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Section - I 1. In a square ABCD of side length 1 unit, an arc is drawn with center at A and radius equal to AB. Another circle is drawn tangent to the arc and the sides BC and CD. A third circle is drawn tangent to the previous circle, the arc and the side CD. What is the radius of this circle?

(1) 2( 2 1)

2−

(2) 2( 2 1)

4+

(3) 0.071 (4) 0.05 (5) none of the above

2.The sum of 19 consecutive positive integers equals p3 where p is a prime number. Then the smallest of these 19 integers is (1) 354 (2) 353 (3) 352 (4) 351 (5) None of these 3.Given quadrilateral ABCD, with BC||AD, AB = BC = CD = 5. What can be the maximum area of the quadrilateral? (1) 25 (2) 32 (3) 18.75 3 (4) 18.25 3 (5) None of these 4. Simpu and Pankaj are going to the Patiala house 20 km from their home. The two of them have one bicycle together. The bicycle can only bear one rider at a time. They decide that Simpu will walk first and Pankaj will go by bike to some point along the way where he puts the bike down and continues on foot. When Simpu reaches that point, he will get on the bike and cycle to the Patiala house. Simpu's speed is 5 km/h on foot and 12 km/h by bike. Pankaj walks at 4 km/h and bikes at 10 km/h. If they start out together, how many kilometers should Pankaj cover by bike so that they get to the Patiala house at the same time? (1) 12.5 km (2) 13.5km (3) 14.5km (4) 10.5km (5) None of these 5. The number 99 999 989 999 is multiplied by itself. What is the number of nines in the result? (1) 8 (2) 9 (3) 10 (4) 11 (5) None of these 6. The Function f has its domain the set of ordered pairs of positive integers. Function f satisfies the following properties: • f(x, x) = x • f(x, y) = f( y, x) • (x + y) f(x, y) = y f(x, x + y) Then the value of f(18, 50) is (1) 180 (2) 360 (3) 420 (4) 450 (5) none of the above 7.The product of two of the four roots of the quartic equation x4 - 256 x3 + kx2 - 494x - 2008 = 0 is 8. Find the value of k. (1) 1255 (2) 1257 (3) 1269 (4) 1271 (5) None of these



8. f(x) is a linear function. If, for all real x, f(f(f( x))) = f(x), How many solutions for f(x) are possible? (1)0 (2) 1 (3) 2 (4) 3 (5) infinite 9.A product of three consecutive integers has the form abcabc. How many sets of such consecutive integers are possible? (1) 1 (2) 2 (3) 3 (4) 4 (5) None of these

10. A triangle has side lengths of 1, 1 and 3 . Three mutually externally tangent circles are then drawn, each centered at one of the three vertices of the triangle. Find the fraction of the triangles area that lies within the circles.

(1) (7 3 6)

2 3−π

(2) (7 3 6)

8 3−π

(3) (17 8 3)

6 3

−π (4)

(7 2 3)4−π

(5) None of these

11. Which one of the following numbers cannot be the area of a triangle with perimeter 60? (1) 96 (2) 121 (3) 144 (4) 169 (5) 175 12. How many two-element subsets {a, b} of {1, 2, 3,… 16} satisfy that ab is a perfect square? (1) 5 (2) 6 (3) 7 (4) 8 (5) None of these 13. Let N denote the largest number satisfying all three of the properties (a) N is a product of three consecutive integers, (b) N is a sum of three consecutive integers, and (c) N < 1000. (d) When N is divided by 9, the remainder obtained is 3. What is the sum of the digits of N? (1) 6 (2) 12 (3) 18 (4) 24 (5) 36 14. The product of a two digit natural number N and the number formed by reversing the digits of N is 1000 more than the product of the digits of N. How many values of N are possible? (1) 2 (2) 4 (3) 3 (4)1 (5) 0 15. In triangle ABC, AB = AC = 208 units. D is a point on AB such that AD = 52 units. Side AC is extended to F such that CF = 156 units. DF intersects BC at E. What is the ratio of the area of ∆CEF to that of ∆BDE?

(1) 2:5 (2) 1:6 (3)1:7 (4)2:7 (5) cannot be ` `` ` determined

16.A hotel gives me 25% commission on every tour package that I sell. And on every 15 packages, it gives me one package for free. What is my effective percentage commission? (1) 31.66 % (2) 31.25 % (3)30 % (4)29.78 % (5)29.68 %



17.A store has four open checkout stands. In how many ways could six customers line up at the checkout stands? (1) 210 (2) 1296 (3) 4096 (4) 60480 (5) 151200 18.A bag contains two hundred slips, marked 1 to 200. How many slips need to be pulled out of the bag in order to be sure that one of the selected slip has a number double or half of one selected earlier? (1) 101 (2) 151 (3) 133 (4) 134 (5) None of these

19.In a right angle triangle with sides 3, 4, and 5 feet, a bug starts at the vertex of the right angle and crawls straight (perpendicular) toward the opposite side. Then it turns and crawls straight towards the closer opposite side. If it keeps turning and crawling to the closer side indefinitely, what total distance does the bug crawl?

(1) 3 feet (2) 4 feet (3) 5 feet (4) 6 feet (5) None of these



Directions for questions 20 to 22: Each question is followed by two statements, I and II. Answer each question using the following instructions: Mark (1) If the question can be answered by using the statement I alone but not by using the statement II alone. Mark (2) If the question can be answered by using the statement II alone but not by using the statement I alone. Mark (3) If the question can be answered by using either of the statements alone. Mark (4) If the question can be answered by using both the statements together but not by either of the statements alone. Mark (5) If the question cannot be answered on the basis of the two statements. 20. N is a n digit palindromic number. Is N a prime number? (A palindromic number is one which reads the same way forwards and backward, such as 14599541.) I. n = 8. II. n = 2008. 21. ABCD is a trapezium with AB and CD as two parallel sides. Diagonals AC and BD intersect at a point O. What is the area of trapezium?

I. CDAB

= 4.

II. CODBOC

∆∆

= 4

22. Let N = pnnnn ++×+×+×+ )4()3()2()1( , such that 2008≥n . Is N a perfect square? I. p is the smallest natural number. II. p is the smallest whole number.

The sum of the series + + ++ + + + + + + +

+3 4 5 20091! 2! 3! 2! 3! 4! 3! 4! 5! 2007! 2008! 2009!

... is

(1) +

×2009! 22 2009!

(2) +

×2009! 12 2009!

(3) 20082009

(4) −

×2009! 22 2009!

(5) −2009! 2

2009!

24. The number of common points shared between the graphs of the equation ⎜x⎜ + ⎜y⎜ = 2 and x2 − y = 2 is (1) 0 (2) 2 (3) 3 (4) 4 (5) 5 25. If 1020000 is divided by 10200 + 7, we get a quotient and a remainder. What is the last digit of the quotient? (1) 0 (2) 1 (3) 3 (4) 7 (5) 9



Space for Rough Work



Section - II Directions for Questions 26 to 28: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. Smith’s basic idea was that business owners seeking to lure customers away from rivals have powerful incentives to introduce improved product designs and cost-saving innovations. These moves bolster innovators’ profits in the short term. But rivals respond by adopting the same innovations, and the resulting competition gradually drives down prices and profits. In the end, Smith argued, consumers reap all the gains. The central theme of Darwin’s narrative was that competition favors traits and behavior according to how they affect the success of individuals, not species or other groups. As in Smith’s account, traits that enhance individual fitness sometimes promote group interests. For example, a mutation for keener eyesight in hawks benefits not only any individual hawk that bears it, but also makes hawks more likely to prosper as a species. In other cases, however, traits that help individuals are harmful to larger groups. For instance, a mutation for larger antlers served the reproductive interests of an individual male elk, because it helped him prevail in battles with other males for access to mates. But as this mutation spread, it started an arms race that made life more hazardous for male elk over all. The antlers of male elk can now span five feet or more. And despite their utility in battle, they often become a fatal handicap when predators pursue males into dense woods. In Darwin’s framework, then, Adam Smith’s invisible hand survives as an interesting special case. Competition, to be sure, sometimes guides individual behavior in ways that benefit society as a whole. But not always. Individual and group interests are almost always in conflict when rewards to individuals depend on relative performance, as in the antlers arms race. In the marketplace, such reward structures are the rule, not the exception. The income of investment managers, for example, depends mainly on the amount of money they manage, which in turn depends largely on their funds’ relative performance. Relative performance affects many other rewards in contemporary life. For example, it determines which parents can send their children to good public schools. Because such schools are typically in more expensive neighborhoods, parents who want to send their children to them must outbid others for houses in those neighborhoods. In cases like these, relative incentive structures undermine the invisible hand. To make their funds more attractive to investors, money managers create complex securities that impose serious, if often well-camouflaged, risks on society. But when all managers take such steps, they are mutually offsetting. No one benefits, yet the risk of financial crises rises sharply. Similarly, to earn extra money for houses in better school districts, parents often work longer hours or accept jobs entailing greater safety risks. Such steps may seem compelling to an individual family, but when all families take them, they serve only to bid up housing prices. As before, only half of all children will attend top-half schools. It’s the same with athletes who take anabolic steroids. Individual athletes who take them may perform better in absolute terms. But these drugs also entail serious long-term health risks, and when everyone takes them, no one gains an edge. If male elk could vote to scale back their antlers by half, they would have compelling reasons for doing so, because only relative antler size matters. Of course, they have no means to enact such regulations.



But humans can and do. By calling our attention to the conflict between individual and group interest, Darwin has identified the rationale for much of the regulation we observe in modern societies — including steroid bans in sports, safety and hours regulation in the workplace, product safety standards and the myriad restrictions typically imposed on the financial sector. Ideas have consequences. The uncritical celebration of the invisible hand by Smith’s disciples has undermined regulatory efforts to reconcile conflicts between individual and collective interests in recent decades, causing considerable harm to us all. If, as Darwin suggested, many important aspects of life are graded on the curve, his insights may help us avoid stumbling down that grim path once again. The competitive forces that mold business behavior are like the forces of natural selection that molded elk. In each case, we see instances of socially benign conduct. But in neither can we safely presume that individual and social interests coincide. 26. The main idea of the above passage is that (1) during competition, individual benefits play more defining roles than group benefits do. (2) relative performance of an individual determines his success in contemporary life. (3) Darwin’s theory of economics produces better results than that of Smith. (4) a group should discourage individual benefits as they are harmful to the group’s benefit as a whole. (5) contrary to Smith’s theory, individual benefits are not always favorable to groups during competition. 27. The author mentions male elks wanting to scale back their antlers in order to (1) showcase relative size of competitions. (2) introduce the merits of regulation. (3) point the superiority of Darwin’s theory. (4) differentiate between humans and animals. (5) suggest unreliability of Smith’s theory.

28. The tone of the author of the passage can said to be (1) critical (2) sardonic (3) analytical (4) factual (5) rhetorical



Directions for Questions 29-32: Each question has a paragraph given with one sentence missing at the end. From among the answer choices given, select the sentence that can fill the blank to form a coherent paragraph. 29. We are still faced by the question why it is that the transvaluation of all values, which is really a permanent phenomenon, has taken such an acute form not in one science, but in many, and perhaps in most. In experimental science facts of the greatest importance are rarely discovered accidentally: more frequently new ideas point the way towards them. The ideas which form the background of the individual sciences have an internal inter connection, _________ (1) though the influences of these ideas can often be traced into unexpected ramifications. (2) but this idea, which is so clearly connected with other tendencies of the times, has opened up vast new

tracts. (3) though these connections are not viewed favourably by even propounders of experimental sciences. (4) but more often than not they are useless, and potentially dangerous at best. (5) but they are also firmly connected with each other and with the ideas of the age in a far more primitive

manner.

30. The Albigenses stood on a totally different standpoint. The procreation of children was for them the supreme sin. A woman with child was described as having a devil, as possessed by the evil one. No one could be saved unless he renounced marriage. Even sins between unmarried folk, or unnatural crimes were looked upon as of less malice than marriage, ________ (1) for marriage was held to be the shameless flaunting of evil under the cover of legality. (2) and there was less hope of repentance for the so-called "wedded" folk. (3) as human nature was too strong to be overcome by such pretences. (4) making earthly life, and above all, marriage, the' perpetuation of life’, intrinsically evil. (5) and thus their "perfect people", their " good people", were those who abstained from marriage. 31. What began as free thought has now developed into freedom from thought. All through history, there have been broad conceptions of the aims of life, tests of morality which masses of men have held and applied with certainty; but in the modern world these various systems have been abandoned and what is left of them is nothing but debris – ___________ (1) scattered at the altars of utilitarianism in the modern society. (2) a collection of broken bits, the ruins of past philosophies. (3) remains of beliefs that behind human consciousness there are realities. (4) a positive poisonous thing resting in the soul of man. (5) painful reminders of freedom and thought.

32. A conscientious examination shows that all the various ways of explaining what is actually meant by a question are, ultimately, nothing but various descriptions of ways in which the answer to the question must be found. Every explanation or indication of the meaning of a question consists, in some way or other, of prescriptions for finding its answer. __________ (1) This principle has proved to be of fundamental importance for the method of science. (2) For what is logically impossible cannot even be described by science. (3) It cannot be expressed by words or other means of communication. (4) Thus a question which is unanswerable in principle can have no meaning. (5) It is logically impossible to give an answer where there is no question.



Directions for Questions 33 to 35: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. HAVE you ever experienced that eerie feeling of a thought popping into your head as if from nowhere, with no clue as to why you had that particular idea at that particular time? You may think that such fleeting thoughts, however random they seem, must be the product of predictable and rational processes. After all, the brain cannot be random, can it? Surely it processes information using ordered, logical operations, like a powerful computer? Actually, no. In reality, your brain operates on the edge of chaos. Though much of the time it runs in an orderly and stable way, every now and again it suddenly and unpredictably lurches into a blizzard of noise. Neuroscientists have long suspected as much. Only recently, however, have they come up with proof that brains work this way. Now they are trying to work out why. Some believe that near-chaotic states may be crucial to memory, and could explain why some people are smarter than others. In technical terms, systems on the edge of chaos are said to be in a state of "self-organised criticality". These systems are right on the boundary between stable, orderly behaviour - such as a swinging pendulum - and the unpredictable world of chaos, as exemplified by turbulence. The quintessential example of self-organised criticality is a growing sand pile. As grains build up, the pile grows in a predictable way until, suddenly and without warning, it hits a critical point and collapses. These "sand avalanches" occur spontaneously and are almost impossible to predict, so the system is said to be both critical and self-organising. Earthquakes, avalanches and wildfires are also thought to behave like this, with periods of stability followed by catastrophic periods of instability that rearrange the system into a new, temporarily stable state. Self-organised criticality has another defining feature: even though individual sand avalanches are impossible to predict, their overall distribution is regular. The avalanches are "scale invariant", which means that avalanches of all possible sizes occur. They also follow a "power law" distribution, which means bigger avalanches happen less often than smaller avalanches, according to a strict mathematical ratio. Earthquakes offer the best real-world example. Quakes of magnitude 5.0 on the Richter scale happen 10 times as often as quakes of magnitude 6.0, and 100 times as often as quakes of magnitude 7.0. These are purely physical systems, but the brain has much in common with them. Networks of brain cells alternate between periods of calm and periods of instability - "avalanches" of electrical activity that cascade through the neurons. Like real avalanches, exactly how these cascades occur and the resulting state of the brain are unpredictable. It might seem precarious to have a brain that plunges randomly into periods of instability, but the disorder is actually essential to the brain's ability to transmit information and solve problems. "Lying at the critical point allows the brain to rapidly adapt to new circumstances," says Andreas Meyer-Lindenberg from the Central Institute of Mental Health in Mannheim, Germany. The idea that the brain might be fundamentally disordered in some way first emerged in the late 1980s, when physicists working on chaos theory - then a relatively new branch of science - suggested it might help explain how the brain works. The focus at that time was something called deterministic chaos, in which a small perturbation can lead to a huge change in the system - the famous "butterfly effect". That would make the brain unpredictable but not actually random, because the butterfly effect is a phenomenon of physical laws that do not depend on chance. Researchers built elaborate computational models to test the idea, but unfortunately they did not behave like real brains. "Although the results were beautiful and elegant, models based on deterministic



chaos just didn't seem applicable when looking at the human brain," says Karl Friston, a neuroscientist at University College London. In the 1990s, it emerged that the brain generates random noise, and hence cannot be described by deterministic chaos. When neuroscientists incorporated this randomness into their models, they found that it created systems on the border between order and disorder - self-organised criticality. More recently, experiments have confirmed that these models accurately describe what real brain tissue does. They build on the observation that when a single neuron fires, it can trigger its neighbours to fire too, causing a cascade or avalanche of activity that can propagate across small networks of brain cells. This results in alternating periods of quiescence and activity - remarkably like the build-up and collapse of a sand pile. 33. A suitable title for the passage would be (1) Anomalies in thoughts- a Hobson’s choice? (2) Deterministic chaos- a cognitive phenomenon? (3) Collapse of thoughts- a natural process? (4) Predicting thoughts- breakthrough in Physics. (5) Randomness, a predictable occurrence. 34. According to the passage calmness in the brain can be achieved by (1) eliminating perturbation to the brain. (2) regulating self organized criticality. (3) predicting the chaos at regular intervals. (4) liminating external cause of stimulation. (5) None of the above.

35. On the basis of the passage, we can say that the absence of ‘self organized criticality’ in our brain will (1) render us sluggish to changing circumstances. (2) make the noise in the brain more pronounced. (3) result in accumulation of thoughts day by day. (4) reduce the numbers of neurons present in the brain. (5) cause none of the above.



Directions for questions 36 to 38: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 36. (A) The survival of the human species is under threat from past and present irresponsible human choices. (B) Throughout recorded history, the insights of typical individual problem-solvers acting alone or in small

groups, have led to adaptive new patterns of human behaviour. (C) Human insight is needed to meet these threats. (D) Therefore, typical insightful individuals ought to be able to go about their lives freely. (E) Sometimes, however, insightful individuals have been at risk for persecution and harm to their person

and/or property because the adaptive changes they espoused were perceived as threats to the established order.

(1) ABECD (2) AEDBC (3) DEACB (4) BEACD (5) CEADB 37.

(A) If I say I don't understand, by what measure may I know that what I say I don't know I actually know?

(B) How should I know? (C) If I say I understand, how can I know whether I don't know what I say I understand? (D) Although that's how it is, I shall nevertheless try to explain.

(1) ABCD (2) ACBD (3) ACDB (4) BDCA (5) DCBA 38. (A) It may take decades before reaching a sustainable equilibrium. (B) Various land, habitat and wildlife conservation groups have sprung up all over the world. (C) However, in the last century or two, there has been a growing awareness of the inherent value of

other species. (D) Industries and governments have begun to take actions to reduce pollution and global warming. (E) Modern technologies make possible the rapid spread of new diseases. (1) BDECA (2) DECBA (3) DEACB (4) EBACD (5) ECBDA



Directions for Questions 39 to 42: The passage given below is followed by a set of four questions. Choose the most appropriate answer to each question. Most questions of whether and how language shapes thought start with the simple observation that languages differ from one another. And a lot! Let's take a (very) hypothetical example. Suppose you want to say, "Bush read Chomsky's latest book." Let's focus on just the verb, "read." To say this sentence in English, we have to mark the verb for tense; in this case, we have to pronounce it like "red" and not like "reed." In Indonesian you need not (in fact, you can't) alter the verb to mark tense. In Russian you would have to alter the verb to indicate tense and gender. So if it was Laura Bush who did the reading, you'd use a different form of the verb than if it was George. In Russian you'd also have to include in the verb information about completion. If George read only part of the book, you'd use a different form of the verb than if he'd diligently plowed through the whole thing. In Turkish you'd have to include in the verb how you acquired this information: if you had witnessed this unlikely event with your own two eyes, you'd use one verb form, but if you had simply read or heard about it, or inferred it from something Bush said, you'd use a different verb form. Clearly, languages require different things of their speakers. Does this mean that the speakers think differently about the world? Do English, Indonesian, Russian, and Turkish speakers end up attending to, partitioning, and remembering their experiences differently just because they speak different languages? For some scholars, the answer to these questions has been an obvious yes. Just look at the way people talk, they might say. Certainly, speakers of different languages must attend to and encode strikingly different aspects of the world just so they can use their language properly. Scholars on the other side of the debate don't find the differences in how people talk convincing. All our linguistic utterances are sparse, encoding only a small part of the information we have available. Just because English speakers don't include the same information in their verbs that Russian and Turkish speakers do doesn't mean that English speakers aren't paying attention to the same things; all it means is that they're not talking about them. It's possible that everyone thinks the same way, notices the same things, but just talks differently. Believers in cross-linguistic differences counter that everyone does not pay attention to the same things: if everyone did, one might think it would be easy to learn to speak other languages. Unfortunately, learning a new language (especially one not closely related to those you know) is never easy; it seems to require paying attention to a new set of distinctions. Whether it's distinguishing modes of being in Spanish, evidentiality in Turkish, or aspect in Russian, learning to speak these languages requires something more than just learning vocabulary: it requires paying attention to the right things in the world so that you have the correct information to include in what you say. 39. Based on the information given in the passage, which of the following statements can be regarded as a

correct inference? (1) The author believes that the language we use shapes our thought process. (2) The author cannot decide whether the language we speak shapes our thoughts or not. (3) The author believes thinks that both schools of thought have equal merits. (4) The author refrains from opining on the veracity of either of the schools of thought. (5) The author believes that the language we use does not shape our thought process.

40. By citing the example of a sentence in the first paragraph the author wants to (1) show the poverty of English language. (2) highlight that different languages require different syntaxes. (3) show that Russian is a more comprehensive language than English. (4) show that out of the three languages mentioned, Turkish is the most complicated. (5) highlight that the complexity of different languages depends on verbs.



41. Based on the information given in the passages, which of the following statements is likely to garner support from the believers of cross-linguistic differences?

(1) Cricket is popular in both England and India, because India was under British rule for a very long

period. (2) The Japanese will savour sea-food more than the Pakistanis, because of Japan’s proximity to sea. (3) Da Vinci’s Mona Lisa will get a different review from a Chinese art critic, than from a Russian art critic. (4) India and Pakistan will fight over Kashmir because both look at it from the same perspective. (5) People of all the countries will value honesty if it were commonly proven to be the greatest virtue. 42. The primary purpose of the passage is to (1) present a commonplace idea and its inaccuracies. (2) describe a situation and its potential drawbacks. (3) explore the implications of a finding. (4) open a debate on a frequent source of disagreement. (5) propose a temporary solution to a problem.

Directions for questions 43 to 47: In each question, the word at the top of the table is used in five different ways, numbered 1 to 5. Choose the option in which the usage of the word is INCORRECT or INAPPROPRIATE. 43. Boot (1) You can bet your boots that I'll be there! (2) The mill-worker died with his boots on. (3) All of the patriot’s sons died in their boots. (4) You should really tighten your boots, as the exams are near. (5) We received an extra week's pay to boot.

44. Sack (1) The small girl loved the sack of candy presented by her father. (2) The baron looked really big in his new sack. (3) The players sacked the quarterback even before he could move. (4) The farmer started sacking up before the rains could arrive. (5) The boy sacked all his belongings together.

45. Bag (1) A stiff breeze made the sails bag out. (2) The wind bagged the curtain. (3) The stay at the prison had made him look like a bag of bones. (4) The hunter put the dead fowl in his game bag. (5) The players bagged up after the match was over.



46. Bone (1) She felt in her bones that it was going to be a momentous day. (2) They boned out the turkey before feasting upon it. (3) The teacher had a bone to pick with him because his homework paper was identical with his

neighbour’s. (4) He makes no bones about his dislike of modern music. (5) The government cut social service programs to the bone. 47. Cry (1) Those people cry down everyone who differs from them. (2) We made arrangements to purchase a house, but the owner cried off at the last minute. (3) The little girl cried her eyes off when her cat died. (4) She always cries up her profession as if she were the best placed amongst us. (5) This treatment is a far cry from that which we received before. Directions for Questions 48 to 50: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question. Enthusiasm is building among scientists for a quite different view—that religion emerged not to serve a purpose but by accident. This is not a value judgment. Many of the good things in life are, from an evolutionary perspective, accidents. People sometimes give money, time, and even blood to help unknown strangers in faraway countries whom they will never see. From the perspective of one's genes this is disastrous—the suicidal squandering of resources for no benefit. But its origin is not magical; long-distance altruism is most likely a by-product of other, more adaptive traits, such as empathy and abstract reasoning. Similarly, there is no reproductive advantage to the pleasure we get from paintings or movies. It just so happens that our eyes and brains, which evolved to react to three-dimensional objects in the real world, can respond to two-dimensional projections on a canvas or a screen. Supernatural beliefs might be explained in a similar way. This is the religion-as-accident theory that emerges from my work and the work of cognitive scientists such as Scott Atran, Pascal Boyer, Justin Barrett, and Deborah Kelemen. One version of this theory begins with the notion that a distinction between the physical and the psychological is fundamental to human thought. Purely physical things, such as rocks and trees, are subject to the pitiless laws of Newton. Throw a rock, and it will fly through space on a certain path; if you put a branch on the ground, it will not disappear, scamper away, or fly into space. Psychological things, such as people, possess minds, intentions, beliefs, goals, and desires. They move unexpectedly, according to volition and whim; they can chase or run away. There is a moral difference as well: a rock cannot be evil or kind; a person can. Where does the distinction between the physical and the psychological come from? Is it something we learn through experience, or is it somehow pre-wired into our brains? One way to find out is to study babies. It is notoriously difficult to know what babies are thinking, given that they can't speak and have little control over their bodies. (They are harder to test than rats or pigeons, because they cannot run mazes or peck levers.) But recently investigators have used the technique of showing them different events and recording how long they look at them, exploiting the fact that babies, like the rest of us, tend to look longer at something they find unusual or bizarre. This has led to a series of striking discoveries. Six-month-olds understand that physical objects obey gravity. If you put an object on a table and then remove the table, and the object just stays there (held by a hidden wire), babies are surprised; they expect the object to fall. They expect objects to be solid, and contrary to what is still being taught in some psychology classes, they understand that objects persist over



time even if hidden. (Show a baby an object and then put it behind a screen. Wait a little while and then remove the screen. If the object is gone, the baby is surprised.) Five-month-olds can even do simple math, appreciating that if first one object and then another is placed behind a screen, when the screen drops there should be two objects, not one or three. Other experiments find the same numerical understanding in nonhuman primates, including macaques and tamarins, and in dogs. Similarly precocious capacities show up in infants' understanding of the social world. Newborns prefer to look at faces over anything else, and the sounds they most like to hear are human voices—preferably their mothers'. They quickly come to recognize different emotions, such as anger, fear, and happiness, and respond appropriately to them. Before they are a year old they can determine the target of an adult's gaze, and can learn by attending to the emotions of others; if a baby is crawling toward an area that might be dangerous and an adult makes a horrified or disgusted face, the baby usually knows enough to stay away. A skeptic might argue that these social capacities can be explained as a set of primitive responses, but there is some evidence that they reflect a deeper understanding. For instance, when twelve-month-olds see one object chasing another, they seem to understand that it really is chasing, with the goal of catching; they expect the chaser to continue its pursuit along the most direct path, and are surprised when it does otherwise. In some work we found that when babies see one character in a movie help an individual and a different character hurt that individual, they later expect the individual to approach the character that helped it and to avoid the one that hurt it. Understanding of the physical world and understanding of the social world can be seen as akin to two distinct computers in a baby's brain, running separate programs and performing separate tasks. The understandings develop at different rates: the social one emerges somewhat later than the physical one. They evolved at different points in our prehistory; our physical understanding is shared by many species, whereas our social understanding is a relatively recent adaptation, and in some regards might be uniquely human. That these two systems are distinct is especially apparent in autism, a developmental disorder whose dominant feature is a lack of social understanding. Children with autism typically show impairments in communication (about a third do not speak at all), in imagination (they tend not to engage in imaginative play), and most of all in socialization. They do not seem to enjoy the company of others; they don't hug; they are hard to reach out to. In the most extreme cases children with autism see people as nothing more than objects—objects that move in unpredictable ways and make unexpected noises and are therefore frightening. Their understanding of other minds is impaired, though their understanding of material objects is fully intact. At this point the religion-as-accident theory says nothing about supernatural beliefs. Babies have two systems that work in a cold-bloodedly rational way to help them anticipate and understand—and, when they get older, to manipulate—physical and social entities. In other words, both these systems are biological adaptations that give human beings a badly needed head start in dealing with objects and people. But these systems go awry in two important ways that are the foundations of religion. First, we perceive the world of objects as essentially separate from the world of minds, making it possible for us to envision soulless bodies and bodiless souls. This helps explain why we believe in gods and an afterlife. Second, as we will see, our system of social understanding overshoots, inferring goals and desires where none exist. This makes us animists and creationists. 48. According to the passage, the word ‘accident,’ in relation to development of religion, means (1) an unforeseen outcome of development of physical and social systems in humans. (2) a byproduct of imposing a physical phenomenon on a social one in human brains. (3) a natural development that is an integral part of human development. (4) a primitive response that is hardwired into human brains. (5) an unexplained occurrence in the social development theory.



49. According to the passage, a baby suffering from autism (1) has understanding of the social phenomenon developing earlier than that of a physical one. (2) will still feel surprised if a ball does not fall towards the earth because of gravity. (3) will react to social bonding in the same way as the other babies in his group. (4) is going to act neutral if an object placed behind a screen disappears when the screen is removed. (5) is going to have his mental faculties extra developed because of lack of the social ones. 50. According to the author, scientists took to studying babies because (1) they are completely new to physical phenomena and hence provide undiluted response. (2) their studies are a challenge over that of rats and pigeons. (3) their studies provide a definite answer to a skeptic’s argument of primitive response. (4) it can decide if the distinction between physical and psychological is experiential or congenital. (5) none of the above.



Section - III

Directions for questions 51 to 54:

Tathagat, a premium CAT (Common Admission Test) coaching institute in Delhi, had 4 running batches- A, B, C & D. All the students of these 4 batches appeared for CAT, which had 3 sections- Quant, Verbal & LRDI. Each of these 3 sections had 25 questions. If a student got an answer right he was awarded with 2 marks, and if he got an answer wrong he got a penalty of .5 marks (deducted from his score). There was no penalty for skipping a question. The cut off in each section was integer. The overall cut off was the sum of the sectional cut offs. The following table shows the performance of Tathagat students in CAT:

Based on the above data answer the following questions:

51. Find the maximum overall cut off if 10 students from each batch in Tathagat cleared all the sectional cut offs. (1)108 (2)111 (3)106 (4)150 (5)None of these

52. Find the minimum overall cut off if 10 students from each batch in Tathagat cleared all the sectional cut offs. (1)-36 (2)-31 (3)-26 (4)0 (5)None of these

53. If the sectional cut offs in Quant, Verbal & LRDI were 43, 31 & 15, respectively, then find out the maximum number of students in Tathagat who could have cleared all the sectional cut offs. (1)51 (2) 41 (3)40 (4)50 (5) None of these 54. Find out the average of maximum and minimum overall cut off if 10 students from each batch in Tathagat cleared all the sectional cut offs. (1)67 (2)57 (3)62 (4)75 (5)41

Average score in different Sections Sections

Number of Students

Quant Verbal LRDI

Batch A 30 6 2 4

Batch B 35 8 6 9

Batch C 30 5 7 7

Batch D 25 10 6 8




Once, Mrs Singh, Mrs Mahajan, Mrs Kumar and Mrs Sharma went shopping together, each with two activities to perform. One of the women had to visit the hardware shop, two needed to go to the bank, two needed to go to the butcher shop, and all but one needed to buy groceries. Their shopping was simplified quite a bit by the fact that they lived in a small town which had only one store of each kind and only one bank. As a result they were soon done and on their way home. It is known that

• Archana didn’t go into the grocery store.

• Both Isha and Mrs Sharma bought meat.

• Tanya came home with more money then she had when she started.

• Mrs Mahajan didn’t go into any of the places where Ritu or Mrs Kumar went.

55. Who didn’t go to the grocery store?

(1)Mrs. Singh

(2)Mrs. Mahajan

(3)Mrs. Kumar

(4)Mrs. Sharma

(5)cannot be determined

56. What’s the first name of Mrs Kumar?

(1)Archana

(2)Tanya

(3)Ritu

(4)Isha


57. Which two places were visited by Mrs Singh?

(1)Grocery & Meat

(2) Hardware & Meat

(3)Grocery & Bank

(4)Meat & Bank





Two or more drinks out of the given five drinks – soda water , orange juice , grape juice, apple juice , and chocolate syrup – are used in making mocktails. To prepare a mocktail the following conditions should be met :

• Chocolate syrup, if used, be least in quantity in comparison to other drinks used for a mocktail.

• A mocktail containing orange juice , should also contain apple juice and the quantity of orange juice and apple juice used should be in the ratio 3:2.

• A mocktail should not have soda water and chocolate syrup together.

• A mocktail containing grape juice should contain grape juice in such a proportion that at least 50 % of the total quantity of mocktail is made up of grape juice.

• A mocktail containing grape juice should also contain chocolate syrup and they should be in the ratio 4:1.

The price of each drink is given below:

Soda water: Rs 40/litre , Orange juice: Rs 90/litre, Apple juice: Rs 130/litre , Grape juice: Rs 180/litre, and Chocolate syrup: Rs 300/litre.

58. If a mocktail is prepared using grape juice, then what is the percentage quantity (p) of chocolate syrup used in the mocktail if it contains at least three drinks.

(1) 12.5<= p < 20

(2) 12.5<= p <= 40/3

(3) 12.5<= p < 40/3

(4) 12.5<= p < 50/3

(5) None of these

59. How many different mocktails can be prepared based on the kind of drinks used?

(1) 8 (2)7 (3)6 (4) 5 (5) None of these

60. If the average price per litre of a mocktail containing grape juice , chocolate syrup & apple juice is Rs 180/litre, then what is the ratio of chocolate syrup: apple juice : grape juice?

(1)4:5:16 (2)5:6:20 (3)3:4:12 (4)5:12:20 (5)Data insufficient

61. How many of the following is/are agreeable combination/s for a mocktail?

• 1 part soda water, 3 parts orange juice , 2 parts apple juice.

• 1 part soda water , 4 parts grape juice , 1 part chocolate syrup.

• 16 parts grape juice, 4 parts chocolate syrup, 3 parts orange juice, 2 parts apple juice.

• 16 parts grape juice, 4 parts chocolate syrup , 9 parts orange juice, 6 parts apple juice.

(1) 0 (2) 1 (3) 2 (4) 3 (5) 4



Directions for question no 62 to 65:

One day I was taking out a print of my DI class which contained 10 pages. Since I wanted to take 44 sets of that material, I put exactly 440 papers in the printer. These papers were numbered 1 to 10 and I kept paper number 1 on the top. After some time I realized that my printer was having some problem- after 8 papers the printer started rolling two papers together and was printing only on the upper most paper (i.e. after paper number 8 it rolled paper number 9 & 10 together but printed only on paper number 9 and paper number 10 came out blank). Then after 8 similar pairs of papers it started rolling three papers together and so on. Based on the above mentioned problem please solve the following questions:

62. In all, how many papers come out blank?

(1) 80 (2) 140 (3) 240 (4) 360 (5) 400

63. After the first set of 9 pages, which of the following page of the class material were printed on the right numbered paper at first?

(1) 4 (2) 5 (3) 6 (4) 8 (5) 10

64. How many pages of DI class were printed on the right numbered paper?

(1) 10 (2) 13 (3) 19 (4) 21 (5) 22

65. If I flip each of the paper and put them back in the printer in the reverse order (from 440 to 1) as I put them initially, how many papers would have same material printed on both the sides. By the way this time my printer is working absolutely right.

(1) 0 (2) 1 (3) 2 (4) 3 (5) 4




Delhi, Mumbai, Chennai & Kolkata are the four cities in India which are having airports. Jumbo Airline, Fly Air, Sky Air and Masala jet are the only four airline operators in India. A route between two cities is known as a sector i.e. route between Delhi and Mumbai is known as Delhi-Mumbai sector. The same airplane flies between the two cities of a particular sector. There are few observations about the number of airplanes and number of sectors, which are as follows:

No two airline operator operates in the same number of sectors.

Sum of the sectors operated by each of the airline is 14

None of the two sectors of a particular airline or any of the two airlines are having same number of flight.

Based on the above Bar graph, answer following questions:

66. Which of the following airline operates in least number of sectors?

(1) Jumbo Airline

(2) Fly Air

(3) Sky Air

(4) Masala Jet

(5) Can not be determined

67. With how many flights does Jumbo air operate in Delhi-Mumbai sector, given that jumbo airline has maximum number of flight in this sector compared to any other operator in this sector?

(1) 2

(2) 4

(3) 8

(4) It does not operate in that sector




68. Which sector is having maximum number of flight ( all operators included)

(1) Delhi – Mumbai

(2) Mumbai – Chennai

(3) Mumbai – Kolkata

(4) Kolkata – Delhi


69. Which of the following airline operates in the maximum number of sectors?

(1) Jumbo Airline

(2) Fly Air

(3) Sky Air

(4) Masala Jet





In a certain apartment house occupied exclusively by young married couples and their children the following facts are known to be true.

• There are more children than adults, more adults than boys, more boys than girls, and more girls than families.

• There are no childless couples, and no two families have the same number of children. • Every girl has at least one brother and at most one sister. • One family has more children than all the others put together.

70. Total how many families are there in the apartment?

(1) 2 (2) 3 (3) 4 (4) 5 (5) Trivial solution

71. Including adults how many people are there in the apartment?


72. How many children are there in the largest family?




Directions for question no 73 to 75

Two friends, Kamal and Anurag are playing a game. They start with an unlimited supply of coins, with denominations of 10, 20, 40 and 50 paisa. They take turns placing a single coin into a pot, which is intially empty. They decide a target amount and amount in the pot should not exceed this target amount. 73. If the winner is the player who puts in the last coin in the pot, reaching the target, then for which of the following as the target amount kamal will win the game, if he starts the game by putting the first coin?

(1) 300 paisa

(2) 330 paisa

(3) 340 paisa

(4) 360 paisa

(5) 390 paisa

74. For which of the following case Anurag will win the game, if the target amount is 650 paisa. And the winner is the player who puts in the last coin in the pot.

(1) Anurag starts by putting 40 paisa coin

(2) Kamal starts by putting 20 paisa coin

(3) Anurag starts by putting 50 paisa coin

(4) (1) and (3) both

(5) (2) and (3) both

75. If the person, who puts in the last coin in the pot loses the game. So for the target amount of 740 paisa, which of the following will surely lead Anurag to win the game.

(1) Anurag starts the game by putting 40 paisa coin

(2) Kamal starts the game by putting 50 paisa coin.

(3) Anurag starts the game by putting 10 paisa coin.

(4) Both (1) & (2)

(5) All the three



Answer Key

Section I ( Quant) Section - II

(Verbal) Section - III (DI) Q. No Ans Q. No Ans Q. No Ans 1 1 26 5 51 1 2 3 27 2 52 3 3 3 28 3 53 2 4 1 29 5 54 5 5 2 30 1 55 2 6 4 31 2 56 4 7 2 32 4 57 3 8 5 33 1 58 4 9 2 34 5 59 1 10 3 35 1 60 4 11 5 36 4 61 2 12 4 37 4 62 4 13 2 38 5 63 4 14 1 39 4 64 5 15 3 40 2 65 5 16 5 41 3 66 3 17 4 42 4 67 3 18 4 43 4 68 5 19 4 44 4 69 1 20 3 45 5 70 2 21 5 46 2 71 4 22 3 47 3 72 4 23 4 48 1 73 3 24 5 49 2 74 3 25 5 50 4 75 5


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