ATOS ORGIN Each digit, 1, 2, 3, 4, 5, 6, 7, 8 and 9 is represented by a different letter A, B, C, D, E, F, G, H and I but not necessarily in this order. Further, each of A + B + C, C + D + E, E + F + G and G + H + I is equal to 13. 1. Find the value of E. a. 5 b. 7 c. 4 d. Cannot be determined 2. What is the sum of C, E and G? a. 7 b. 9 c. 11 d. Cannot be determined 3. How many different sum’s of A, D, F and I are possible? a. 1 b. 2 c. 4 d. Cannot be determined In the M. sc. Nuclear Physics class of Presidency Collage there are 151 students. They must choose either two or three out of 4 optional subjects, Nuclear Thermo Dynamics, Nuclear Field Theory, Nuclear Radiation, Nuclear Reaction in their combination. Given below are some clues about breakup of 2004-05 classes Number of students taking 2 subject combination = 132 students. Students taking only Nuclear Thermo Dynamics & Nuclear Field Theory = 12 Students taking only Nuclear Field Theory & Nuclear Reaction = 33 Students taking only Nuclear Theory Dynamics & Nuclear Radiation = 31 Students taking only Nuclear Radiation & Nuclear Reaction = 46 4. What is the number of students who took nuclear Thermo Dynamics in their combination? a. less than 75 b. 75 c. more than 75 d. can’t be determined e) 23 5. What is the number of students who took Nuclear Radiation in their combination? a. less than 95 b. 95 c. more than 95 d. 54 e. can’t be determined 6. Which subject was taken up by maximum number of students? a. Nuclear Thermo Dynamics b. Nuclear Field Theory c. Nuclear Reaction d. Nuclear Radiation e. None of these Long ago, King Ashoka, organized a horse riding competition. The entry fee for participation was one gild coin and the total number of coins collected would be distributed among the first four winners. All the four winners were awarded with a different number of coins; however the winner in the first position got the maximum coins and so on, so that the winner in the fourth position got the least number of coins. A, B, C, D were the first four winners in the competition so that; I. A did not come first, B did not come second, C did not come third and D did not come fourth. II. B won more coins than C. III. D won more coins than B. 7. C, one of the four winners ended the competition in position number. a. 4 b. 2 c. 1 d. Cannot be determined 8. If 12 participants took part in the competition, then how many coins did B win? a. 2 b. 3 c. 4 d. Cannot be determined 9. If 13 participants took part in the competition and A won 4 coins, how many coins did d win? a. 7 b. 5 c. 6 d. Cannot be determined 10. The average age of a woman and her daughter is 16 years. The ratio of their ages in 7 : 1 respectively. What is the woman’s age? a. 4 years b. 28 years c. 32 years d. 6 years e. None of these 11. Deven Invests Rs. 2,34,558 which is 25% of his annual income, in National Saving schemes. Whar is his monthly income? a. Rs. 9,38,232 b. Rs. 78,186 c. Rs. 4,69,116 d. Rs. 2,34,558 e. None of these 12. A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the stream is a. 10 km/h b. 5 km/h c. 4 km/h d. 6 km/h e. None of these 13. Tow-third of one-seventh of a number is 87.5% of 240. Whar is the number? a. 2670 b. 2450 c. 2205 d. 1470 e. None of these 14. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immeresed. The water level in the vessel will rise by a. 9/2 cm b. 9/4 cm c. 4/9 cm d. 2/9 cm e. None of these 15. At what rate perscent per annum of simple interest, will a sum of money double itself in 12 years? a. 7 1/2% b. 8% c. 9% d. 8 1/3% e. None of these 16. If (20)² is subtracted from the square of a number, the answer so obtained is 4321. What is the number? a. 110 b. 111 c. 112 d. 113 e. None of these P, Q and R run on the tracks made in the shape of a star, pentagon and circle, respectively. The radius of the circle is ‘r’ and side of the pentagon = 2a and OX = 2OL = 2b. O is the centre of the figure 17. Find distance traveled by ‘P’. a. 5(r² + 3a²)½ b. 10(r² + 3a²/2)½ c. 10(r² + 2a²)½ d. 10(r² + 3a²/4)2 18. If a + b = r 10 km and P travels at a speed of 10 km/hr. Find time taken by P to complete one round. a. 6.52 hours. b. 8.5 hours c. 8 hours d. 7.21 hours 19. What is the ratio of the time taken by R to complete one round to the time taken by Q to complete one round around their respectively tracks if the speed of Q is two thirde that of R? (Use data from the previous questions) a. 0.698 b. 0.85 c. 0.5 d. 1.43 There are 3 bottles and a jug. The bottles each have a capacity of 5 liters but are partially filled with water. The jug also has some water in it. The sum of the water in the jug and water in the first bottle is half of the total jug capacity. When the first bottle and third bottle are emptied into the jug, it contains 6 liters of water. When the second and the third bottle are emptied into the jug, it contains 7 liters of water. When all the bottles are poured into the jug, it’s filled to it’s capacity. The first and second bottles contain a total of 7 liters. 20. what percentage of total capacity of the bottles is filled with water? a) 20% – 40% b) 40% – 60% c) 60% – 80% d)30% – 50% e) Can’t be determined. 21. What is the capacity of the jug? (In liters) a) 7 b) 8 c) 9 d) 10 e) 11 22. How much water does the jug already contain (in liters)? a) 3 b) 4 c) 1 d) 2 e) 5 23.A thief escaped from police custody. Since he was a sprinter, he could run at a speed of 40 km/hr. The police realized it after 3 hr and started chasing him in the same direction at 50km/hr. The police had a dog, which could run at 60 km/hr. The dog would run to the thief and then return back to the police and then would turn back towards the thief. It kept on doing so till the police caught the thief. Find the total distance traveled by the dog in the direction of the thief? Here are the options - a) 720 km b) 600 km c) 660 km d) 360 km e) 230 km A cricket tournament was to be organized in Mumbai in which six teams were to participate. The six teams are A, B, C, D, E and F. Each team had to play each of the other teams once. The tournament is scheduled to be held between 25th to August to 4th September 1998. Following information are given: (i) There has to be a gap of at least 1 day between the matches played by a particular team. (ii) There cannot be more than two matches on any given day. (iii) Team C has to play the 1st match of the tournament on 25th August and the last match is to be held on 4th September. (iv) A plays C on 3rd September and D on 31st August. (v) D plays C on 25th August, F on 27th August, E on 29th August and play their last match on 4th September. (vi) No matches are to be held on 26th August and 2nd September. Only 1 match is to be held on 4th September. 24. Which of the following matches cannot be held on 25th August? a. C vs B b. B vs A c. B vs F d. None of these 25. E vs F match cannot be scheduled on a. 30th August b. 31st August c. 1st September d. 3rd September 26. The last Match for A is scheduled on a. 1st September b. 2nd September c. 3rd Septermber d. 4th September 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 batsmen 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 highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order. \27. How many players among those listed definitely scored less than Yuvraj in the tournament? a.0 b.1 c.2 d. More than 2 e. none 28. Which of the players had the best M-index from the tournament? a.Rahu1 b.Saurav c.Virender d. Yuvraj e. Cannot be determined. 29. For how many Indian players is it possible to calculate the exact M-index? a.0 b.1 c. 2 d. More than 2 e. Cannot be determined 30. Among the players mentioned, who can have the lowest R-index from the tournament? a. Only Kaif, Rahul or Yuvraj b. Only Kaif or Rahul c. Only Kaif or Yuvraj d. Only Kaif e. Only Yuvraj In a cricket game, 3 batsman A , B and C performed well . The runs are scored in 6’s , 4’s and 1’s only. The number of B’s sixes are greater by 50% than that of C and less by 25% than that of A. The number of B’s fours are greater by 50% than that of A and less by 25% than that of C. Maximum numbers of one’s is scored by C which is 50% greater than that of A, and B’s is 25% greater than that of A . The number of balls and number of runs scored are same. Also 276 runs are scored in the game. Runs scored from 6’s are 75% of the runs scored from 4’s . A score 40 ones.

31. Who scores maximum runs ? a) A b) B c) C d) A & B e ) B & C 32. How many balls were dot balls? a) 126 b) 150 c) 76 d) 99 e) 121 A, B, C and D are four football teams taking in the ULFA Cup. Each team is required to play against all the other teams once. The matches will be played on grounds P, Q, R and S. You as the coordinator of the ULFA Cup are required to allot matches to the four grounds. To allot the matches, you must meet the following conditions: I. Grounds P and Q can host matches only on Sundays and grounds R and S can host matches only on Saturday. II. Team A can play its matches either on ground P or R and on no other grounds. III. Team B can play its matches either on ground P or Q and on no other grounds. IV. Team C can play its matches on all grounds except P. V. All grounds must host at least one match. 33. On which one of the following grounds will the match between b and C be played? a. P b. Q c. R d. S 34. Which one of the following set of teams must play the match on a Saturday? a. C and D b. A and B c. A and D d. A and C 35. Which one of the following set of teams will not play the match on a Saturday? a. C and D b. A and B c. A and D d. A and C 36. What will be the total number of matches played in the tournament? a. 3 b. 4 c. 5 d. 6 37. Which one of the following set of teams can play the match on ground P and Q? a. B and C b. B and D c. A and B d. A and C Eight friends A, B, C, D, E, F, G and H are playing a game. The game involves many rounds initially all of them stand forming a circle according to the alphabetical order of their names in clockwise arrangement. In each round exactly three players exchange their position and in a round one player can exchange his position only once. Nobody can exchange position with his adjacent players and so player can exchange position in two consecutive rounds. 38. Which players can possibly play the first round? a. A, D, E b. B, C, F c. F, G, H d. A, F, L 39. If the first round is played by B, G and E then which player cannot play in the third round? a. F b. B c. C d. A 40. If C, E and G played the first round then which of the following statements must be true? I. Both F and D will play the second round. II. Both F and D cannot play the third round. III. Atleast one out of F and D cannot play the third round. a. I only b. II only c. III only d. I and II only 41. If H, B and E played the first round then anyone out of the following can play in the their round except: a. G b. A c. C d. F Harish and Sachin are playing a game of matchsticks. There are N matchsticks on the table to start with. Each player, in his turn, picks up at least one matchstick and at most eight matchsticks. The two players take turn alternately. The player who clears the table loses. Assume that each player plays intelligently with an objective of winning. The first move is Haris’s. No player is allowed to pass his turn without picking up any matchsticks. 42. If, for some N, it is known that the number of matchsticks up by Harish in his first four moves were 6, 4, 3 and 6 respectively, then how many matchsticks would Sachin have picked up in his third move? Assume that Harish wins the game? a. 3 b. 5 c. 6 d. insufficient data. 43. If it is known that the game was completed in 8 moves (by each of the two players), what is the maximum possible value for N? a. 63 b. 71 c. 72 d. 81 Four boys and four girls sit around a round to discuss strategies to improve their performance in CAT. Each one of them likes two of the three sections English, Maths and DI and is weak in the third section which they dislike. Also, 1. Namrata is equidistant from Manju and Ritu and likes Maths and DI. 2. Sachin is equidistant from Abhay and Swati but not adjacent and does not like English. 3. Person sitting two places to the right of Amar does not like English. 4. Swapnil likes Maths and sits to the immediate left of Namrata and to the immediate tight of Manju. 5. Person opposite Ritu likes only one of the sections that Ritu likes. 6. Abhay and the person sitting opposite him don’t like Maths. 7. Person to the immediate left of Swati likes DI and English. 44. Which are the two sections that Manju likes? a. English and Maths b. English and DI c. [a] and [c] d. and [c] 45. Who sits opposites Namrata? a. Sachin b. Amar c. Swati d. Manju 46. Which is the section that Ritu does not like? a. Maths b. Di c. English d. DI or Maths 47. Which is the common section in which Ritu and Swapnil are weak? a. Maths b. English or maths c. Maths or DI d. DI There are 3 bottles and a jug. The bottles each have a capacity of 5 liters but are partially filled with water. The jug also has some water in it. The sum of the water in the jug and water in the first bottle is half of the total jug capacity. When the first bottle and third bottle are emptied into the jug, it contains 6 liters of water. When the second and the third bottle are emptied into the jug, it contains 7 liters of water. When all the bottles are poured into the jug, it’s filled to its capacity. The first and second bottles contain a total of 7 liters. 48. What percentage of total capacity of the bottles is filled with water? a) 20% – 40% b) 40% – 60% c) 60% – 80% d) 30% – 50% 49. What is the capacity of the jug? (In liters) a) 7 b) 8 c) 9 d) 10 50. How much water does the jug already contain (in liters)? a) 3 b) 4 c) 1 d) 2 51. Four cups of milk are to be poured into a 2-cup bottle and a 4-cup bottle. If each bottle is to be filled to the same fraction of its capacity, how many cups of milk should be poured into the 4-cup bottle? a) 2/3 b)7/3 c) 5/2 d) 8/3 e) 3 52. 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 will they meet each other? a) 7 hours b) 10 hours c) 35 km from A d) Midway between A & B e) 6 hours S = {a, b, c, d, e}. A binary operation * is defined by the following table, which had been partially filled up. For all x, y belonging to S, x * y = y * x. The operation * is so defined that every x belonging to S occurs exactly once in each row and each column of the table. 53. If a * b = e and a * a = d, what is the value of c * d? a. a b. b c. c d. e 54. If a * a = b and b * b = c, what is the value of c * d? a. a b. b c. c d. e 55. If a * b = d and c * d = b, then d * d = a. c b. a c. d d. b 56.What would be the remainder when (1!)3 + (2!)3 + (3!)3 + (4!)3 + (5!)3 +…+ (n!)3 is divided by 5. Where n is the largest 3 digit number . A. 0 B. 1 C. 3 D. 2 E. 4 57.Find the greatest number consisting of 6 digits , which on being divided by 6,7,8,9,10 leaves 4,5,6,7,8 as remainders respectively. A. 997922 B. 997920 C. 997918 D. 997928 E. 997912 58.A watermelon weighs 5000 gm. 99% of its weight is water. It is kept in a drying room and after some time it turns out that only 98% of its weight is water. What is the weight now? A. 2450 B. 4851 C. 4500 D. 2500 E. None of these . 59.A cask of wine when fully filled holds 10 liters. 2 liters of wine is removed and filled with water. Then 4 liters in the solution is replaced with water. Then 6 and 8 liters respectively. At the end of the 4th operation , the ratio of wine to water is. A. 4! / (5) 4 B. 4! / (5 4 - 4! ) C. 8! / 10 4 D. 8! / (10 4 – 8! ) E. None of these 60.A hare pursued by a hound who is 50 of her own leaps before him. When the hare takes 4 leaps, the hound takes 3. in one leap , the hare goes 1¾ meters and the hound 2¾ meters. In how many leaps will the hound overtake the hare? A. 70 leaps B. 36 leaps C. 210 leaps D. 328 leaps E. 140 leaps.

Direction for next 2 questions: Answer the questions on the basis of the text given below If A and B are running in a circular track in a direction opposite to that in which C is running. C is running at twice and thrice the speed of A and B respectively and on the same track. They start running from the same point and A’s average speed is 3m/s and the track is 120 m. 61.When, after the start, will B find himself equidistant and between A and C for the first time? A. 120/9 see B. 17 1/7 C. 15 sec D. 25 2/3 sec E. None of these 62.When all three meet for the first time , how many complete rounds have been made by C ? A. 4 B. 9/2 C. 5 D. 6 E. 3 63.A monkey climbing up a greased pole ascends 10 meters and slips down 2 meters in alternate minutes. If the pole is 64 meters high how long will it take him to reach the top? A. 16 min B. 12 min C. 14 min D. 18 min E. None of these 64.The average of (54,820)2 and (54,822)2 is. A. (54,821)2 B. (54,821.5)2 C. (54,820.5)2 D. (54,821)2 + 1 E. (54,821)2 – 1 65.a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc? A. 16 B. 13 C. 5 D. 3 E. none of the above 66.11+22+33+...+1010 is divided by 5. What is the remainder? A. 0 B. 1 C. 2 D. 3 E. 4 67.If n is an integer greater than 0, what is the remainder when 912n+3 is divided by 10? A. 0 B. 1 C. 2 D. 7 E. 9 68.Each of 435 bags contains at least one of the following three items: raisins, almonds, and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain only almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is one-fifth the numbers of bags that contain only almonds. 210 bags contain almonds. How many bags contain only one kind of item? A. 256 B. 260 C. 316 D. 320</ E. can’t be determined 69.If a = 2x 3y and b = 2l 3m and all of x, y, l, m are positive integers. What is the probability that a/b is an integer? A. 1/2 B. 1/6 C. 1/4 D. 3/4 E. 2/3 70 A rectangle plank √2 m wide is placed symmetrically on the diagonal of a square of side 8m as shown in the figure. The area of the plank is? A. (16√2-3)m2 B. 7√2m2 C. 98m2 D. 14m2 E. 13√3m2 71.The largest integer that always divides n5 – 5n3 + 4n for all natural n is A. 40 B. 60 C. 24 D. 120 E. 30 72.Two printers are installed to print some pages. First printer’s work is directly proportional and the other’s is inversely proportional to the temperature. If the total work done at 15o C is 20 pages and at 20o C is 25 pages, what is the work done at 35o C? A. 41.2 pages B. 43.2 pages C. 40 pages D. 39.7 pages. E. 40.7 pages. 73. In the given figure, OX and OY are tangents and A and C are the centers of the circles. Find (∠ p - ∠q). A. 6° B. 7° C. 8° D. 9° E. 5° 74.The value of y = (x2)/(x4 + 1) lies in which of the following inequality? A. 0<y<1/2 B. 0<y<=1/2 C. 0<=y<=α D. -1/2<=y<=1/2 E. -α<y<0 75.If a, b, c are in G.P (a, b, c >0) and log(5c/a), log(3b/5c) and log(a/3b) are in A.P then a, b, c are sides of A. an acute angled triangle B. an equilateral triangle C. a right angled triangle D. Isosceles triangle E. None of these.