COMMON ADMISSION TEST(CAT) Entrance Examination Question Paper -2006

COMMON ADMISSION TEST(CAT) Entrance Examination Question Paper -2006 Instructions: 1. This test has three sections that examine various abilities. Each section has 25 questions. You will be given two and half hours to complete the test. In distributing the time over the three sections, please bear in mind that you need to demonstrate your competence in all three sections. 2. Directions for answering the questions are given before each group of questions. Read these direactions carefully and answer the questions by darkening the appropriate circles on the Answer sheet. There is only one correct answer of each question. 3. Each section carries 100 marks. All questions carry four marks each. Each wrong answer will attract a penalty of one mark. 4. Do your rough work only on the Test Booklet and NOT on the Answer Sheet. 5. Follow the instructions of the invigilator. Candidates found violating the instructions will be disqualified. Section - I

Section - I has 25 questions. 1 Q. K,L,M,N,O,P,Q,R,S,U and W are the only ten members in a department. There is a proposal to from within the members of the department, subject to the following conditions: 1. A team must include exactly one among P,R and S. 2. A team must include either M or Q, but not both. 3. If a team includes K, then it must also include the other two. 4. If a team includes one among S,U and W, then it must also include the other two. 5. L and N cannot be members of the same team. 6. 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. 5 (5) Who can be a member of a team of size 5 ? A. K B. L C. M D. P 2 Q. Mathematicans are assigned a number called Erdos number (named after the famous mathematician, Paul Erdos).Only Paul Erdos himself has an Erdos number of Zero. Any mathematician who has written a research paper with Erdos has an Erdos number of 1. For other mathematicians, the calculation of his/her Erdos 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 Erdos number. Let the Erdos number of Y be y. Then X has an Erdos number of y + 1. Hence any mathematician with no co-authotship chain connected to Erdos has an Erdos number of infinity. In a seven day long mini-conference organized in memory of Paul Erdos, 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 Erdos number. Nobody had an Erdos 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 Erdos number of the group of eight mathematicians to 3. The Erdos number of B,D,E,G and H remained uncharged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdos number of the group of eight to as low as 3. At the end of the third days, five members of this group had identical Erdos numbers distinct from each other. On the fifth day, E co-authored a paper with F which reduced the group's average Erdos number by 0.5. The Erdos numbers of the remaining six were unchanged with the writing of this paper. No other paper was written during the conference. 5 (2) How many participants had the same Erdos number at the beginning of the conference ? A. 2 B. 3 C. 4 D. 5 3 Q. 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 decision 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 addition 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 share 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. 5 (2) What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day ? A. Rs 3700 B. Rs 4000 C. Rs 4700 D. Rs 5000 4 Q. Answer Questions 1 to 5 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. 5 (5) 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% of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to T under this policy will be : A. Rs 7 B. Rs 9 C. Rs 10 D. Rs 13 5 Q. In a Class X Board examination, ten papers are distributed over five Groups -PCB, Mahematics, 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. 5 (4) Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups ? A. 1 B. 2 C. 3 D. 4

Section - II

Section - II has 25 questions. 6 Q. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees ? A. 75 B. 90 C. 150 D. 120 7 Q. The passage given below is followed by a set of five questions. Choose the most appropriate answer to each question. Fifteen years after communism was officially pronounced dead, its spectre seems once again to be haunting Europe. Last month, the Council of Europe's parliamentary assembly voted to condemn the "crimes of totalitarian communist regimes," linking them with Nazism and complaining that communist parties are still "legal and active in some countries." Now, Goran Lindblad, the conservation Swedish MP behind the resolution, wants to go further. Demands that European Ministers launch a continent-wide anti-communist campaign-including school textbook revisions, official memorial days, and museums-only narrowly missed the necessary two-thirds majority. Mr.Lindblad pledged to bring the wider plans back to the council of Europe in the coming months. He has chosen a good year for his ideological offensive : this is the 50th anniversary of Nikita Khrushchev's denunciation of Josef Stalin and the subsequent Hungarian uprising, which will doubtless be the cue for further excoriation of the communist record. Paradoxically, given that there is no communist government left in Europe outside Moldova, the attacks have if anything, become more extreme as time has gone on. A clue as to why that might be can be found in the rambling report by Mr.Lindblad that led to be Council of Europe declaration. Blaming class struggle and public ownership, he explained "different elements of communist ideology such as equality or social justic still seduce many" and "a sort of nostalgia for communism is still alive." Perphaps the real problem for Mr.Lindblad and his right wing allies in Eastern Europe is that communism is not dead enough-nd they will only be content when they have driven a stake through its heart. The fashionable attempt to equate communism and Nazism is in reality a moral and historical nonsense. Despite the cruelties of the Stain terror, there was no Soviet Terblinka or Sorbibor, no extermination camps built to murder millions. Nor did the Soviet Union launch the most devastating war in history at a cost of more than 50 million lives-in fact it played the decisive role in the defeat of the German war machine. Mr.Lindblad and the Council of Europe adopt as fact th ewildest estimates of those "killed by communist regimes"(mostly in famines) from the fiercely contested Black Book of communism, which also underplays the number of deaths attributable to Hitler. But, in any case, none of this explains why anyone might be nostalgic in former communist states, now enjoying the delights of capitalist restoration. The dominant account gives no sense of how communist regimes renewed themselves after 1956 or why Western leaders feared they might overtake the capitalist world well into the 1960s. For all its brutalities and failures, communism in the Soviet Union, Eastern Europe and elsewhere delivered rapid industrialization, mass education, job security, and huge advances in social and gender equality. Its existence helped to drive up welfare standards in the west, and provided a powerful counterweight to Western global domination. 5 (5) Which of the following cannot be inferred as a compelling reason for the silence of the Council of Europe on colonial atrocities ? A. The Council of Europe being dominated by erstwhile coloialists. B. Generating support for condemning communist idology. C. Unwillingness to antagonize allies by raking up an embarrassing issue D. Greater value seemingly placed on European lives 8 Q. Each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way. 10 (5) Age has a curvilinear relationship with the exploitation of opportunity. Initially, age will increase the likelihood that a person will exploit an enterpreneurial opportunity because people gather much of the knowledge necessary to exploit opportunities oner the course of thier lives, and because age provides credibility in transmitting that information to others. However, as people become older, their willingness to bear risks declines, thier opportunity costs rise, and they become less receptive to new information. A. As a result,people transmit more information rather than experiment with new ideas as they reach an advanced age. B. As a result,people are reluctant to experiment with new ideas as they reach an advanced age. C. As a result,only people with lower opportunity costs exploit opportunity when they reach an advanced age. D. As a result,people become reluctant to expliot entrepreneurial opportunities when they reach an advanced age. 9 Q. Each question has a set of four Sequentialy ordered statements.Each statement can be classified as one of the following: 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 option 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') Select the answer option that best describes the set of four statements 2 (2) (1) Inequitable distribution of all kinds of resources is certainly one of the strongest and most sinister sources of conflict. (2) Even without war, we know that conflicts continue to trouble us - they only change in character. (3) Extensive disarmament is the only insurance for our future, imagine the amount of resources that can be released and redeployed. (4) The economies of the industrialized western world derive 20% of their income from the sale of all kinds of arms. A. IJJI B. JIJF C. IIJF D. JIIF 10 Q. 8 (5) Which of the following situations best represents the idea of justice as fairness, as argued in the passage ? A. All individuals are paid equally for the work they do. B. Everyone is assigned some work for his or her livelihood. C. All acts of theft are penalized equally. D. All children are provided free education in similar schools. 11 Q. 1 (1) In the context of science, according to the passage, the interaction of dogmatic beliefs and critical attitude can be best described as : A. A duel between two warriors in which one has die. B. The effect of a chisel on a marble stone while making a sculpture. C. The feeddtock(natural gas) in fertilizer industry being transformed into fertilizers. D. A predator killing its prey.

Section - III

Section - III has 25 questions. 12 Q. 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? A. 3 B. 6 C. 5 D. 4 13 Q. The Sum of the four Consecutive two -digit odd number , when divided by 10 ,become a perfect square . which of the following can possibly be one of these four number? A. 21 B. 25 C. 41 D. 67 14 Q. Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40 and 60 km/hr, 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 ? A. 3 B. 3.5 C. 4 D. 4.5 15 Q. The length, breadth and hieght of a room are in the ratio 3:2:1. If the breadth and height are havled while the lenght is doubled, then the total area of the four walls of the room will: A. remain the same B. decrease by 30% C. decrease by 15% D. decrease by 18.75% 16 Q. Consider a sequence where the nth term, tn = n/(n + 2), n= 1,2 , ....... . The value of t3*t4*t5*.........*t53 equals : A. 2/495 B. 2/477 C. 12/55 D. 1/1485 17 Q. Consider the set S = {1,2,3,.....,1000}. How many arithmatic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements ? A. 3 B. 4 C. 6 D. 7 18 Q. the sum of four consecutive two-digit odd numbers when divided by 10 ,becomes a perfect square.which of the following can possible be one of these four numbers? A. 5 B. 6 C. 7 D. 8 19 Q. There are 6 task and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or to person 4. Every person is to be assigned one task. In how many ways can the assignment be done ? A. 144 B. 180 C. 192 D. 360 20 Q. 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: 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 excatly two consecutive issues(out of the three)? A. 7 B. 9 C. 12 D. 14 21 Q. When you reverse the digits of the number 13,the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed ? A. 5 B. 6 C. 7 D. 10 22 Q. The number of solutions of the equation 2x + y= 40, where both x and y are positive integers and x ≤ y is : A. 7 B. 13 C. 14 D. 18 23 Q. What values of x satisfy x2/3 + x1/3 -2 ≤ 0 ? A. -8 ≤ x ≤ 1 B. -1 ≤ x ≤ 8 C. 1 < x < 8 D. 1 ≤ x ≤ 8 24 Q. Which among 21/2, 31/3, 41/4, 61/6 and 121/12 is the largest ? A. 21/2 B. 31/3 C. 41/4 D. 61/6