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.