Page 1 MOCK CAT SECTION – A 1. If m 2 a 2 + (n 2 + 1) b 2 + c 2 = 2b(mna – c), then which of the following statement(s) is/are necessarily true? I. ma = nb II. ma = – nc III. ma = nc (1) I only (2) only II and III (3) Only I and II (4) None of these 2. In the adjacent figure ABCDEF is a regular hexagon. Find the ratio of the radius of C large to that of radius of C small . (1) 1 2 1 2 - + (2) 3 2 3 2 - + (3) 1 2 (4) Can’t say Directions for questions 3 – 4: Refer to the following data for the following questions. There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A & C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 22 routes between B & C. 3. How many direct roads are there between A & B? (1) 4 (2)3 (3) 6 (4) 2 4. How many direct roads are there between B & C? (1) 4 (2)3 (3) 5 (4) 1 5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many days would the pasture last if 20 cows were to graze on it. (1) 90 days (2) 80 days (3) 100 days (4) 120 days Directions for questions 6 – 8: Refer to the following data for the following questions. A polynomial of the from a 1 1 n x + a 2 2 n x + ……. + a i i n x + …….. + a k k n x where n 1 > n 2 > …… > n k and a 1 ? 0 and 0 = I < k is represented by the sequence (a 1 , n 1 , a 2 , n 2 , a 3 , n 3 , ….., a k , n k ) 6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is (1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) (3) (4, 5, 2, 3, 5, 1) (4) None of these 7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is (1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) (3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these • A B F D E C C large C small Page 2 MOCK CAT SECTION – A 1. If m 2 a 2 + (n 2 + 1) b 2 + c 2 = 2b(mna – c), then which of the following statement(s) is/are necessarily true? I. ma = nb II. ma = – nc III. ma = nc (1) I only (2) only II and III (3) Only I and II (4) None of these 2. In the adjacent figure ABCDEF is a regular hexagon. Find the ratio of the radius of C large to that of radius of C small . (1) 1 2 1 2 - + (2) 3 2 3 2 - + (3) 1 2 (4) Can’t say Directions for questions 3 – 4: Refer to the following data for the following questions. There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A & C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 22 routes between B & C. 3. How many direct roads are there between A & B? (1) 4 (2)3 (3) 6 (4) 2 4. How many direct roads are there between B & C? (1) 4 (2)3 (3) 5 (4) 1 5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many days would the pasture last if 20 cows were to graze on it. (1) 90 days (2) 80 days (3) 100 days (4) 120 days Directions for questions 6 – 8: Refer to the following data for the following questions. A polynomial of the from a 1 1 n x + a 2 2 n x + ……. + a i i n x + …….. + a k k n x where n 1 > n 2 > …… > n k and a 1 ? 0 and 0 = I < k is represented by the sequence (a 1 , n 1 , a 2 , n 2 , a 3 , n 3 , ….., a k , n k ) 6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is (1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) (3) (4, 5, 2, 3, 5, 1) (4) None of these 7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is (1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) (3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these • A B F D E C C large C small 8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y = (1) (1, 1, 2, 0) (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these 9. For some digit ‘a’ we have 0.a25a25a25 ... = 810 K , where K is a positive integer. Find the hundred place of K. (1) 5 (2)7 (3) 9 (4) 3 10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by 1000? (1) 240 (2) 312 (3) 120 (4) 100 11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now guess at this stage how many buses with Blue number plates are there? (1) 50 (2) 60 (3) 75 (4)90 12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the time now? (1) 8 : 07 (2) 8 : 09 (3) 8 : 45 (4) None of these 13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to ensure each received an equal amount. But when we counted & found that each had 18 except one who had only 12. I calculated that if the number of children was subtracted from the total number of chocolates, it would equal to 1014. So guess how many children came in my birthday party? (1) 17 (2) 55 (3) 60 (4)65 14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10 more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of pants, shirts & T-shirts are respectively. (1) 170, 120, 180 (2) 150, 130, 190 (3) 120, 150, 200 (4) None of these 15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. Find the 1000th term. (1) 1038 (2) 1028 (3) 1039 (4) 1041 16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5% and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30% of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of the total time allotted is the time wasted by Munish? (1) 38.33% (2) 39.4545% (3) 49.09% (4) Cannot be determined Page 3 MOCK CAT SECTION – A 1. If m 2 a 2 + (n 2 + 1) b 2 + c 2 = 2b(mna – c), then which of the following statement(s) is/are necessarily true? I. ma = nb II. ma = – nc III. ma = nc (1) I only (2) only II and III (3) Only I and II (4) None of these 2. In the adjacent figure ABCDEF is a regular hexagon. Find the ratio of the radius of C large to that of radius of C small . (1) 1 2 1 2 - + (2) 3 2 3 2 - + (3) 1 2 (4) Can’t say Directions for questions 3 – 4: Refer to the following data for the following questions. There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A & C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 22 routes between B & C. 3. How many direct roads are there between A & B? (1) 4 (2)3 (3) 6 (4) 2 4. How many direct roads are there between B & C? (1) 4 (2)3 (3) 5 (4) 1 5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many days would the pasture last if 20 cows were to graze on it. (1) 90 days (2) 80 days (3) 100 days (4) 120 days Directions for questions 6 – 8: Refer to the following data for the following questions. A polynomial of the from a 1 1 n x + a 2 2 n x + ……. + a i i n x + …….. + a k k n x where n 1 > n 2 > …… > n k and a 1 ? 0 and 0 = I < k is represented by the sequence (a 1 , n 1 , a 2 , n 2 , a 3 , n 3 , ….., a k , n k ) 6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is (1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) (3) (4, 5, 2, 3, 5, 1) (4) None of these 7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is (1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) (3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these • A B F D E C C large C small 8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y = (1) (1, 1, 2, 0) (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these 9. For some digit ‘a’ we have 0.a25a25a25 ... = 810 K , where K is a positive integer. Find the hundred place of K. (1) 5 (2)7 (3) 9 (4) 3 10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by 1000? (1) 240 (2) 312 (3) 120 (4) 100 11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now guess at this stage how many buses with Blue number plates are there? (1) 50 (2) 60 (3) 75 (4)90 12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the time now? (1) 8 : 07 (2) 8 : 09 (3) 8 : 45 (4) None of these 13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to ensure each received an equal amount. But when we counted & found that each had 18 except one who had only 12. I calculated that if the number of children was subtracted from the total number of chocolates, it would equal to 1014. So guess how many children came in my birthday party? (1) 17 (2) 55 (3) 60 (4)65 14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10 more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of pants, shirts & T-shirts are respectively. (1) 170, 120, 180 (2) 150, 130, 190 (3) 120, 150, 200 (4) None of these 15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. Find the 1000th term. (1) 1038 (2) 1028 (3) 1039 (4) 1041 16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5% and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30% of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of the total time allotted is the time wasted by Munish? (1) 38.33% (2) 39.4545% (3) 49.09% (4) Cannot be determined 17. An electronic lock has 10 digit codes. A combination is any subset of 5 digits. It can be opened by the combination in any order. Let there be X combinations possible. Suppose it is redesigned to allow a combination to be any subset of 1 to 9 digits. What is the approx. percentage increase in total combinations? (1) 210 (2) 305 (3) 83 (4) 350 18. If M = 107, N = 108, O = 109, P = 110 then the square root of (1 + (M + 1)(N + 1)(O + 1)(P + 1)) (1) 11989 (2) 11909 (3) 10979 (4) 9069 19. Five consecutive positive integers are such whose sum is a cube and sum of the middle three is a square, find the smallest possible middle integer. (1) 27 (2) 125 (3) 675 (4) 225 20. If 16 101 + 8 101 + 4 101 + 2 101 + 1 is divided by 2 100 + 1, then the remainder is (1) 0 (2) 11 (3)4 (4) 2 21. At how many points does the graph of y = (x – 2) (2x 2 – 5x + 4) (2x 2 – 7x + 4) intersect the x-axis? (1) 0 (2) 1 (3) 2 (4) 3 22. A child starts counting all the natural numbers starting from one. After sometime he stops and finds that he has not counted one of the numbers and also that he has counted one other number thrice. To his surprise he finds that the final count is the same as he would have got without making any mistake. What is the total number of such combinations possible if the count was 496? (1) 14 (2) 15 (3) 16 (4) None of these 23. Give that 1025/1024 = 1.0009765625, what is the sum of the digits of 5 10 ? (1) 36 (2) 40 (3)41 (4) 50 24. f(x, y) is defined for positive integers x, y and satisfies f(x, x) = x, f(x, y) = f(y, x), f(x, x + y) = (1 + x/y) f(x, y). Find f(14, 52). (1) 246 (2) 424 (3) 190 (4) 364 25. A biased coin has probability p of coming up tails. If it is tossed five times, the probability of just two tails is the same as the probability of just one tail. Find the probability of just three tails in five tosses. (1) 5 3 40 (2) 16 5 (3) 5 3 25 (4) 5 3 10 Page 4 MOCK CAT SECTION – A 1. If m 2 a 2 + (n 2 + 1) b 2 + c 2 = 2b(mna – c), then which of the following statement(s) is/are necessarily true? I. ma = nb II. ma = – nc III. ma = nc (1) I only (2) only II and III (3) Only I and II (4) None of these 2. In the adjacent figure ABCDEF is a regular hexagon. Find the ratio of the radius of C large to that of radius of C small . (1) 1 2 1 2 - + (2) 3 2 3 2 - + (3) 1 2 (4) Can’t say Directions for questions 3 – 4: Refer to the following data for the following questions. There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A & C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 22 routes between B & C. 3. How many direct roads are there between A & B? (1) 4 (2)3 (3) 6 (4) 2 4. How many direct roads are there between B & C? (1) 4 (2)3 (3) 5 (4) 1 5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many days would the pasture last if 20 cows were to graze on it. (1) 90 days (2) 80 days (3) 100 days (4) 120 days Directions for questions 6 – 8: Refer to the following data for the following questions. A polynomial of the from a 1 1 n x + a 2 2 n x + ……. + a i i n x + …….. + a k k n x where n 1 > n 2 > …… > n k and a 1 ? 0 and 0 = I < k is represented by the sequence (a 1 , n 1 , a 2 , n 2 , a 3 , n 3 , ….., a k , n k ) 6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is (1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) (3) (4, 5, 2, 3, 5, 1) (4) None of these 7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is (1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) (3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these • A B F D E C C large C small 8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y = (1) (1, 1, 2, 0) (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these 9. For some digit ‘a’ we have 0.a25a25a25 ... = 810 K , where K is a positive integer. Find the hundred place of K. (1) 5 (2)7 (3) 9 (4) 3 10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by 1000? (1) 240 (2) 312 (3) 120 (4) 100 11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now guess at this stage how many buses with Blue number plates are there? (1) 50 (2) 60 (3) 75 (4)90 12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the time now? (1) 8 : 07 (2) 8 : 09 (3) 8 : 45 (4) None of these 13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to ensure each received an equal amount. But when we counted & found that each had 18 except one who had only 12. I calculated that if the number of children was subtracted from the total number of chocolates, it would equal to 1014. So guess how many children came in my birthday party? (1) 17 (2) 55 (3) 60 (4)65 14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10 more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of pants, shirts & T-shirts are respectively. (1) 170, 120, 180 (2) 150, 130, 190 (3) 120, 150, 200 (4) None of these 15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. Find the 1000th term. (1) 1038 (2) 1028 (3) 1039 (4) 1041 16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5% and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30% of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of the total time allotted is the time wasted by Munish? (1) 38.33% (2) 39.4545% (3) 49.09% (4) Cannot be determined 17. An electronic lock has 10 digit codes. A combination is any subset of 5 digits. It can be opened by the combination in any order. Let there be X combinations possible. Suppose it is redesigned to allow a combination to be any subset of 1 to 9 digits. What is the approx. percentage increase in total combinations? (1) 210 (2) 305 (3) 83 (4) 350 18. If M = 107, N = 108, O = 109, P = 110 then the square root of (1 + (M + 1)(N + 1)(O + 1)(P + 1)) (1) 11989 (2) 11909 (3) 10979 (4) 9069 19. Five consecutive positive integers are such whose sum is a cube and sum of the middle three is a square, find the smallest possible middle integer. (1) 27 (2) 125 (3) 675 (4) 225 20. If 16 101 + 8 101 + 4 101 + 2 101 + 1 is divided by 2 100 + 1, then the remainder is (1) 0 (2) 11 (3)4 (4) 2 21. At how many points does the graph of y = (x – 2) (2x 2 – 5x + 4) (2x 2 – 7x + 4) intersect the x-axis? (1) 0 (2) 1 (3) 2 (4) 3 22. A child starts counting all the natural numbers starting from one. After sometime he stops and finds that he has not counted one of the numbers and also that he has counted one other number thrice. To his surprise he finds that the final count is the same as he would have got without making any mistake. What is the total number of such combinations possible if the count was 496? (1) 14 (2) 15 (3) 16 (4) None of these 23. Give that 1025/1024 = 1.0009765625, what is the sum of the digits of 5 10 ? (1) 36 (2) 40 (3)41 (4) 50 24. f(x, y) is defined for positive integers x, y and satisfies f(x, x) = x, f(x, y) = f(y, x), f(x, x + y) = (1 + x/y) f(x, y). Find f(14, 52). (1) 246 (2) 424 (3) 190 (4) 364 25. A biased coin has probability p of coming up tails. If it is tossed five times, the probability of just two tails is the same as the probability of just one tail. Find the probability of just three tails in five tosses. (1) 5 3 40 (2) 16 5 (3) 5 3 25 (4) 5 3 10 SECTION – B Directions for questions 26 – 28: Read the following and answer the questions that follow the BSNL announced a cut in the STD rates on 27 December 2001. The new rates and slabs are given in the table below and are to be implemented from the 14 January 2002. SLAB DETAILS Rates (Rs./min) Distance Peak Rates Off Peak Old New Old New 50 – 200 4.8 2.4 1.2 1.2 200 – 500 11.6 4.8 3 2.4 500 – 1000 17.56 9.00 4.5 4.5 1000+ 17.56 9.00 6 4.5 26. The maximum percentage reduction in costs will be experienced for calls over which of the following distances? (1) 50-200 (2) 500-1000 (3) 1000+ (4) 200-500 27. The percentage difference in the cost of a set of telephone calls made on the 13 th and 14 th January having durations of 4 minutes over a distance of 350 km, 3 minutes for a distance of 700 km and 3 minutes for a distance of 1050 kms is (if all the three calls are made in peak times) (1) 51.2% (2) 51.76% (3) 59.8% (4) Cannot be determined 28. If one of the three calls in question 48 were made in an off peak time on both days, then the percentage reduction in the total cost of the calls between 13 th and 14 th January will (1) Definitely reduce (2) Definitely increase (3) Will depend on which particular call was made in an off peak time (4) Cannot be determined Directions for questions 29 – 31: Refer to the graphs below: 2869.7 2330.8 2135.5 3352.1 3790.9 93-94 92-93 91-92 90-91 89-90 Flls & Public 40.29% Fls 42.84% Tata Group 7% Directors 0.03% Foreign Companies 1.50% Other Companies 4.14% Bank & Mutual Funds 4.17 Govt Companies 0.03% 180.8 127.1 214.1 160.1 148.5 93-94 92-93 91-92 90-91 89-90 SHARE HOLDING PATTERN SALES FOR ALL THE YEARS PROFIT Figures in Rs. Crores Figures in Rs. Crores Page 5 MOCK CAT SECTION – A 1. If m 2 a 2 + (n 2 + 1) b 2 + c 2 = 2b(mna – c), then which of the following statement(s) is/are necessarily true? I. ma = nb II. ma = – nc III. ma = nc (1) I only (2) only II and III (3) Only I and II (4) None of these 2. In the adjacent figure ABCDEF is a regular hexagon. Find the ratio of the radius of C large to that of radius of C small . (1) 1 2 1 2 - + (2) 3 2 3 2 - + (3) 1 2 (4) Can’t say Directions for questions 3 – 4: Refer to the following data for the following questions. There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A & C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 22 routes between B & C. 3. How many direct roads are there between A & B? (1) 4 (2)3 (3) 6 (4) 2 4. How many direct roads are there between B & C? (1) 4 (2)3 (3) 5 (4) 1 5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many days would the pasture last if 20 cows were to graze on it. (1) 90 days (2) 80 days (3) 100 days (4) 120 days Directions for questions 6 – 8: Refer to the following data for the following questions. A polynomial of the from a 1 1 n x + a 2 2 n x + ……. + a i i n x + …….. + a k k n x where n 1 > n 2 > …… > n k and a 1 ? 0 and 0 = I < k is represented by the sequence (a 1 , n 1 , a 2 , n 2 , a 3 , n 3 , ….., a k , n k ) 6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is (1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) (3) (4, 5, 2, 3, 5, 1) (4) None of these 7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is (1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) (3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these • A B F D E C C large C small 8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y = (1) (1, 1, 2, 0) (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these 9. For some digit ‘a’ we have 0.a25a25a25 ... = 810 K , where K is a positive integer. Find the hundred place of K. (1) 5 (2)7 (3) 9 (4) 3 10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by 1000? (1) 240 (2) 312 (3) 120 (4) 100 11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now guess at this stage how many buses with Blue number plates are there? (1) 50 (2) 60 (3) 75 (4)90 12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the time now? (1) 8 : 07 (2) 8 : 09 (3) 8 : 45 (4) None of these 13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to ensure each received an equal amount. But when we counted & found that each had 18 except one who had only 12. I calculated that if the number of children was subtracted from the total number of chocolates, it would equal to 1014. So guess how many children came in my birthday party? (1) 17 (2) 55 (3) 60 (4)65 14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10 more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of pants, shirts & T-shirts are respectively. (1) 170, 120, 180 (2) 150, 130, 190 (3) 120, 150, 200 (4) None of these 15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. Find the 1000th term. (1) 1038 (2) 1028 (3) 1039 (4) 1041 16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5% and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30% of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of the total time allotted is the time wasted by Munish? (1) 38.33% (2) 39.4545% (3) 49.09% (4) Cannot be determined 17. An electronic lock has 10 digit codes. A combination is any subset of 5 digits. It can be opened by the combination in any order. Let there be X combinations possible. Suppose it is redesigned to allow a combination to be any subset of 1 to 9 digits. What is the approx. percentage increase in total combinations? (1) 210 (2) 305 (3) 83 (4) 350 18. If M = 107, N = 108, O = 109, P = 110 then the square root of (1 + (M + 1)(N + 1)(O + 1)(P + 1)) (1) 11989 (2) 11909 (3) 10979 (4) 9069 19. Five consecutive positive integers are such whose sum is a cube and sum of the middle three is a square, find the smallest possible middle integer. (1) 27 (2) 125 (3) 675 (4) 225 20. If 16 101 + 8 101 + 4 101 + 2 101 + 1 is divided by 2 100 + 1, then the remainder is (1) 0 (2) 11 (3)4 (4) 2 21. At how many points does the graph of y = (x – 2) (2x 2 – 5x + 4) (2x 2 – 7x + 4) intersect the x-axis? (1) 0 (2) 1 (3) 2 (4) 3 22. A child starts counting all the natural numbers starting from one. After sometime he stops and finds that he has not counted one of the numbers and also that he has counted one other number thrice. To his surprise he finds that the final count is the same as he would have got without making any mistake. What is the total number of such combinations possible if the count was 496? (1) 14 (2) 15 (3) 16 (4) None of these 23. Give that 1025/1024 = 1.0009765625, what is the sum of the digits of 5 10 ? (1) 36 (2) 40 (3)41 (4) 50 24. f(x, y) is defined for positive integers x, y and satisfies f(x, x) = x, f(x, y) = f(y, x), f(x, x + y) = (1 + x/y) f(x, y). Find f(14, 52). (1) 246 (2) 424 (3) 190 (4) 364 25. A biased coin has probability p of coming up tails. If it is tossed five times, the probability of just two tails is the same as the probability of just one tail. Find the probability of just three tails in five tosses. (1) 5 3 40 (2) 16 5 (3) 5 3 25 (4) 5 3 10 SECTION – B Directions for questions 26 – 28: Read the following and answer the questions that follow the BSNL announced a cut in the STD rates on 27 December 2001. The new rates and slabs are given in the table below and are to be implemented from the 14 January 2002. SLAB DETAILS Rates (Rs./min) Distance Peak Rates Off Peak Old New Old New 50 – 200 4.8 2.4 1.2 1.2 200 – 500 11.6 4.8 3 2.4 500 – 1000 17.56 9.00 4.5 4.5 1000+ 17.56 9.00 6 4.5 26. The maximum percentage reduction in costs will be experienced for calls over which of the following distances? (1) 50-200 (2) 500-1000 (3) 1000+ (4) 200-500 27. The percentage difference in the cost of a set of telephone calls made on the 13 th and 14 th January having durations of 4 minutes over a distance of 350 km, 3 minutes for a distance of 700 km and 3 minutes for a distance of 1050 kms is (if all the three calls are made in peak times) (1) 51.2% (2) 51.76% (3) 59.8% (4) Cannot be determined 28. If one of the three calls in question 48 were made in an off peak time on both days, then the percentage reduction in the total cost of the calls between 13 th and 14 th January will (1) Definitely reduce (2) Definitely increase (3) Will depend on which particular call was made in an off peak time (4) Cannot be determined Directions for questions 29 – 31: Refer to the graphs below: 2869.7 2330.8 2135.5 3352.1 3790.9 93-94 92-93 91-92 90-91 89-90 Flls & Public 40.29% Fls 42.84% Tata Group 7% Directors 0.03% Foreign Companies 1.50% Other Companies 4.14% Bank & Mutual Funds 4.17 Govt Companies 0.03% 180.8 127.1 214.1 160.1 148.5 93-94 92-93 91-92 90-91 89-90 SHARE HOLDING PATTERN SALES FOR ALL THE YEARS PROFIT Figures in Rs. Crores Figures in Rs. Crores 29. If profits have to be distributed in the ratio of the shareholding, the difference of profit of Tata Group in 90-91 and profit of Banks and mutual funds in 93-94, will be (Rs.) : (1) 3.66 crores (2) 4.98 crores (3) 3.15 crores (4) 2.34 crores 30. The angles subtended by the FIs and FIIs & public (at the center of the pie chart) differ by : (1) 8.36 o (2) 8.8 o (3) 9.18 o (4) 9.36 o 31. The approximate Average annual growth rate of ‘sales’ from 89-90 to 92-93 is: (1) 19% (2) 21% (3) 17% (4) 22% Directions for questions 32 – 36: The chart below shows the distances in km between four villages A, B, C and D which are connected by straight roads. – A B C D A – 15 13 24 B 15 – 12 28 C 13 12 – 21 D 24 28 21 – 32. If a health visitor has to visit all the villages starting form B and to return to B, which is the shortest route he should take? (1) B A C D B (2) B A D C B (3) B D C A B (4) B D A C B 33. Health camps have to be set up in two of the four villages, so that the distances from the remaining two villages to the health camps may be the least. Which two villages should be selected? (1) B and C (2) A and C (3) A and D (4) C and D 34. If a village E is 8 km from A on the road to B, what is E’s distance from C? (1) 10 km (2) 18 km (3) 9 km (4) 20 km 35. If the bus fare along route ABD is Re.0.25 per km and along ACD it is Re.0.18 per km, which route is less expensive and by how much? (1) ABD by Rs. 2.83 (2) ACD by Rs. 4.63 (3) ABD by Rs. 1.25 (4) ACD by Rs. 1.35 36. If a village is equidistant from B, C and A, what is its distance from B? (1) 10 km (2) 12 km (3) 8 km (4) 16 km Directions for questions 37 – 41: Study the data and answer the following questions. Two machines X and Y can produce three different types of spare parts A, B and C for motor vehicles. X can produce 1, 4 and 3 of A, B and C respectively in one hour while Y takes ½, 3/8, and 1/8 hour respectively to produce one A, B and C. Each machine can produce only one article at a time and can work for 20 hours per day. 37. 70 of A, 30 of B and 60 of C are required to be produced. Which machine will take less time to produce these? (1)X (2) Y (3) Both will take same time (4) Cannot be foundRead More

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