M has five siblings 93. A game consists of tossing a coin successively. There is an entry fee of Rs. 10 and an additional fee of Rs. 1 for each toss of the coin. The game is considered

A. B. 94.

A. B. 95. If B

A. B.

to have ended normally when the coin turns heads on two consecutive throws. In this case the player is paid Rs.100. Alternatively, the player can choose to terminate the game prematurely after any of the tosses. Ram has incurred as loss of Rs. 50 by playing this game. How many times did he toss the coin? (2003C) The game ended normally The total number of tails obtained in the game was 138 Each packet of Soap costs Rs. 10. Inside each packet is a gift coupon labelled with one of the letter S,O, A and P. If a customer submits four such coupons that make up the word Soap the customer gets a free Soap packet. Ms X kept buying packet after packet of Soap till she could get one set of coupons that formed the world Soap. How many coupons with lable P did she get in the above process (2003C) The last label obtained by her was S and the total amount spent was Rs. 210 The total number of vowels obtained was 18 If A and B run a race, then A wins by 60 seconds. and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed, what is the time taken by C to finish the race (2003C) A and C run the same race and A wins by 375 meters The length of the race is 1 km

Directions for Questions 96 to 99 : These questions are based on the information given below. Each question is followed by two statements, A and B. Answer each question using the following instructions : Choose (a), if the question can be answered by using statement A alone but not by using B alone. Choose (b), if the question can be answered by using statement B alone but not by using A alone. Choose (c), if the question can be answered by using any one of the two statements alone. Choose (d), if the question can be answered by using both the statements together but not by either statement alone. 96. In a cricket match, the‘man of the match’ award is given to the player scoring the highest number of runs. In case of a tie, the player (out of those locked in the tie) who has taken the higher number of catches is chosen. Even thereafter if there is a tie, the player (out of those locked in the tie) who has dropped fewer catches is selected. Aakash, Biplab, and Chirag who were contenders for the award

dropped at least one catch each. Biplab dropped 2 catches more than Aakash did, scored 50, and took 2 catches. Chirag got two chances to catch and dropped both. Who was the ‘man of the match’? (2003) A. Chirag made 15 runs less than both Aakash and Biplab B. The catches dropped by Biplab are 1 more than the catches take by Aakash 97. Four friends A, B, C and D got the top four ranks in a competitive examination, but A did not get the first, B did not get the second, C did not get the third, and D did not get the fourth rank. Who secured which rank? (2003) A. Neither A nor D were among the first 2 B.

Neither B nor C was third or fourth

98. The members of a local club contribute equally to pay Rs. 600 towards a donation. How much did each one pay? (2003) A. If there had been five fewer members, each one would have paid an additional Rs. 10 B.

There were at least 20 members in the club, and each one paid no more than Rs. 30 99. A family has only one kid. The father says “after ‘n’ years my age will be 4 times the age of my kid”. The mother says “after ‘n’ years, my age will be 3 times that of my kid”. What will be the combined ages of the parents after ‘n’ years? (2003) A. The age difference between the parents is 10 years B.

After ‘n’ years the kid is going to be twice as old as she is now

Directions for Questions 100 to 105 : These questions are based on the information given below. Each question is followed by two statements, A and B. Answer each question using the following instructions : Choose (a), if the question can be answered by using one of the statement alone but not by using the other statement alone. Choose (b), if the question can be answered by using either of the statement alone. Choose (c), if the question can be answered by using both statements together but not by either statement alone. Choose (d), if the question cannot be answered on the basis of the two statements. 100. Ravi spent less than Rs. 75 to buy one kilogram each of potato, onion, and gourd. Which one of the three vegetables bought was the costliest? (2004) A : 2 kg potato and 1 kg gourd cost less than 1 kg potato and 2 kg gourd.

B : 1 kg potato and 2 kg onion together cost the same as 1 kg onion and 2 kg gourd. 101. Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses a coin. If it comes up heads, he moves one step to the right; otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stop? (2004) A : He stops after 21 coin tosses. B : He obtains three more tails than heads. 102. Nandini paid for an article using currency notes of denomination Re. 1, Rs. 2, Rs. 5, and Rs. 10 using at least one note of each denomination. The total number of five and ten rupee notes used was one more than the total number of one and two rupee notes used. What was the price of the article? (2004) A : Nandini used a total of 13 currency notes. B : The price of the article was a multiple of Rs. 10. 103. Four candidates for an award obtain distinct scores in a test. Each of the four casts a vote to choose the winner of the award. The candidate who gets the largest number of votes wins the award. In case of a tie in the voting process, the candidate with the highest score wins the award. Who wins the award? (2004) A : The candidates with top three scores each vote for the top scorer amongst the other three. B : The candidate with the lowest score votes for the player with the second higest score. 104. In a class of 30 students, Rashmi secured the third rank among the girls, while her brother Kumar studying in the same class secured the sixth rank in the whole class. Between the two, who had a better overall rank? (2004) A : Kumar was among the top 25% of the boys merit list in the class in which 60% were boys. B : There were three boys among the top five rank holders, and three girls among the top ten rank holders. 105. Zakib spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25%, and 13%. Who spends more on children’s education? (2004) A : Zakib spends more on recreation than Supriyo. on healthcare than Zakib.

B : Supriyo spends more

Directions for Questions 106 through 109 : Each question is followed by two statements A and B. Indicate your responses based on the following directives: (1) if the question can be answered using A alone but not using B alone. (2) if the question can be answered using B alone but not using A alone. (3) if the question can be answered using A and B together, but not using either A or B alone. (4) if the question cannot be answered even using A and B together. 106. The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI, of Section I is smaller than the average weight, WII, of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes WII and that of Section II becomes WI. What is the weight of Poonam? (2007) A : WII – WI = 1.0 B : Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal. 107. Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z2? A: x + y + z = 89 B: Among x, y, z two are equal. (2007) 108. Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square? A: The length of OM is twice that of OL. B: The length of OM is 4 cm. (2007) 109. ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC’s requirements?

A: The inner diameter of the tank is at least 8 meters. B: The tank weights 30,000 kg when empty, and is made of a material with density of 3gm/cc. (2007) Directions for Questions 110 to 113 : Each question is followed by two statements, A and B. Answer each question using the following instructions : (a)

if the question can be answered by using the statement A alone but not by using the statement B alone.

(b)

if the question can be answered by using the statement B alone but not by using the statement A alone.

(c)

if the question can be answered by using either of the statements alone.

(d)

if the question can be answered by using both the statements together but not by either of the statements alone.

(e)

if the question cannot be answered on the basis of the two statements.

110. In a football match, at the half–time, Mahindra and Mahindra Club was trailing by three goals. Did it win the match? (2007) A: In the second–half Mahindra and Mahindra Club scored four goals. B: The match.

opponent

scored

four

goals

the

111. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school? (2007) A: Sixty per cent of the top academic performers were not athletes. B: All the top academic performers were not necessarily athletes. 112. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who participated in a quiz contest. They were ranked based on their scores in the contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank as compared to Chetan. Chetan’s rank was lower than the median. Who among the five got the highest rank? (2007) A: Atul was the last rank holder. B: Bala was not among the top two rank holders. 113. Thirty per cent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background? (2007)

A: Twenty five per cent of the employees have engineering background. B: Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background. Directions for Questions 114 and 115 : Mark (a) if Q can be answered from A alone but not from B alone. Mark (b) if Q can be answered from B alone but not from A alone. Mark (c) if Q can be answered from A alone as well as from B alone. Mark (d) if Q can be answered from A and B together but not from any of them alone. Mark (e) if Q cannot be answered even from A and B together. In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subjects to the following rules : (a)

(b)

If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a mach against each other and the winner moves on to the next round. If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n – 1) players are grouped into (n – 1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n + 1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament. 114. Q : What is the number of matches played by the champion? A : The entry list for the tournament consists of 83 players. B : The champion received bye.

one (

2008) 115. Q : If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n? A : Exactly one player, received a bye in the entire tournament. B : One player received a bye while moving on to the fourth round from the third round. (2008) 1.

(d) We have time taken from O - H & H - C is same but speed from C - H is less therefore distance H - C should be less than O - H

(a) No matter who starts the work, the work will be completed in the same number of days. 3. (b) 2G + 3B = 20 and 2B + 3G = 20 so G and B can be formed by these equations 4. (b) Let S.P be S C.P be C Volume of sales is V Profit = (S -C)V ....(i) it S.P is increased by 10% the new S.P = S + 10% ofS = 1.1 S and new cost price be C + 10% C and V changes to V – 10% V = 0.9 V then new profit = 0.9 V (1.15S – 1.1C) = .99V ( S – C) ....(ii) from (i) and (ii) we can say if C is constant, change in profit can not be found. 5. (d) Since previous average weight is unknown then new can not be found so ques. can not be answered 6.

(b)

and PB > RE from A also B and E lies an P Q and RS respectively from B hence we say 7. (b) Suppose first boy has x toffees then second has x + 4 and third has x+ 8 Geometric progression be

So the question can be answered with the help of II alone. 8. (a) Let number of sheep last year was x then

(using I st. statement) x can be calculated from here

(d) Since dimensions of each tile are not given so number of tiles can not be found hence total cost can not be found as cost of a single tile has been given. 10. (d) It is not given that mangoes stolen by each boy form a series, hence total number can not be found 11. (a) x can be obtained by using the information provided by both ‘I’ & ‘II’ using ‘I’ we get x= 4 , 12 Using ‘II’ we get that x is only a multiple of 2 and not of 3. Using both we get x = 4 OR pdt of two nos.

12. 13.

14. 15.

16.

(d) (I) shows that x, y and z all are odd so it answers z – x. But from (II) it is not possible exactly to comment on x, y and z (b) (I) gives infinite values for x & y ; eg: 2, 4; 4, 6 etc. (II) shows that x + y < 10, which will be satisfied by 2 & 4 only. But we can not say which is x & which is y. (d) It is clear that only (I) answers the question (a) (I) shows that × b = 48 (II) shows 2 + b2 = 100 ( by pythagorous theorem) Hence using both we can get (c) (I) is useless (II) gives the price of bananas, which is double the price for 48 bananas

17. (d) (II) is useless (a) (I) shows that the two integers on squaring add up to 116 < 112 which means the integers are less than 10. We further find that the nos. are 10 and 4. 18. (c) (II) shows that both t & z are odd. (I) shows that x + y + t is even. 19. (a) If the altitude to the base of an isosceles triangle is known, the base can be found, and hence the area. So both the statements are required. 20. (a) From statement (i) and (ii) , we cannot find out the cost price of the particle. We are only able to find the ratio of SP and CP. 21. (d) The given in equality reduces to Both the statements are required to determine the outcome. Hence option (d) is correct in this case 22. (b) We cannot find out SP of the article from statement (i). However statement (ii) is sufficient to answer the given query. Hence (b) is the correct option.

23. 24. 25.

(a) None of the statements alone or together are sufficient to determine the radius of the rear wheel. (a) In this question also, it is not possible to find the ratio of the two liquids in the three vessels. (a) The statements that are given hold good for any quadratic equation of the given form. From the given statements, the value of can be expressed in terms of a and b.

26.

(c)

0.16 y = 2, 000

27.

28. 29.

30.

(a) Anil age was a prime number in 1996 and 1998. So Anil’s age can be two consecutive primes with a difference of 2. The pairs can be ( 3,5), (5, 7) (11,13) -----and so on. It is not possible to find a unique solution. (d) We can find the total worth of Lakhiram’s assets by calculating the given data in both the statements. Hence (d) is the correct option. (a) Different triangles that can be formed by 16 non - parallel but coplanar lines cannot be found because the lines may be interacting at a single point. Thus it is not possible to find the number of triangles. (d)

Since

31.

32.

are not uniquely determined we can’t find a & b nor we can uniquely determine (a+ b), so we cant even apply formula. Hence cannot be determined even with the help of both statements. (b) The number is divisible by 99 if its reverse is divisible by 9 and 11 and also it will be divisible by 9 and 11, this is property of divisibility test of 9 and 11. Hence if reverse is divisible by 9 and 11, then number is also divisible. (b) Since both the statements can be used to solve the distance between Mali & Pali

Distance =

from I

Distance

from II

Both the statement in dependently tell us the distance 33. (d) Since both the equations ......(1) Multiply (1) by 3.5 and 10.5x + 7y = 157.5 ......(2) Both are same equations i.e equations of parallel lines, hence their solution cannot be found even using both the equation. 34. (d) Say Q is wearing Black hat So R is wearing White and P is wearing Black if Q white R Black P white so using the two given statements, we can not comment regarding the colour of hat. 35. (c) Let speed of motorcycle be = x Speed of Car = x + 10

using this equation we can find valid value of x . Hence, the speed cannot be found using any one independently, while both the equation have to be used to find solution. 36. (b) Since both the statements tell the ratio of dimensions, hence any one statement independtly can help. 37. (c) Statement I gives us the point of Intersection of the two lines (3,2) statement II give us the equation of one line passing through (0, 4) & pt ( 3, 2) also since two lines are perpendicular, we can find its slope also . Hence we can find the area with the help of both the statements. 38. (d) Let the cost prices of the chair and the table be Rs X and Rs Y respectively from. Therefore, corresponding selling prices are Rs. 1.15X Rs. 1.2Y and profit is Rs (0.15X + 0.2Y) From II the profit is Rs. 0.05 X hence Which can’t be solved. Therefore, even both statements together are not sufficient to answer the question. 39. (d) From the two statements we can obtain a relation between the times taken by Tez and Gati to complete one lap. But, we do not know the direction in which they are moving they would require less time if they are moving in opposites direction then they when moving in the some direction.

∴ Even both the statement together are not sufficient to answer the question. 40. (d) Since Hence therefore we need both the length or any other relation since OACB is a rectangle Hence OC = AB Therefore radius = AB Hence, only statement I can give us the answer 41. (c) If n is divisible by 3, 5, 7 and 9 i.e n is divisible by 315 (LCM of 3, 5 7, 9 ) But, it is not necessary that it is odd unless and until n < 316 Since n < 400, hence we can say that n is an odd number become as n exceeds 400 then any even multiple of 315 will be even. Hence both statements are required 42. (a) To find , we need to define . That can be done by statement II which says . Statement I can’t help in final answer so, statement II alone will 43.

44.

give answer (d) Since no data is given about number of question, i.e question attempted by any one of them. Hence, even both the statement can’t help in finding the number of question. (c) Let price of tea be

so price of coffee = Rs x + 5 from II, x + 5 = 3x - 5 Hence, both the statements are require to find the price of tea 45. (d) Let a be 3x and b be 5x so, obviously ratio of 2a :b = 6: 5 Hence, even both the statements would not help in finding out the solution. As both the statements are some. 46. (a) 150 students Let number of girls be x number of boys = 150 -x so from I,

from II, this gives no solution. So, we can solve only using statement I.

47.

(a) from (i) we know that L2 is in envelope I so C2 will open E1 from (ii) we have no idea where L2 is . Hence using (i) only we can find the letter of C2

48.

49.

(a) 1 2 3 4 Rack from (1) IInd book is in 3rd rack so 4th book can be only in Ist rack from (2) we can’t tell about 2nd and 4th book so, only (1) can give is the answer (a) From (i) xy = a2

from (ii) So we cant find in terms of a. So only statement (1) can give us answer.

50.

(c)

from (1) from (2) Hence, from (1) & (2) we can find r1 & r2. Both the statements together give the solution.

51.

(b)

(i) if radius (r) is given we know side area = 2r2 from (ii) so if length of tangent is given we know r, hence any statement can individually, give us the answer.

52. 53.

54.

55.

56.

57.

58. 59.

60.

61.

62.

63.

(d) By one of the options we can say that there are atleast 10 white seeds but no conclusion can be arrived at, about the number of black seeds even with the help of both the statement. (c) From first statement alone we can’t deduce any thing as we don’t know the radius of the sphere. From second statement alone we can’t conclude anything as it gives information only about outer volume. Considering both the statements together the volume can be found. (d) From the first statement it gives that mathematician can never add 2 number correctly, but it is quite possible that apart from mathematician, others can also do the same mistake. The same logic is applied for the second statement as mathematician is given. If it is only mathematician then we can answer with the help of both the statements. (c) From statement 1, the relation comes to , where the solution set is given by 4, 16, 64 .... From the second statement alone too, nothing can be said, but when considered together, the answer comes to be (d). (c) The first statement states the polygon is rectangle but we don’t know anything about the sides of the rectangle and by combining both the statements we can have solution. (a) From the question itself, the shape of the figure is known and the only thing remaining is the orientation of the fig. The first statement fixes the position of the point D, which defines the orientation. The second statement gives us four sets of values, which can’t uniquely answer the query. (a) The answer can be arrived with the help of first statement alone. (d) Statement 1 doesn’t give us anything towards the number of students. Statement two also can’t oblige as it itself is an inference from the data already encountered. (b) Statement one implies that both the equations are basically the same, which gives the number of solution sets as infinite, but +ve integral solution sets are limited and will depend on the particular values of the coefficients. Statement 2 implies that the set of equations is inconsistent, which give number of solution set as nil. (c) Statement 1 gives that A & B have passed, nothing is definite about the other two. Statement 2 alone is also not enough to determine the passed students exactly, which only means that none of C & D have passed. But when combined, they conclude that A & B have passed and C & D have failed. (c) Statement I gives you the length of none of sides of the ∆PQR. Statement II gives you ‘n’ no. of right triangles inscribed in the semicircle. Combining the two statements we can say that for the given right triangle and inradius, we can have only one triangle of which you know the hypotenuse. This is possible to find the summation of the other two sides. (c) Statement I gives us no relation between Y and Z.

Statement II gives us no relation between X and Z. Combining the two, we can say that X>Y>Z. 64. (a) Statement I gives us the ratio of cost price and selling price. So we can find out the profit percentage which will remain independent of the money invested. Statement II cannot lead to any conclusions. 65. (a) Statement I gives . Statement II gives x < 0 or x < 3 Hence statement I can give us an answer. Hence answer option is (a). 66. (b) Statement I gives us that ac = ae. Similarly, Statement II also gives ac = ae. Refer the diagram

So, the answer is (b). (c) Neither of the statements alone can give us any answer. But combining the two statements we can say that f (0,1) = f(1,0)....................from statement I f (1,0) = 0....................from statement II Hence answer option is (c). 68. (c) Neither statement alone gives us any solution. 67.

Z = 100 ..... from question Y = 100 ..... from Statement I X+Y+Z = 1500 .....form Statement II Combining the two we get x = 1300. 69. (d) Neither of the statement alone or in combination can provide us any solution. We could have decided on the answer. Only if we are given the numerical value or the ratio of corresponding constants. 70. (d) Neither of the statements are sufficient as we are given neither direction nor the relation for the local time. 71. (b) Statement I gives us nothing new as we know that the hypotenuse will be the longest when the right triangle is isosceles.

Statement II gives us the length of the isosceles sides. Hence statement II alone is sufficient. 72. (c) It can be answered using both the statements. n even & m odd product = 30 = 15 × 2 is the only possible according to I 73. (d) I Rise in X for past 5 years = 5% annually Rise in Y for past 5 years = 6% annually Five years ago, GDP of X > GDP of Y. It cannot be said whether X’GPP was higher or not till we know the actual values of GDP’s. 74. (b) (A) X & Y are unequal even integer X < 10 , Y < 10 an odd integer ∴ X = 6, Y = 2 is only combination possible (B) X & Y both are even X < 10, Y < 10 XY = 12 Hence solution is 6, 2 But independently, it cannot be said which one is X and which one is Y. So only (a) can give us value of X not B. 75. (a) (A) The boat can carry 200 passenger of any time, but we don’t how many did it carry for trips. So (I) can’t tell about number of trips (B) Statement II gives the number of trips Say X trips for each trip time = 80 + 40 = 120 min So, boat makes 6 trips 76. (c) Transfer rate = 6 Kb / see size = 4.5 ×103 kb

Hence, it can be solved with the help of both equation 77.

(b)

Diameter

or R

Side of square = 25, so, bath area can be calculated & difference can be calculated from II side = 25 Dia

Hence it can be calculated Hence it can be answered from any of the statements. 78.

(d) (a) No. of apples of Ram

(apples of Gopal)

(b) Total stock of Dealer = 500. Even using both the statements. The question cannot be answered. 79. (d) Suppose before last five minutes score was India 0 & Korea 2 Considering both (A) & (B) statements final score becomes India 0 + 3 = 3 Korea 2 + 1 = 3 So given ques. Can not be answered by either of the statement 80. (a) If 12 students were added then total number of students will be 16, hence teacher would be able to divide her students evenly into dance team of 8. 81.

(a)

; ;

or ⇒

; Hence statement (1) gives the answer.

But from IInd statement, 82.

(b) Let listed price = using (A) statement

, so it is not sure that x = y , whole sale cost = w or

also it is given that

......(1) ......(2)

using (1) & (2) w can be determined it we use only (B) statement then we can be calculated (d) 500 is the arithmetic mean it does not show how many people above 500 and how many are below. If 500 would have been median then it would be true. The second statement do not provide any useful information. Therefore answer can be not given by either of the statement. 84. (d) A. | x | < 1 B. | x | < 2 From A statement, – 1< x < 1, for which | x–2 | < 1 is always true From B statement, –1 < x < 3, which does not clearly says about |x – 2| < 1 83.

85.

86.

(c)

Shaded portion = only French = 300 – 196 – 58; so both A & B are necessary (c) Let P unit receive Rs P Girish Rs G Jagdish Rs J ......(1)

, But A alone do not say anything about P & G

Therefore both A & B are necessary 87. (d) 244 < b11 . Even if b > 16 , we cannot say whether b is an integer or not. (b) Sum of roots = –b/4 and product of roots = c/4 From Statement I : Sum of roots = 0 and product of roots = –1/4 From this, b and c can be found out. Statement II : c/b = 1 or c = b Put x = – 1/2 in the equation . Hence b can be found out. Answer is obtained through either statement. 89. (d) We cannot get the answer from both the statements. 90. (a) Statement I is not enough. 88.

From statement II : We get x = Hence LHS > RHS. (b) From statement I, we get ABC as equilateral triangle, hence ∆DEF can be found out. Similarly we can get the answer from statement II as well. 92. (c) The data shows F has two siblings and M has five. M has 2 brothers, if. F has two brothers. So it can be answered Using option (a) alone. Option (b) is useless and do not provide any resent. 93. (b) It can be answered using option (a) alone 91.

Option (b) can not give any exact answer. 94. (c) Combining the statements, we get (A) : number of coupons = 21, and (B) : number of vowels = 18. The last letter being S, it leaves 2 blanks, which must be P’s Hence answer is (c). 95. (a) To find C’s time, we need total distance and C’s speed. These 2 variables are given by statement (A) and (B) combined. 96. (d) Runs Catches Catches Dropped A 50 At least 2 , say x B 50 2 , x+2 C 35 0 , atleast 2 From second statement, as catches dropped by Biplab are one more then catches taken by Akash. So Akash has taken atleast 2 catches. For the man of match, we require both the statements [A[ and [B] 97.

Using

; we get solution ;

; we get solution.

So we get the solution using either A or B. 98. (a) B statement does not give any useful conclusion. From A : nx = 600 and ( n – 5) (x + 10) = 600, which can solved to get an answer. 99. (a) Father mother after n years Using A, we get x + n = 10, so combined ages can be found. Using B, x + n = 2x or x = n; so ages can not be found. 100. (c) 2 p + 1g < 1p + 2g or p < g ......(i) 1p + 2O = 1O + 2g or 1p + 1O = 2g using (i), we get O > g So none of the statements alone can’t give the answer but on combining we get the answer. 101. (b) Here the answer can be obtained from both the statements individually. In A : 21 tosses takes him to a mark which is possible only with 12 Tails & 9 Heads and he reaches the blue mark. In B : In this case ha clearly reaches the blue mark. 102. (d) For 13 notes, we can not find the no. of Rs. 1, Rs. 2, Rs. 5 & Rs. 10 notes individually. Even after combining with B statement, we can get various

combinations of the given currency notes. 103. (a) This can be answered using A alone. As when the top 3 scorers will vote the topper will clearly get 2 votes. 104. (a) A says there were 18 boys and 12 girls, and Kumar was among top 5 boys but his rank among them is not known. So A can not answer the question. As per B, there were 3 boys in top 5, hence remaining 2 were girls. As Kumar is 6th so Rasmi is definitely behind him. 105. (a) A does not give the answer as 0.2 Z > 0.25 S or Z > 1.25 s which does not tell that 0.3 Z is greater or less than 0.4 S. From B, 0.13 S > 0.10 Z or Z < 1.3 S; which show that 0.3 Z < 0.4S 106. (c) Let weight of Deepak = D kg and weight odd Poonam = P kg If Deepak of section II is moved to section I and Poonam of Section I is moved to Section II, then and D – P = 50(WII – WI) and D – P = 50(WII – WI) Total weight of 100 students of the class = 4500 kg 50W1 + 50W2 = 4500 WI + WII = 90 ...(i) On using statement (A), we get WII – WI = 1 ...(ii) On solving equation (i) and (ii), we get WI = 44.5 kg, WII = 45.5 kg D – P = 50 (45.5 – 44.5) D – P = 50 From this, we can not get the age of Poonam Now, on using statement (B), we get

...(iii)

10D = 255WII – 245WI 10D = 255 × 45.5 – 245 × 44.5 D = 70 (iv) From this, we also can not get the age of Poonam Now, on combining statements (A) and (B), i.e., Using equation (iii) and (iv), we get P = 20 Therefore, on using both statements (A) and (B), we get the solution. 107. (a) A: x + y + z = 89 For x2 + y2 + z2 to be minimum, each of x, y, z must take integral value nearest to 89/3.

Let x = 30, y = 30, z = 29 ∴ Minimum value of x2 + y2 + z2 = (30)2 + (30)2 + (29)2 = 2641 Hence statement A alone is sufficient to answer the question. Hence, [a].

108. (b)

Length OM is maximum, when point O concides with point K. In this case OM become a diagonal and OL become the a side of the square. Hence, maximum length of OM = OL But according to the statement (A), Length of OM = 2.OL, which is not possible That’s why, Rahim unable to draw the square. From statement (B), we can not get any useful information. 109. (b) Outer radius = 5m According to the statement (A), Inner radius is at least 4 m If V be the capacity of the tank, then

(approx.) Thus, we can’t say that the capacity of the tank is at least 400 kilolitres. 110. (e) The question cannot be answered. A – If M & M scored 4 goals then still it will lose if the opponent scores 2 or more goals. As the goals scored by the opponent is not known so we cannot answer this. B – The opponent scores 4 goals in the match. The half time score can be 3 – 0 or 4 – 1. We do not know the goals scored by M & M in B. If we combine the two, A & B, there is a possibility of draw, if the half time score is 3 – 0. So, we can not answer the question. 111. (a) A answers the questions, as it gives the top performers, who are not atheletes. By adding the 10 athelete who are top academic performer. We will know the total top academic performers. B is redundant and do not provide any information.

112. (d) A says that Atul was ranked 5th. The median is 3, so Chetan was ranked 4th. But we do not know anything about the positions of D, B & E, which can be D E B or D B E or B D E. B says Bala was not 1st or 2nd, so he can be 3rd or 4th as C has to be 4th and 5th respectively. So, B alone do not tell us anything. On combining the 2, we see that only D E B satisfiesA and B among the 3 options possible – D E B, D B E, B D E. 113. (c) The question can be answered using any of the options, A or B, alone. A → We know the total students with Engineering background. By subtracting the Female Engineers. we calculate the Male Engineers. B → As the number of Female Engineers is known so, we can calculate the Male Engineers. 114. (d) (A) If there are 83 players, then one player get bye before first, second and fourth round each because before the first, second and fourth round each, the number of players is odd. Hence, there may be a player who get more than one bye. Therefore, statement (A) is not possible. (B) We are unable to give the answer from the given information. By combining the two statements we can get the answer. 115. (d) (A) This statement is not possible. For example, if number of players is 127, then there are more than one bye. (B) This statement is not possible. For example, if number of players is 80, then there is no player, who receive any bye. By combining the two statements, we can get the answer n = 72.

Directions for Questions 1 to 10 : From the alternatives, choose the one which correctly classifies the four sentences as a F J I 1. B. C. D. (a) (b) (c) (d) 2. B. C. D. (a) (b) (c) (d) 3.

: Fact : If it relates to a known matter of direct observation, or an existing reality or something known to be true. : Judgement : If it is an opinion or estimate or anticipation of common sense or intention. : Inference : If it is a logical conclusion or deduction about something, based on the knowledge of facts. A. If India has embarked on the liberalization route, she cannot afford to go back (1994) Under these circumstances, being an active supporter of WTO policies will be a good idea. The WTO is a truly global organization aiming at freer trade. Many member countries have already drafted plans to simplify tariff structures. FJFI IFJF IJFF IFIF A. The Minister definitely took the wrong step (1994) Under the circumstances, he had many other alternatives. The Prime Minister is embarrassed due to the Minister’s decision. If he has put the government in jeopardy, the Minister must resign. JFFI IFJI FFJI IFIJ A. The ideal solution will be to advertise aggressively (1994 ) One brand is already popular amongst the youth.

C. D. (a) (b) (c) (d) 4. B. C. D. (a) (b) (c) (d) 5. B. C. D. (a) (b) (c) (d) 6. B. C. D. (a) (b) (c) (d) 7.

Reducing prices will mean trouble as our revenues are already dwindling. The correct solution will be to consolidate by aggressive marketing. JFIJ FJJI IJFF JJIF A. If democracy is to survive, the people must develop a sense of consumerism (1994) Consumerism has helped improve the quality of goods in certain countries. The protected environment in our country is helping the local manufacturers. The quality of goods suffers if the manufacturers take undue advantage of this. IJFJ JFJI IJJF IFJJ A. Unless the banks agree to a deferment of the interest, we cannot show profits this year (1994) This would not have happened had we adopted a stricter credit scheme. The revenues so far cover only the cost and salaries. Let us learn a lesson : we cannot make profits without complete control over credit. IIJF IJFI FJIF FJFI A. Qualities cannot be injected into one’s personality (1994) They are completely dependent on the genetic configuration that one inherits. Hence changing our inherent traits is impossible as the genes are unalterable. The least one can do is to try and subdue the “bad qualities”. FIJI JFFI JFIJ JIFI A. Everything is purposeless

B. C. D. (a) (b) (c) (d) 8. B. C. D. (a) (b) (c) (d) 9. B. C. D. (a) (b) (c) (d) 10. B. C. D. (a) (b) (c) (d)

(1994) Nothing before and after the existence of the universe is known with certainty. Man is a part of the purposeless universe; hence man is also purposeless. There is only one way of adding purpose to the universe : Union with Him. JFIJ FJJI JFFI IJFJ A. Everyday social life is impossible without interpersonal relationships (1994) The root of many misunderstandings has been cited in poor relations among individuals. Assuming the above to be true, social life will be much better if people understand the importance of good interpersonal relations. A study reveals that interpersonal relations and hence life in general can be improved with a little effort on the part of individuals. FJIJ JFIF FIFJ IFFJ A. The prices of electronic goods are falling (19 94) Since we have substantial reductions in import duties, this is obvious. The trend is bound to continue in the near future. But the turnover of the electronic industry is still rising, because the consumers are increasing at a rapid rate. IFJF FJII FIJF JIFF A. In the past, it appears, wealth distribution, and not wealth creation has dominated economic policy (1994) Clearly, the government has not bothered to eradicate poverty. Today’s liberalization is far from the hitherto Nehruvian socialism. Results are evident in the form of a boom in the manufacturing sector output and turnover of all Industries. FJIF FIFJ IJIF JIFF

Directions for Questions 11 to 15 : Each question has a set of four sequentially ordered statements. Each statement can be classified as one of the following : • • • 11. 2. 3. 4.

(a) (b) (c) (d) (e) 12. 2. 3. 4.

(a)

Facts, which deal with pieces of information that one has heard, seen or read, and which are open to discovery or verification (the answer option indicates such a statement with an ‘F’). Inferences, which are conclusions drawn about the unknown, on the basis of the known (the answer option indicates such a statement with an ‘I’). Judgements, which are opinions that imply approval or disapproval of persons, objects, situations and occurrences in the past, the present or the future (the answer option indicates such a statement with a ‘J’). 1. We should not be hopelessly addicted to an erroneous belief that corruption in India is caused by the crookedness of Indians. The truth is that we have more red tape - we take eighty-nine days to start a small business, Australians take two. Red tape leads to corruption and distorts a people’s character. Every red tape procedure is a point of contact with an official, and such contacts have the potential to become opportunities for money to change hands. (2006) JFIF JFJJ JIJF IFJF JFJI 1. Given the poor quality of service in the public sector, the HIV/AIDS affected should be switching to private initiatives that supply antiretroviral drugs (ARVs) at a low cost. The government has been supplying free drugs since 2004, and 35000 have benefited up to now - though the size of the affected population is 150 times this number. The recent initiatives of networks and companies like AIDSCare Network, Emcure, Reliance-Cipla-CII, would lead to availability of much-needed drugs to a larger number of affected people. But how ironic it is that we should face a perennial shortage of drugs when India is one of the world’s largest suppliers of generic drugs to the developing world. (2006) JFIJ

(b) (c) (d) (e) 13. 2. 3. 4.

(a) (b) (c) (d) (e) 14. 2. 3. 4. (a) (b) (c) (d) (e) 15. 2. 3.

JIIJ IFIJ IFFJ JFII 1. According to all statistical indications, the Sarva Shiksha Abhiyan has managed to keep pace with its ambitious goals. The Mid-day Meal Scheme has been a significant incentive for the poor to send their little ones to school, thus establishing the vital link between healthy bodies and healthy minds. Only about 13 million children in the age group of 6 to 14 years are out of school. The goal of universalisation of elementary education has to be a prerequisite for the evolution and development of our country. (2006) IJFJ JIIJ IJFJ IJFI JIFI 1. Inequitable distribution of all kinds of resources is certainly one of the strongest and most sinister sources of conflict. Even without war, we know that conflicts continue to trouble us - they only change in character. Extensive disarmament is the only insurance for our future; imagine the amount of resources that can be released and redeployed. The economies of the industrialized western world derive 20% of their income from the sale of all kinds of arms. (2006) IJJI JIJF IIJF JIIF IJIF 1. So much of our day-to-day focus seems to be on getting things done, trudging our way through the tasks of living - it can feel like a treadmill that gets you nowhere; where is the childlike joy? We are not doing the things that make us happy; that which brings us joy; the things that we cannot wait to do because we enjoy them so much. This is the stuff that joyful living is made of - identifying your calling and committing yourself wholeheartedly to it.

(a) (b) (c) (d) (e)

When this happens, each moment becomes a celebration of you; there is a rush of energy that comes with feeling completely immersed in doing what you love most. (2006) IIIJ IFIJ JFJJ JJJJ JFIl

Directions for Questions 1 to 39 : In the questions below, choose the option, which represents a legitimate argument, i.e where the third sentence is a conclusion that can be arrived at from the previous two sentences. For instance All cigarettes are harmful for health. Brand X is a cigarette. Brand X is health. (1994) 1. A. All vegetarians eat meat B. All those who eat meat are not vegetarians C. All those who eat meat are herbivorous D. All vegetarians are carnivorous E. All those who eat meat are carnivorous F. Vegetarians are herbivorous (a) BCE (b) ABE (c) ACD (d) ACF 2. A. All roses thorns (1994) B. All roses have nectar. C. All plants with nectar have thorns D. All shrubs have roses E. All shrubs have nectar

harmful

for

have

F. (a) (b) (c) (d) 3.

B. C. D. E. F. (a) (b) (c) (d) 4.

B. C. D. E. F. (a) (b) (c) (d) 5.

B. C. D. E. F. (a) (b) (c)

Some roses have thorns BEF BCF BDE ACF A. No spring season (1994) Some seasons are springs Some seasons are autumns No seasons are autumns Some springs are not autumns All springs are autumns DFA BEF CEB DEB A. All high (1994) All falcons are blind. All falcons are birds. All birds are yellow. All birds are thirsty. All falcons are yellow. ABC CDF DEF BCA A. No hooks (1994) Some springs are hooks. All springs are wires Some hooks are not wires No hook is a spring All wires are springs AED BCF BEF

falcons

fly

wires

are

(d) ACE 6. A. Some dabra

abra

are

(1994) B. C. D. E. F. (a) (b) (c) (d) 7. B. C. D. E. F. (a) (b) (c) (d) 8. B. C. D. E. F. (a) (b) (c) (d) 9.

All abra are cabra. All dabra are abra. All dabra are cabra. Some cabra are abra. Some cabra are dabra. AEF BCF ABD BCE A. No plane chain (1994) All manes are chains. No mane is a plane. Some manes are not planes. Some planes are manes. Some chains are not planes. ACD ADF ABC CDF A. All nice (1994) All toys are nice All toys are dolls Some toys are nice Some nice things are dolls No doll is nice CDE CEF ACD BEF A. Some buildings scrappers (1994)

dolls

are

not

sky-

B. C. D. E. F. (a) (b) (c) (d) 10.

B. C. D. E. F. (a) (b) (c) (d) 11.

2. 3. 4. 5. 6. (a) (b) (c) (d) 12.

2. 3. 4. 5. 6.

Some sky-scrappers are not buildings. No structure is a sky-scrapper All sky-scrappers are structures Some sky-scrappers are buildings Some structures are not buildings ACE BDF CDE ACF A. All bins buckets (1994) No bucket is a basket No bin is a basket Some baskets are buckets Some bins are baskets No basket is a bin BDE ACB CDF ABF 1. Some bad (1995) All men are sad All bad things are men All bad things are sad Some sad things are men Some sad things are bad 165 236 241 235 1. No tingo bingo (1995) All jingoes are bingoes No jingo is a tingo Some jingoes are not tingoes Some tingoes are jingoes Some bingoes are not tingoes

are

men

are

(a) (b) (c) (d) 13.

2. 3. 4. 5. 6. (a) (b) (c) (d) 14.

2. 3. 4. 5. 6. (a) (b) (c) (d) 15.

2. 3. 4. 5. 6. (a) (b) (c)

123 132 461 241 1. All bright

Toms

(1995) No bright Toms are Dicks Some Toms are Dicks Some Dicks are bright No Tom is a dick No Dick is a Tom 123 256 126 341 1. Some bubbles dubbles (1995) Some dubbles are not bubbles No one who is rubbles is dubbles All dubbles are rubbles Some dubbles are bubbles Some who are rubbles are not bubbles. 146 456 123 246 1. All witches nasty (1995) Some devils are nasty All witches are devils All devils are nasty Some nasty are devils No witch is nasty. 234 341 453

are

not

are

(d) 653 16. 1. An eggs

ostrich

lays

(1996) 2. 3. 4. 5. 6. (a) (b) (c) (d) 17.

2. 3. 4. 5. 6. (a) (b) (c) (d) 18.

2. 3. 4. 5. 6. (a) (b) (c) (d)

All birds lay eggs Some birds can fly An ostrich cannot fly An ostrich is a bird An ostrich cannot swim 251 125 453 532 1. Some wood (1996) All wood is good All that is good is wood All wood is paper All paper is good Some paper is good 254 246 612 621 1. Some pins tin (1996) All tin is made of copper All copper is used for pins Some tin is copper Some pins are used for tin Some copper is used for tin 123 356 345 125

paper

are

made

19. 1. All tricks 2. 3. 4. 5. 6. (a) (b) (c) (d) 20.

2. 3. 4. 5. 6. (a) (b) (c) (d) 21.

2. 3. 4. 5. 6. (a) (b) (c) (d) 22.

(1996) Some tricks are shrieks Some that are shrieks are bricks Some tricks are not bricks All tricks are shrieks No tricks are shrieks 513 234 123 543 1. Some band (1996) All sandal is sand All band is sandal No sand is sandal No band is sand Some band is sandal 231 165 453 354 1. No wife life (1996) All life is strife Some wife is strife All that is wife is life All wife is strife No wife is strife 256 632 126 245 1. Poor girls want boys

bricks

are

sand

marry

rich

2. 3. 4. 5. 6. (a) (b) (c) (d) 23.

2. 3. 4. 5. 6. (a) (b) (c) (d) 24. 2. 3. 4. 5. 6. (a) (b) (c) (d) 25. B. C. D. E.

(1996) Rich girls want to marry rich boys Poor girls want to marry poor girls Rich boys want to marry rich girls Poor girls want to marry rich girls Rich boys want to marry poor girls 145 123 234 456 1. Six five (1996) Five is not four Some five is ten Some six is twelve Some twelve is five Some ten is four 145 123 156 543 1. Some flies (1996) Some flies are mosquitoes All mosquitoes are flies Some owls are flies All owls are mosquitoes Some mosquitoes are not owls 123 356 145 542 A. No viviparous (1997) All mammals are viviparous Bats are viviparous No bat is a bird No bird is a mammal

crows

bird

are

F. (a) (b) (c) (d) 26.

B. C. D. E. F. (a) (b) (c) (d) 27.

B. C. D. E. F. (a) (b) (c) (d) 28. B. C. D. E. F. (a) (b) (c) (d)

All bats are mammals ADC ABE FBA AFC A. No nurse

mother

(1997) Some nurses like to work No woman is a prude Some prude are nurses Some nurses are women All women like to work ABE CED FEB BEF A. Oranges sweet (1997) All oranges are apples Some sweets are apples Some oranges are apples All sweets are sour. Some apples are sour DAC CDA BCA FEC A. Zens Marutis (1997) Zens are fragile Marutis are fragile All stable are weak Marutis can beat Opels Opels are stable ACB EFD CEA ABC

are

29. A. Dogs open

sleep

the

(1997) B. C. D. E. F. (a) (b) (c) (d) 30. B. C. D. E. (a) (b) (c) (d) 31. B. C. D. E. (a) (b) (c) (d) 32. B. C. D. E. (a) (b)

Sheep stay indoors Dogs are like sheep All indoors are sheep Some dogs are not sheep Some open are not sheep DEF DCA EAF FBD A. All software companies employ knowledge workers (1999) Tara Tech employs knowledge workers. Tara Tech is a software company. Some sofware companies employ knowledge workers Tara Tech employs only knowledge workers ABC ACB CDB ACE A. Traffic congestion increase carbon monoxide in the environment (1999) Increase in carbon monoxide is hazardous to health Traffic congestion is hazardous to health. Some traffic congestion does not cause increased carbon monoxide. SomeTraffic congestion is not hazardous to health CBA BDE CDE BAC A. Apples are not sweets (1999) Some apples are sweet All sweets are tasty Some apples are not tasty No apple is tasty. CEA BDC

B. C. D. E. (a) (b) (c) (d) 35.

B. C. D. E. (a) (b) (c) (d) 36.

towns

(1999) All polluted towns should be destroyed Town Meghana should be destroyed Town Meghana is polluted Some towns in India should be destroyed BDE BAE ADE CDB A. No patriot criminal (1999) No Bundledas is a criminal Bundledas is a patriot Bogusdas is a patriot Bogusdas is a criminal ACB ABC ADE ABE A. Ant ants (1999) Boys are ant eaters Balram is an ant eater Balram likes ants Balram may eat ants DCA ADC ABE ACD A. All handsome (1999) Some actors are popular

India

are

eaters

actors

are

C. D. E. (a) (b) (c) (d) 37.

B. C. D. E. (a) (b) (c) (d) 38. B. C. D. E. (a) (b) (c) (d) 39.

B. C. D. E. (a) (b) (c)

Ram is handsome Ram is a popular actor Some popular people are handsome ACD ABE DCA EDC A Modern industry is driven 1999) BTI is a modern industry. BTI is a technology driven BTI may be technology driven Technology driven industry is modern ABC ABD BCA EBC A All Golmal islanders are blue people Some smart people are not blue coloured people. Some babies are blue coloured Some babies are smart Some smart people are not Golmal islanders BCD ABE CBD None of these A. MBA’s are in demand (1999) Ram and Sita are in great demand Ram is in great demand Sita is in great demand Ram and Sita are MBA’s ABE ECD AEB

technology (

colured (1999)

great

(d) EBA

Directions for Questions 1 to 14 : In each of the following sentences, the main statement is followed by four sentences each. Select the pair of sentences that relate logically with the given statement. 1.

Either drunk

Sam

ill;

loses (1997)

has

(1997) A. B. C. D. (a) (b) (c) (d) 2. A. B. C. D. (a) (b) (c) (d) 3. A. B. C. D. (a) (b) (c) (d) 4.

Sam is ill. Sam is not ill. Sam is drunk Sam is not drunk AB DA AC CD Whenever Ram hears sleep Ram heard of a tragedy Ram did not hear of a tragedy Ram lost sleep Ram did not lose sleep CA BD DB AD Either the train derailed (1997) The train is late The train is not late The train is derailed The train is not derailed AB DB CA BC When I read a nightmare

horror

tragedy,

late;

story

have

A. B. C. D. (a) (b) (c) (d) 5. A. B. C. D. (a) (b) (c) (d) 6.

(1997) I read a horror story I did not read a horror story I did not have a nightmare I had a nightmare CB AD BC AC When I eat rashes (1997) I ate berries I did not get rashes I did not eat berries I got rashes DA BC CB AD Either Sita is careless

berries

sick

get

she

(1998) A. B. C. D. (a) (b) (c) (d) 7. A. B. C. D. (a) (b) (c) (d)

Sita is not sick Sita is not careless Sita is sick Sita is careless AB AD BA DA Ram gets a swollen hamburgers ) Ram gets a swollen nose Ram does not eat hamburgers Ram does not get a swollen nose Ram eats hamburgers AB DC AC BC

nose

whenever

eats (1998

8. A. B. C. D. (a) (b) (c) (d) 9. A. B. C. D. (a) (b) (c) (d) 10. A. B. C. D. (a) (b) (c) (d) 11. A. C. D. (a) (b) (c) (d) 12.

Either the employees have no confidence in the management or they are hostile by nature (1998) They are hostile by nature They are not hostile by nature They have confidence in the management They have no confidence in the management. BA CB DA BD Whenever Ram reads late into the night, his father beats him up (1998) His father does not beat Ram Ram reads late into the night Ram reads early in the morning Ram’s father beats him in the morning CD BD AB None of the above All irresponsible parents shout if their children do not cavort (1998) All irresponsible parents do not shout Children cavort Children do not cavort All irresponsible parents shout AB BA CA All of the above Either the orangutan is not angry, or he frowns upon the world (1999) The orangutan frowns upon the world. B. The orangutan is not angry. The orangutan does not frown upon the world. The orangutan is angry. CB only DA only AB only CB and DA Either Ravan is a demon, or he is a hero

A. C. (a) (b) (c) (d) 13. A. C. (a) (b) (c) (d) 14. A. B. C. (a) (b) (c) (d)

(1999) Ravan is a demon. B. Ravan is not a demon Ravan is a hero D. Ravan is not a hero DA BC DB Both a and b Whenever Rajeev uses the internet, he sees a spider in his dream (1999) Rajeev sees a spider in his dream. B. Rajeev uses the internet. Rajeev does not see a spider in his dream. D. Rajeev does not use the internet. BA CD AB Both a and b If he talks to the professor, he will not need medicine (1999) He talks to the professor. He will not need medicine He does not talk to the professor. D. He will need medicine AD AB BA DC

Directions for Questions 1 to 14 : Each of the questions below contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two. 1. A. Some Xs are Ps; Some Ps are Ys; Some Xs are Ys (1998) B. All Sonas are bright; Some bright are crazy; Some Sonas are crazy. C. Some Cs are funny; All funny are wild; Some Cs are wild. D. No faith is strong; some strong have biceps; no faith has biceps. (a) A and D (b) C only (c) D only

(d) None of the above 2. A. Some icicles are cycles; all cycles are men; some icicles are men (1998) B. All girls have teeth; no teeth are yellow; no girls have yellow teeth. C. No hand is foot; some foot are heads; some heads are not hands D. Every man has wife; all wives are devoted; no devoted wife has a husband. (a) A, B and C only (b) A and B (c) C and B (d) A, B and C and D 3. A. No sun is not white; all moon is sun; all moon is white (1998 ) B. All windows are open; No open space is allocated; all window is closed space C. Some As can sleep late; some Bs wake up early; some As wake up early. D. No German can fire; all Americans bombard; both Germans and Americans can fight. (a) A only (b) B only (c) C only (d) D only 4. A. All Ts are square; all square are rectangular; all Ts are rectangular (1998) B. Some fat are elongated; some elongated things are huge; some fat are huge. C. Idiots are bumblers; bumblers fumble; Idiots fumble D. Water is good for health; health foods are rare; water is rare (a) D only (b) C only (c) Both A & C (d) All of the above 5. A. No cowboys laugh. Some who laugh are sphinxes. Some sphinxes are not cowboys (1999) B. All ghosts are fluorescent. Some ghosts do not sing. Some singers are not fluorescent. C. Cricketers indulage in swearing. Those who swear are hanged. Some who are hanged are not cricketers. D. Some crazy people are pianists. All crazy people are whistelers. some whistlers are pianists. (a) A and B (b) C only

(c) A and D (d) D only 6. A. All good peoples are knights. All warriors are good people. All knights are warriors (1999) B. No footballers are ministers. All footballers are tough. Some ministers are players C. All pizzas are snacks. Some meals are pizzas. Some meals are snacks. D. Some barkers are musk-dear. All barkers are sloth bears. Some sloth bears are musk deer (a) C and D (b) B and C (c) A only (d) C only 7. A. Dinosaurs are pre-historic creatures Water buffaloes are not dinosaures Water buffaloes are not pre historic creatures B. C. D. (a) (b) (c) (d) 8. B. C. D. (a) (b) (c) (d) 9. B. C. D. (a)

(1999) All politicians are frank. No frank people are crocodiles. No crocodiles are politicians No diamond is quartz. No opal is quartz. Diamonds are opals. All monkeys like bananas. Some GI joes like bananas. Some GI joes are monkeys. C only B only A and D B and C A. All earthquakes cause havoc. Some landslides cause havoc. Some earthquakes cause landslides (1999) All glass things are transparent. Some curios are glass things. Some curios are transparent. All clay objects are brittle. All XY are clay objects. Some XY are brittle No criminal is a patriot. Ram is not a patriot. Ram is a criminal D only B only C and B A only A. MD is an actor.Some actors are pretty. MD is pretty (1999) Some man are cops. All cops are brave. Some brave people are cops. All cops are brave. Some men are cops. Some men are brave. All actors are pretty. MD is not an actor. MD is not pretty. A and B

(b) (c) (d) 10. B. C. D. (a) (b) (c) (d) 11. B. C. D. (a) (b) (c) (d) 12. B. C. D. (a) (b) (c) (d) 13.

C and D A only C only A. All IIMs are in India. No BIMs are in India. No IIMs are BIMs (1999) All IIMs are in India.No BIMs are in India. Some brave people are cops Some IIMs are not in India. Some BIMs are not in India. Some IIMs are BIMs. Some IIMs are not in India. Some BIMs are not in Indai. Some BIMs are IIMs. A and B C and D A only B only A. Citizens of Yes Islands speak only the truth. Citizens of Yes islands are young people. Young people speak only the truth (1999) Citizens of Yes islands speak only the truth. Some Yes Islands are in the Atlantic. Some citizens of Yes islands are in Atlantic. Citizens of Yes Islands speak only the truth. Some young people are citizens of yes islands. Some young people speak only the truth. Some people speak only the truth. Some citizens of yes islands speak only the truth. Some people who speak only the truth are citizens of yes Islands. A only B only C only D only A. All mammals are viviparous. Some fish are viviparous. Some fish are mammals (1999) All birds are oviparous. Some fish are not oviparous. Some fish are birds No mammal is oviparous. Some creatures are oviparous and some are not. Some creatures are not mammals. Some creatures are mammals. Some creatures are viviparous. Some mammals are viviparous. A only B only C only D only A. Many singers are not writers. All poets are singers. Some poets are not writers (1999)

B. C. D. (a) (b) (c) (d) 14. B. C. D. (a) (b) (c) (d)

Giants climb beanstalks. Some chicken do not climb beanstalks. Some penguins are explorers All exploers live in snowdrifts. Some penguins live in snowdrifts. Some penguins are explorers. Amar is taller than Akbar. Anthony is shorter than Amar. Akbar is shorter than Anthony. A only B only B and C None of the above A. A few farmers are rocket scientists. Some rocket scientists catch snakes.A few farmers catch snakes (1999) Poonam is a kangaroo. Some kangaroos are made of teaks. Poonam is made of teak. No bulls eat grass. All matadors eat grass. No matadors are bulls. Some skunks drive cadillacs. All skunks are polar bears. Some polar bears drive cadillacs B only A and C C only C and D

Directions for Questions 1 - 3 : A robot moves on a co-ordinate plane as per the following instructions : GOTO (x, y) WALKX(p)

WALKY (p)

Robot reaches instructions

Robot directly moves to the point (x,y) from its initial position. Robot moves the distance ‘p’ parallel to the X - axis in the positive X direction for positive values of p and in the negative X direction for negative values of p. Robot moves the distance ‘p’ parallel to the Y - axis in the positive Y direction for positive values of p and in the negative Y direction for negative values of p. (6,6) following the given set of (1999)

(i) GOTO (x,y) ; (ii) WALKX(2) ; (iii) WALKY (4) Find out position of the robot after instruction (i). (a) (2, 4) (b) (4, 2) (c) (–4, –2) (d) Both (b) & (c) 2. If use of GOTO instruction is not allowed & the robot is currently at (x ,y) such that then what is the minimum number of instructions required to bring the robot to origin? (1999) (a) 1 (b) 2 (c) 3 (d) 4 3. Robot goes from point A(2,6) to point B( 7, 6) to point C (2, –4) and then back to point A. Which of the following points doesn’t lie on the path of the Robot? (1999) (a) (2, 0) (b) (3, 6) (c) (0, 6) (d) (4, 0) Directions for questions 4 & 5 : Read the information given below and answer the questions that follow : There are three vessels A, B and C with capacities 5, 3 and 2 respectively. There is a computer program that can perform certain functions as described below: Drain (Y) : drains the liquid in a vessel Y. Fill (X, Y) : fill amount from Y into X such that the amount of liquid withdrawn from Y is equal to the liquid in X. Empty (X,Y) : empty amount from Y into X such that the amount left in Y is equal to the amount of liquid in X. 4. The following operations are performed in succession (2000 ) 1. Fill k(C, A) 2. ..................... 3. Fill (C, A)

What should the second operation be if after the three operations A should contain one litre of liquid ? (a) Empty (C, B) (b) Empty (B, C) (c) Fill (C, B) (d) Fill (B, C) 5. In addition to the three operations in above problem, the fourth operation performed is Drain A. What operations should follow so that A contains four litres of liquid ? (2000) (a) Empty (B,A) , Drain (c) (b) Empty (B, A), Empty (C, A) (c) Fill (B, A), Fill (C, A) (d) Fill (A, B), Fill (A, C) Directions for questions 6 & 8 : Study the information below and answer questions based on it. Everyday Miss Yadav, Miss Sharma, Miss Toppo, and Miss Hussain go to a park for morning walk. One day, they reach the gate of the park at the same time and immediately start walking on the only circular track adjacent to the gate. Miss Yadav, Miss Toppo and Miss Hussain go on a clockwise direction while Miss Sharma goes anti-clockwise. Miss Hussain who is asthmatic is the slowest among the four and soon others move away from her. Like every day she could walk only one round taking almost the same time as others to complete their morning walk. After her walk Miss Hussain reads the following instruction written at the gate while others join her one after another. “Walkers are requested to use only the 500 m walking track. Plucking of flowers and leaves are strictly prohibited. The park will remain closed from 6 pm to 5 am.” While walking Miss Yadav overtakes Miss Hussain twice; once near the fountain and the other time at the signature rock. Miss Toppo and Miss Sharma cross her three times. (2009) 6. What is the total distance covered by Miss Sharma and Miss Toppo together? (a) 3500 m (b) 4000 m (c) 2500 m (d) 3000 m 7. How many times Miss Yadav and Miss Sharma crossed each other on the track? (a) Twice (b) Three times (c) Four times

(d) 8. (a) (b) (c) (d)

Five times How many times Miss Toppo would overtake Miss Yadav? Never Once Twice Three times

Directions for questions 9 - 11 : Answer the questions on the basis of the information given below. H1, H2, H3 and H4 are four horses that participated in each of the four different races – Race-I, Race-II, Race-III and Race-IV – during an annual horse-racing event in Goa. Each horse is owned by a different owner among Rahul, Dharma, Dablu and Ritesh, in no particular order. None of the four horses finished at the same position in more than two of the four races. In each race the four horses were given ranks 1, 2, 3 and 4 according to the positions at which they finished in the race. It is also known that: (2009) (i) In Race-I, H2 finished third and Ritesh’s horse finished first. Interestingly, in Race-II, H2 finished first and Ritesh’s horse finished third. (ii) In Race-IV, H2 finished third and H3 finished fourth. (iii) Dablu’s horse finished at the same position in Race-I and Race-II, and also in Race-III and Race-IV. (iv) In Race-IV, H1 and H3 interchanged the positions at which they had finished in Race-II. (v) In Race-III, H3 finished fourth and H4 finished second. (vi) Rahul’s horse did not finish first in any of the four races. 9. Who are the owners of H3 and H4 respectively? (a) Ritesh and Rahul (b) Dablu and Ritesh (c) Rahul and Dablu (d) Cannot be determined 10. Whose horse finished third in Race-III? (a) Rahul (b) Ritesh (c) Dharma (d) Either Rahul or Dablu 11. If the horse with the lowest sum of ranks in the four races won a Jackpot of `1 crore, which horse won the Jackpot? (a) H1 (b) H2 (c) H3 (d) H4

Directions for questions 12 & 13 : Go through the situation and the accompanying table, and pick up the best alternative to answer. There are five sets of digits; Set A, Set B, Set C, Set D and Set E; as shown in given diagram. Set A contains one digit, Set B contains two digits, Set C contains three digits. Set D contains two digits, and Set E contains one digit. Rearrange the digits, across the sets, such that the number formed out of digits of Set C is multiple of the numbers formed from digits in sets on either side. For example; in the given diagram, Set C is a multiple of digits in Set A and Set B but not of Set D and Set E. (2010)

12. What is the minimum number of rearrangements required to arrive at the solution? A rearrangement is defined as an exchange of positions between digits across two sets. For example, when 1 from Set C is exchanged with 5 of Set E, it is counted as one rearrangement? (a) 5 (b) 2 (c) 8 (d) 3 (e) 7 13. Which of the following pairs of digits would occupy Set A and E? (a) 2 and 6 (b) 3 and 6 (c) 3 and 9 (d) 4 and 8 (e) 2 and 4 Directions for questions 14 & 15 : Answer the questions on the basis of the information given below. During a political rally, seven leaders of a party – Ajeet, Ambika, Azad, Kamal, Kapil, Mukul and Pranab– are sitting on seven chairs arranged in a row, not necessarily in the same order. It is also known that: (i) Ambika is sitting beside Kapil. (ii) Pranab is the party president and so he is sitting in the middle of the row. (iii) Either Ajeet or Kamal, but not both, is sitting at one of the ends of the row. (iv) Azad and Mukul are sitting as far as possible from each other, without violating other conditions. (2011) 14. If ‘n’ represents the number of leaders sitting between Ajeet and Azad, which of the following is not a possible value of ‘n’? (a) 0 (b) 2

(c) 3 (d) 5 15. Which two leaders, among the given pairs, cannot sit adjacent to each other? (a) Mukul and Kamal (b) Azad and Ambika (c) Kamal and Kapil (d) Ajeet and Mukul

ANSWERS WITH SOLUTIONS TYPE - A 1.

6. 7. 8.

(c) Clearly out of the four statements C and D are facts as they already exist and are known. B is a judgement as it is an opinion that it will be a good idea. A is an inference as it is a logical conclusion of the fact that the world is moving towards free trade (liberalisation). (a) A is clearcut an opinion (judgement) about somebody else’s decision. D is a conclusion (inference) about the minister’s future action. B and C are facts as C is something known and B is a known matter of direct observation. (a) A and D are judgements as they talk about two opinions/solutions in a specific situation. B is a fact as it is known. C is an inference as it is clearly a logical conclusion. (b) B is clearly a fact - something known/observed. D is inference - logical conclusion - as quality will go down if manufacturers took undue advantage of the situation. A and C are judgements. (d) A is a fact because we know that profits won’t come until the bank agrees. C is also a fact as it is a known observation. D is a clear cut lesson/inference. B is a judgement as “If we would have done this, it wouldn’t have happened” - an opinion. (c) B is a fact - something known to be true. C is an inference as it is clearly dependent on the fact B. A and D are judgements. (a) Out of the four statements, only B can be a fact. A and D are judgements as they are opinions. C is an inference. (b) B and D are facts – D is clearly a study report and B is an observation. Clearly C is inference (clear from the language, “Assuming the above to be true). A is a judgement. (c) A and D are facts. B is an inference based on the fact A (prices are falling because of reductions in import duties). C is a judgement as it is an estimate.

10. (d) A is not a fact but a judgement (clear from the language ‘it appears’). C and D are facts. B is an inference based on the fact C. 11. (e) The first statement is a judgement, it uses the modal ‘should’ which has a judgemental, dogmatic use. The statement shows an opinion on the ‘erroneous belief’ and, thus, is a judgement made by the writer. This eliminates option (d). The second statement is a fact. It gives us a piece of information, statistics, figures, plain verifiable truth. Infact, the statement begins with ‘The truth is that’ and continues to give figures on days needed to start a small business. Thus, option (c) is eliminated. The third statement is not a fact, it does not give information but an opinion, it is a judgement. It is neither a verifiable truth nor a conclusion drawn from other statements but an opinion, thus, the third statement is a judgement. So, we have only to choose between (b) and (e). The last statement is an inference as it is a conclusion drawn from facts. ‘Contact with official’ and ‘money changing hands’ are known truths about Red tapeism on basis of which this conclusion is drawn. Thus, (e) is the right answer. 12. (d) The first statement is an inference, a conclusion drawn from the given statements. The given information is mentioned in the statement - ‘the poor quality of service in public sector’ and the conclusion drawn, thus, is ‘HIV/AIDS affected should be switching to private initiatives’. The second statement is a fact, it’s a verifiable truth stating statistics and figures about the time since free drugs have been supplied by the government, number of benefitted people etc. The third statement is an inference statement, a conclusion based on given facts. The facts in the statement being ‘recent initiatives of networks and companies like AIDS Care Network...’ and the conclusion drawn from this is that it ‘would lead to availability of much needed drugs....’. The fourth statement is a clear judgement. This statement gives the opinion of the author i.e. the shortage of drugs in India is “Ironic”. So, the right answer will be (c). 13. (a) The first statement is an inference, it uses the phrase ‘According to all statistical indication’, thus, it is a conclusion drawn from the statistical information mentioned in the sentence. The second statement, also, is an inference, use of the word. ‘Thus’ shows it is a conclusion. The first part of the statement is a given fact while the second part is the drawn conclusion, so, the statement is an inference. The third statement is a fact, it states figures, statistics and gives plain, true information. The fourth statement is a judgement. It is not a fact for it does not give verifiable information. It can be confused as an inference but one should keep in mind that the statement is not a conclusion drawn from

given facts but a personal opinion of the writer. The writer believes that the goal of universalisation of elementary education should be evolution and development of the country. Thus, it is a judgement. Thus, the correct answer is (a). 14. (b) The first statement is a judgement, it is not a conclusion derived from objective, known facts but an opinion of the author. The second statement is an inference because it is based on some previously known facts ‘we know’, conflicts continue to trouble us even without war and the conclusion drawn from this is that they change in character. So, this statement is an inference. The third statement is a judgement. There is no fact stated on basis of which the conclusion is drawn, rather it is simply a personal opinion and not an objective truth. The fourth statement is a fact which gives verifiable information, figures or statistics. Thus, the right answer is (b). 15. (d) The first statement is a judgement though it might appear as an inference on first reading but it is an opinion not a conclusion. A subjective statement is always a judgement while an objective statement can either be a fact or an inference. The second statement is also a judgement. It is a personal opinion, you may or may not agree with this opinion, thus, it is a judgement. The third statement is also a judge, this too an opinion of the writer and not an objective statement. The fourth statement is also a judgement, it is an author’s opinion that doing what you love makes each moment a celebration. So, all the four statements are judgements. Thus, answer is (d).

TYPE - B 1.

(d)

(c)

(a)

(b)

(d)

(b)

(c)

(a)

(b)

10. (d)

11.

(b)

12.

(a)

13. (c)

14. (d)

15. (b)

16. (a)

17. (b)

[Note : the arrow shows that one is a subset of other. The one with arrow towards itself is the bigger set] 18. (c)

19. (a)

20. (a)

21. (d)

22. (a) It clearly follow from :

23. (a)

24. (b)

25. (b)

26. (c)

27. (a)

28. (a)

29. (c)

30. (b)

31. (d)

32. (a)

33. (d)

34. (a)

35. (d)

36. (b)

37. (a)

38. (d) None of the options form a logical sequence. It can be verified by drawing venn diagrams.

39. (c)

TYPE - C 1. 2.

3. 4.

6. 7. 8.

9. 10. 11. 12. 13. 14.

(b) The two statements mean that atleast one of the two, i.e. “Sam is ill” or “he is drunk” is true, which clearly follows in DA. (c) The statement means that Ram did not lose sleep if he did not hear of a tragedy. Clearly DB follows. BD is not sure as he might lose sleep because of something as well. (d) The two statements mean that atleast one of the two, i.e. “train is late” or “it has derailed” is true, which clearly follows in BC. (a) The given statement means, ‘I did not have a nightmare if I did not read a story’. CB follows but BC is not sure as he might have a nightmare because of something else. (b) AD is not correct as rashes can be because of something else as well. The only conclusion which is true is BC, which states that, “I did not get rashes, which definitely means I did not eat berries”. (b) The given statement means if Sita is not sick, then, she is careless and vice-versa. Clearly option AD follows. (d) DC and AC are clearly wrong. AB is not sure. BC is the correct option. (b) Clearly BA and DA are wrong. The given statement means if they have confidence, then, they are hostile by nature and vice-versa. So CB follows. (d) CD and BD - irrelevant. AB not correct as ‘A’ must be followed by ‘Ram didn’t read late in the night’. (a) AB is true but BA is not sure. CA is definitely wrong. (d) If orangutan is angry he frowns upon the world and vice-versa. Both CB and DA are true. (d) If Ravan is not a demon then he is a hero and vice-versa. Clearly BC and DA are correct. (d) AB is not sure. Both BA and CD are correct. (d) AD is clearly wrong. BA is not sure. Out of DC and AB, DC seems to be more close to the given statement.

TYPE - D

(b)

(a)

(c)

(a)

(b)

(d)

10.

(c)

11.

(c)

12. (c) 13. (d) Can be foundout by drawing Venn diagrams. None is correct.

14. (d)

TYPE - E 1.

2. 3.

(b) Final Position = (6, 6) Position after instruction (ii) = (6, 2) Position after instruction (i) = (4, 2) (b) Clearly we use two instructions to reach the origin. One condition for Xa-axis and one condition for Y-axis. (c) Points using on the path of the Robot : From A to B : (3, 6), (4, 6), (5, 6), (6, 6) From B to C : (6, 4), (5, 2), (4, 0), (3, –2)

From C to A : (2, –3), (2, –2), (2, –1), (2, 0), ...... (2, 5) Hence, (0, 6) doesn’t lie on the path. (d) From the first operation Fill (C, A) water is taken out from vessel A and vessel C is filled . Now in the second operation water from the vessel C is filled in vessel B this operation can be written as fill (B,C). (d) After the above steps vessel A has one litre, vessel B and C has two litters each. After drain A it is empty now there can be four liters in A only if the liquids from C and B are emptied into A. This will happen by the commands Fill (A, C) and Fill (A, B).

6 - 10 : Solution for the set: 1. 2.

Total distance of the walking track = 500 m Distance covered by Miss Hussain = 500 m = 1 round

Since Miss Yadav over takes Miss Hussain two times so the number of rounds she covered = 3

Miss Toppo overtakes Miss Hussain 3 times so the number of rounds covered by her = 4 Miss Sharma crosses Miss Hussain 3 times so the number of rounds by her =3

5. 6. 7. 8.

(a) Total distance travelled by both the ladies = 3 x 500 + 4 x 500 = 3500 m (d) They both were walking in opposite direction so they cross each other 5 times ,3 times in the mid and two times at the end point (c) Two times , because Miss Toppo completed 4 rounds and Miss Yadav completed 3 rounds So first cross would be on the 2nd round and second cross would be on the third round.

(b) Dablu and Ritesh

10. (a) Rahul 11. (d) The sum of the ranks of H4 was the lowest and was equal to 7. Hence, H4 must have won the jackpot. 12. (d) According to question, Set A

Set B

Set C

Set D

Set E

196

Now in the first rearrangement, 7 from set A is exchanged with 2 of set B to get the following : Set A

Set B

Set C

Set D

Set E

196

Now in the second rearrangement, 4 from set D is exchanged with 5 of set E to get the following : Set A

Set B

Set C

Set D

Set E

196

Now in the third rearrangement, 9 from set C is exchanged with 5 of set D to get the following : Set A

Set B

Set C

Set D

Set E

156

Thus, a minimum of 3 rearrangement are required. So, option (d) is the correct answer. 13. (e) From the previous solution we get that Set A and Set E contains 2 and 4. So, option (e) is the correct answer. 14. (b) The value of ‘n’ cannot be 2. 15. (c) Kamal and Kapil can never sit adjacent to each other.

Directions for Questions 1 to 4 : Study the information below and answer questions based on it. A leading socialite decided to organise a dinner and invited a few of her friends. Only the host and the hostess were sitting at the opposite ends of a rectangular table, with three persons along each side. The pre-requisite for the seating arrangement was that each person must be seated such that atleast on one side it has a person of opposite sex. Maqbool is opposite Shobha, who is not the hostess. Ratan has a woman on his right and is sitting opposite a woman. Monisha is sitting to the hostess’s right, next to Dhirubhai. One person is seated between Madhuri and Urmila who is not the hostess. The men were Maqbool, Ratan, Dhirubhai and Jackie, while the women were Madhuri, Urmila, Shobha and Monisha. 1. The eighth person present, Jackie, must be (1994) I. the host II. seated to Shoba’s right III. seated opposite Urmila (a) I only (b) III only (c) I and II only (d) II and III only 2. Which of the following persons is definitely not seated next to a person of the same sex? (1994) (a) Maqbool (b) Madhuri (c) Jackie (d) Shobha

If Ratan would have exchanged seats with a person four places to his left, which of the following would have been true after the exchange? (1994) I. No one was seated between two persons of the opposite sex. (e.g. no man was seated between two women) II. One side of the table consisted entirely of persons of the same sex. III. Either the host or the hostess changed seats. (a) I only (b) II only (c) I and II only (d) II and III only 4. If each person is placed directly opposite his or her spouse, which of the following pairs must be married? (1994) (a) Ratan and Monisha (b) Madhuri and Dhirubhai (c) Urmila and Jackie (d) Ratan and Madhuri Directions for Questions 5 to 7 : Study the information below and answer questions based on it. Five of India’s leading models are posing for a photograph promoting “y’know, world peace and understanding”. But then, Rakesh Shreshtha the photographer is having a tough time getting them to stand in a straight line, because Aishwarya refused to stand next to Sushmita because Sushmita had said something about her in a leading gossip magazine. Rachel and Anu want to stand together because they are “such good griends, y’know”. Manpreet on the other hand cannot get along well with Rachel, because there is some talk about Rachel scheming to get a contract already awarded to Manpreet. Anu believes her friendly astrologer who has asked her to stand at the extreme right for all group photographs. Finally, Rakesh managed to pacify the girls and got a beautiful picture of five beautiful

5. (a) (b) (c) (d) 6.

girls smiling beautifully in a beautiful straight line, promoting world peace. If Aishwarya is standing to the extreme left, which is the girl standing in the middle? (1994) Manpreet Sushmita Rachel Can’t say If Aishwarya stands to the extreme left, which is the girls who stands second from left? (1994)

(a) Can’t say (b) Sushmita (c) Rachel (d) Manpreet 7. If Anu’s astrologer tells her to stand second from left and Aishwarya decides to stand second from right, then who is the girl standing on the extreme right? (1994) (a) Rachel (b) Sushmita (c) Can’t say (d) Manpreet Directions for Questions 8 to 11 : Study the information below and answer questions based on it.

A, B, C, D, E, F and G are brothers. Two brothers had an argument and A said to B “You are as old as C was when I was twice as old as D, and will be as old as E was when he was as old as C is now”. B said to A, “You may be older than F but G is as old as I was when you were as old as G is, and D will be as old as F was when F will be as old as G is”. Who is the eldest brother?

(1994) (a) (b) (c) (d) 9.

(a) (b) (c) (d) 10.

A E C Can’t be determined Who is brother? (1994) B D F Can’t be determined Which two twins

the

youngest

are

probably

(1994) (a) (b) (c) (d) 11.

D and G E and C A and B Can’t be determined Which of false?

the

following

(1994) (a) (b) (c) (d)

G has 4 older brothers A is older than G but younger than E B has three older brothers There is a pair of twins among the brothers

Directions for Questions 12 to 15 : Study the information below and answer questions based on it. The primitive tribes-folk of the island of Lexicophobos have recently developed a language for themselves, which has a very limited vocabulary. In fact, the words can be classified into only three types : the Bingoes, the Cingoes and the Dingoes. The Bingoes type of words are : Grumbs, Harrumphs, Ihavitoo

The Cingoes type of words are : Ihavitoo, Jingongo, Koolodo The Dingoes type of words are : Lovitoo, Metoo, Nana They have also devised some rules of grammar : I. Every sentence must have only five words II. Every sentence must have two Bingoes, one Cingo and two Dingoes. III. If Grumbs is used in a sentence, Ihavitoo must also be used and vice versa. IV. Koolodo can be used in a sentence only if Lovitoo is also used. 12. Which choice of words in a sentence is not possible, if no rules of grammar are to be violated? (1994) (a) Grumbs and Harrumphs as the Bingoes and Ihavitoo as the Cingo (b) Harrumphs and Ihavitoo as the Bingoes (c) Grumbs and Ihavitoo as the Bingoes and Lovitoo and Nana as the Dingoes (d) Metoo and Nana as the Dingoes 13. If Grumbs and Harrumphs are the Bingoes in a sentence, and no rule of grammar is violated, which of the following is/are true? (1994) I. Ihavitoo is the Cingo II. Lovitoo is the Dingo III. Either Lovitoo or Metoo must be one of - or both - the Dingoes (a) I only (b) II only (c) III only (d) I & III only 14. Which of the following is a possible sentence if no grammar rule is violated? (1994) (a) Grumbs harrumphs ihavitoo lovitoo metoo (b) Grumbs harrumphs ihavitoo jingongo lovitoo (c) Harrumphs ihavitoo jingongo lovitoo metoo (d) Grumbs ihavitoo koolodo metoo nana 15. If in a sentence Grumbs is the Bingo and no rule of grammar is violated, which of the following can be true? (1994) (a) Harrumphs must be a Bingo

(b) Ihavitoo must be a Bingo (c) Lovitoo must be used (d) All three Bingoes are used. Directions for Questions 16 to 19 : Study the information below and answer questions based on it. Bankatlal works x hours a day and rests y hours a day. This pattern continues for 1 week, with an exactly opposite pattern next week, and so on for four weeks. Every fifth week he has a different pattern. When he works longer than he rests, his wage per hour is twice what he earns per hour when he rests longer than he works. The following are his daily working hours for the weeks numbered 1 to 13 1st week

5th week

9th week

13th week

16. (a) (b) (c) (d) 17.

Rest

Work

A week consist of six days and a month consists of 4 weeks If Bankatlal is paid Rs. 20 per working hour in the 1st week, what is his salary for the 1st month? (1994) 1440 2040 1320 1680 Referring to the data given in previous question, Bankatlal’s average monthly salary at the end of the first four months will be (1994)

(a) (b) (c) (d) 18.

1760 2040 1830 1680 The new manager Khushaldas stipulated that Rs 5 be deducted for every hour of rest and Rs 25 be paid per hour starting 9th week, then what will be the change in Bankatlal’s salary for the 3rd month?

(Hourly deductions and salaries are constant for all weeks starting 9th week) (1994) (a) 540 (b) 480 (c) 240 (d) 0 19. Using the data in the previous questions, what will be the total earning of Bankatlal at the end of sixteen weeks (1994) (a) 7320 (b) 7800 (c) 8400 (d) 7680 Directions for Questions 20 to 23 : Study the information below and answer questions based on it.

20.

(a) (b) (c) (d) 21.

(a) (b) (c) (d) 22.

Four sisters Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other player. They played four games and each sister lost one game in alphabetical order. At the end of fourth game each sister had Rs 32. Who started with the lowest amount? (1995) Suvarna Tara Uma Vibha Who started with the highest amount? (1995) Suvarna Tara Uma Vibha What was the amount with Uma at the end of the second round? (1995)

(a) (b) (c) (d) 23.

36 72 16 None of these. How many with?

rupees

did

Suvarna

starts

(1995) (a) (b) (c) (d)

60 34 66 28

Directions for Questions 24 to 28 : Study the information below and answer questions based on it. Machine M1 as well as Machine M2 can independently produce either Product P or Product Q. The times taken by machines M1 and M2 (in minutes ) to produce one unit of product P and Q are given in the table below : (Each machine works 8 hours per day).

24. What is the maximum number of units that can be manufactured in one day? (1995) (a) 140 (b) 160 (c) 120 (d) 180 25. If the number of units of P are be 3 times that of Q, what is the minimum idle time for maximum total units manufactured? (1995) (a) 0 minutes (b) 24 minutes (c) 1 hour (d) 2 hours 26. If equal quantities of both are to be produced, then out of the four choices given below, the least efficient way would be ... (1995)

(a) (b) (c) (d) 27.

48 of each with 3 minutes idle 64 of each with 12 minutes idle 53 of each with 10 minutes idle 71 of each with 9 minutes idle If M1 works at half its normal efficiency, what is the maximum number of units produced, if at least one unit of each must be produced? (1995) (a) 96 (b) 89 (c) 100 (d) 119 28. What is the least number of machine hours required to produce 30 pieces of P and 25 pieces of Q? (1995) (a) 6 hours 30 minutes (b) 7 hours 24 minutes (c) 5 hours 48 minutes (d) 4 hours 6 minutes Directions for Questions 29 to 33 : Study the information below and answer questions based on it. A manufacturer can choose from any of the three types of tests available for checking the quality of his product. The graph that follows gives the relative costs for each of these tests for a given percentage of defective pieces.

29. Adopting Test-2 will be feasible if the percentage of defective pieces (p) lies between (1996) (a) 0.10 to 0.20 (b) 0.20 to 0.30 (c) 0.05 to 0.20 (d) 0.00 to 0.05 30. If p is equal to 0.2, then which test will be feasible? (1996) (a) either 1 or 2 (b) 2 only (c) 3 only (d) either 2 or 3 31. When will Test-3 be feasible? (1996) (a) p > 0.2 (b) 0.1 < p < 0.2 (c) 0.05 < p < 0.1

(d) p < 0.05 32. When feasible?

Test

-1

(1996) (a) (b) (c) (d) 33.

p < 0.05 0.0 < p < 0.2 0.1 < p < 0.2 0.05 to 0.2 If p < be

0.2,

then

the

best

alternative

will

(1996) (a) Test -2 (b) Test-3 (c) Test-1 (d) Not Test -3 Directions for Questions 34 & 35 : Study the information below and answer questions based on it. In a locality, there are five small towns, A, B, C, D and E. The distances of these towns from each other are as follows: AB = 2 km AC = 2km AD > 2km AE > 3km BC = 2km BD = 4 km BE = 3km CD = 2km CE= 3km DE > 3km 34. If a ration shop is to be set up within 2 km of each city, how many ration shops will be required? (1996) (a) 2 (b) 3 (c) 4 (d) 5 35. If a ration shop is to be set up within 3 km of each city, how many ration shops will be required? (1996) (a) 1 (b) 2 (c) 3 (d) 4

Directions for Questions 36 to 38 : Study the information below and answer questions based on it. A certain race is made up of three stretches A, B and C, each 2 km long, and to be covered by a certain mode of transport. The following table gives these modes of transport for the stretches, and the minimum and maximum possible speeds (in kmph) over these stretches. The speed over a particular stretch is assumed to be constant. The previous record for the race is ten minutes. A

Car

Motorcycle

Bicycle

36. Anshuman travels at minimum speed by car over A and completes stretch B at the fastest. At what speed should he cover stretch C in order to break the previous record? (1997) (a) Max. speed for C (b) Min. speed for C (c) This is not possible (d) None of these 37. Mr. Hare completes the first stretch at the minimum speed and takes the same time for stretch B. He takes 50% more time than the previous record to compete the race. What is Mr. Hare’s speed for the stretch C? (1997) (a) 10.9 kmph (b) 13.3 kmph (c) 17.1 kmph (d) None of these 38. Mr. Tortoise completes the race at an average speed of 20 kmph. His average speed for the first two stretches is 4 times that for the last stretch. Find his speed over stretch C (1997) (a) 15 kmph

(b) 12 kmph (c) 10 kmph (d) This is not possible Directions for Questions 39 & 40 : Study the information below and answer questions based on it. The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate. 39. Raja starts working on February 25th, 1996 and finishes the job on March 2nd, 1996. How much time would T and J take to finish the same job if both start on the same day as Raja? (1997) (a) 4 days (b) 5 days (c) 3½ days (d) Insufficient data 40. Starting on February 25th, 1996, if Raja had finished his job on April 2nd, 1996, when would T and S have completed the job, had they started on the same day as Raja? (1997) (a) March 15th, 1996 (b) March 14th, 1996 (c) March 22nd, 1996 (d) Insufficient data Directions for Questions 41 & 42 : Study the information below and answer questions based on it. Production pattern for no. of units (in cubic feet) per day For a truck that can carry 2000 cubic feet, hiring cost per day is Rs 1000. Storing cost per cubic feet is Rs 5 per day. 41. If all the units should be sent to the market, on which days should the truck be hired to minimize the cost? (1998)

(a) (b) (c) (d) 42.

2nd, 4th, 6th, 7th 7th 2nd, 4th, 5th, 7th None of these If storage cost reduced to Rs 0.8 per cubic feet per day, then on which days should the truck be hired to minimize the cost? (1998) (a) 4th (b) 7th (c) 4th and 7th (d) None of these Directions for Questions 43 to 45 : Study the information below and answer questions based on it. A, B, C, D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place. 43. Which of the following must be false? (1998) (a) A is at the first place (b) A is at the second place (c) A is at the third place (d) A is at the fourth place 44. If A is not at the third place, then C has the following option only (1998) (a) the first place only (b) the third place only (c) the first and the third place only (d) any of the places 45. If A and B are together then which of the following must be necessarily false (1998) (a) C is not at the first place (b) A is at the second place (c) D is at the first place (d) C is at the first place Directions for Questions 46 to 48 : Study the information below and answer questions based on it.

A, B, C, D collected one rupee coins following the given pattern. (i) Together they collected 100 coins (ii) Each one of them collected even no. of coins (iii) Each one of them collected at least 10 coins (iv) No two of them collected the same no. of coins 46. The maximum number of coins collected by any one of them cannot exceed (1998) (a) 64 (b) 36 (c) 54 (d) None of these 47. If A collected 54 coins, then the difference in the number of coins between the one who collected maximum number of coins and the one who collected the second highest number of coins must be at least (1998) (a) 12 (b) 24 (c) 30 (d) None of these 48. If A collected 54 coins and B collected two more coins than the twice of the number of coins collected by C. Then the number of coins collected by B could be (1998) (a) 28 (b) 20 (c) 26 (d) 22 Directions for Questions 49 & 50 : Study the information below and answer questions based on it. Amar, Akbar, Anthony are three friends. Only three colors are available for their shirts, viz. Red, Green and Blue. Amar did not wear red shirt. Akbar did not wear green shirt. Anthony did not wear blue shirt. 49. If Akbar and Anthony wear the same colour, then which of the following is not true? (1998)

(a) (b) (c) (d) 50.

Amar wears blue and Akbar wears green Amar wears green and Akbar wears red. Amar wears blue and Akbar does not wear blue Anthony wears red If two of them wear the same colour then how many of the following must be false (1998) I. Amar wears blue and Akbar does not wear green II. Amar does not wear blue and Akbar wears blue. III. Amar does not wear blue and Akbar does not wear blue IV. Amar wears green. Akbar does not wear red. Anthony does not wear green (a) 0 (b) 1 (c) 2 (d) 3 Directions for Question 51 : Study the information and answer question. 51. My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates he wishes. But then he must have biscuits twice the number of chocolates and apples more than biscuits and chocolates together. Each chocolate costs Re. 1. The cost of apple is twice of chocolate and four biscuits are worth of one apple. Then which of the following can be the amount that I spent on that evening on my son? (1998) (a) Rs 34 (b) Rs 33 (c) Rs 8 (d) None of these Directions for Questions 52 to 55 : Study the information below and answer questions based on it. Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms. Andhra Pradesh, Ms. Uttar Pradesh, Ms. West Bengal and Ms. Maharashtra. Mrs. Bankatlal, who was very anxious about the result asked him about it as soon as he was back home. Bankatlal just told that the one who was wearing the yellow saree

won the contest. When Mrs. Bankatlal pressed for further details, he elaborated as follows: I. All of them were sitting in a row II. All of them wore sarees of different colors, viz. Green, Yellow, White, Red III. There was only one runner up and she was sitting beside Ms. Maharashtra IV. The runner up was wearing the Green saree V. Ms. West Bengal was not sitting at the ends and was not a runner up VI. The winner and the runner up are not sitting adjacent to each other VII. Ms. Maharashtra was wearing white saree VIII. Ms. Andhra Pradesh was not wearing the Green saree IX. Participants wearing Yellow saree and White saree were at the ends 52. Who wore the Red saree? (1998) (a) Ms. Andhra Pradesh (b) Ms. West Bengal (c) Ms. Uttar Pradesh (d) Ms. Maharashtra 53. Ms. West Bengal was sitting adjacent to.......................... (1998) (a) Ms. Andhra Pradesh and Ms. Maharashtra (b) Ms. Uttar Pradesh and Ms. Maharashta (c) Ms. Andhra Pradesh and Ms. Uttar Pradesh (d) Ms. Uttar Pradesh only 54. Which saree was worn by Ms. Andhra Pradesh? (1998) (a) Yellow (b) Red (c) Green

(d) White 55. Who up?

was

the

runner

(1998) (a) (b) (c) (d)

Ms. Andhra Pradesh Ms. West Bengal Ms. Uttar Pradesh Ms. Maharashta

Directions for Questions 56 to 60 : Study the information below and answer questions based on it. Krishna distributed 10 acre of land to Gopal and Ram who paid him the total amount in the ratio 2:3. Gopal invested further Rs2 lac in the land and planted coconut and lemon trees in the ratio 5:1 on equal area of land. There were a total of 100 lemon trees. The cost of one coconut was Rs 5. The crop took 7 years to mature and when the crop was reaped in 1997, the total revenue generated was 25% of the total amount put in by Gopal and Ram together. The revenue generated from the coconut and lemon tress was in the ratio 3:2 and it was shared equally by Gopal and Ram as the initial amount spent by them were equal. 56. What was the total output of coconuts? (1998) (a) 24000 (b) 36000 (c) 18000 (d) 48000 57. What was the value of output per acre of lemon trees planted (in lakh/ acre )? (1998) (a) 0.72 (b) 2.4 (c) 24 (d) Cannot be determined

58. What 1997?

was

the

amount

received

Gopal

tree

for

(1998) (a) (b) (c) (d) 59.

Rs1.5 lac Rs 3.0 lac Rs 6 lac None of these What was coconuts?

the

value

output

per

(1998) (a) (b) (c) (d) 60. (a) (b) (c) (d)

36 360 3600 240 What was the ratio of yields per acre of land for coconuts and lemons? (1998) 3:2 2:3 1:1 Cannot be determined Directions for Questions 61 & 62 : Study the information below and answer questions based on it.

There are six people A, B, C, D, E and F. Two of them are housewives, one is an accountant, one is an architect, one is a lawyer and one is a lecturer. A, the lawyer is married to D & E is not the housewife. None of the females is the architect or the accountant. There are two married couples. C is the accounant, Married to the lecturer F. 61. What is the profession of E (1999) (a) Accountant (b) Lecturer (c) Architect

(d) None of these 62. How there

many

males

are

(1999) (a) (b) (c) (d)

2 3 4 can’t be determined

Directions for Questions 63 to 66 : Answer the questions based on the following information. Ten coins are distributed among four people P, Q, R and S such that one of them gets one coin, another gets two coins, the third gets three coins and the fourth gets four coins. It is known that Q gets more coins than P, and S gets fewer coins than R. 63. If the number of coins distributed to Q is twice the number distributed to P, then which one of the following is necessarily true? (a) R gets an even number of coins. (b) R gets an odd number of coins. (1999) (c) S gets an even number of coins. (d) S gets an odd number of coins. 64. If R gets at least two more coins than S, then which one of the following is necessarily true? (1999) (a) Q gets at least two more coins than S. (b) Q gets more coins than S. (c) P gets more coins than S. (d) P and Q together get at least five coins. 65. If Q gets fewer coins than R, then which one of the following is not necessarily true? (1999) (a) P and Q together get at least four coins. (b) Q and S together get at least four coins. (c) R and S together get at least five coins. (d) P and R together get at least five coins. 66. If R receives 3 coins then number of coins received by Q is (1999 )

(a) (b) (c) (d)

2 3 4 All of these

Directions for Questions 67 & 68 : Study the information below and answer questions based on it.

67.

(a) (b) (c) (d) 68. (a) (b) (c) (d)

Seven players A, B, C, D,E, F & G have to take dinner sitting on the same side of a rectangular table. Both A & G want to leave early so they must sit on the extreme right positions. B has to receive the man of the match award so he must sit in the middle. C & D don’t like each other so they must sit as far from each other as possible . E & F are very good friends & so they must sit together. With the help of this information answer the following questions. Which of the following two person can not sit together (1999) C&A G&C E&F E&G Which of the following persons can not sit on either of the extreme positions (1999) A D G F

Directions for Questions 69 to 71 : Answer the questions based on the following information. A young girl Roopa leaves home with x flowers, goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river. The number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to

69. (a) (b) (c) (d) 70. (a) (b) (c) (d) 71 (a) (b) (c) (d)

the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand. If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is (1999) 30 31 32 33 The minimum number of flowers that could be offered to each deity is (1999) 0 15 16 Cannot be determined The minimum number of flowers with which Roopa leaves home is (1999) 16 15 0 Cannot be determined

Directions for Questions 72 to 74 : Study the information below and answer questions based on it. Ghosh Babu goes to a casino in Kay - Kay islands where he comes across an interesting game of cards. The visitor playing the game is called the player & the clubman is called the dealer. The rules of the game are as follows: First the player picks the card. This card is called the base card & the number on the face of the card is called the base value of the card. Ace, King, Queen & Jack all have base value of 10. The dealer pays the player same number of rupees as the base value of the card. Now the dealer picks a card &. This is called the top card. If topcard is of the same suite then the player pays the dealer double the amount of base value. If it is of the same colour but not the same suite then the player pays the dealer the

amount of a bse value. If it is of different colour then the dealer pays the player the amount of base value. Ghosh Babu plays the game 4 times. First time, he draws 8 of club & the dealer draws jack of club. Second time he draws 10 of hearts & the dealer draws 2 of spade. Third time he draws 6 of diamond & the dealer draws 1 of heart. Finally, Ghosh Babu draws 8 of spade and the dealer draws ace of the spade. 72. If Ghosh Babu should leave the game when his profit is maximum then what is that profit (1999) (a) 12 (b) 18 (c) 20 (d) None of these 73. If Ghosh Babu did not have to borrow any money from anyone then what is the minimum amount that he could have started with (1999) (a) (b) (c) (d) 74. (a) (b) (c) (d) 75.

16 24 8 None of these If Ghosh Babu is left with 100 rupees now what is the amount that he had started with (1999) 120 104 96 None of these In a bag a person can carry 10 books. The books are mathematics physics, management and fiction. If a person carries a book of management, he has to carry two or more books of fiction. If he carries a book of mathematics he has to carry two or more books of physics. In carrying books he used to get certain points. To carry a book of management, mathematics, physics and fiction each the points he got were 4, 3, 2, 1 respectively. He has to carry a book of each subject. So what is the maximum no of points a person can

get (2000) (a) 20 (b) 21 (c) 22 (d) 23 76. Five persons P, Q , T, S, M lives in a hut, palace hotel, cottage, penthouse not necessarily in tha order. Each of them like two colours out of red, green, yellow, blue and black. P likes red and blue. Q lives in a hut. T likes yellow and black and S likes the colour liked by P. The person who lives in a palace doesn’t like blue or black colour where does M stay? (2000) (a) palace (b) hut (c) cottage (d) pent house 77. There are ten animals-two each of lion, panther, bison, bear, and deer-in a zoo. The enclosures in the zoo are named X, Y, Z, P and Q and each enclosure is allotted to one of the following attendants Jack, Mohan, Shalini, Suman and Rita. Two animals of different species are housed in each enclosure. A lion and a deer cannot be together. A panther cannot be with either a deer or a bison. Suman attends to animals from among bison, deer, bear and panther only. Mohan attends to a lion and a panther. Jack does not attend to deer, lion or bison. X, Y and Z are allotted to Mohan, Jack and Rita respectively. X and Q enclosures have one animal of the same species. Z and P have the same pair of animals. The animals attended by Shalini are (2000) (a) bear & bison (b) bison & deer (c) bear & lion (d) bear & panther 78. Eighty kilograms (kg) of store material is to be transported to a location 10 km away. Any number of couriers can be used to transport the material can be packed in any number of units of 10, 20 or 40 kg. Courier charges are ` 10 per hour. Couriers travel at the speed of 10 km/hr if they are not carrying any load, at 5 km/hr if carrying 10 kg, at 2 km/hr if carrying 20 kg and at 1 km/hr if carrying

40 kg. A courier cannot carry more than 40 kg of load. The minimum cost at which 80 kg of store material can be transported will be (2000) (a) ` 180 (b) ` 160 (c) ` 140 (d) ` 120 79. Four persons A, B, C and D live in four houses which are Red, Green Blue and Yellow in colour. A doesn’t live adjacent to the yellow house. B lives in the Yellow house. The Yellow house is adjacent to the Green and the Red house. What is the colour of A’s house? (2000) (a) Red (b) Green (c) Blue (d) can’t be determined 80. In some code, letters a, b, c, d and e represents numbers 2, 4, 5, 6 and 10. We just don’t know which letter represents which number. Consider the following relationships : I.

a + c = e,

II.

b – d = d and

III. e + a = b Which true?

statement

below

(2001) (a) b = 4, d = 2 (b) a = 4, e = 6 (c) b = 6, e = 2 (d) a = 4, c = 6 81. At a village mela, the following six nautanki (plays) are scheduled as shown in the table below (2001)

You like to see all the six nautankis. Further, you wise to ensure that you get a lunch break from 12:30 p.m. to 1:30 p.m Which of the following ways can you do this? (a) Sati-Savitri is viewed first; Sunder kand is viewed third and Jhansi Ki Rani is viewed last. (b) Sati-Savitri is viewed last; Veer Abhimanyu is viewed third and Reshma aur Shera is viewed first. (c) Sati-Savitri is viewed first; Sunder Kand is viewed third and Joru ka Ghulam is viewed fourth. (d) Veer Abhimanyu is viewed third; Reshma aur Shera is viewed fourth and Jhansi ki Rani is viewed fifth. 82. Mrs. Ranga has three children and has difficulty remembering their ages and the months of their birth. The clues below may help her remember (2001) * The boy, who was born in June, is 7 years old * One of the children is 4 years old, but it is not Anshuman * Vaibhav is older than Suprita * One of the children was born in September, but it was not Vaibhav * Supritas birthday is in April * The youngest child is only 2 years old. Based on the above clues, which one of the following statements is true? (a) Vaibhav is the oldest, followed by Anshuman who was born in September, and the youngest is Suprita who was born in April. (b) Anshuman is the oldest being born in June , followed by Suprita who is 4 years old, and the youngest is Vaibhav who is 2 years old (c) Vaibhav is the oldest being 7 years old, followed by Suprita who was born in April, and the youngest is Anshuman who was born in

September (d) Suprita is the oldest who was born in April, followed Vaibhav who was born in June, and Anshuman who was born in September. 83. The Bannerjees, the Sharmas, and the Pattabhiramans each have a tradition of eating Sunday lunch as a family. Each family serves a special meal at a certain time of day. Each family has a particular set of chinaware used only for this meal. Use the clues below to answer the following question (2001) * The Sharma family eats at noon * The family that serves fried brinjal uses blue chinaware * The Bannerjee family eats at 2 o’clock * The family that serves sambar does not use red chinaware * The family that eats at 1 o’clock serves fried brinjal * The Pattabhiraman family does not use white chinaware * The family that eats last likes makkai-ki-roti Which one of the following statements is true? (a) The Bannerjees eat makkai-ki-roti at 2 o’clock, the Sharmas eat fried brinjal at 12 o’clock and the Pattabhiramans eat sambar from red chinaware. (b) The Sharmas eat sambar served in white chinaware, the Pattabhiramans eat fried brinjal at 1 o’ clock, and the Bannerjees eat makkai-ki-roti served in blue chinaware. (c) The Sharmas eat sambar at noon, the Pattabhiramans eat fried brinjal served in blue chinaware, and the Bannerjees eat makkai-ki-roti served in red chinaware. (d) The Bannerjees eat makkai-ki-roti served in white chinaware, the Sharmas eat fried brinjal at 12o’ clock and the Pattabhiramans eat sambar form red chinaware. 84. While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat of the counter and ran out. Balbir was mad when he realised what had happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers

really didn’t want to help Balbir. So each of them made a statement which contained one truth and one lie (2001) * Shopkeeper Number 1 said - “The dog had black hair and a long tail”. * Shopkeeper Number 2 said - “The dog had a short tail and wore a collar.” * Shopkeeper Number 3 said- “The dog had white hair and no collar.” Based on the above statements, which of the following could be a correct descriptions? (a) The dog had white hair, short tail and no collar (b) The dog had white hair, long tail and a collar (c) The dog had black hair, long tail and a collar (d) The dog had black hair, long tail and no collar Directions for Questions 85 & 87 : Answer the following questions based on the information given below. Elle is three times older than Yogesh. Zaheer is half the age of Wahida. Yogesh is older than Zaheer. 85. Which of the following can be inferred? (2001) (a) Yogesh is older than Wahida. (b) Elle is older than Wahida (c) Elle may be younger than Wahida. (d) None of the above 86. Which of the following information will be sufficient to estimate Elle’s age? (2001) (a) Zaheer is 10 years old (b) Both Yogesh and Wahida are older than Zaheer by the same number of years (c) Both (a) and (b) above (d) None of the above 87. P, Q, R, S are four statements. Relation between these statements is as follows (1998) If P is true then Q must be true

If Q is true then R must be true If S is true then either Q is false or R is false Then which of the following must be true. (a) If P is true then S is false (b) If S is false then Q must be true (c) If Q is true then P must be true (d) If R is true then Q must be true Directions for Questions 88 to 90 : Study the information below and answer questions based on it.

88.

(a) (b) (c) (d) 89.

(a) (b) (c) (d) 90.

(a) (b)

A group of three or four has to be selected from seven persons. Among the seven are two women: Fiza and Kavita, and five men : Ram, Shyam, David, Peter and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group. Which of the following is a feasible group of three? (2001) David, Ram, Rahim Peter, Shyam, Rahim Kavita, David, Shyam Fiza, David, Ram Which of the following is a feasible group of four? (2001) Ram, Peter, Fiza, Rahim Shyam, Rahim, Kavita, David Shyam, Rahim, Fiza, David Fiza, David, Ram, Peter Which of the following statements is true? (2001) Kavita and Ram can be part of a group of four A group of four can have two women

(c) A group of four can have all four men (d) None of these 91. On her walk through the park, Hamsa collected 50 coloured leaves, all either maple or oak. She sorted them by category when she got home, and found the following : (2001) * The number of red oak leaves with spots is even and positive * The number of red oak leaves without any spot equals the number of red maple leaves without spots * All non-red oak leaves have spots, and there are five times as many of them as there are red spotted oak leaves * There are no spotted maple leaves that are not red * There are exactly 6 red spotted maple leaves * There are exactly 22 maple leaves that are neither spotted nor red How many oak leaves did she collect? (a) 22 (b) 17 (c) 25 (d) 18 92. Eight people carrying food baskets are going for a picnic on motorcycles. Their names are A, B, C, D, E, F, G and H. They have four motorcycles, M1, M2, M3, and M4 among them. They also have four food baskets O, P, Q, and R of different sizes and shapes and each can be carried only on motorcycles M1, M2, M3, or M4, respectively. No more than two persons can travel on motorcycle and no more than one bakset can be carried on a motorcycle. There are two husband - wife pairs in this group of eight people and each pair will ride on a motorcycle together. C cannot travel with A or B. E cannot travel with B or F. G cannot travel with F, or H, or D. The husband-wife pairs must carry baskets O and P. Q is with A and P is with D. F travels on M1and E travels on M2 motorcycles. G is with Q, and B cannot go with R. Who is travelling with H? (2001) (a) A (b) B

(c) C (d) D 93. In a family gathering there are two males who are grandfathers and four males who are fathers. In the same gathering there are two females who are grandmothers and four females who are mothers. There is at least one grandson or granddaughter present in this gathering. There are two husband-wife pairs in this group. These can either be a grandfather and a grandmother, or a father and a mother. The single grandfather (whose wife is not present) has two grandsons and a son present. The single grandmother (whose husband is not present) has two granddaughters and a daughter present. A grandfather or a grandmother present with their spouses does not have any grandson or grand daughter present. What is the minimum number of people present in this gathering. (2001) (a) 10 (b) 12 (c) 14 (d) 16 94. I have a total of Rs, 1000. Item A costs Rs. 110, item B costs Rs 90, C costs Rs 70, item D costs Rs 40 and item E costs Rs 45. For every item D that I purchase, I must also buy two of item B. For every item A, I must buy one of item C. For very item E, I must also buy two of item D and one of item B. For every item purchased I earn 1000 points and for every rupee not spent I earn a penalty of 1500 points. My objective is to maximise the points I earn. What is the number of items that I must purchase to maximise my points? (2001) (a) 13 (b) 14 (c) 15 (d) 16 95. Four friends Ashok, Bashir, Chirag and Deepak are out shopping. Ashok has less money than three times the amount that Bashir has. Chirag has more money than Bashir. Deepak has an amount equal to

the difference of amounts with Bashir and Chirag. Ashok has three times the money with Deepak. They each have to buy at least one shirt, or one shawl, or one sweater, or one jacket that are priced Rs 200, Rs 400, Rs 600 and Rs 1000 a piece, respectively. Chirag borrows Rs 300 from Ashok and buys a jacket. Bashir buys a sweater after borrowing Rs 100 from Ashok and is left with no money. Ashok buys three shirts . What is the costliest item that Deepak could buy with his own money? (2001) (a) A shirt (b) A shawl (c) A sweater (d) A jacket 96. In a “keep-fit” gymnasium class there are fifteen females enrolled in a weight - loss program. They all have grouped in any one of the five weight-groups W1, W2, W3, W4 and W5. One instructor is assigned to one weight-group only. Sonali, Shalini, Shubhra, and Shahira belong to the same weight-group. Sonali and Rupa are in one weightgroup, Rupali and Renuka are also in one weight-group. Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight-groups. Somya cannot be with Ritu, and Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu. Shahira is in W1 and Somya is in W4 with Ruchika. Sweta and Jyotika cannot be with Rupali, but are in a weight-group with total membership of four. No weight-group can have more than five or less than one member. Amita, Babita, Chandrika, Deepika and Elina are instructors of weight-groups with membership sizes 5, 4, 3, 2, and 1, respectively. Who is the instrutor of Radha? (2001) (a) Babita (b) Elina (c) Chandrika (d) Deepika 97. A king has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He

decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three persons selected (2001) M1 likes fishing and smoking, but hates gambling, M2 likes smoking and drinking, but hates fishing, M3 likes gambling, but hates smoking, M4 likes mountaineering , but hates drinking, M5 likes drinking, but hates smoking and mountaineering M6 likes fishing, but hates smoking and mountaineering M7 likes gambling and mountaineering, but hates fishing, and M8 likes smoking and gambling, but hates mountaineering. Who are the four people selected by the king? (a) M1, M2, M5, M6 (b) M3, M4, M5, M6 (c) M4, M5, M6, M8 (d) M1, M2, M4, M7 Directions for questions 98 to 100 : Read the information given below and answer the questions that follow : Answer these question based on the pipeline diagram below. The following sketch shows the pipelines carrying material from one location to another. Each location has a demand for material. The demand at Vaishali is 400, at Jyotishmati is 400, at Panchal is 700, and at Vidisha is 200. Each arrow indicates the direction of material flow through the pipeline. The flow from Vaishali to Jyotishmati is 300. The quantity of material flow is such that the demands at all these locations are exactly met. The capacity of each pipeline is 1000.

98. The is

quantity

moved

from

Avanti

Vidisha

(2001) (a) (b) (c) (d) 99.

200 800 700 1000 The free capacity available at the Avanti -Vaishali pipeline is (2001) (a) 0 (b) 100 (d) 200 (d) 300 100. What is the free capacity available in the Avanti - Vidisha pipeline? (2001) (a) 300 (b) 200 (c) 100 (d) 0 101. Four students (Ashish, Dhanraj, Felix and Sameer) sat for the Common Entrance Exam for Management (CEEM). One student got admission offers from three National Institutes of Management (NIM), another in two NIMs, the third in one NIM, while the fourth got none. Below are some of the facts about who got admission offers from how many NIMs and what is their educational background (2002)

(i) The one who is an engineer didn’t get as many admissions as Ashish (ii) The one who got offer for admissions in two NIMs isn’t Dhanraj nor is he a chartered accountant (iii) Sameer is an economist (iv) Dhanraj isn’t an engineer and received more admission offers than Ashish (v) The medical doctor got the most number of admission offers Which one of the following statements is necessarily true? (a) Ashish is a chartered accountant and got offer for admission in three NIMs (b) Dhanraj is a medical doctor and got admission offer in one NIM (c) Sameer is an economist who got admission offers in two NIMs (d) Felix who is not an engineer did not get any offer for admission 102. Five boys went to a store to buy sweets. One boy had Rs 40. Another boy had Rs30. Two other boys had Rs20 each. The remaining boy had Rs10. Below are some more facts about the initial and final cash positions (2002) (i) Alam started with more than Jugraj (ii) Sandeep spent Rs 1.50 more than Daljeet (iii) Ganesh started with more money than just only one other person (iv) Daljeet started with 2/3 of what Sandeep started with (v) Alam spent the most, but did not end with the least (vi) Jugraj spent the least and ended with more than Alam or Daljeet (vii) Ganesh spent Rs 3.50. (viii) Alam spent 10 times more than what Ganesh did. In the choices given below, all statements except one are false. Which one of the following statements can be true? (a) Alam started with Rs 40 and ended with Rs9.50 (b) Sandeep started with Rs 30 and ended with Rs 1.00 (c) Ganesh started with Rs 20 and ended with Rs 4.00 (d) Jugraj started with Rs 10 and ended with Rs 7.00 103. In a hospital there were 200 Diabetes, 150 Hyperglycaemia and 150 Gastro-enteritis patients. Of these, 80 patients were treated for both Diabetic and Hyperglycaemia. Sixty patients were treated for Gastro-

enteritis and Hyperglycaemia, while 70 were treated for Diabetes and Gastro-enteritis. Some of these paitents have all the three diseases. Doctor Dennis treats patients with only Diabetes. Doctor Hormis treats patients with only Hyperglycaemia and Doctor Gerard treats patients with only Gastro-enteritis. Doctor Paul is a generalist. Therefore, he can treat patients with multiple diseases. Patients always prefer a specialist for their disease. If Dr. Dennis had 80 patients, then the other three doctors can be arranged in terms of the number of patients treated as (2002) (a) Paul > Gerard > Hormis (b) Pual > Hormis > Gerard (c) Gerard > Paul > Hormis (d) None of these 104. Three children won the prizes in the Bournvita Quiz contest. They are from the schools : Loyola, Convent and Little Flowers, which are located at different cities. Below are some of the facts about the schools, the children and the city they are from

(2002) * Loyola

One of the children is Bipin School’s contestant did not come first * Little Flower’s contestant was named Riaz * Convent School is not in Hyderabad * The contestant from Pune took third place * The contestant from Pune is not from Loyola School * The contestant from Bangalore did not come first * Convent School’s contestant’s name is not Balbir Which of the following statements is true? (a) 1st prize : Riaz (Little Flowers), 2nd prize : Bipin (Convent), 3rd prize : Balbir (Loyola) (b) 1st prize : Bipin (Convent), 2nd prize : Riaz (Little Flowers), 3rd prize : Balbir (Loyola)

(c) 1st prize : Riaz (Little Flowers), 2nd prize : Balbir (Loyola), 3rd prize : Bipin (Convent) (d) 1st prize : Bipin (Convent), 2nd prize : Balbir (Loyola), 3rd prize : Riaz (Little Flowers) 105. Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of father of the younger boy. Similarly, if we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divided the figure by 2, we get the age of mother of the younger boy. The mother of the younger boy is younger to his father, by 3 years. Then, what is the age of the younger boy (2002) (a) 3 (b) 4 (c) 2 (d) None of these 106. Flights A and B are scheduled from an airport within the next one hour. All the booked passengers of the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of 200, out of which 10% remained vacant. 40% of the waiting passengers are ladies. When boarding announcements came, passengers of flight A left the hall and boarded the flight. Seating capacity of each flight is two-third of the passengers who waited in the waiting hall for both the flights put together. Half the passengers who boarded flight A are women. After boarding for flight A, 60% of the waiting hall seats became empty. For every twenty of those who are still waiting in the hall for flight B, there is one airhostess in flight A. Then, what is the ratio of empty seats in flight B to number of airhostesses in flight A? (2002) (a) 1 : 3 (b) 2 : 4

(c) 3 : 2 (d) none of these Directions for Questions 107 to 110 : Study the information below and answer questions based on it. A country has the following types of traffic signals. 3 red lights = stop; 2 red lights = turn left; 1 red light = turn right; 3 green lights = go at 100 kmph speed; 2 green lights = go at 40 kmph speed; 1 green light = go at 20 kmph speed. A motorist starts at a point on a road and follows all traffic signals literally. His car is heading towards the north. He encounters the following signals (the time mentioned in each case below is applicable after crossing the previous signal). Starting Point - 1 green light; after half an hour, 1st signal - 2 red & 2 green lights; after 15 minutes, 2nd signal - 1 red light; after half an hour, 3rd signal - 1 red & 3 green lights; after 24 minutes, 4th signal - 2 red & 2 green lights; after 15 minutes, 5th signal - 3 red lights; 107. The total distance travelled by the motorist from the starting point till the last signal is (2002) (a) 90 km (b) 100 km (c) 120 km (d) None of these 108. What is the position (radial distance) of the motorist when he reaches the last signal (2002) (a) 45 km directly north of Starting Point (b) 30 km directly to the east of the Starting Point (c) 50 km away to the northeast of the Starting Point (d) 45 km away to the northwest of the Starting Point 109. After the starting point if the 1st signal were 1 red and 2 green lights, what would be the final poisition of the motorist (2002)

(a) 30 km to the west and 20 km to the south (b) 30 km to the west and 40 km to the north (c) 50 km to the east and 40 km to the north (d) Directly 30 km to the east 110. If at the starting point, the car was heading towards south, what would be the final position of the motorist (2002) (a) 30 km to the east and 40 km to the south (b) 50 km to the east and 40 km to the south (c) 30 km to the west and 40 km to the south (d) 50 km to the west and 20 km to the north 111. The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally? (2002) (a) 40 (b) 36 (c) 25 (d) None of these 112. A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked,“How many gold coins do we have?” After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 48 times the difference between the two numbers equals the difference between the squares of the two numbers.” The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins the merchant has? (2002) (a) 96 (b) 53 (c) 43 (d) None of these 113. Shyam visited Ram on vacation. In the mornings, they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e., either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did

nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram? (2002) (a) 32 (b) 24 (c) 30 (d) None of these 114. Six persons are playing a card game. Suresh is facing Raghubir who is to the left of Ajay and to the right of Pramod. Ajay isto the left of Dhiraj. Yogendra is to the left of Pramod. If Dhiraj exchanges his seat with Yogendra and Pramod exchanges with Raghubir, who will be sitting to the left of Dhiraj? (2002) (a) Yogendra (b) Raghubir (c) Suresh (d) Ajay Directions for Questions 115 to 117 : Study the information below and answer questions based on it. A boy is asked to put in a basket one mango when ordered ‘One’, one orange when ordered ‘Two’, one apple when ordered ‘Three’ and is asked to take out from the basket one mango and an orange when ordered ‘Four’. A sequence of orders is given as : 12332142314223314113234 115. How many total oranges were in the basket at the end of the above sequence? (2002) (a) 1 (b) 4 (c) 3 (d) 2 116. How many total fruits will be in the basket at the end of the above order sequence? (2002) (a) 9 (b) 8

(c) 11 (d) 10 117. Three travelers are sitting around a fire, and are about to eat a meal. One of them has five small loaves of bread, the second has three small loaves of bread. The third has no food, but has eight coins. He offers to pay for some bread. They agree to share the eight loaves equally among the three travelers, and the third traveler will pay eight coins for his share of the eight loaves. All loaves were the same size. The second traveler (who had three loaves) suggests that he be paid three coins, and that the first traveler be paid five coins. The first traveler says that he should get more than five coins. How much the first traveler should get? (a) 5 (b) 7 (c) 1 (d) None of these (2002) Directions for Questions 118 & 119 : Study the information below and answer questions based on it. New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Budhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3 projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved. 118. What is the number of projects in which Gyani alone is involved? (2003C) (a) Uniquely equal to zero (b) Uniquely equal to 1 (c) Uniquely equal to 4 (d) Cannot be determined uniquely 119. What is the number of projects in which Medha alone is involved?

(2003C) (a) Uniquely equal to zero (b) Uniquely equal to 1 (c) Uniquely equal to 4 (d) Cannot be determined uniquely. Directions for Questions 120 & 121 : Study the information below and answer questions based on it. Some children were taking free throws at the basketball court in school during lunch break. Below are some facts about how many baskets these children shot? (i) Ganesh shot 8 baskets less than Ashish (ii) Dhanraj and Ramesh together shot 37 baskets (iii) Jugraj shot 8 baskets more than Dhanraj (iv) Ashish shot 5 baskets more than Dhanraj (v) Ashish and Ganesh together shot 40 baskets 120. Which of the following statements is true? (2003C) (a) Dhanraj and Jugraj together shot 46 baskets (b) Ganesh shot 18 baskets and Ramesh shot 21 baskets (c) Dhanraj shot 3 more baskets than Ramesh (d) Ramesh and Jugraj together shot 29 baskets 121. Which of the following statements is true? (2003C) (a) Ramesh shot 18 baskets and Dhanraj shot 19 baskets (b) Ganesh shot 24 baskets and Ashish shot 16 baskets (c) Jugraj shot 19 baskets and Dhanraj shot 27 baskets (d) Dhanraj shot 11 baskets and Ashish shot 16 baskets Directions for Questions 122 to 124 : Study the information below and answer questions based on it. Seven versity basketball players (A, B, C, D, E, F and G) are to be honoured at a special luncheon. The players will be seated on the dais in a row. A and G have the luncheon early and so must be seated at the extreme right. B will receive the most valuable player’s trophy and

so must be in the centre to facilitate presentation. C and D are bitter rivals and therefore must be seated as far apart as possible. 122. Which of the following pairs cannot occupy the seats on either side of B? (2003C) (a) F & D (b) D & E (c) E & G (d) C & F 123. Which of the following pairs cannot be seated together? (2003C) (a) B & D (b) C & F (c) D & G (d) E & A 124. Which of the following cannot be seated at either end? (2003C) (a) C (b) D (c) F (d) G Directions for Questions 125 to 127 : Study the information below and answer questions based on it. A, B, C, D, E and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professsor. A is married to a housewife. E is not a housewife. 125. How many members of the group are males ? (2003C) (a) 2 (b) 3

E’s (2003C)

(a) Engineer (b) Lawyer (c) Professor (d) Accountant 127. Which of couples?

the

following

one

the

married

(2003C) (a) (b) (c) (d)

A&B B&E D&E A&D

Directions for Questions 128 to 130 : Study the information below and answer questions based on it. Rang Barsey paint Company (RBPC) is in the business of manufacturing paints, RBPC buys Red, Yellow, White, Orange and Pink paints. Orange paint can be also produced by mixing Red and Yellow paints in equal proportions. Similarly, Pink paint can also be produced by mixing equal amounts of Red and White paints. Among other paints , RBPC sells Cream paint, (formed by mixing White and Yellow in the ratio 70:30) Avocado paint (formed by mixing equal amounts of Orange and Pink paint ) and Washedorange paint (formed by mixing equal amounts of Orange and White paint.) The following table provides the price at which RBPC buys paints .

128. The cheapest way to manufacture avocado paint would cost (2003 C) (a) Rs 19.50 per litre (b) Rs 19.75 per litre (c) Rs 20.00 per litre (d) Rs 20.25 per litre 129. Washedorange can be manufactured by mixing (2003C) (a) Cream and Red in the ratio 14:10 (b) Cream and Red in the ratio 3:1 (c) Yellow and Pink in the ratio 1:1 (d) Red, Yellow and White in the ratio 1:1:2 130. Assume that Avocado, Cream and Washedorange each sells for the same price . Which of the three is the most profitable to manufacture? (2003C) (a) Avocado (b) Cream (c) Washedorange (d) Sufficient data is not available Directions for Questions 131 & 132 : Study the information below and answer questions based on it. The Head of a newly formed government desires to appoint five of the six elected members A, B, C, D, E and F to portfolios of Home, Power , Defence, Telecom and Finance, F does not want any portfolio if D gets one of the five. C wants either Home or finance or no portfolio. B says

that if D gets either Power or Telecom then she must get the other one. E insists on a portfolio if A gets one. 131. If A gets Home and C gets Finance, then which is not a valid assignment for defence and Telecom? (2003C) (a) D-Power, B-Telecom (b) F-Defence , B-Telecom (c) B-Defence, E-Telecom (d) B-Defence, D-Telecom 132. Which is

valid

assignment?

(2003C) (a) A-Home, (b) Finance (c) A-Home, (d) Finance

B-Power,

C-Defence, D-Telecom, E-Finance C-Home, D-Power, A-Defence, B-Telecom, E-

B-Power,

E-Defence, D-Telecom, F-Finance B-Home, F-Power, E-Defence, C-Telecom, A-

Directions for Questions 133 to 135 : Study the information below and answer questions based on it. Five friends meet every morning at Sree sagar restaurant for an idli-vada breakfast. Each consumes a different number of idils and vadas. The number of idlis consumed are 1, 4, 5, 6 and 8 while the number of vadas consumed are 0, 1, 2, 4, and 6. Below are some more facts about who eats what and how much. (i) The number of vadas eaten by Ignesh is three times the number of vadas consumed by the person who eats four idlis (ii) Three persons, including the one who eats four vadas, eat without chutney (iii) Sandeep does not take any chutney (iv) The one who eats one idli a day does not eat any vadas or chutney. Further he is not Mukesh (v) Daljit eats idli with chutney and also eats vada

(vi) Mukesh, who does not take chutney, eats half as many vadas as the person who eats twice as many idlis as he does (vii) Bimal eats two more idlis than Ignesh, but Ignesh eats two more vadas than Bimal 133. Which of the following statements is true? (2003C) (a) Mukesh eats 8 idlis and 4 vadas but no chutney (b) The person who eats 5 idlis and 1 vada does not take chutney (c) The person who eats equal numbers of vadas and idlis also takes chutney (d) The person who eats 4 idlis and 2 vadas also takes chutney 134. Which of the following statements is true? (2003C) (a) Sandeep eats 2 vadas (b) Mukesh eats 4 vadas (c) Ignesh eats 4 vadas (d) Bimal eats 4 vadas 135. Which one of the following statements is true? (2003C) (a) Daljit eats 5 idlis (b) Ignesh eats 8 idlis (c) Bimal eats 1 idli (d) Bimal eats 6 idlis Directions for Questions 136 to 137 : Study the information below and answer questions based on it. Five women decided to go shopping to M.G.Road, Banglore. They arrived at the designated meeting place in the following order : (1) Archana, (2) Chellamma, (3) Dhenuka, (4) Helen, and (5) Shahnaz. Each woman spent at least Rs 1000. Below are some additional facts about how much they spent during their shopping spree. (i) The woman who spent Rs 2234 arrived before the lady who spent Rs 1193 (ii) One woman spent Rs 1340 and she was not Dhenuka

(iii) One woman spent Rs 1378 more than Chellamma (iv) One woman spent Rs 2517 and she was not Archana (v) Helen spent more than Dhenuka (vi) Shahnaz spent the largest amount and Chellamma the smallest 136. What was the amount spent by Helen? (2003C) (a) Rs 1193 (b) Rs 1340 (c) Rs 2234 (d) Rs 2517 137. Which of the following amount was spent by one of them? (2003C) (a) Rs 1139 (b) Rs 1378 (c) Rs 2571 (d) Rs 2718 138. The woman who spent Rs 1193 is (2003C) (a) Archana (b) Chellamma (c) Dhenuka (d) Helen Directions for Questions 139 to 142 : Study the information below and answer questions based on it.

The plan above shows an office block for six officers A, B, C, D, E and F. Both B and C occupy offices to the right of the corridor (as one enters the office block) and A occupies an office to the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F’s office is further down the corridor than A’s, but on the same side. 139. If E sits in his office and faces the corridor, whose office is to his left? (2003) (a) A (b) B (c) C (d) D 140. Whose office faces A’s office? (2003) (a) B (b) C (c) D (d) E 141. Who is/are F’s neighbour(s)? (2003) (a) A only (b) A and D (c) C only (d) B and C 142. D was heard telling someone to go further down the corridor to the last office on th right. To whose room was he trying to direct that person? (2003) (a) A (b) B (c) C (d) F

Directions for Questions 143 & 144 : Study the information below and answer questions based on it. LAYOUT OF MAJOR STREETS IN A CITY

Two days (Thursday and Friday) are left for campaigning before a major election, and the city administration has received requests from five political parties for taking out their processions along the following routes. Congress : A-C-D-E BJP : A-B-D-E SP : A-B-C-E BSP : B-C-E CPM : A-C-D Street B-D cannot be used for a political procession on Thursday due to a religious procession. The district administration has a policy of not allowing more than one procession to pass along the same street on the same day. However, the administration must allow all parties to take out their processions during these two days. 143. Congress procession can be allowed (2003) (a) only on Thursday (b) only on Friday (c) on either day (d) only if the religious procession is cancelled. 144. Which of the following is NOT true?

(a) (b) (c) (d)

(2003) Congress and SP can take out their processions on the same day The CPM procession cannot be allowed on Thursday The BJP procession can only take place on Friday Congress and BSP can take out their processions on the same day

Directions for Questions 145 to 148 : Study the information below and answer questions based on it. Seven faculty members at a management institute frequent a lounge for strong coffee and stimulating conversation. On being asked about their visit to the lounge last Friday we got the following responses. JC : I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and VR were present in the lounge. DG left with me JP : When I entered the lounge with VR, JC was sitting here. There was someone else, but I cannot remember who it was SM : I went to the lounge for a short while, and met JC, SS, and DG in the lounge that day SS : I left immediately after SM left DG : I met JC, SS, SM, JP and VR during my first visit to the lounge. I went back to my office with JC. When I went to the lounge the second time, JP and VR were there PK : I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left. JP and DG were the only people in the lounge while I was there VR :No comments 145. Based on the responses, which of the two, JP or DG, entered the lounge first? (2003) (a) JP (b) DG (c) Both entered together (d) Cannot be deduced 146. Who was sitting with JC when JP entered the lounge? (2003) (a) SS (b) SM (c) DG

(d) PK 147. How many of the seven members did VR meet on Friday in the lounge? (2003) (a) 2 (b) 3 (c) 4 (d) 5 148. Who were the last two faculty members to leave the lounge? (2003) (a) JC and DG (b) PK and DG (c) JP and PK (d) JP and DG Directions for Questions 149 to 153 : Study the information below and answer questions based on it. Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answer-key. All the others create their answer - key in the following manner. They obtain the answer key from one or two people who already possess the same. The people are called his/her “sources”. If the person has two sources, then he/she compares the answer-keys obtained form both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source’s answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key. The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.

149. Which one sources?

among

the

following

must

have

two

(2003) (a) A (b) B (c) C (d) D 150. How many people (excluding the mastermind) needed to make answer - keys before C could make his answer-key? (2003) (a) 2 (b) 3 (c) 4 (d) 5 151. Both G and H were sources to (2003) (a) F (b) B (c) 1 (d) None of these 152. Which of the following statements is true? (2003) (a) C introduced the wrong answer to question 27 (b) E introduced the wrong answer to question 46 (c) F introduced the wrong answer to question 14 (d) H introduced the wrong answer to question 46

153. Which of the following two groups of people had identical sources? (2003) (I) A, D and G (II) E and H (a) Only (I) (b) Only (II) (c) Neither (I) nor (II) (d) Both (I) and (II) Directions for Questions 154 to 157 : Study the information below and answer questions based on it. Four families decided to attend the marriage ceremony of one of their colleagues. One family has no kids, while the others have at least one kid each. Each family with kids has atleast one kid attending the marriage. Given below is some information about the families, and who reached when to attend the marriage. The family with 2 kids came just before the family with no kids. Shanthi who does not have any kids reached just before Sridevi’s family Sunil and his wife reached last with their only kid. Anil is not the husband of Joya Anil and Raj are fathers. Sridevi’s and Anita’s daughter go to the same school. Joya came before Shanthi and met Anita when she reached the venue. Raman stays the farthest from the venue. Raj said his son could not come because of his exams. 154. Which third?

woman

arrived

(2003) (a) Shanthi (b) Sridevi (c) Anita (d) Joya 155. Name wife?

the

correct

pair

husband

and

(2003) (a) Raj and Shanthi (b) Sunil and Sridevi (c) Anil and Sridevi (d) Raj and Anita 156. Of the following pairs, whose daughters go to the same school? (2003) (a) Anil and Raman (b) Sunil and Raman (c) Sunil and Anil (d) Raj and Anil 157. Whose family is known to have more than one kid for certain? (2003) (a) Raman’s (b) Raj’s (c) Anil’s (d) Sunil’s Directions for Questions 158 & 159 : Answer the questions on the information given below. In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the question in group A together carry at least 60% of the total marks. 158. If group B contains 23 questions, then how many questions are there in group C? (2004 - 2marks) (a) 1 (b) 2 (c) 3 (d) Cannot be determined 159. If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group

B? (2004 - 2marks) (a) (b) (c) (d)

11 or 12 12 or 13 13 or 14 14 or 15 Directions for Questions 160 to 163 : Answer the questions on the basis of the information given below.

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsman got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his higest and lowest scores in the 3 games while the Mindex is the middle number, if his scores are arranged in a nonincreasing order.

160. Which of the tournament? (2004 - 2marks) (a) Rahul (b) Saurav (c) Virender (d) Yuvraj

players

had

the

best

M-index

from

the

161. Among the players mentioned, who can have the lowest R-index from the tournament? (2004 2marks) (a) Only Kaif, Rahul or Yuvraj (b) Only Kaif or Rahul (c) Only Kaif or Yuvraj (d) Only Kaif 162. For how many Indian players is it possible to calculate the exact Mindex? (2004 - 2marks) (a) 0 (b) 1 (c) 2 (d) More than 2 163. How many players among those listed definitely scored less than Yuvraj in the tournament? (2004 2marks) (a) 0 (b) 1 (c) 2 (d) More than 2 Directions for Questions 164 to 167 : Answer the questions on the basis of the information given below. Twenty one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation. The following five facts about the participants are given. I. The number of labour experts in the camp was exactly half the number of experts in each of the three other categories. II. Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category. III. None of the continents sent more than three experts in any category. IV. If there had been one less Australasian expert, then the America would have had twice many experts as each of the other

continents. V. Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia. 164. Which of the following numbers cannot be determined from the information given? (2004 2marks) (a) Number of labour experts from the Americas. (b) Number of health experts from Europe. (c) Number of health experts from Australasia. (d) Number of experts in refugee relocation from Africa. 165. Which of the following combinations is NOT possible? (2004 - 2marks) (a) 2 experts in population studies from the Americas and 2 health experts from Africa attended the conference. (b) 2 experts in population studies from the Americas and 1 health expert from Africa attended the conference. (c) 3 experts in refugee relocation from the Americas and 1 health expert from Africa attended the conference. (d) Africa and America each had 1 expert in population studies attending the conference. 166. If Ramos is the lone America expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents? (2004 - 2marks) (a) There is one expert in health from Africa. (b) There is one expert in refugee relocation from Africa. (c) There are two experts in health from the Americas. (d) There are three experts in refugee relocation from the Americas. 167. Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex? (2004 - 2marks) (i) At least one (ii) Atmost two (a) Only (i) and not (ii)

(b) Only (ii) and not (i) (c) Both (i) and (ii) (d) Neither (i) nor (ii) Directions for Questions 168 to 171 : Answer the questions on the basis of the information given below. The year was 2006, All six teams in Pool A of World Cup hockey, play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goal For - Goals Against) qualifies. In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below. Pool A

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches (A) Spain won both the fourth and fifth round matches. (B) Both Argentina and Germany won their fifth round matches by 3 goals to 0. (C) Pakistan won both the fourth and fifth round matches by 1 goal to 0. 168. Which one of the following statement is true about matches played in the first two rounds? (2004 - 2 marks) (a) Pakistan beat South Africa by 2 goals to 1 (b) Argentina beat Pakistan by 1 goal to 0 (c) Germany beat Pakistan by 2 goals to 1 (d) Germany beat Spain by 2 goals to 1 169. Which one of the following statements is true about matches played in the first two rounds? (2004 - 2 marks) (a) Germany beat New Zealand by 1 goal to 0

(b) Spain beat New Zeland by 4 goals to 0 (c) Spain beat South Africa by 2 goals to 0 (d) Germany beat Spain by 2 goals to 1 170. If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified? (2004 - 2 marks) (a) Argentina (b) Germany (c) Spain (d) Cannot be determined 171. Which team finished at the top of the pool after five rounds of matches? (2004 - 2 marks) (a) Argentina (b) Germany (c) Spain (d) Cannot be determined Directions for Questions 172 to 175 : Answer the questions on the basis of the information given below. Venkat, a stockbroker, invested a part of his money in the stock of four companies — A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the-time of investment, the price of each stock was Rs l00. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30% and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or[ the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies.

Which do not announce extraordinarily good results, the returns realized during the year were the same as initially expected. 172. What is the minimum average return Venkat would have earned during the year? (2005) 1. 30% 2. 31¼% 3. 32½% 4. Cannot be determined 173. If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true? I. Company A belonged either to Auto or to Steel Industry. (2005) II. Company B did not announce extraordinarily good results. III. Company A announced extraordinarily good results. IV. Company D did not announce extraordinarily good results. 1. I and II only 2. II and III only 3. III and IV only 4. II and IV only 174. If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true? I. Company C belonged either to Auto or to Steel Industry. (2005) II. Company D belonged either to Auto or to Steel Industry. III. Company A announced extraordinarily good results. IV. Company B did not announce extraordinarily good results. 1. I and II only 2. II and III only 3. III and IV only 4. II and IV only 175. If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true? (2005) I. Venkat earned not more than 36.25% return on average. II. Venkat earned not less than 33.75% return on average.

III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results. IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry. (a) I and II only (b) II and IV only (c) II and III only (d) III and IV only Directions for Questions 176 to 179 : Answer the questions on the basis of the information given below : The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A,B,C and D, in no particular order.

Further, it is known that : • In the state of MP, Truthful Ltd. has the highest market share. • Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs. 5 million. 176. What can be said regarding the following two statements? Statement 1: Honest Ltd. has the highest share in the UP market. Statement 2: Aggressive Ltd. has the highest share in the Bihar market. (2005) (a) Both statements could be true. (b) At least one of the statements must be true. (c) At most one of the statements is true. (d) None of the above. 177. What can be said regarding the following two statements? Statement 1 : Aggressive Ltd.’s lowest revenues are from MP. Statement 2 : Honest Ltd.’s lowest revenues are from Bihar.

(2005) (a) If Statement 2 is true then Statement 1 is necessarily false. (b) If Statement I is false then Statement 2 is necessarily true. (c) If Statement I is true then Statement 2 is necessarily true. (d) None of the above. 178. What can be said regarding the following two statements? Statement 1: Profitable Ltd. has the lowest share in MP market. Statement 2 : Honest Ltd.’s total revenue is more than Profitable Ltd. (2005) (a) If Statement 1 is true then Statement 2 is necessarily true. (b) If Statement 1 is true then Statement 2 is necessarily false. (c) Both Statement 1 and Statement 2 are true. (d) Neither Statement 1 nor Statement 2 is true. 179. If Profitable Ltd.’s lowest revenue is from UP, then which of the following is true? (2005) (a) Truthful Ltd.’s lowest revenues are from MP. (b) Truthful Ltd.’s lowest revenues are from Bihar. (c) Truthful Ltd.’s lowest revenues are from UP. (d) No definite conclusion is possible. Directions for Questions 180 to 183 : Answer the questions on the basis of the information given below. In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No.1 of first round; the 2nd seeded player plays the 31 st seeded player which is designated match No.2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No.1 of first round plays the winner of match No. 16 of first round and is designated match No.1 of second round. Similarly, the winner of match No.2 of first round plays the winner of match No. 15 of first round, and is designated match No.2 of second

round. Thus, for instance, match No.8 of the second round is to be played between the winner of match No.8 of first round and the winner of match No.9 of first round. The same pattern is followed for later rounds as well.

180. If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals? (2005 - 2 marks) (a) Dinara Safina (b) Justine Henin (c) Nadia Petrova (d) Patty Schnyder 181. If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final? (2005 - 2 marks) (a) Amelie Mauresmo (b) Elena Dementieva (c) Kim Clijsters (d) Lindsay Davenport 182. If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals? (a) Justine Henin

(b) Nadia Petrova (c) Patty Schnyder (d) Venus Williams (2005 - 2 marks) 183. If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals? (2005 - 2 marks) (a) Anastasia Myskina (b) Flavia Pennetta (c) Nadia Petrova (d) Svetlana Kuznetsova Directions for Questions 184 to 187 : Answer the questions on the basis of the information given below. Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project. • A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone. is equal to the volunteers having additional involvement in the ER project. • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. • 17 volunteers are involved in the TR project. , • The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone. • Ten volunteers involved in the TR project are also involved in at least one more project. 184. Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is : (2005 - 2 marks) (a) 1

(b) 3 (c) 4 (d) 5 185. Which of the following additional information would enable to find the exact number of volunteers involved in various projects? (a) Twenty volunteers are involved in FR. (2005 - 2 marks) (b) Four volunteers are involved in all the three projects. (c) Twenty three volunteers are involved in exactly one project. (d) No need for any additional information. 186. After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows? (2005 - 2 marks) (a) The lowest number of volunteers is now in TR project. (b) More volunteers are now in FR project as compared to ER project. (c) More volunteers are now in TR project as compared to ER project. (d) None of the above. 187. After the withdrawal of volunteers, as indicated in Question 85, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers? (2005 2 marks) (a) ER (b) FR (c) TR (d) Cannot be determined

Directions for Questions 188 to 191 : Answer the questions on the basis of the information given below. The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC. • In any round of voting; the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event. • A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities(s) he voted for in earlier rounds are out of contention in that round of voting.) • A member is also ineligible to cast a vote in a round if the city(s) he represents is in contention in that round of voting. • As long as the member is eligible,(s)he must vote and vote for only one candidate city in any round of voting. The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds.

It is also known that : • All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well. • Those who voted for New York in round 1, voted either for Beijing or Paris in round 2. • The difference in votes cast for the two contending cities in the last round was 1.

•

50% of those who voted for Beijing in round 1, voted for Paris in round 3. 188. What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2? (2005

marks) (a) 33.33 (b) 50 (c) 66.67 (d) 75 189. What is the number of votes cast for Paris in round I? (2005 - 2 marks) (a) 16 (b) 18 (c) 22 (d) 24 190. What percentage of members from among those who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London? (2005 2 marks) (a) 33.33 (b) 38.10 (c) 50 (d) 66.67 191. Which of the following statements must be true? (2005 - 2 marks) (a) IOC member from New York must have voted for Paris in round 2. (b) IOC member from Beijing voted for London in round 3. (a) Only a (b) Only b (c) Both a and b (d) Neither a nor b Directions for Questions 192 to 196 : Answer the questions on the basis of the information given below.

Two traders, Chetan and Michael, were involved in the buying and selling of MCS shares over five trading days. At the beginning of the first day, the MCS share was priced at Rs 100, while at the end of the fifth day it was priced at Rs 110. At the end of each day, the MCS share price either went up by Rs 10, or else, it came down by Rs 10. Both Chetan and Michael took buying and selling decisions at the end of each trading day. The beginning price of MCS share on a given day was the same as the ending price of the previous day. Chetan and Michael started with the same number of shares and amount of cash, and had enough of both. Below are some additional facts about how Chetan and Michael traded over the five trading days. • Each day if the price went up, Chetan sold 10 shares of MCS at the closing price. On the other hand, each day if the price went down, he bought 10 shares at the closing price. • If on any day, the closing price was above Rs 110, then Michael sold 10 shares of MCS, while if it was below Rs 90, he bought 10 shares, all at the closing price. 192. If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3? (2006) (a) Rs 90 (b) Rs 100 (c) Rs 110 (d) Rs 120 (e) Rs 130 193. If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of the share at the end of day 3? (2006) (a) Rs 90 (b) Rs 100 (c) Rs 110 (d) Rs 120 (e) Rs 130 194. What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth

day? (2006) (a) Rs 3700 (b) Rs 4000 (c) Rs 4700 (d) Rs 5000 (e) Rs 6000 195. If Chetan ended up with Rs 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4? (2006) (a) Rs 90 (b) Rs 100 (c) Rs 110 (d) Rs 120 (e) Not uniquely determinable 196. If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan (at the end of day 5)? (2006) (a) Michael had 10 less shares than Chetan. (b) Michael had 10 more shares than Chetan. (c) Chetan had 10 more shares than Michael. (d) Chetan had 20 more shares than Michael. (e) Both had the same number of shares. Directions for Questions 197 to 201 : Answer the questions on the basis of the information given below. A significant amount of traffic flows from point S to point T in the one-way street network shown below. Points A, B, C, and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.

Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost, then motorists are indifferent between them. Hence, the traffic gets evenly distributed among all the least cost routes. The government can control the flow of traffic only by levying appropriate toll at each junction. For example, if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs 14 (i.e., Rs 9 + Rs 5) plus the toll charged at junction A. 197. If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is: (2006) (a) 0, 5, 4, 1 (b) 0, 5, 2, 2 (c) 1, 5, 3, 3 (d) 1,5,3,2 (e) 0, 4, 3, 2 198. If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is: (2006) (a) 1, 5, 3, 3 (b) 1, 4, 4, 3

(c) 1, 5, 4, 2 (d) 0, 5, 2, 3 (e) 0, 5, 2, 2 199. If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is: (2006) (a) 2, 5, 3, 2 (b) 0, 5, 3, 1 (c) 1, 5, 3, 2 (d) 2, 3, 5, 1 (e) 1, 3, 5, 1 200. If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is: (2006) (a) 0, 5, 2, 2 (b) 0, 5,4, 1 (c) 1, 5, 3, 3 (d) 1, 5, 3, 2 (e) 1, 5, 4, 2 201. The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be: (2006) (a) Rs 7 (b) Rs 9 (c) Rs 10 (d) Rs 13 (e) Rs 14

Directions for Questions 202 to 206 : Answer the questions on the basis of the information given below. Mathematicians are assigned a number called Erdös number (named after the famous mathematician, Paul Erdös). Only Paul Erdös himself has an Erdös number of zero. Any mathematician who has written a research paper with Erdös has an Erdös number of 1. For other mathematicians, the calculation of his/her Erdös number is illustrated below: Suppose that a mathematician X has co-authored papers with several other mathematicians. From among them, mathematician Y has the smallest Erdös number. Let the Erdös number of Y be y. Then X has an Erdös number of y + 1. Hence any mathematician with no coauthorship chain connected to Erdös has an Erdös number of infinity. In a seven day long mini-conference organized in memory of Paul Erdös, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdös number. Nobody had an Erdös number less than that of F. • On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdös number of the group of eight mathematicians to 3. The Erdös numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdös number of the group of eight to as low as 3. • At the end of the third day, five members of this group had identical Erdös numbers while the other three had Erdös numbers distinct from each other. • On the fifth day, E co-authored a paper with F which reduced the group’s average Erdös number by 0.5. The Erdös numbers of the remaining six were unchanged with the writing of this paper. • No other paper was written during the conference. 202. The Erdös number of C at the end of the conference was: (2006) (a) 1 (b) 2

(c) 3 (d) 4 (e) 5 203. The Erdös number of E at the beginning of the conference was: (2006) (a) 5 (b) 5 (c) 6 (d) 7 (e) 8 204. How many participants had the same Erdös number at the beginning of the conference? (2006) (a) 2 (b) 3 (c) 4 (d) 5 (e) cannot be determined 205. The person having the largest Erdös number at the end of the conference must have had Erdös number (at that time): (2006) (a) 5 (b) 7 (c) 9 (d) 14 (e) 15 206. How many participants in the conference did not change their Erdös number during the conference? (2006) (a) 2 (b) 3 (c) 4 (d) 5 (e) cannot be determined Directions for Questions 207 to 211 : Answer the questions on the basis of the information given below.

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions : • A team must include exactly one among P, R and S. • A team must include either M or Q, but not both. • If a team includes K, then it must also include L, and vice versa. • If a team includes one among S, U and W, then it must also include the other two. • L and N cannot be members of the same team. • L and U cannot be members of the same team. The size of a team is defined as the number of members in the team. 207. Who can be a member of a team of size 5? (2006) (a) K (b) L (c) M (d) P (e) R 208. Who cannot be a member of a team of size 3? (2006) (a) L (b) M (c) N (d) P (e) Q 209. What could be the size of a team that includes K? (2006) (a) 2 or 3 (b) 2 or 4 (c) 3 or 4

(d) Only 2 (e) Only 4 210. In how many ways a team can be constituted so that the team includes N? (2006) (a) 2 (b) 3 (c) 4 (d) 5 (e) 6 211. What would be the size of the largest possible team? (2006) (a) 8 (b) 7 (c) 6 (d) 5 (e) cannot be determined Directions for Questions 212 to 215 : Answer the questions on the basis of the information given below. The proportion of male students and the proportion of vegetarian students in a school are given below. The school has a total of 800 students, 80% of whom are in the Secondary Section and rest equally divided between Class 11 and 12. (M) Class 12 Class 11

Male Vegetarian (V) 0.60

0.55 0.50

Secondary Section 0.55 Total

0.475 0.53

212. What is the percentage of vegetarian students in Class 12? (2007) (a) 40 (b) 45 (c) 50 (d) 55 (e) 60 213. In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male nonvegetarians? (2007) (a) less than 8 (b) 10(c) 12 (d) 14 (e) 16 214. What is the percentage of male students in the secondary section? (2007) (a) 40 (b) 45(c) 50 (d) 55 (e) 60 215. In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct? (2007) (a) Except vegetarian males, all other groups have same number of students. (b) Except non-vegetarian males, all other groups have same number of students.

(c) Except vegetarian females, all other groups have same number of students. (d) Except non-vegetarian females, all other groups have same number of students. (e) All of the above groups have the same number of students. Directions for Questions 216 to 219 : Answer the questions on the basis of the information given below. A health–drink company’s R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R and S), which can be used in different proportions in the formulations. The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O: 150, P:50, Q: 200, R: 500, S: 100.

216. The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible? (2007) (a) O and P (b) R and S (c) P and S (d) Q and R (e) O and S 217. For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many

different ways can we prepare this diet by mixing at least two ingredients? (2007) (a) One (b) Two (c) Three (d) Four (e) None 218. Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? The diet has to be formed by mixing two ingredients. (2007) (a) P and Q (b) P and S (c) P and R (d) Q and S (e) R and S 219. In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost? (2007) (a) 2:1:3 (b) 4:1:2 (c) 2:1:4 (d) 3:1:2 (e) 4:1:1 Directions for Questions 220 & 221 : Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000, Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss. 220. Which of the following cannot be true?

(2008) (a) At least two horses finished before Spotted (b) Red finished last (c) There were three horses between Black and Spotted (d) There were three horses between White and Red (e) Grey came in second 221. Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true? (2008) (a) Spotted came in first (b) Red finished last (c) White came in second (d) Black came in second

ANSWERS WITH SOLUTIONS 1.

(c)

Jakie is the host and seated to shobha’s right (d) Shobha is a person who is seated between Dhirubhai and Jackie (a) Only statement (I) would be true if (a) Ratan and Monisha are sitting just opposite to each other. Hence, they must be married. (b)

6. 7.

If Aishwarya is a girl in extreme left then, the girl in the middle is Sushmita. (d) Manpreet (from above) (d)

2. 3. 4.

Manpreet is on the extreme right. For Qs. 8-11. B is as old as C was when I was twice as old as D

......(i) B will be as old as E was when he was as old as C is now ......(ii) A may be older than F but G is as old as B was when A was as old as G is and A = B ......(iii) D will be as old as F was when F will be as old as G is ......(iv) From (i), (ii), (iii) and (iv) 8. 9. 10. 11. 12. 13.

14. 15. 16.

(b) (b) (c) (c) (b)

Eldest brother - E Youngest brother - D Twins - A & B B has only 2 elder brothers Ihavitoo must be used together with Grumbs only, so (b) is not possible. (d) As per the given rules Ihavitoo must be used together with Grumbs. Lovitoo or Metoo or both can be used as Dingos, hence, (d) is the correct answer. (a) Two Bingos, one Cingo and two Dingos are been used in (a) & other rules are being satisfied, so, (a) is the correct answer. (d) Only (d) i.e. all the three bingos are used can be true. (a) Salary in the first week = Rs 20 per working hour As the working pattern changes next week, so wage/hr for the 2nd and fourth week

Work and Rest hrs/day for the 2nd and 4th weeks respectively are 2 and 5 hrs. A week consist of 6 days and a month of 4 week Salary from 1st and 3rd week = 20 × 5 × 2 × 6 = Rs 1200 Salary for 2nd and 4th week = 2 × 10 × 6 × 2 = Rs 240 Salary for 1st month = 1200 + 240 = Rs 1440 17. (c) Salary for 5th and 7th week = 2 × 7 × 20 × 6 = Rs 1680 Salary for 6th and 8th week = 2 × 3 × 10 × 6 = Rs 360 Salary for 2nd month = 1680 + 360 = Rs 2040 Similarly salary for 3rd month

= 2(6 × 20 × 6) + 2 ( 4 × 10 × 6) = 1440 + 480 = Rs 1920 Salary for 4th month = 2(8 × 20 × 6) + 2 (0) = Rs 1920 Salary at the end of 4 months = 1440 + 2040 + 1920 + 1920 = Rs 7320 ∴ Average monthly salary 18. (b) Under new scheme salary for 9th and 11th week = 2 (25 × 6 – 5 × 4 ) × 6 = Rs 1560 Now salary for 10th and 12th week = 2( 25 × 4 – 5 × 6 ) × 6 = Rs 840 Total salary for 3rd month = 1560 + 840 = Rs 2400 Under previous scheme total salary for 3rd month = Rs 1920 Difference = 2400 – 1920 = Rs 480 19. (b) According to conditions salary for first 3 months = 1440 + 20 40 + 2400 = Rs 5880 Salary for 4th month (13th to 16th week) = = 2400 – 480 = Rs 1920 Total salary for 16 weeks = 5880 + 1920 = Rs 7800 For Qs. 20-23. S, T, U and V each has Rs 32 after 4th round i.e. They have a total of 32 × 4 = Rs 128 among themselves after each round of game.

20. 21. 22. 23. 24.

(d) Vibha (a) Suvarna (b) at the end of the second round Uma has Rs 72 with her. (c) Suvarna started with Rs 66. (b) One day = 8 × 60 = 480 minutes Both machines can independently produce P &Q ∴ Total available hours To produce maximum units we produce only Q

∴ No. of units 25. (a) P = 3Q For machine For machine But P takes less time to produce on M2. So, as to manufacture maximum units we produce P through M2. No. of units of P through Time taken to produce 20 Q from M1 Now time left = 480 – 120 = 360 minutes for machine M1 : 10P + 6Q = 360 or Q = 10 Hence, no idle time 26. (c) To compare the four options take the LCM of 48, 64, 53 and 71, which comes out to be 722496. Now we have to find the case which will take maximum idle machine hours to manufacture 722496 units. So, idle machine hours for (a) = (722496 × 3) / 48 = 45156 minutes (b) = (722496×12) / 64 = 135468 minutes (c) = (722496 × 10) / 53 = 136320 minutes (d) = (722496 × 9) / 71 = 91584 minutes As (c) takes maximum idle hours, it is the least efficient. 27. (d) For For For maximum no. of units, 1 unit of P is produced on M2 and rest Q is produced. Hence, For M1 : For M2 : units + 4 hr idle time Hence, total units 28. (a) 30 P and 25 Q for least machine hours, P must be produced on M2.

⇒ Total time

29.

30. 31. 32. 33.

34.

35.

or 6 hrs 30 min (c) Let the feasibility be decided by the costs involved i.e., if the relative cost is lower than any other test, than the test can be said to be feasible. Hence by looking at the options the percentage of defective pieces lie between 0.05 and 0.20 the test 2 to be feasible. (d) Test 2 and test 3 have same relative costs for p = 0.2, hence either of them can be adopted. (a) Test 3 will be feasible for p > 0.2 because it has the lowest relative cost. (a) Test 1 will be feasible when p < 0.05 because it has the lowest relative cost. (d) When p < 0.2, then alternatives which can be feasible is either test 1 or test 2 . But from the given data, it is not possible to say which test is the best. But it is definitely clear that test 3 in the most unfeasible test. (a) We do not know the exact distances in case of AD, AE and DE. Since these three cities form a triangle, AC + CD > AD hence, AD < 4. Now let us find about A-C-E. AC + CE > AE . Hence, AE < 5. Now considering C - D -E, we have CD + CE > DE. Hence, DE < 5. Thus, the minimum distance between any two cities is 2 km and the maximum distance does not exceed 5 kms. If we want a ration shop within 2km of each city, we will require one shop as long as the distance between any two cities does not exceed 4 km. The only cities which can be more than 4 km from each other are AE and DE. Since city E is common to both. Hence, one shop will be able to cater to these three. Hence, total number of shops required = 2. (a) If we want a ration shop within 3 km of each city, we will require only one ration shop (This is because distance between no two cities is more than 6 km).

36. (c) Let speed of C be x km/hr time taken by Time taken by

Time taken by Total time taken

min

For new record total time < 10 min

which is not possible 37. (b) Time for Time for Let speed for C be x km/hr ∴ Total time also, total time After solving we get,

38. (c) Let times for A, B, C stretches by

and t3 hrs. respectively

Average Speed

Average speed for first two stretches

Hence, Average speed for stretch C = 10 kmph

39. (a) Since 1996 is a leap year. 25th Feb, 96 will be Wednesday. Since Raja doesn’t have any holidays, he completes the job in 7 days. So, one person can do

th of the work per day therefore on 25th T

and J complete

th of the day. T will not work on 26th i.e.

Thursday. So,

work done on 26th. Now

job remains

which will be done on Friday and Saturday. ∴T and J complete the job in 4 days. 40. (c) Raja doesn’t take any holiday so he complete job in 38 days each person by himself can complete the job in 38 days if he would not take any holiday. In one day, T and S together can complete

th of the work. Sine T takes holiday on Tuesday and

Thursday and S takes holiday on Saturday and Sunday. Therefore, in the one week they can do

th of the work.

In the 3rd weeks In the 4th week Hence, it is completed on 22nd March. 41. (c) Day Units Accumulated Units Produced (a) (b) (c) 1 150 150 150 150 2 180 0 330 0 3 120 120 450 120 4 250 0 700 0 5 160 160 860 0 6 120 0 980 120 7 150 0 0 0 Storage cost @ 5 2150 17350 1950 Hiring Cost 4000 1000 4000

So the correct option is (c). 42. (a) Day Units Accumulated Units (a) (b) (c) 1 150 150 150 150 2 180 330 330 330 3 120 450 450 450 4 250 0 700 0 5 160 160 860 160 6 120 280 980 280 7 150 430 0 0 Storage cost 1440 2776 1096 @ 0.8 per sq. ft. Cost of truck 1000 1000 2000 Total cost 2440 3776 3096 The minimum cost is in option (a). 43. (a) If A is the first, then B will be either at 2nd or at 4th place and in both the cases, there is a contradiction i.e. C, D sitting together. 44. (c) If A is not at the third place C can only be at the first or third place

45. (b) If A and B must be together A cannot be at the second place because if A is at the second place then B has to be at the first place and hence C, D are together which should not be true. Hence, A cannot be at second place. 46. (a) To find maximum number of coins collected by one, we find the minimum number of coins collected by other three Hence, maximum 47. (c) A collected 54 Coins No. of coins for rest of the three = 46 to find the second highest i.e. highest amongst these three, we use the same method as above: Hence, second highest = 46 – ( 10 +12) = 24 Difference between highest and second highest = 54 – 24 = 30 48. (d) A = 54 coins So, no. of coins collected by B, C, D = 100 – 54 = 46

If no. of coins collected by C = x ∴ by B = 2x + 2 ∴ 2x + 2 + x + y = 46 where y is the no. of coins which D have. Minimum value of y is 10. ∴ 3x + 2 < 36 and y = 12 and or B have 22. Hence, coin collected by B = 22 For Qs. 49-50

49. (a) From option (a), Amar — Blue Akbar — Green (not possible) From option (b), Akbar — Red Anthony — Red From option (c), Amar — Blue Akbar — except blue (red) Anthony — Red From option (d), Amar — Green or Blue Akbar — Red Anthony — Red Thus only option (a) is not possible. 50. (a) According to above table statement II and IV are false. 51. (a) If number of chocolates is NC then those of biscuitsNB = 2NC and number of apples i.e NA > 3NC also, total amount spent = (note that amount of money spent is even number) option (b) 33 = 8 + 24 + 1 but option (c) is not possible minimum Rs that can be spent = 10[ 4 × 2 + 1 × 1 + 2×1/2] So, option (a) 34 = 8+ 24 + 2

So, option (a) is correct 52. (b) So, Ms. West Bengal wore red saree. 53. (c) From the above solved table Ms. West Bengal was sitting together with Ms. A and Ms. U. 54. (a) Ms. AP has worn yellow saree. 55. (c) Ms. U was runner up. For Qs. 56-60. Gopal paid = 40% Ram paid = 60% Let total cost be Rs x

∴ Total amount put in by Ram and Gopal = 10,00,000 + 2,00,000 = 12,00,000

So, if 100 lemon trees Hence, 500 coconut trees So, Revenue generated Revenue for coconut Revenue for lemon 56. (b) Total output of coconuts

57. (a) From lemon trees

= 3 lac.

Land for lemon trees

acres

Output per acre of lemon trees planted = 0.72 lakh / acre 58. (a) In 1997, amount received by Gopal of total revenue 59. (b) Total output of coconuts =

. 1,80,000

Hence, output per tree 60. (a) Ratio of yields from coconut and lemons was 3:2, further the coconut and lemon trees were planted on the equal area of the total 10 acres of land. Therefore the ratio of yields per acre of land for coconuts and lemon was 3:2. For Qs. 61-62. The information provided in the problem can be tabulated as follows :

E can only be the architect, hence has to be male. D can only be a housewife, which means that A is a male. Consequently, B also has to be a housewife. The males are A, C and E. 61. (c) E is architect 62. (b) There are three males in all. For Qs. 63-66. the coins distributed are : 1, 2, 3, 4 Q > P and S < R. 63. It is given that Q > P and R > S.

The distribution of coins can be of two types in both the cases, S gets an odd number. 64. Option (b) is the answer as it is one of the conditions mentioned in the question itself. 65.

Looking at the possible distribution of coins, we find that option (a) is not always true. 66. (c) R = 3 S = 1 or 2 Again Q > P, so P can be 1 or 2. But 1 and 2 values can be taken by P and S Hence Q = 4 For Qs. 67-68. From the conditions,

So E & G cannot sit together. F cannot sit on extreme position. 67. (d) 68. (d) For Qs. 69-71.

Starting from the fourth place of worship and moving backwards, we find that number of flowers before entering the first place of worship is

Hence, number of flowers before doubling = (but this is equal to 30)

Hence, y = 32 Answer for 69 is (c) The minimum value of y so that

is a whole number is 16.

Therefore, 16 is the minimum number of flowers that can be offered. Answer for 70 is (c). For y = 16, the value of Hence, the minimum number of flowers with which Roopa leaves home is 15. Answer for 71 is (b). 69. (c) 70. (c) 71. (b) For Qs. 72-74.

If the Ghosh Babu leaves the game after he has played it twice his gain will be maximum i.e. Rs 12. Because 1st the dealer pays the base amount, Ghosh Babu, has to start with Rs 8. as minimum. So, that he can pay Rs 16 at the end of 1st game. Net result = Gain of Rs 4 to Ghosh Babu. So, he must start with Rs 96. 72. (a) 73. (c) 74. (c) 75. (c) The task with the person is to optimize his points. If he takes a book of 1 management +2 fictions 1 mathematics + 2 physics There are no restrictions on carrying either fiction or physics alone. So to maximize the no. of points , he will carry 1 management +2 fictions = 6 2 × (1mathematics + 2 physics) = 14 1 Physics = 2 so total = 22. 76. (a) The given clues can be arranged as follows :

Hence, we find that only Q and M can stay in the palace. Since Q stays in the hut, M stays in the palace. Hence, the answer option is (a). 77. The attendants of X, Y and Z are to be Mohan, Jack and Rita. The animals under Mohan’s care is given in the data. Since Jack does not attend to deer, lion and bison, the following table can be created using the data given.

The data for Mohan and Jack can be filled directly. Similarly, X, Y, Z can be filled directly from data given. The key after filling in these animals is that Z and P have the same pair of animals, the only option is deer and bison. 78. By trial and error, we can make different combinations and find the cost. Like 20 kg × 2 + 10 kg × 4, the cost would be ` 180. The minimum cost comes in the case of 10 kg × 8, i.e. ` 160. 79. (c) Since A doesn’t live in the yellow house or in the green or the Red houses adjacent to it, he has to stay in the Blue house. 80. (b) a, b, c, d and e represent numbers 2, 4, 5 , 6 and 10 From (I), a + c = e From (II), or d = 5 accepted From (III), a + e = b From above we have,

Hence, a = 4; b = 10; c = 2; d = 5; e = 6 is the required solution. 81. (c) The perfect schedule is as follows :

So, option (c) is correct answer 82. (c) Hence, (c) is the right answer. 83. (c) Fried brinjal — Blue Chinaware Sambar — White Chinaware Makkai-ki-roti — Red Chinaware. The family that eats at 10’clock serves fried brinjal, hence Pattabhiraman serves fried brinjal. The family that eats last like makkai-ki-roti so, Banerjees like makkai-ki-roti. Sharmas are left with samber. Sharma – 12:00 – Samber – White Pattabhiraman – 1:00 – Fried brinjal – Blue Bannerjees – 2:00 – Makkai-ki-roti – Red 84. (b) We had two options. Black hair, Short tail and no collar. And white hair, long tail and a collar Hence (b) is right answer. For Qs. 85-87. From the given statement E = 3Y ....(1) Z= Y>Z

.....(2) .....(3)

85. (b) (a) gives Y >

, which is not true from the above equations.

For (b), From (1), (2), (3);

or E > 1.5W,

which is true. (c) is clearly wrong as can be seen above. 86. (c) (a) gives Z = 10, which alone is not sufficient. (b) gives Y = W, which again is not sufficient. On combining (a) and (b), W = Y = 2Z = 20; Z = 10 ⇒ E = 3Y = 60 Hence (c) is the correct option. 87. (a) (a) is correct as if P is true it means Q and R are true which further means S is false (from the given statements). (b) is wrong because it gives that either Q or R is true, which is not sure. (c) & (d) can’t be sure. For Qs. 88-90.

88. (b) Peter, Shyam and Rahim is become feasible if Shyam is there & Ram is not there Shyam & Rahim together If Peter no David No David, no Kavita. 89. (c) Shyam, Rahim, Fiza, David Shyam and Rahim together Shyam with no Ram David without Peter Fiza with David’s demand 90. (d) If Kavita david is there No Peter No Ram Hence (a) is not possible If Kavita then David, no Peter no Ram. Fiza will be the fourth member . Again not possible

A group of 4 cannot be possible. So, none of the options is correct 91. (b)

6 + 22 + x + x + y + 5y = 50 2x + 6y = 22 x + 3y = 11 As y is even, so, y = 2, x = 5. Oak leaves = x + y + 5y = x + 6y = 5 + 12 = 17

92. (c)

93. (b)

The two married couples are GF2 & GM2 and F2 and M2. Thus, we have 2 grandfathers GF1, GF2 4 fathers GF1, GF2, F1 and F2. 2 grandmothers GM1, GM2 4 mothers GM1, GM2, M1 and M2. Thus, minimum number will be 12. 94. (b) ....(i) ....(ii) ....(iii) (Since for every D there are 2B)

As there is no condition with C, so the average cost in any scheme shall be less than 70, so as to maximise the points. Otherwise, C would be preferred. Scheme (i), Average Cost = Scheme (ii), Average Cost = Scheme (iii), Average Cost = But following the 3rd scheme, I need to buy atleast Which fetches 30 × 1500 –ve points. Which is not possible. So, maximum points can be attained in case of buying ∴ No. of items purchased = 14 95. (b) From question we have A < 3B C>B D=|B–C|=C–B A = 3D

C buys Jacket for Rs 1000, with Rs 300 borrowed from A C had atleast 1000 – 300 = Rs 700 B buys Sweater for Rs 600 with Rs 100 borrowed from A B had 600 – 100 = Rs 500 As A buys 3 shirts A had atleast 600 + 300 + 100 = Rs 1000 atleast As shirt, jacket and sweater has already been bought, a Shawl is left. D buys a Shawl worth Rs 400 and A = 3 × 400 = Rs 1200

96. (b) W1 = Wx = Sonali, Shalini, Shubhra, Shahira, Rupa Somya ≠ Ritu ≠ Wb Wy = Rupali, Renuka, Komal Tara ≠ Radha ≠ Wz Wz = Radha Komal ≠ Radha, Somya, Ritu W4 = Wa = Ruchika, Somya, Sweta, Jyotika Rupali ≠ Sweta, Jyotika ≠ Wy Wb = Ritu, Tara Komal is in Wy as W1 is full Hence, Elina is the instructor of Radha.

97. (d)

(a) M1, M2, M5, M6 - not possible because M1 hates Gambling which is not a liking of any of the rest three. (b) M3, M4, M5, M6 - not possible because none of them share a liking with each other. (c) M4, M5, M6, M8 - not possible because none of them share a liking with each other. (d) M1, M2, M4, M7 - correct. For Qs. 98 to 100.

98. (d) Clearly since each pipeline can have maximum of 1000.So, here we have put the values according to demand of the places 99. (d) Avanti – Vaishali = 700 So, free capacity = 1000 – 700 = 300 100. (d) Avanti – Vidisha = 1000 Free capacity = 0 101. (c) Conclusion comes out from all five statements that Sameer is an Economist who got admission offers in two NIMs 102. (d) Given that A > J, S = D + 1.50, G > only one person , A spent the most but did not end with the least J spent least, J’ > A’ or D’, G’ = 3.50, A = 10 G therefore conclusion comes out that Jugraj started with Rs 10 and ended with Rs 7.00

103. (a)

or 80 = 50 + x or x = 30 Patients for hyperglycaemia only = 150 – ( 80 – x + x + 60 – x) = 10 + x Patients for Gastroenteritis only = 20 + x

Dr Paul had 50 + 30 + 40 + 30 = 150 Patients Dr Dennis had 80 Patients Dr Gerard had 50 Patients D Hormis had 40 Patients Paul > Gerard > Hormis

104. (c)

105. (c) Let age of younger boy = y years and age of elder boy = x years According to given conditions Age of father Age of mother =

Put or

106. (a) Seating capacity of hall = 200 Vacant seats in hall = 20 Waiting ladies passenger Seating capacity of each flight After boading for flight A, vacent seats in hall = Passengers who boarded flight A Now passengers waiting for flight B = 180 – 100 = 80 Air hostess in flight Empty seats in flight B = 120 – 80 = 40 Required ratio 40 : 4 = 10 : 1. 107. (a) Total distance travelled from starting point till last signal = 10 + 20 + 20 + 40 + 0 = 90 km to west in 20 km to south F in situated at 30 km to west in 40 km to south

108. (c)

109. (a)

110. (c)

Final position be 30 km to west to 20 km to south 111. (b) Let he stole originally 8x diamond According to question Diamonds given to first watchman Now, thief has diamonds

= 4x + 2

Diamonds given to second watchman = 2x + 1 = (2x – 3) diamonds

Now, thief has

Diamonds given to third watchman Now, remaining diamonds =

According to question or Originally he theft 112. (d) Suppose two unequal numbers of coins are x and y, then according to question

But

(since

)

total coins = 48 113. (c) They did nothing on 24 mornings They did nothing on 14 evenings ∴ They played tennis on (24 – 14) = 10 evenings The remaining playouts, i.e., 22 – 10 = 12 can be done in 6 days, i.e., 6 mornings and 6 evenings. So, Shyam stayed for 30 days.

114. (c)

After interchanging the seats it is clear from the fig. that Suresh (S) is to the left of Dhiraj (D) 115. (d) 1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4 there are six ‘2’ in the sequence and four ‘4’. Therefore, 6 oranges are put and 4 oranges are taken out. So, total oranges at the end of sequence = 6 – 4 = 2 116. (c) There are six ‘1’ in the sequence ∴ 6 mangoes are put There are six ‘2’ in the sequence ∴ 6 oranges are put There are seven ‘3’ in the sequence ∴ 7 apples are put Total fruits put = 6 + 6 + 7 = 19 There are four ‘4’ in the sequence ∴ 4 mangoes and 4 oranges are taken out ∴ Taken out fruits = 8 Total fruits at the end of sequence = 19 – 8 =11 117. (b) Share of each traveller 1st traveller gave to 3rd traveller 2nd traveller gave to 3rd traveller 3rd traveller pays 8 coins for his share ∴ For

bread = 8 coins

bread

coins

Therefore, 1st traveller should get 7 coins. 118. (d) G + B = M + 16 .....(i)

Total number of projects = 2 ( 8 + 6 + 3 + 2) – 1 = G + M + B + 19 Hence, G + M + B = 18 .....(ii) Using (i) & (ii), we can solve for M but cannot find G. 119. (b) Using (i) & (ii), we get M = 1 For Qs. 120-121. G=A–8 Again, Again, Again, 120. (a) D + J = 27 + 19 = 46, (a) is true. Clearly (b), (c) and (d) are wrong 121. (a) is true For Qs. 122-124. From the data provided, the two possible options are

122. (c) E and G as G can not be on B’s adjacent side. 123. (d) E and A as in option (i), A’s adjacent position has to be occupied by C or D 124. (c) Clearly F. For Qs. 125-127. Following information can be inferred from the given data:

125. 126. 127. 128.

(b) (a) (d) (b)

3 Males E - Engineer A and D Cost of 1litre Avocado paint

= Cost of = 11 + cost of = 11 + 5 + 3.75 = Rs 19.75 129. (d) 1 litre of washed orange can be produced by mixing and

litre white or

yellow

orange

litre white or 1:

1 : 2 in red, yellow & white colour respectively. 130. (b) Cost of 1 litre cream = 0.7 × 15 + .3 × 25 = 10.5 + 7.5 = Rs 18 Cost of 1litre Avocado = Rs 19.75 (From Q. 40) Cost of 1litre washed orange

= Rs 18.50

Hence, cream is the cheapest 131. (d) A = home, then C = finance, D and B must have power and telecom, hence (d) is wrong.

132. (b) C gets home or finance, hence (a) and (d) are wrong.. Statement (c) is also wrong as D and F cannot come together. For Qs. 133-135.

133. (c) Ignesh takes 6 Idli and 6 Vada and takes Chutney. 134. (d) Clearly, Ignesh eats and Vadas. 135. (a) We get the following table :

For Qs. 136-138.

136. (b) A= 137. (a) 138. (c) 139. (c)

We get S = 2517 . Then C = 2517 – 1378 = 1139 2234, D = 1193 and H = 1340 . Rs 1139 Dhenuka The given facts can be formulated in the following figure:

So, C’s office is to the left of E. 140. (d) E and A face each other 141. (a) A only 142. (b) Office of B is right and in the corner.

143. (a) SP and BSP clash routes, so, separate days. Congress and CPM clash routes, so, separate days. Political Parties take out their processions from following days :

Congress should be allowed on Thursday 144. (d) Congress on Thursday and BSP on Friday So, not on the same day 145. (b) The order of events as given in the problem can be written as: JC (e); SS (e); SM (e); DG (e); SM (l); SS (l); VR (e), JP(e); JC(l) DG(l); DG(e2); VR (l); PK (e); PK (l); JP (l); DG (l) where e shows entered, l shows left and e2 show entered 2nd time. So, DG entered before JP 146. (c) DG was sitting with JC, when JP entered 147. (b) 3 members whom VR met were JC, DG and JP 148. (d) JP and DG were the last to leave 149. (b) A and D have no blank answers, so, they may have only one source C has copied from 1source only (as there are 2 wrong answers) B has copied from 2 sources as there is only 1 worng answer (which has been done by himself) and rest blank answers (which have not matched in the 2 sources) 150. (c) C has 2 wrong answers and 3 blank answers. This means one wrong answer has been done by himself and the other from the source, say S, from where he copied. 3 blank answer mean that they were present in S’s answer key too. This means S has got it from two sources – S2, one with one wrong answer and the other S3, with 2 wrong answers. The one haveing 1 wrong answer could have got it from the master mind but the other one has to

get it from a single source S1, ( who has got it from MM) with one wrong answer. So, 4 people before him

151. (d) If G and H would be sources to some one than he should have 25, 46 and 92 as blanks which is not there in any case 152. (c) (a) False, as 27 was introduced by I (b) False, as 46 was introduced by A (c) True (d) False 153. (d) (I) A, D, and G have the same source as the mastermind as they have only one wrong answer and no blank answers (II) E and H have no blank answers so it means they both have got their answers from one single source, i.e. A. So, both (I) & (II) had identical sources. For Qs. 154-157. The data provided in the question can be tabulated in the following form.

154. 155. 156. 157. 158.

(a) (b) (c) (b) (a)

Table shows that Shanthi was the third one to arrive. Sunil and Sridevi Sridevi and Anita, so, Sunil and Anil Raj has two kids. Question is group B = 23 ≡ 46 marks

If c = 1 then total marks = 76 + 46 + 3 = 125 whose 60% is 75. As marks of A > 75, so, c = 1 satisfy but for any c > 1, then % marks of A will be less than 60%. 159. (c) If C has 8 question, it has 24 marks. Then if B has 12 question, A must have 80 questions. Percentage of marks in B = 24/128 = 18.75%, hence the first two choices are wrong since it must be 20%. If B has 13 questions, percentage = 26/129 > 20%, and if B has 14 questions, percentage = 28/130 > 20%. For Qs. 160-163.

198 175 192 Inning Total 220 250 240 160. (b) From the above table it is clear that Saurav has the highest Mindex 161. (a) The players who can have the lowest R-index can be seen from the table Saurav’s R-index will be > 53 and Virender’s R-index > 82, so both can not have the lowest R-index. Kaif’s R- index lies between 23-51, so he definitely falls in the category of lowest R-index. Rahul (between 33-55) and Yuvraj (47-87) also fall in this category. 162. (c) It is only possible to calculate the M-index for Rahul and Saurav, i.e., 2 players. 163. (b) The above table shows that Rahul definitely scores less than Yuvraj. Kaif scores ≤ 127 in all the three matches whereas Yuvraj scores 127 in 2 matches. In case Yuvraj scores 0 in the 3rd match and Kaif scores 48 in the 3rd match they both score 127. So, nothing can be said for Kaif. For Qs. 164-167. Top 3 Batsmen

x + 2x + 2x + 2x = 21 = 7x ⇒x=3 y + 2y + y + 1 + y = 21 = 5y + 1 ⇒y=4 164. (a) No. of Labour experts from the Americas = 1 No. of health experts from the Europe = 1 No. of health experts from the Australasia = 1 No. of Refugee relocation from the Africa can not be found. 165. (d) Clearly from the table option (d) is not possible as no. of expert in Africa and America has to be 6 –3 = 3. 166. (c) American expert in population studies the above table becomes L H PS R Africa 0 1 2 1 America 1 3 1 3 Australasia 1 1 2 1 Europe 1 1 1 1 Option (c) is not true. 167. (c) From the top table it is clear that the Refugee relocation experts in America can be at the most 3. So both (i) and (ii) are correct. 168. (d) Best done by elimination. (a) If true, then NZ lost the second game by 5-1, which does not match. (b) If Spain beats NZ by 4-0, then in the next game it should lose by 1-2 (c) If Spain beats SA by 2-0, then it should win the next game by 3-2, but it lost the other game. Only (d) is possible. 169. (b) As above (a). If Pakistan has 2-1, it should draw the next game 0-0,which is not true. (b) is possible. (c) same as in the first choice. 170. (d) The question is inconsistent. If Pakistan wins the last two rounds, and we are also told in (a) to (c) that Spain, Argentina,

Germany and Pakistan won their fifth round matches. This is not possible, since there can be only three winners. 171. (d) We can say nothing about the winner. 172. (a) One of the companies with extraordinary results belongs to cement or IT industry (double return) stored and the other one belong to steel or auto industry (

times return)

173. (b)

So, II and III are correct. 174. (c) So I & IV are correct. 175. (b) So clearly II and IV are true. For Qs. 176-179.

Hence it is clear from condition (2) that B and C have their names between Aggressive ltd. & Honest Ltd.

176. (c) If statement (1) is true then B is Honest Ltd. If statement (2) is true then B is Aggressive Ltd. So (c) i.e., at most one of these is true. 177. (c) As per 1 B is Aggressive Ltd. As per 2, C is Honest Ltd. So if 1 is true than 2 has to be true. 178. (b) As per 1, B is profitable Ltd. As per 2, C should be Honest Ltd., Which has the highest aggregate revenue of 222 m. But as per the given condition in M.P, Truthful Ltd, has the highest market share. So 2 is necessarily false. 179. (c) If profitable Ltd.’s is lowest revenue is form UP, then it is either A or D. In either case the other one (A or D) is truthful Ltd. Hence the lowest revenue is from up again. 180. (c) In the second sound, Elena Dementieva (≠6) will lose to the winner of Patty Schnyder (≠ 11) and Dinara(≠ 22) and Serena Williams (≠8) will lose to Nadia Petrova (≠9). Further in round 3 (quarter finals), Nadia Petrova will play with Maria Sharapova and defeat her. 181. (c) In question final Maria will defeat Serena and play with the winner of ≠ 4 and ≠ 5 and will defeat her in the semi finals. So she will definitely not play Kim Clijsters in the finals. 182. (d) In the IInd round there will be the top 16 players. As there is upset in the 6th, 7th and 8th match of the 2nd round, so the quarter finalists will be : ≠1, ≠2, ≠3, ≠4, ≠5, ≠9, ≠10, ≠11. So Lindsay Davenport (≠2) plays ≠10 (Venus Williams) in the quarters. 183. (a) The line up for second round becomes 1, 31, 2, 29, 5, 27, 7, 25, 9, 23, 11, 21 , 13, 19, 15, 17 The line up for 3rd round is : 1, 15, 3, 13, 5, 11, 7, 9 So, in the semifinal Maria Sharapova will meet ≠ 13 or ≠ 5. Hence, Anastasia Myskina is the answer. 184. (c) n (TR) = 17 n (involved in TR & atleast 1 more) = 10 n (only TR) = 17 – 10 = 7; n(only ER) = 7 + 1 = 8

n (FR only) = n (FR volunteers involved in ER) = b + 4

n (FR TR but not ER) = c = 6 – a ......(1) Total volunteers = 37 ⇒ 17 + 8 + 4 + 2b = 37 ⇒ 2b = 8 or b = 4 From (1), a + c = 6 As FR has to have maximum volunteers so c can have the following possible values (1) c = 4, a = 2 (2) c = 5, a = 1 But for minimum volunteers in FR & TR, c = 4. 185. (a) Only 1st option is useful 20 = 4 + 4 + 8 + c or c = 4 Using the value of c and b we can get all required values. 186. (b) The Venn-diagram looks like,

Now the 4 students common to all the three projects are asked to shift. 1 moves from TR and remains in ER & FR 1 moves from ER and remains in FR& TR 2 moves from FR and in remains in ER & TR So, the new diagram becomes

n (TR) = 10 + a + c n (FR) = 9 + 5 + c = 14 + c n (ER) = 8 + 5 + a + 2 = 15 + a Further, a + c = 6 for which either c = 5 & a = 1 or c = 4 & a = 2 Thus, FR has maximum volunteers for any values of c & a.

187. (a)

a+2=5⇒a=3 a+c=6⇒c=3 n (TR) = 8 + 4 + 5 = 17 n (FR) = 8 + 5 + 4 = 17 n (ER) = 8 + 5 + 5 = 18 So, maximum volunteers are in ER = 18 For Qs. 188-191.

In all 9 members could not vote in round 3 [ 83 – (75 –1)] as both the countries they voted for — New York & Beijing lost in the first two rounds. So the remaining members who voted for Beijing in round 2 (i.e., 21 – 9= 12) are equivalent to the 75% of members who voted Beijing in round 1. Hence Members voting for Beijing in round 1 = Total votes in round 1 = 83 – 1 = 82 188. (d) Members who voted for NY in round 1 but for Beijing in round 2 = 189. (d) Votes for Paris in round 1 = 24 190. (d) Voters who voted for London in round 3 but voted for Beijing in round 2 (Note : 9 out of 21 members of Beijing left) 191. (a) Clearly the new member from NY voted for Paris in round 2. Further the new member from Beijing also voted for Paris in round 3. 192. (c) The opening price on day 1 was Rs 100. The closing price on day 5 was Rs 110. Chetan sold 10 shares of MCS on 3 consecutive days and Michael sold 10 shares only once during the 5 days. The possible trend of the closing price of MCS shares is:

So the closing price at the end of day 3 was Rs 110/193. (a) Michael ended up with 20 more shares than Chetan at the end of day 5. The various possibilities in this situation for the given options are :

So it is clear from the above table that Michael had 20 more shares than Chetan for option 1, where the closing prices were, 90, 80, 90, 100 and 110. So the price at the end of day 3 was Rs 90. 194. (d) The maximum possible increase in combined cash balance of Chetan and Michael would be in the case when both Chetan and Michael sell their shares and that too at higher prices. Further for Michael to sell his shares the price has to be above 110. This will be possible when the closing prices are : 110, 120, 130, 120 and 110. Day Chetan Michael 1110 1100 –

2120 1200 1200 3130 1300 1300 4120 – 1200 1200 5110 – 1100 – Total 1300 3700 So total increase in combined cash balance = 1300 + 3700 = Rs 5000 195. (b) The various possible cases of price variation are given below.

So in four cases II, IV, VIII and IX, Chetan had 1300 Rs more than Michael. In all the four cases, the closing price of day 4 is Rs 100/-. 196. (e) From the above table it is clear that Michael had Rs 100 less cash than Chetan in case III, V and X. In all the three cases we see that Chetan sold 30 shares and bought 20 shares. But Michael only sold 10 shares. So finally both had the same number of shares. 197. (d) For the traffic to be evenly distributed at S, the cost on the routes SAT, SBAT, SBCT, SDCT, and SDT has to be the same.

Option (e) is ruled out as the traffic moves only on SBAT. Again (3) is ruled out as the traffic do not move to the SD route. Similarly in (2) and (4) the traffic can not be equally divided as there are various paths possible which makes the distribution unequal. But in (1), there are only three routes SAT, SBAT and SDT, which among themselves can divide the traffic equally. 198. (e) Street DT is not functional. For equal traffic through junctions A and C, the cost on routes SAT, SBAT, SBCT and SDCT shall be equal so that the traffic gets evenly distributed. This is true in case of option (e). Route Fuel cost Total cost SAT 14 14 + 0 = 14 SBAT 9 9 + 5 + 0 = 14 SBCT 7 7 + 5 + 2 = 14 SDCT 10 10 + 2 + 2 = 14 199. (b) Again the costs on all routes SAT SBAT, SDCT and SDT have to be equal so that all motorist pay the same amount. Route Fuel cost Total cost SAT 14 14 + 0 = 14 SBAT 9 9 + 5 + 0 = 14 SBCT 10 10 + 1 + 3 = 14 SDT 13 13 + 1 = 14 This is possible in option (b). 200. (d) In this case cost on all the 5 routes has to be the same.

So clearly (d) is the correct option. 201. (c) The minimum cost to the commuters is Rs 7 for the route SBCT with 100% traffic flowing through it. If we increase this cost by a Re (using tolls 0, 0, 1, 0), i.e. the minimum cost becomes Rs 8, still 100% traffic flows through B. Further increasing the minimum cost to 9 (using tolls 0, 0, 2, 0) the traffic flows through SBAT (2 + 2 + 5 = 9) and SBCT (2 + 3 + 2 + 2 = 9), but still 100% traffic flows through B. Again increasing the minimum cost to 10, the traffic can move through SBAT, SBCT and SDCT. The various situations are Route Cost Cost Cost (Toll) (0, 1, 2,0) (1, 0, 3, 0) (0, 3, 0, 0) SBAT 10 10 12 SBCT 10 10 10 SDCT 12 13 10 Traffic 100% 100% 50% through B So for minimum cost of Rs 10, the situation is fulfilled. For Qs. 202-206.

As the total Erdos no. of the group changes from 24 to 20, i.e. a difference of 4 and the Erdos no. of E becomes f + 1 after 5th day, it means the Erdos no of E was f + 1 + 4 = f + 5 after the third day. After 3rd day 5 mathematician have similar Erdos no. and the rest of 3 have distinct Erdos no. Hence 5 people have Erdos no. = f + 1 5(f + 1) + f + f + 5 + x = 24 7f + x = 14

The only values of f and x which satisfy this equation are f = 1 and x = 7 Note : The condition no other co-authorship among any 3 members would have reduced the avg. Erdos no to 3 means A followed by C had the largest Erdos no. at the beginning of the conference. 202. (b) The Erdos no. of C at the end of conference was f + 1 = 1 + 1= 2. 203. (c) The Erdos no. of E at the beginning of conference was f + 5 = 1 +5=6 [Note : that the Erdos no. of E did not changed till the third day as he did not co-authored any paper.] 204. (b) After 3rd day 5 participants had Erdos no. of f + 1. But A and C changed their Erdos no. to f + 1 on the third day itself. So, at the beginning of the conference only 3 participants had the same Erdos no. 205. (b) As calculated above, the Erdos no. of one of the participants was 7 (x) which do not change after the 5th day. 206. (d) During the conference, A and C changed their Erdos no. on the 3rd day and E changed its Erdos no. on the 5th day. So in all 5 participants do not change their Erdos no. 207. (c) Making K as a member Not included N, U, W Making M as a member Q, P, R, K, L So from above grids it is clear that K, L, P and R can not be a member of a team of size 5. 208. (a) Making L as a member This can not be a 3 member team as one from M/Q and R/P/S each has to be there. M can be member of a team of 3, viz. MPN, P and N again are members of MPN Q can be a member of QPN, QRN etc. 209. (e) If K is there, L has to be there. So N and U are out. Again as U is out so S and W will be out. So N, U, S and W are out. Now

from M and Q only one has to be there. Again from P, R, S only one has to be there. But S is out. So team can be so a team of only 4. 210. (e) If N is there, L is out and so K is also out. Also, one from M or Q has to be there. Similarly one from P, R and S has to be there. So teams using N, are NMP N M S UW NMR NQP NQR NQSUW Hence 6 teams can be constituted. 211. (d) The largest team size would be 5. For the largest team SUW has to be there. So P, R, K, L are out and only one from M or Q can be there. 212. (a) Total students = 800 Students in secondary section = Students in class XI/XII = Let the proportion of vegetarian students in XII = x ⇒ 80 × x + 80 × 0.5 + 640 × 0.55 = 0.53 × 800 ⇒ 80x = 424 – 40 – 352 = 32 ⇒ x= ∴

Percentage of vegetarian students in XII = 40%

213. (e) Vegetarian in class XII = ∴

Male vegetarians =

∴ Female vegetarians = 32 – 8 = 24 Males in class XII = 0.6 × 80 = 48

∴ Male non-vegetarians = 48 – 8 = 40 ⇒ Required difference = 40 – 24 = 16 214. (b) 80 × 0.6 + 80 × 0.55 + 640 × x = 0.475 × 800 ⇒ 48 + 44 + 640x = 380 ⇒ x= Percentage of male students in secondary section = 45% 215. (b) THIS QUESTION IS WRONG. 50% students in Secondary section are vegetarian males is not possible as we have just calculated that there are 45% males in the secondary section. Consider that 50% of vegetarian students of secondry section are males. Vegetarian students = 0.55 × 640 = 352 ∴

So, MVS = FVS = 176 Non-vegetarian students = 640 – 352 = 288 Total males = 288 (from above question) ∴ MN-VS = 288 – MVS = 288 – 176 = 112 Further F N-VS = NVS – MN-VS = 288 – 112 = 176 So, (2) is correct as MN-VS = 112 but MVS = FVS = FN-VS = 176. 216. (e) Carbohydrates Protein Fat Minerals (≥ 30%) (≥ 30%) (< 25%) (≥ 5%) (1) O & P 65% 25% 5% 5% (2) R & S 25% 50% 20% 5% (3) P & S 62.5% 35% 0% 2.5% (4) Q & R 7.5% 40% 45% 7.5% (5) O & S 47.5% 40% 5% 7.5% 217. (a) As the diet contains 10% minerals, it can be prepared only by mixing ingredients containing 10% mineral content. As none of the ingredients contains more than 10% minerals so we cannot

formulate a diet using an ingredient containing less than 10% minerals in whatever ratio we mix it. 218. (d) As we require 10% fat content so it cannot be formulated by mixing any two out of O, P and S as O contain 10% and P & S contain less than 10% fat content. So (b) is wrong. Similarly P and Q can not be mixed to give ≥ 30% protein content. So (a) is out. Diet Fat (10%) Ratio Cost P&R

10%

3:1

Q&S

10%

1:4

R&S

10%

1:3

[Note: For P & R, Ratio of mix = P : R ⇒ ⇒

30R = 10P or

219. (e) Ratio (a) 2 : 1 : 3

40R = 10P + 10R

⇒ ]

Carbohydrate content

Cost

—

(b) 4 : 1 : 2 × = 100 (c) 2 : 1 : 4

—

(d) 3 : 1 : 2

—

(e) 4 : 1 : 1 × = 83.3 220. (d) There may be an order in which the five horses finished the race as given in the different options: For option (a)

For option (b)

For option (c) For option (e)

For each of the above mentioned order so far option (a), (b), (c) and (e) respectively, total winning amount is Rs. 6000. That means there is no profit and no loss. Hence option (a), (b), (c) and (e) can be true. For option (d), two cases are possible : W ....................... R ....(i) R ......................... W ..(ii) In each cases winning amount is greater than Rs. 6000. Therefore, option (d) is not possible.

221. (c) There may be an order in which the five horses finished the race as given in the different options. For option (a)

For option (b)

For option (d)

For option (e)

For each of the above mentioned orders for option (a), (b), (d) and (e) respectively, total winning amount is Rs. 6000. That means there is no profit and no loss. Hence, option (a), (b), (d) and (e) can be true. Now for option (c), There are two cases arises Case (i) : If one of the two positions I and III occupied by spotted horse then the remaining of the two positions I and III will be occupy by one of the red or black horse. i.e., SWRG ....(i) SWBG ....(ii) RWSG ....(iii) BWSG ....(iv) For each (i), (ii), (iii) and (iv) order, winning amount is more than Rs. 6000. Case (ii) : If spotted horse comes at V position then the I and III positions occupied by the red and black horses in any order i.e., RWBGS ...(i) BWRGS ...(ii)

For each (i) and (ii) order, winning amount is more than Rs. 6000 Hence, option (c) is not possible. 222. (c) Since, Charlie got calls from only two colleges. So, the aggregate cut off marks of these two colleges will be mininum i.e. 171 and 175. Therefore, the two colleges from which Charlie got the calls are college 2 and 3. Now, the minimum marks obtained by Charlie in a section (say section A) can be find out by maximising the marks obtained in remaining three sections (B,C and D) like

If minimum marks obtained in a section is 21, then Charlie will get the call only from college 3. If minimum marks obtained in a section is 25, then Charlie will get the call from two colleges 2 and 3. 223. (b) Since, Bhama got calls from all colleges, hence minimum aggregate marks obtained by her = Sum of maximum cut-off of each section = 45 + 45 + 46 + 45 = 181. 224. (c) Four colleges have cut off for section C and the remaining two colleges have cut off for section D. Since, Aditya did not get a call from even a single college therefore, Aditya get less than the minimum cut off marks in section C (42) and less than the minimum cut off marks for section D (44). Hence, maximum aggregate marks obtained by Aditya = 50 (Section A) + 50 (Section B) + 41 (Section C) + 43 (Section D) = 184. For Qs. 225-228: As each team plays 3 matches in stage I and 2 matches in stage II so in stage I there would be 9 matches and in stage II there would be 6 matches. Stage I : There is one team which won all the matches in stage I, so it cannot be D, E, B, C or F as they all lost matches as per the observations of stage I. So A wins all 3 matches. • A, B, D & E won atleast one match. So it is C and F who lost all 3 matches.

• •

D has 2 wins (against C & F) and one loss (to A). E has 2 wins (against C & F) and one loss (to B). Hence, the situation after stage I observations is : A—3W D — 2W, 1L E — 2W, 1L C—3L F—3L B — 2 W, 1L i.e. 9W and 9L in all ( 9 matches.) Stage II : A lost its next 2 matches. • Out of C & F one wins its next two matches and the other loses the next 2 matches. As F did not play against A in stage I, so he will win against A in stage II. Thus F wins both matches and C loses both matches in stage II. • Out of the remaining 3 teams, viz. B, D and E, one team loses both matches. As there have to be 6 wins in all, so the other two will win both their matches. • E has played with B, C and F in stage I, so he plays with A and D in stage II. Thus E wins both its matches. • D played with A, C and F in stage I, so he plays with B & E in stage II. As E has won both its matches so D lost both its matches. Situation after stage II Stage I Stage II A 3W 2L B 2W, 1L 2W C 3L 2L D 2W, 1L 2L E 2W, 1L 2W F 3L 2W 225. (e) The teams which won exactly 2 matches in the event are D & F. 226. (e) The team with most wins are B and E (4 wins each). 227. (b) The matches in stage I : Plays with (wins or lose)

A — D (L) B — E (L) C — D (W), E (W) D — A (W), C (L), F (L) E — B (W), C (L), F (L) F — D (W), E (W) As F did not play with the top team (A) in stage I so only B, C, D and E can play with A. As E plays its matches with B, C and F so A plays with B,C and D in stage I and with E and F in stage II. Hence, E & F defeats A in stage II. 228. (d) B, E & F wins both their matches in stage - II. 229. (e) From the given information it is clear that U P1 and P10 > P3 Since price at 12 noon was lower than the opening price. So P10 > P12 Thus,

P10 > P12 > P1 > P3 > P2 > P11

Thus P10 is the highest share price which is at 10 am. 236. (a, d) From above,

P10 > P12 > P1

> P3 > P2 > P11 So, option (a) is necessarily false as P2 > P11. Also, (d) is necessarily false as P12 > P1.

Directions for questions 1 to 22 : From the given alternatives, select the one in which the pairs of words have a relationship similar to the one between the bold words. 1.

LYING

PERJURY (1994)

(a) (b) (c) (d) 2.

statement : seeing : taking : eating : PREHISTORIC

testimony observing stealing dining : MEDIEVAL (1994)

(a) (b) (c) (d) 3.

Akbar : present : Shakespeare : colossus : LOUD

British future Tennyson elephant : STENTORIAN (1994)

(a) mild (b) painful (c) adjective (d) bright 4. BUILDING

: : :

noisy prickly descriptive resplendent : STOREY (1995)

(a) book (b) sentence

: :

chapter adjective

: :

stem tusk :

ALLEVIATE (1995)

(a) (b) (c) (d) 6.

hint revolt collapse question SECRET

: : : :

allocate repudiate rise interrogate : CLANDESTINE (1995)

(a) (b) (c) (d) 7.

overt covert open news LIMPID

: : : :

furtive stealthy closed rumour : MURKY (1995)

(a) (b) (c) (d) 8.

dazed obscure bright nebulous DRAMA

: : : :

clouded vague gloomy dim : AUDIENCE (1995)

(a) (b) (c) (d) 9.

brawl obscure art movie LIQUIDITY

: : : :

vagabonds vague critics actors : GASEOUSNESS (1996)

(a) (b) (c) (d) 10.

serum humid thaw smoke DOUBT

: : : :

fume arid distil cloud : FAITH (1996)

(a) (b) (c) (d) 11.

atheist sceptic iconoclast apostate FISSION

: : : :

religious pious idol state : FUSION (1996)

(a) (b) (c) (d) 12.

implosion separation intrusion enemy ACTION

: : : :

explosion togetherness extrusion friend : REACTION (1996)

(a) (b) (c) (d) 13.

introvert assail diseased death DULCET

: : : :

extrovert defend treatment rebirth : RAUCOUS (1996)

(a) (b) (c) (d) 14.

sweet : crazy : palliative : theory : MALAPROPISM :

song sane exacerbating practical WORDS (1996)

(a) (b) (c) (d) 15.

anachronism : ellipsis : jinjanthropism : catechism : ANTERIOR

time sentence apes religion : POSTERIOR (1996)

(a) (b) (c) (d)

in top head front

: : : :

out bottom tail rear

16. BRICK

BUILDING (1996)

(a) (b) (c) (d) 17.

word alphabet platoon idiom PEEL

: : : :

dictionary letter soldier language : PEAL (1997)

(a) (b) (c) (d) 18.

coat laugh rain brain DOGGEREL

: : : :

rind bell reign cranium : POET (1997)

(a) (b) (c) (d) 19.

symphony prediction wine pulp fiction PREMISE

: : : :

composer astrologer vintner novelist : CONCLUSION (1997)

(a) (b) (c) (d) 20.

assumption hypothesis knowledge brand BARGE

: : : :

inference theory ideas marketing : VESSEL (1997)

(a) (b) (c) (d) 21.

shovel book rim training LOVE

: : : :

instrument anthology edge preparation : AFFECTION (1997)

(a) (b) (c) (d)

happiness amity enemy sorrow

: : : :

joy harmony hatred misery

22. PARADIGM

PATTERN (1997)

(a) (b) (c) (d)

skeleton method plant dinosaur

: : : :

flesh system genus tyrannosaurus

Directions for questions 23 to 27 : In each of the following questions a related pair of words or phrases is followed by five lettered pairs of words or phrases. Select the lettered pair that best expresses a relationship that is least similar to the one expressed in the original pair. 23. XENOPHOBIA

FOREIGNERS (1995)

(a) (b) (c) (d) 24.

claustrophobia : anglophobia : bibliophobia : hemophobia : SAIL

foreigners Englishmen book blood : SHIP (1995)

(a) (b) (c) (d) 25.

propeller radar hydrogen accelerator CANINE

: : : :

dog satellite balloon car : DOG (1995)

(a) (b) (c) (d) 26.

feline acquatic serpentine vulpine COSMIC

: : : :

cat parrot cobra fox : UNIVERSE (1995)

(a) (b) (c) (d)

terrestrial lunar connubial annular

: : : :

earth moon youth rumour

27. GERMANE

PERTINENT (1995)

(a) (b) (c) (d)

apt quick dull excited

: : : :

appropriate urgent sluggish serene

Directions for questions 1 to 21 : In the following questions, a set of four words is given. Three of the words are related in some way, the remaining word is not related to the rest. You have to pick the word which does not fit in the relation and mark that as your answer. 1. (b) (c) (d) 2. (b) (c) (d) 3. (b) (c) (d) 4. (b) (c) (d) 5. (b) (c) (d) 6. (b)

(a) quell ruffle allay pacify (a) couple sever rend lacerate (a) eulogy panegyric ignominy glorification (a) cease launch initiate commence (a) adroit adept dexterous awkward (a) brink hub

(1995)

(c) (d) 7. (b) (c) (d) 8. (b) (c) (d) 9. (b) (c) (d) 10. (b) (c) (d) 11. (b) (c) (d) 12. (b) (c) (d) 13. (b) (c) (d) 14. (b) (c) (d) 15. (b)

verge brim (a) detest abhor ardour loathe (a) fanatic zealot maniac rational (a) sporadic frequent intermittent scarce (a) taciturn reserved clamorous silent (a) hiatus break pause end (a) effusion intrusion percolation effluence (a) duplicity guilelessness artfulness shrewdness (a) impetuosity equanimity zealousness effervescence (a) taxi cruise

(1995)

(1996)

amble cab (a) keen kin enthusiastic willing (a) adept adapt skillful proficient (a) ring round bell circle (a) computer internet grid network (a) suffer endure ordeal withstand (a) break hiatus chasm bridge

(1996)

(1997)

Directions for questions 1 to 10 : For the word given at the top of each table, match the dictionary definitions on the left (A, B, C, D) with their corresponding usage on the right (E, F, G, H). Out of the four possibilities given in the boxes below the table, select the one that has all the definitions and their usages correctly matched.

Exceed (2001)

Infer (2001)

Mellow (2001)

Relief (2001)

Purge (2001)

Measure (2002)

Bound (2002)

Catch (2002)

Deal (2002)

10. Turn (2002)

Directions for questions 1 to 5 : For each of the words below, a contextual usage is provided. Pick the word from the alternatives given, that is most inappropriate in the given context. 1.

Specious : A specious argument is not simply a false one but one that has the ring of truth. (2001) (a) Deceitful (b) Fallacious (c) Credible (d) Deceptive 2. Obviate : The new mass transit system may obviate the need for the use of personal cars. (2001) (a) Prevent (b) Forestall (c) Preclude (d) Bolster 3.

Disuse : Some words fall into disuse as technology makes objects obsolete. (2001)

(a) Prevalent (b) Discarded (c) Obliterated (d) Unfashionable 4.

Parsimonious : The evidence parsimonious scraps of information. (a) Frugal

was

constructed

from very (2001)

(b) Penurious (c) Thrifty (d) Altruistic 5. Facetious : When I suggested that war is a method of controlling population, my father remarked that I was being facetious. (2001) (a) Jovian (b) Jovial (c) Jocular (d) Joking Directions for questions 6 to 10 : For each of the words below, a contextual usage is provided. Pick the word from the alternatives given, that is closest in meaning in the given context. 6.

Opprobrium : The police officer appears oblivious to the opprobrium generated by his blatantly partisan conduct. (2002)

(a) Harsh criticism (b) Acute distrust (c) Bitter enmity (d) Stark oppressiveness 7. Portends : It appears to many that the US “war on terrorism” portends trouble in the Gulf. (2002) (a) Introduces (b) Evokes (c) Spells (d) Bodes

Prevaricate : When a videotape of her meeting was played back to her and she was asked to explain her presence there, she started prevaricating. (2002)

(a) Speaking evasively (b) Speaking violently (c) Lying furiously (d) Throwing a tantrum 9. Restive : The crowd became restive when the minister failed to appear even by 10 p.m. (2002) (a) Violent (b) Angry (c) Restless (d) Distressed 10. Ostensible : Manohar’s ostensible job was to guard the building at night. (2002) (a) Apparent (b) Blatant (c) Ostentatious (d) Insidious Directions for Questions 11 to 14 : Each of the following questions has a paragraph with one italicized word that does not make sense. Choose the most appropriate replacement for that word from the options given below the paragraph. 11.

Intelligent design derives from an early 19th-century explanation of the natural world given by an English clergyman, William Paley. Paley was the populariser of the famous watchmaker analogy. Proponents of intelligent design are crupping Paley’s argument with a new gloss from molecular biology. (2005) (a) destroying (b) testing

(c) resurrecting (d) questioning 12. Women squat, heads covered, beside huge piles of limp fodder and blunk oil lamps, and just about all the cows in the three towns converge upon this spot. Sinners, supplicants and yes, even scallywags hand over a few coins for a crack at redemption and a handful of grass. (2005) (a) shining

(b) bright

(c) sputtering (d) effulgent 13. It is klang to a sensitive traveler who walks through this great town, when he sees the streets, the roads, and cabin doors crowded with beggars, mostly women, followed by three, four, or six children, all in rags and importuning every passenger for alms. (2005) (a) amusing (b) irritating (c) disgusting (d) distressing 14. Or there is the most fingummy diplomatic note on record: when Philip of Macedon wrote to the Spartans that, if he came within their borders, he would leave not one stone of their city, they wrote back the one word - “If’. (2005) (a) witty (b) rude (c) simple (d) terse

Directions for Questions 1 to 5 : Four statements with blanks have been given. These statements are followed by four alternatives. Choose the one which fits into the set of statements the maximum number of times. 1. B.

A. Professional studies has become the ___________ of the rich. (1994) Every citizen has the ___________ to speak, travel and live as he pleases.

C. He has a definite ___________ over all his rivals. D. Sheron no longer has the ___________ of the company’s bungalow and car. (a) advantage (b) privilege (c) right (d) concession 2.

A. People .

sensed

___________

(1994) A bad ___________ case had come in - a person with a smashed arm.

C. And then, without warning, ___________ struck. D. The dogs were the first to recognize the signs of oncoming ___________ . (a) tragedy (b) accident (c) disaster (d) calamity 3. B.

A. The men there have fought ___________ and emotional withdrawal, and were more capable of helping Jim (1994) But ___________ does occasionally inflict all the adults.

C. A person who is deeply hurt feels very ___________ . D. It is hard to survive this feeling of ___________ .

(a) dejection (b) lonely (c) trouble (d) depression 4. A. I have . (1994)

had

small

power

___________

Down with a very high fever, he suffers from frequents fits of ___________ . C. They are now bitter enemies - all because of a small ___________ . D. Her ___________ is the most creative thing she has ever possessed. (a) illusion (b) imagination (c) hallucination (d) misunderstanding 5.

A. Communism states that every individual must live for the ___________ . (1994)

The ___________ of the affairs of the nation is deplorable.

___________ have been laid down by the United States : states The Statesman.

D. No ___________ has succeeded in gaining complete autonomy from the Federal government. (a) state (b) nation (c) government (d) condition

Directions for Questions 1 to 54 : In each of the following questions, a part / two of a sentence has been left blank. You are to select from among the four options given below each question, the one which

would best fill the blanks. In case of more than one blanks, the first word in the pair, given in the choices, should fill the first gap. 1. (a) (b) (c) (d) 2. (a) (b) (c) (d) 3. (a) (b) (c) (d) 4. (a) (b) (c) (d) 5.

(a) (b) (c) (d)

One dark night a Darvesh ___________ passing by a dry well. (1994) wasn’t happened to be discovered in found to Nordisk have recently ___________ a product called Glucometer. (1994) started commissioned launched begun I had already published a novel and it was an unexpected success. I thought my ___________ . (1994) days were up chances were good lady luck was happy fortune was made The neighbour grabbed the boy, and rolled him on the road to ___________ the flames. (1994) smother kill burn out fizz out Sam asked me to keep this secret ___________ . (1994) secret in myself amongst us between us

6. (a) (b) (c) (d) 7. (a) (b) (c) (d) 8. (a) (b) (c) (d) 9.

(a) (b) (c) (d) 10. (a) (b) (c) (d)

Sometimes the greatest inventions ___________ an idea of startling simplicity. (1994) stumbles upon hinge upon starves without lacks Real friends, genuinely wanting the best for the organization, ___________ different garbs. (1994) come in clad in dressed in clothed in I am an entertainer, ___________ , I have to keep smiling because in my heart laughter and sorrow have an affinity. (1996) even if I have tears in me even though I am depressed inside while entertaining people in the entertainment business Political power is just as permanent as today’s newspaper. Ten years down the line, ___________, who the most powerful man in any state was today. (1996) who cares nobody will remember what was written in today’s newspaper or few will know, or care about when a lot of water will have passed under the bridge, who will care When we call others dogmatic, what we really object to is ___________ . (1996) their giving the dog a bad name their holding dogmas that are different from our own the extremism that goes along with it the subversion of whatever they actually believe in concomitantly

11.

(a) (b) (c) (d) 12.

(a) (b) (c) (d) 13. (a) (b) (c) (d) 14. (a) (b) (c) (d) 15. (a) (b) (c) (d) 16.

Although it has been more than 50 years since Satyajit Ray made Pather Panchali, ___________ refuse to go away from the mind. (1996) the haunting images its haunting images its haunted images the haunt of its images ___________, the more they remain the same. (1996) People all over the world change The more people change The more they are different The less people change The stock markets ___________. The state they are in right now speaks volumes about this fact. (1996) is the barometer of public confidence are the best indicators of public sentiment are used to trade in expensive shares are not used to taking stock of all markets An act of justice closes the book on a misdeed; an act of vengeance ___________ . (1997) writes one of its own opens new books reopens the first chapter writes an epilogue This is about ___________ a sociological analysis can penetrate. (1997) as far as the outer limit that just how far into the subject just the relative distance that I am always the first to admit that I have not accomplished everything that I ___________ achieve five years ago. (1997)

(a) (b) (c) (d) 17. (a) (b) (c) (d) 18. (a) (b) (c) (d) 19. (a) (b) (c) (d) 20.

(a) (b) (c) (d) 21.

(a)

set out to went to thought to thought of This is not the first time that the management has done some ___________ . (1997) tough talk tough talking firm talk firm talking In India the talent is prodigious, really, and it increases ___________ (1997) each year year by year annually progressively The present Constitution will see ___________ amendments but its basic structure will survive. (1997) much more many more too many more quite a few more Taking risks, breaking the rules, and being a maverick have always been important for companies, but, today, they are ___________ . (1997) more crucial than ever more crucial much more crucial very crucial Education is central because electronic networks and software-driven technologies are beginning to ___________ the economic barriers between nations. (1997) break down

(b) (c) (d) 22. (a) (b) (c) (d) 23.

(a) (b) (c) (d) 24.

(a) (b) (c) (d) 25. (a) (b) (c) (d) 26.

break crumble dismantle Football evokes a ___________ response in India compared to cricket, the almost ___________ the nation. (1998) tepid, boiling lukewarm, electrifies turbid, fascinating apocryphal, genuinely fascinates Social studies, science matters of health and safety, the very atmosphere of the classroom - these areas are few of the ___________ for the ___________ of proper emotional reactions. (1998) things, growth fertile areas, basis fertile fields, inculcation important areas, formation When children become more experienced with words as visual symbols, they find that they can gain meaning without making ___________ sounds. (1998) aural audible vocal intelligible Learning is more efficient when it is ___________, less efficient when it is ___________ . (1998) fast, slow rapid, turtle-slow tedious, like a joy ride fun, drudgery To a greater or lesser degree all the civilized countries of the world are made up of a small class of rulers, ___________ , and of a large class of subjects,

___________. (a) (b) (c) (d) 27. (a) (b) (c) (d) 28. (a) (b) (c) (d) 29. (a) (b) (c) (d) 30.

(a) (b) (c) (d) 31.

(1998) formed by a small minority, who are uncivilized powerfully corrupt, pointless crusaders corrupted by too much power, corrupted by too much passive obedience who are ruled, who ruled Simple arithmetic tells us that there is more ___________ than ___________ . (1998) imitation, innovation improvisation, improvement impracticality, knowledge improbability, probability As a step towards protesting against the spiralling prices, the farmers have decided to stage a picket in an effort to ___________.(1998) show their virility make themselves heard curb the prices topple the government Science is a sort of news agency comparable ___________ to other news agencies. (1998) principally in principle in principal in spirit and form Most political leaders acquire their position by causing a large number of people to believe that these leaders are ___________ by altruistic desires. (1998) actuated convinced categorised led Every one will admit that swindling one’s fellow beings is a necessary practice; upon it, is based really sound commercial success

___________. (1998) (a) (b) (c) (d) 32.

sell what you cannot buy back buy what you will sell to another at a higher price buy cheap and sell dear sell what you can, do not buy from a competitor Though one eye is kept firmly on the___________, the company now also promotes ___________ contemporary art. (2000)

(a) present, experimental (b) future, popular (c) present, popular (d) market, popular 33. The law prohibits a person from felling a sandalwood tree, even if it grows on one’s own land, without prior permission from the government. As poor people cannot deal with the government this legal provision leads to a rip-roaring business for ___________, who care neither for the ___________ , nor for the trees. (2000) (a) middlemen, rich (b) the government, poor (c) touts rich (d) touts, poor 34. It will take some time for many South Koreans to ___________ the conflicting images of North Korea, let alone to___________ what to make of their northern cousins. (2000) (a) reconcile, decide (b) understand, clarify (c) make out, decide (d) reconcile, understand

35. In these bleak and depressing times of ___________ prices, nonperforming governments and ___________ crime rates, Sourav Ganguly has given us, Indians, a lot to cheer about. (2000) (a) escalating, increasing (b) spiralling, booming (c) spiralling, soaring (d) ascending, debilitating 36. The manners and ___________ of the nouveau riche is a recurrent ___________ in the literature. (2000) (a) style, motif (b) morals, story (c) wealth, theme (d) morals, theme 37. But ___________ are now regularly written not just for tools, but well - established practices, organisations and institutions, not all of which seem to be ___________ away. (2001) (a) reports, withering (b) stories, trading (c) books, dying (d) obituaries, fading 38. The Darwin who ___________ is most remarkable for the way in which he ___________ the attributes of the world class thinker and head of the household. (2001) (a) comes, figures (b) arises, adds (c) emerges, combines (d) appeared, combines

39. Since her face was free of ___________ there was no way to ___________ if she appreciated what had happened. (2001) (a) make-up, realise (b) expression, ascertain(c) emotion, diagnose (d) scars, understand 40. In this context, the ___________ of the British labour movement is particularly ___________ .(2001) (a) affair, weird (b) activity, moving (c) experience, significant (d) atmosphere, gloomy 41. Indian intellectuals may boast, if they are so inclined, of being ___________ to the most elitist among the intellectual ___________ of the world. (2001) (a) subordinate, traditions (b) heirs, cliques (c) ancestors, societies (d) heir, traditions 42. Companies that try to improve employees’ performance by ___________ rewards encourage negative kind of behavior instead of ___________ a genuine interest in doing the work well. (2003C) (a) withholding, fostering (b) conferring, discrediting (c) bestowing, discouraging (d) giving, seeking 43. A growing number of these expert professionals ___________ having to train foreigners as the students end up ___________ the teachers who have to then unhappily contend with no jobs at all or new jobs with drastically reduced pay packets. (2003C)

(a) are, supplanting (b) welcome, assisting (c) resist, challenging (d) resent, replacing 44. The___________ regions of Spain all have unique cultures, but the ___________ views within each region make the issue of an acceptable common language of instruction an even more contentious one. (2003C) (a) different, competing (b) divergent, distinct (c) distinct, disparate (d) different, discrete 45. Early___________ of maladjustment to college culture is ___________ by the tendency to develop friendship networks outside college which mask signals of maladjustment. (2003C) (a) prevention, helped (b) identification, complicated (c) detection, facilitated (d) treatment, compounded 46. The British retailer, M&S, today formally ___________ defeat in its attempt to ___________ King’s, its US subsidiary, since no potential purchasers were ready to cough up the necessary cash. (2003C) (a) ratified, auction (b) announced, dispose (c) conceded, offload (d) admitted, acquire 47. This simplified ___________ to the decision-making process is a must read for anyone ___________ important real estate, personal, or professional

decisions. (2003) (a) primer, maximizing (b) tract, enacting (c) introduction, under (d) guide, facing 48. Physicians may soon have ___________ to help paralyzed people move their limbs by bypassing the ___________ nerves that once controlled their muscles. (2003) (a) instruments, detrimental damaged (c) reason, involuntary

(b) ways,

(d) impediments, complex 49. The Internet is a medium where users have nearly ___________ choices and ___________ constraints about where to go and what to do. (2003) (a) unbalanced, nonexistent (b) embarrassing, no (c) unlimited, shocking

minimal

(d) choking,

50. The best punctuation is that of which the reader is least conscious; for when punctuation, or lack of it, ___________ itself, it is usually because it ___________. (2003) (a) obtrudes, offends (b) enjoins, fails (c) conceals, recedes (d) effaces, counts

51. The argument that the need for a looser fiscal policy to ___________ demand outweighs the need to ___________ budget deficits is persuasive. (2003) (a) assess, minimize (b) outstrip, eliminate (c) stimulate, control (d) restrain, conceal 52. The Athenians on the whole were peaceful and prosperous; they had ___________ to sit at home and think about the universe and dispute with Socrates, or to travel abroad and ___________ the world. (2003) (a) leisure, explore (b) time, ignore (b) ability, suffer (d) temerity, understand 53. Their achievement in the field of literature is described as ___________; sometimes it is even called ___________. (2003) (a) magnificent, irresponsible (b) insignificant, influential (c) significant, paltry (d) unimportant, trivial 54. From the time she had put her hair up, every man she had met had groveled before her and she had acquired a mental attitude toward the other sex which was a blend of ___________ and ___________. (2003) (a) admiration, tolerance (b) indifference, contempt (c) impertinence, temperance (d) arrogance, fidelity Directions for Questions 55 to 58 : Each of the following questions has a sentence with two blanks. Given below each question are five

pairs of words. Choose the pair that best completes the sentence. 55. The genocides in Bosnia and Rwanda, apart from being misdescribed in the most sinister and _________ manner as ‘ethnic cleansing’, were also blamed, in further hand-washing rhetoric, on something dark and interior to __________ and perpetrators alike. (2008) (a) innovative; communicator (b) enchanting; leaders (c) disingenuous; victims (d) exigent; exploiters (e) tragic; sufferers 56. As navigators, calendar makers, and other _________ of the night sky accumulated evidence to the contrary, ancient astronomers were forced to __________ that certain bodies might move in circles about points, which in turn moved in circles about the earth. (a) scrutinizers; believe (b) observers; agree (2008) (c) scrutinizers; suggest (d) observers; concede (e) students; conclude 57. Every human being, after the first few days of his life, is a product of two factors: on the one hand, there is his __________ endowment; and on the other hand, there is the effect of environment, including _________. (2008) (a) constitutional; weather (b) congenital; education (c) personal; climate (d) economic; learning (e) genetic; pedagogy 58. Exhaustion of natural resources, destruction of individual initiative by governments, control over men’s minds by central _________ of education and propaganda are some of the major evils which appear to be on the increase as a result of the impact of science upon minds

(a) (b) (c) (d) (e)

suited by ___________ world. tenets; fixation aspects; inhibitions institutions; inhibitions organs; tradition departments; repulsion

earlier (2008)

kind

Directions for questions 1 to 16 : Fill in the blanks, numbered [1], [2] ......up to [16], in the passages below with the most appropriate word from the options given for each blank. Be guided by the author’s overall style and meaning when you choose the answers. ☛

Von Nuemann and Morgenstern assume a decision framework in which all options are thoroughly considered, each option being independent of the others, with a numerical value derived for the utility of each possible outcome (these outcomes reflecting, in turn, all possible combinations of choices). The decision is then made to maximize the expected utility. [1], such a model reflects major simplifications of the way decisions are made in the real world. Humans are not able to process information as quickly and effectively as the model assumes; they tend not to think [2] as easily as the model calls for; they often deal with a particular option without really assessing its [3], and when they do assess alternatives, they may be extremely nebulous about their criteria of evaluation.

(a) Regrettably

(b) Firstly (c) Obviously (d) Apparently 2.

(a) Quantitatively

(b) Systematically

(2002)

(a) Implications

(b) Disadvantages (c) Utility (d) Alternatives ☛

(2002)

In a large company, [4] people is about as common as using a gun or a switch-blade to [5] an argument. As a result, most managers have little or no experience of firing people, and they find it emotionally traumatic; as result, they often delay the act interminably, much as an unhappy spouse will prolong a bad marriage. And when the firing is done, it’s often done clumsily, with far worse side effects than are necessary.

Do the world-class software organizations have a different way of firing people? No, but they do the deed swiftly, humanely, and professionally. The key point here is to view the fired employee as a “failed product” and to ask 4. (b) (c) (d) 5. (b) (c) (d) 6. (b) (c) (d) ☛

how the process [6]such a phenomenon in the first place. (a) dismissing punishing firing admonishing (2002) (a) resolve thwart defeat close (2002) (a) derived engineered produced allowed (2002) At that time the White House was as serene as a resort hotel out of season. The corridors were [7]. In the various offices, [8] gray men in

waistcoats talked to one another in low-pitched voices. The only color, or choler, curiously enough, was provided by President Eisenhower himself. Apparently, his [9] was easily set off; he scowled when he [10] the corridors. 7. (a) striking (b) hollow (c) empty (d) white 8. (a) quiet (b) faded (c) loud (d) 9. (b) (c) (d) 10. (b) (c)

(2004 - ½ mark)

stentorian (2004 - ½ mark) (a) laughter curiosity humour temper (2004 - ½ mark) (a) paced strolled stormed

(d) prowled (2004 - ½ mark) ☛ “Between the year 1946 and the year 1955, I did not file any income tax returns.” With that [11] statement, Ramesh embarked on an account of his encounter with the Income Tax Department . “I originally owed Rs. 20,000 in unpaid taxes. With [12] and [13], the 20,000 became 60,000. The Income Tax Department then went into action, and I learned first hand just how much power the Tax Department wields. Royalties and trust funds can be [14]; automobiles may be [15], and auctioned off. Nothing belongs to the [16] until the case is settled.” 11.

(a) devious

(b) blunt

pretentious (2004 - ½ mark) (a) interest taxes principal returns (2004 - ½ mark) (a) sanctions refunds fees

(d) 14. (b) (c) (d) 15. (b) (c)

fines (2004 - ½ mark) (a) closed detached attached impounded (2004 - ½ mark) (a) smashed seized dismantled

(d) 16. (b) (c)

frozen (2004 - ½ mark) (a) purchaser victim investor

(d) offender

(2004 - ½ mark)

Directions for Questions 1 to 16 : In each question, the word at the top is used in four different ways, numbered (a) to (d). Choose the option in which the usage of the word is Incorrect or Inappropriate. 1.

SORT (2003C)

HOST (2003C)

IMPLICATION (2003C)

DISTINCT (2003C)

BUNDLE (2003C)

HELP (2003)

REASON (2003)

PAPER (2003)

BUSINESS (2003)

10. SERVICE (2003)

11.

BOLT (2004)

12. PASSING (2004)

13. FALLOUT (2004)

14. FOR (2005)

15. HAND (2005)

16. NEAR (2005)

Directions for Questions 17 to 20 : In each of the questions, a word has been used in sentences in five different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate. 17. RUN (2008)

18. ROUND (2008)

19. BUCKLE (2008)

20. FILE (2008)

Directions for Questions 1 to 4 : In each question, there are five sentences. Each sentence has a pair of words that are italicized and highlighted. From the italicized and highlighted words, select the most appropriate words (A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may be selected to correctly complete the set of sentences. From the options given, choose the most appropriate one. 1.

The cricket council that was [A] / were [B] elected last March is [A] / are [B] at sixes and sevens over new rules.

The critics censored [A] / censured [B] the new movie because of its social unacceptability. Amit’s explanation for missing the meeting was credulous [A] / credible [B]. She coughed discreetly [A] / discretely [B] to announce her presence. (2007) (a) BBAAA (b) AAABA (c) BBBBA (d) AABBA (e) BBBAA 2.

The further [A] /farther [B] he pushed himself, the more disillusioned he grew.

For the crowds it was more of a historical [A] / historic [B] event; for their leader, it was just another day. The old man has a healthy distrust [A] / mistrust [B] for all new technology. This film is based on a real [A] / true [B] story. One suspects that the compliment [A] / complement [B] was backhanded. (2007) (a) BABAB (b) ABBBA (c) BAABA

(d) BBAAB (e) ABABA 3.

Regrettably [A] / Regretfully [B] I have to decline your invitation.

I am drawn to the poetic, sensual [A] / sensuous [B] quality of her paintings. He was besides [A] / beside [B] himself with age when I told him what I had done. After brushing against a stationary [A] / stationery [B] truck my car turned turtle. As the water began to rise over [A] / above [B] the danger mark, the signs of an imminent flood were clear. (2007) (a) BAABA (b) BBBAB (c) AAABA (d) BBAAB (e) BABAB 4.

Anita wore a beautiful broach (A)/brooch(B) on the lapel of her jacket.

If you want to complain about the amenities in your neighbourhood, please meet your councillor (A)/counsellor (B). I would like your advice(A)/advise(B) on which job I should choose. The last scene provided a climactic(A)/climatic(B) ending to the film. Jeans that flair(A)/flare(B) at the bottom are in fashion these days. (2008) (a) BABAA (b) BABAB (c) BAAAB (d) ABABA (e) BAABA

The cake had lots of currents(A)/currants(B) and nuts in it.

If you engage in such exceptional(A)/exceptionable(B) behaviour, I will be forced to punish you. He has the same capacity as an adult to consent(A)/assent(B) to surgical treatment. The minister is obliged(A)/compelled(B) to report regularly to a parliamentary board. His

analysis of (A)/genuine(B).

the

situation

far

too

sanguine

(2008) (a) BBABA (b) BBAAA (c) BBBBA (d) ABBAB (e) BABAB 6.

She managed to bite back the ironic(A)/caustic(B) retort on the tip of her tongue.

He gave an impassioned and valid(A)/cogent(B) plea for judicial reform. I am not adverse(A)/averse(B) to helping out. The coupé(A)/coup(B) broke away as the train climbed the hill. They

heard wide.

the

bells

peeling(A)/pealing(B)

far and (2008)

(a) BBABA (b) BBBAB (c) BAABB (d) ABBAA (e) BBBBA 7.

We were not successful in defusing(A)/diffusing(B) the Guru’s ideas.

The students baited(A)/bated(B) the instructor with irrelevant questions.

The hoard(A)/horde(B) rushed into the campus. The prisoner’s interment(A)/internment(B) came to an end with his early release. The hockey team could not deal with his unsociable (A)/unsocial(B) tendencies. (2008) (a) BABBA (b) BBABB (c) BABAA (d) ABBAB (e) AABBA

ANSWERS WITH SOLUTIONS TYPE - A 1.

3. 4.

(a) Perjury means to swear falsely under oath. The relationship between the two words therefore is of degree. Similarly testimony means a statement under oath. While other pairs either differ in meaning or manner. (b) The relation between the two words is that of chronology, prehistory came before medieval times just as present comes before future. Even though Akbar came before British and Shakespeare before Tennyson these are people, while the given pair of words are divisions of time. (d) The relation between the pair is that of degree. Stentorian means very loud just as resplendent means very bright. Other pair do not have a relationship of degree. (a) The relation between the two words is that of component and whole, like a building is made of many storeys, a book is made of many chapters, a sentence is not made of many adjectives, it also has other different components, same for tree-stem and elephant-tusk pairs. (d) The relation between the two words is that of degree. Alleviate means the same as ease but higher in degree, just as interrogate is higher in degree to question. Repudiate means to reject or

(b)

(c)

(a)

10. (b)

11.

(b)

12. (b) 13. (b)

14. (a) 15. (d) 16. (a)

disown and allocate means to assign. No other pair has a similar relationship. The relation between the two words is synonyms. Secret and Clandestine are synonyms just as covert and stealthy are synonyms, furtive means stealthy, overt means obvious. Relation between the words is of antonym. Limpid means clear and murky means dark, unclear. Dazed means stunned or bewildered, clouded means unclear or confused. Obscure means indirect, indistinct and vague means not clear, nebulous means indistinct. Gloomy and bright are also antonyms. Drama is done for audience and the two are intrinsically connected just as Art is for the gaze of the critic. Brawl is a fight. The given words are two different states of matter — Liquid and gas. Serum and fume also are in different states of matter like liquid and gas. Arid means dry and humid means moist. Relation between the two words is of antonyms. Sceptic is a person with doubt and pious is the person with faith. Atheist is a person who does not believe in god, hence there is no doubt. Iconoclast is a person who attacks cherished belief. Fission means breaking while fusion is combining. Separation and togetherness also have the same relation with each other. Intrusion means to come uninvited and extrusion is to squeeze out. Reaction is in response to an action just as a defence is in response to an attack. All other pairs have a different relationship. Dulcet means sounding sweet, raucous means loud and harsh, the two words are thus antonyms. Palliative means to excuse and exacerbate means to irritate or make worse, crazy and sane are antonyms. Malapropism means comical confusion of words, similarly anachronism is related to time, ellipsis is a kind of punctuation. Catechism is a series of questions. Posterior means the rear and anterior means the front. Relation is of component to whole. Words together constitute a dictionary. Letter also constitute an alphabet just as soldiers form a platoon, but in these pairs the relation is reverse whole : component.

17. (c) The given pair are homophones, i.e., they have the same sound, same as rain & reign. 18. (d) Doggerel is written by a poet just as symphony is made by a composer but Doggerel is a bad poem just as pulp fiction is bad writing by a novelist. 19. (a) A conclusion is drawn from a premise, similarly an inference can be drawn from an assumption. Hypothesis is also an assumption but a theory is a usually drawn from proofs. 20. (a) A barge is a kind of vessel. A similar relation is between shovel and instrument. A book can be an anthology (a collection of works) but it is not necessarily so. 21. (d) The relation in the given pair of words is that of degree. Affection is higher degree of love. Just as misery is a higher degree for sorrow. Joy and happiness are simply synonyms. 22. (b) Paradigm is an example or a model for something. So a pattern can be a type of paradigm. Method and system have a similar relation to each other just as there can be various methods of a particular process, and a system of doing it. None of the other pairs have a similar relation. 23. (a) Xenophobia is fear for foreigners, anglophobia is fear of Englishmen, bibliophobia is fear of book and hemophobia is fear of blood but claustrophobia is fear of closed spaces and thus this does not have the same relation as in given pair. 24. (a) Sail helps a ship move. Same is the relation between all the pair except propeller and dog. 25. (b) Dog belongs to category of Canine mammals. Parrot does not belong to the acquatic category (water inhabiting animals). 26. (c) Cosmic is related to universe; cosmic means “of the universal”, just as terrestrial means “of the land”. Connubial means of the marriage and not youth. Thus this pair has a relation different from the given one. 27. (d) Germane and pertinent are synonyms as are all pairs except excited and serene which are antonyms. TYPE - B 1. (b) Ruffle means to disarrange, while quell, allay and pacify all mean to harmonise, suppress or bring to peace. 13. (d) Seeing the wretched condition of the state no one can be amused (happy). Among irritated (annoyed), disgusting

14.

(sickening, distasteful) and distressing (disturbing, painful, traumatic) the last one seems to be most appropriate in the given context. (d) The context here is diplomatic, so simple is ruled out as a simple statement or remark can not be diplomatic similarly a rude remark can not be diplomatic as it is straightforward and tactless. Witty is also ruled out as a witty remark must contain an element of humour. So the correct option is ‘terse’, which means to the point, laconic. Moreover use of ‘most’ is also an important indicator.

(b)

(c)

(d)

(b)

(a)

TYPE - E Privilege is the only word that can fit in 3 sentences, A, B & D. Right fits into B & D but not in other 2, advantage fits only in C, concession fits in none. Disaster fits in A, C, D. Accident fits only in B, tragedy in A & C and calamity in C. Depression fits in A, B and D while lonely only fits in C. Dejection can fit in A and D, trouble does not fit in any of the blanks. Imagination fits in A and D, hallucination fits in B and misunderstanding fits in C. The word state fits in A, B & D even though in different usage, government may fit in D and condition fits in C. TYPE - F

1. 2. 3. 4. 5. 6.

(b) Discovered or found should be preceded by an auxiliary verb like was, wasn’t cannot be an apt word. (c) A product is launched not commissioned or even started. (d) Fortune was made means he was settled as a success. Days were up suggests an ending, chances are talked of before the result. Lady luck cannot fit as mentioned here. (a) Flames can only be smothered to be put out, so the answer is (a). (d) The answer is between us (d), as the secret was between Sam and the Speaker. Amongst is used for more than two people. (b) The answer is (b), as the sentence is based on the fact that success depends upon (hinge upon) a simple idea. The other three choices suggest a negative relationship between invention and simplicity.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

20. 21. 22.

(a) Although garb means cloth and thus option b, c & d will appear as probable answer. In this sentence the use of garb goes well with ‘come’. Real friends come in different clothes (forms, appearances etc.) (b) Since the speaker talks both of laughter and sorrow, and uses ‘have to keep smiling’ instead of ‘I keep smiling’ there must be mention of sorrow in the first part of the sentence. (c) As political power in transient, i.e. lasting for a short time thus few people will know or care about people currently in power ten years hence. (b) Dogma means a set of principle, dogmatic usually refers to being strict about one’s own belief and not very accepting of different voices. (b) ‘its’ refer to the film, the images are ‘haunting’ and not ‘haunted’. (b) The sentence builds a sense of paradox, suggesting that with change similarities also increase and not the other way round. (b) The stock market reflects public sentiments. (c) An act of justice puts an end to a misdeed thus closing the chapter but an act of vengeance can trigger another cycle of violence and misdeed so going back to the first chapter. (a) If ‘just’ is to be used in the sentence it should be before ‘about’. ‘As far as’ is the only grammatically correct option. (a) ‘Set out to’ means set the goal of, thought of should have been followed by ‘achieving’ not ‘achieve’. (b) ‘tough talking’ is an expression usually used to suggest strict attitude of a management towards employees. (b) ‘Year by year’ fits better than all other choices with ‘prodigious’ talent. Annually implies once in a year. Progressively is used for individual talent. (b) The amendments would be many more, keeping the basic structure of the constitution the same. ‘Much’ is used with uncountable noun and amendments are countable, too many more and quite a few more are wrong grammatical usages. (a) Taking risks, breaking the rules and being a maverick are ‘more crucial than ever’. (a) The economic barrier will break down. Crumble is not used with barrier. (b) The response to football is lukewarm, while to cricket is electrifying. Lukewarm means mild or mellow.

23. (d) Social studies, science, matters of health and safety are all fields which will aid in the formation of emotional reactions. 24. (b) Audible sounds are those which can be heard. 25. (d) Efficient learning is fun whereas dull work or drudgery makes learning less efficient. 26. (c) Rulers are corrupted by power whereas subjects are corrupted by passive obedience. 27. (a) Innovations are much rare whereas imitations are much more common. Arithmetic deals with operation on numbers where some numbers are operated on for different results but there is rarely an innovation. 28. (b) The farmers want their protests against the spiralling prices, to be heard and that is the purpose of the staging of a picket. Other options are not suitable. 29. (b) As a news agency science is comparable in principle to other news agencies. Both share the principle of reaching and exposing the truth. 30. (a) Political leaders make a large number of people believe that they are actuated (motivated) by the desire to do good. 31. (c) Commercial success is based upon buying cheap and selling dear. This also entails swindling, that is, cheating. Only through sly moves and fooling others can you sell a cheap product at a high cost. 2. (a) Couple means to bring two things together. Other terms suggest a separation or cutting away. 3. (c) Ignominy is to cause disgrace, eulogy, panegyric and glorification means to praise excessively. 4. (a) Cease means to stop; commence, initiate, launch all mean to start. So cease is odd one among these. 5. (d) Adroit, adept and dexterous are synonyms and means skillful. 6. (b) Brink, verge and brim are synonyms and mean edge while hub means in between. 7. (c) Detest, abhor and loathe mean to hate while ardour means love, affection. 8. (d) Rational is person with balance of mind while a maniac, fanatic and zealot have irrational and imbalanced surge of emotion. 9. (d) Scarce means little, while the other words means unstopped, quick, spo

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