2Common Proficiency Test Model Paper 3

dy 172. if y = x log (log x); then is dx (a) y ⎡ ⎣log ( logx )+1⎤ ⎦ (b) x ⎡ ⎣log ( logx )+1⎤ ⎦ x y (c) − x ⎡ ⎣log ( logx )+1⎤ ⎦ (d) None of these y 1 x+ , dy 1 173. If y = x+ then is dx x x4+x2+2 x4+x2+2 (a) (x2+1)2 (b) x2+1 (x4+x2+2)2 (c) x2+1 (d) None of these y x dy + =6,then is 174. If x y dx x+17y x−17y (a) 17x+y (b) 17x+y x−17y (c) 17x−y (d) None of these ∑3 47c + 50-jc 175. Evaluate : 4 3 j=0 (a) 249900 (b) 24990 (c) 249000 (d) None of these Common Proficiency Test (CPT) Volume - II 269 © The Institute of Chartered Accountants of India MODEL TEST PAPER - 10 176. The first term of an A.P. is 100 and the sum of whose first 6 terms is 5 times the sum of the next 6 terms, then the c.d. is – (a) –10 (b) 10 (c) 5 (d) None of these 177. The sum of n terms of an A.P. is 3n2+n; then its pth term is (a) 6P + 2 (b) 6P – 2 (d) 6P – 1 (d) None of these 178. The sum of first m terms of an A.P. is same as the sum of first n terms, where m¹ n; then the sum of first (m+n) terms is: (a) 0 (b) 1 (c) –1 (d) None of these -9 -7 179. Which term of the sequence, ,-2, , ................ is zero. 4 4 (a) 9th term (b) 10th term (c) 12th term (d) None of these 180. If 6 times of 6th term of an A.P. is equal to 15 times the 15th term, then its 21st term. (a) 1 (b) –1 (c) 0 (d) None of these 181. The average of n numbers is x. If each of the numbers is multiplied by (n+1); then the average of new set of numbers is x (a) x (b) n+1 (c) (n + 1).x (d) None of these 182. The average weight of 8 person increases by 1.5 kg, if a person weighing 65 kg replaced by a new person, what would be the weight of the new person? (a) 76 kg (b) 80 kg (c) 77 kg (d) None of these 183. The average of marks obtained by 120 students in a certain examination is 135. If the average marks of passed students is 39 and that of the failed students is 15; what is the number of students who passed in the examination? (a) 100 (b) 150 (c) 200 (d) None of these 270 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 184. The average of 17 numbers is 45. The average of first 9 of these numbers is 51 and the last 9 of these numbers is 36. Find the 9th number? (a) 5 (b) 14 (c) 18 (d) None of these 185. The average of 11 results is 30, that of the first five is 25 and that of the last five is 28. Find the value of the 6th number? (a) 60 (b) 65 (d) 75 (d) None of these 186. There are ……………. Tests for Index Number (a) Four (b) Three (c) Five (d) None of these 187. Laspeyre’s & Paasche’s Index Number satisfy the time reversal test. (a) True (b) False (c) Either (a) or (b) (d) None of these 188. If one card is drawn at random from a pack of playing cards; find the probability it is neither a hearts nor a club: 1 3 (a) (b) 2 4 1 (c) (d) None of these 8 189. Three balls are drawn at random from a bag containing 6 blue and 4 red balls. What is the chance that 2 balls are blue and 1 is red? 1 3 (a) (b) 4 4 1 (c) (d) None of these 2 190. Find the probability of 53 Mondays in a leap year? 2 3 (a) (b) 7 7 4 (c) (d) None of these 7 Common Proficiency Test (CPT) Volume - II 271 © The Institute of Chartered Accountants of India MODEL TEST PAPER - 10 1 3 191. If A & B are independent events and P(A) = & P(B) = ; then P(AUB) is 3 4 2 5 (a) (b) 6 6 1 (c) (d) None of these 6 192. Two letters are drawn at random from the word “HOME” Find the probability that both the letters are vowel? 1 5 (a) (b) 6 6 2 (c) (d) None of these 3 193. Two letters are drawn at random from the word “HOME” Find the probability that at least one is vowel? 5 1 (a) (b) 6 6 1 (c) (d) None of these 3 194. Two letters are drawn at random from the word “HOME” Find the probability that one of the letters selected should be M. 1 1 (a) (b) 4 2 3 (c) (d) None of these 4 195. A and B are two mutually exclusive events of an experiments. If P (‘not A’) = 0.65, P (AUB) = 0.65 and P(B) = p. Then the value of p is (a) 0.35 (b) 0.60 (c) 0.3 (d) None of these 196. Find the sum of n terms of the given series (a) 2n–n–1 (b) 1–2–n (c) n+2–n–1 (d) 2n–1 272 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 197. Let f(x) be a polynomial function of second degree and a , a , a are in A.P. then 1 2 3 f’ (a ) and f’ (a ) are in 2 3 (a) A.P. (b) G.P. (c) Either A.P. or G.P. (d) None of these 198. A man borrows Rs. 20,000 at interest rate 4% per annum compounded annually and agrees to pay both the principal and the interest in 10 equal instalments at the end of each year. Find the value of each instalment (approx.) (Given log 104 = 2.0170 and log 6761 = 3.8300). (a) Rs. 2,470 (b) Rs. 3,470 (d) Rs. 5,470 (d) None of these 199. Two regression coefficient bxy and byx are 1.2 and –0.5. This is (a) True (b) False (c) Either (a) or (b) (d) None of these 200. The mean of Poisson distribution is 1.6 and variance is 2. This is (a) True (b) False (c) Either (a) or (b) (d) None of these Common Proficiency Test (CPT) Volume - II 273 © The Institute of Chartered Accountants of India © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 1 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (d) 2. (d) 3. (b) 4. (a) 5. (d) 6. (a) 7. (b) 8. (a) 9. (c) 10. (b) 11. (c) 12. (a) 13. (d) 14. (b) 15. (a) 16. (d) 17. (b) 18. (a) 19. (b) 20. (d) 21. (c) 22. (c) 23. (b) 24. (c) 25. (a) 26. (b) 27. (b) 28. (d) 29. (b) 30. (c) 31. (b) 32. (c) 33. (a) 34. (a) 35. (c) 36. (d) 37. (a) 38. (c) 39. (b) 40. (a) 41. (b) 42. (b) 43. (c) 44. (a) 45. (c) 46. (b) 47. (d) 48. (a) 49. (c) 50. (b) 51. (c) 52. (a) 53. (b) 54. (a) 55. (b) 56. (d) 57. (a) 58. (c) 59. (d) 60. (b) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (c) 62. (d) 63. (a) 64. (b) 65. (a) 66. (a) 67. (d) 68. (c) 69. (c) 70. (b) 71. (a) 72. (a) 73. (a) 74. (b) 75. (a) 76. (c) 77. (d) 78. (c) 79. (b) 80. (b) 81. (a) 82. (a) 83. (c) 84. (d) 85. (d) 86. (a) 87. (b) 88. (b) 89. (a) 90. (a) 91. (a) 92. (d) 93. (b) 94. (b) 95. (b) 96. (b) 97. (c) 98. (d) 99. (b) 100. (a) Common Proficiency Test (CPT) Volume - II 275 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 1 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (d) 121 (b) 131 (c) 141 (b) 102 (a) 112 (d) 122 (a) 132 (b) 142 (c) 103 (c) 113 (a) 123 (c) 133 (d) 143 (b) 104 (a) 114 (c) 124 (d) 134 (c) 144 (a) 105 (a) 115 (b) 125 (b) 135 (b) 145 (b) 106 (b) 116 (c) 126 (c) 136 (a) 146 (b) 107 (c) 117 (b) 127 (b) 137 (b) 147 (d) 108 (a) 118 (a) 128 (d) 138 (c) 148 (b) 109 (d) 119 (b) 129 (c) 139 (b) 149 (a) 110 (b) 120 (c) 130 (c) 140 (c) 150 (d) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (a) 152. (c) 153. (d) 154. (b) 155. (a) 156. (a) 157. (c) 158. (a) 159. (b) 160. (c) 161. (b) 162. (d) 163. (b) 164. (a) 165. (a) 166. (b) 167. (c) 168. (a) 169. (c) 170. (b) 171. (c) 172. (a) 173. (c) 174. (a) 175. (b) 176. (a) 177. (c) 178. (d) 179. (b) 180. (a) 181. (a) 182. (c) 183. (b) 184. (a) 185. (a) 186. (a) 187. (b) 188. (a) 189. (b) 190. (a) 191. (b) 192. (a) 193. (b) 194. (c) 195. (b) 196. (b) 197. (a) 198. (b) 199. (a) 200. (c ) 276 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 2 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (c) 2. (d) 3. (a) 4. (b) 5. (c) 6. (a) 7. (c) 8. (b) 9. (a) 10. (c) 11. (b) 12. (d) 13. (c) 14. (b) 15. (c) 16. (a) 17. (a) 18. (c) 19. (b) 20. (b) 21. (c) 22. (d) 23. (d) 24. (a) 25. (c) 26. (b) 27. (c) 28. (a) 29. (d) 30. (b) 31. (c) 32. (a) 33. (b) 34. (a) 35. (b) 36. (b) 37. (c) 38. (d) 39. (c) 40. (a) 41. (a) 42. (b) 43. (d) 44. (c) 45. (a) 46. (c) 47. (a) 48. (a) 49. (b) 50. (a) 51. (c) 52. (a) 53. (d) 54. (b) 55. (c) 56. (a) 57. (b) 58. (d) 59. (a) 60. (c) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (a) 62. (b) 63. (a) 64. (a) 65. (b) 66. (a) 67. (c) 68. (d) 69. (d) 70. (c) 71. (a) 72. (d) 73. (c) 74. (a) 75. (c) 76. (c) 77. (c) 78. (c) 79. (c) 80. (b) 81. (a) 82. (d) 83. (b) 84. (b) 85. (a) 86. (c) 87. (d) 88. (a) 89. (b) 90. (c) 91. (a) 92. (a) 93. (d) 94. (a) 95. (c) 96. (a) 97. (d) 98. (a) 99. (c) 100. (c) Common Proficiency Test (CPT) Volume - II 277 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 2 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (a) 111 (b) 121 (a) 131 (b) 141 (a) 102 (c) 112 (d) 122 (b) 132 (c) 142 (c) 103 (c) 113 (b) 123 (d) 133 (a) 143 (d) 104 (d) 114 (b) 124 (d) 134 (c) 144 (a) 105 (b) 115 (a) 125 (c) 135 (a) 145 (c) 106 (c) 116 (d) 126 (d) 136 (d) 146 (c) 107 (d) 117 (c) 127 (a) 137 (a) 147 (d) 108 (d) 118 (d) 128 (b) 138 (b) 148 (b) 109 (d) 119 (b) 129 (a) 139 (d) 149 (d) 110 (d) 120 (a) 130 (b) 140 (a) 150 (a) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (a) 152. (b) 153. (a) 154. (a) 155. (c) 156. () 157. (c) 158. (b) 159. (a) 160. (c) 161. (a) 162. (b) 163. (b) 164. (a) 165. (b) 166. (b) 167. (b) 168. (c) 169. (b) 170. (b) 171. (c) 172. (a) 173. (c) 174. (d) 175. (b) 176. (a) 177. (a) 178. (b) 179. (a) 180. (a) 181. (b) 182. (b) 183. (a) 184. (c) 185. (b) 186. (b) 187. (a) 188. (c) 189. (a) 190. (b) 191. (b) 192. (a) 193. (a) 194. (b) 195. (c) 196. (a) 197. (b) 198. (a) 199. (c) 200. (b) 278 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 3 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (a) 2. (c) 3. (c) 4. (c) 5. (a) 6. (a) 7. (b) 8. (b) 9. (a) 10. (b) 11. (d) 12. (d) 13. (d) 14. (c) 15. (a) 16. (a) 17. (a) 18. (a) 19. (a) 20. (c) 21. (b) 22. (a) 23. (c) 24. (d) 25. (a) 26. (c) 27. (a) 28. (d) 29. (b) 30. (b) 31. (b) 32. (a) 33. (c) 34. (d) 35. (a) 36. (d) 37. (d) 38. (a) 39. (c) 40. (a) 41. (b) 42. (c) 43. (c) 44. (c) 45. (c) 46. (b) 47. (a) 48. (c) 49. (d) 50. (b) 51. (b) 52. (a) 53. (b) 54. (b) 55. (d) 56. (b) 57. (d) 58. (a) 59. (b) 60. (c) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (c) 62. (d) 63. (d) 64. (d) 65. (c) 66. (b) 67. (d) 68. (a) 69. (c) 70. (a) 71. (a) 72. (c) 73. (c) 74. (d) 75. (a) 76. (a) 77. (b) 78. (a) 79. (b) 80. (c) 81. (b) 82. (a) 83. (b) 84. (c) 85. (c) 86. (c) 87. (b) 88. (c) 89. (d) 90. (b) 91. (b) 92. (a) 93. (c) 94. (c) 95. (c) 96. (a) 97. (c) 98. (b) 99. (b) 100. (a) Common Proficiency Test (CPT) Volume - II 279 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 3 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (d) 111 (a) 121 (d) 131 (d) 141 (b) 102 (b) 112 (d) 122 (c) 132 (a) 142 (d) 103 (b) 113 (c) 123 (b) 133 (c) 143 (d) 104 (c) 114 (c) 124 (c) 134 (a) 144 (a) 105 (c) 115 (b) 125 (a) 135 (d) 145 (b) 106 (a) 116 (d) 126 (c) 136 (a) 146 (c) 107 (b) 117 (a) 127 (a) 137 (a) 147 (b) 108 (b) 118 (c) 128 (d) 138 (b) 148 (d) 109 (c) 119 (a) 129 (c) 139 (d) 149 (b) 110 (d) 120 (d) 130 (b) 140 (c) 150 (c) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (b) 152. (c) 153. (a) 154. (b) 155. (c) 156. (c) 157. (a) 158. (b) 159. (b) 160. (c) 161. (b) 162. (a) 163. (b) 164. (a) 165. (b) 166. (c) 167. (b) 168. (c) 169. (a) 170. (b) 171. (d) 172. (a) 173. (c) 174. (b) 175. (a) 176. (a) 177. (c) 178. (a) 179. (c) 180. (a) 181. (a) 182. (a) 183. (a) 184. (d) 185. (c) 186. (b) 187. (a) 188. (c) 189. (a) 190. (a) 191. (c) 192. (b) 193. (a) 194. (b) 195. (a) 196. (a) 197. (c) 198. (b) 199. (a) 200. (c) 280 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 4 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (b) 2. (d) 3. (b) 4. (c) 5. (d) 6. (b) 7. (d) 8. (d) 9. (b) 10. (a) 11. (c) 12. (c) 13. (b) 14. (b) 15. (c) 16. (a) 17. (a) 18. (c) 19. (a) 20. (d) 21. (a) 22. (d) 23. (c) 24. (a) 25. (c) 26. (a) 27. (d) 28. (b) 29. (b) 30. (d) 31. (c) 32. (c) 33. (c) 34. (a) 35. (d) 36. (a) 37. (d) 38. (c) 39. (b) 40. (c) 41. (a) 42. (c) 43. (a) 44. (a) 45. (c) 46. (b) 47. (c) 48. (b) 49. (b) 50. (b) 51. (a) 52. (c) 53. (b) 54. (a) 55. (b) 56. (b) 57. (b) 58. (d) 59. (a) 60. (b) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (d) 62. (c) 63. (a) 64. (c) 65. (c) 66. (a) 67. (d) 68. (d) 69. (b) 70. (c) 71. (b) 72. (d) 73. (c) 74. (c) 75. (b) 76. (b) 77. (d) 78. (a) 79. (c) 80. (d) 81. (c) 82. (b) 83. (c) 84. (b) 85. (b) 86. (a) 87. (c) 88. (b) 89. (b) 90. (a) 91. (c) 92. (b) 93. (b) 94. (a) 95. (c) 96. (d) 97. (b) 98. (a) 99. (b) 100. (b) Common Proficiency Test (CPT) Volume - II 281 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 4 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (c) 111 (d) 121 (d) 131 (a) 141 (a) 102 (c) 112 (c) 122 (c) 132 (a) 142 (c) 103 (a) 113 (c) 123 (b) 133 (b) 143 (b) 104 (c) 114 (d) 124 (a) 134 (a) 144 (c) 105 (c) 115 (d) 125 (c) 135 (b) 145 (b) 106 (c) 116 (a) 126 (b) 136 (d) 146 (c) 107 (d) 117 (b) 127 (d) 137 (b) 147 (b) 108 (a) 118 (b) 128 (d) 138 (c) 148 (a) 109 (a) 119 (d) 129 (b) 139 (c) 149 (a) 110 (d) 120 (a) 130 (a) 140 (b) 150 (c) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (a) 152. (c) 153. (a) 154. (c) 155. (c) 156. (b) 157. (a) 158. (a) 159. (b) 160. (a) 161. (a) 162. (b) 163. (a) 164. (a) 165. (a) 166. (a) 167. (d) 168. (d) 169. (a) 170. (b) 171. (b) 172. (b) 173. (a) 174. (b) 175. (a) 176. (c) 177. (a) 178. (c) 179. (a) 180. (b) 181. (c) 182. (a) 183. (a) 184. (a) 185. (b) 186. (a) 187. (b) 188. (c) 189. (a) 190. (b) 191. (a) 192. (a) 193. (b) 194. (a) 195. (b) 196. (b) 197. (a) 198. (b) 199. (b) 200. (b) 282 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 5 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (a) 2. (d) 3. (c) 4. (d) 5. (b) 6. (a) 7. (d) 8. (a) 9. (c) 10. (b) 11. (d) 12. (b) 13. (a) 14. (c) 15. (d) 16. (a) 17. (d) 18. (c) 19. (c) 20. (d) 21. (a) 22. (b) 23. (c) 24. (b) 25. (a) 26. (c) 27. (d) 28. (c) 29. (a) 30. (b) 31. (c) 32. (a) 33. (d) 34. (d) 35. (a) 36. (c) 37. (b) 38. (c) 39. (c) 40. (b) 41. (b) 42. (d) 43. (a) 44. (a) 45. (d) 46. (c) 47. (a) 48. (b) 49. (c) 50. (b) 51. (a) 52. (d) 53. (a) 54. (b) 55. (c) 56. (c) 57. (b) 58. (b) 59. (b) 60. (d) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (a) 62. (b) 63. (d) 64. (d) 65. (b) 66. (b) 67. (b) 68. (d) 69. (c) 70. (b) 71. (a) 72. (c) 73. (a) 74. (b) 75. (b) 76. (d) 77. (a) 78. (c) 79. (d) 80. (b) 81. (a) 82. (c) 83. (a) 84. (c) 85. (a) 86. (a) 87. (c) 88. (b) 89. (c) 90. (b) 91. (b) 92. (d) 93. (d) 94. (c) 95. (a) 96. (a) 97. (a) 98. (b) 99. (b) 100. (b) Common Proficiency Test (CPT) Volume - II 283 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 5 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (b) 121 (c) 131 (b) 141 (d) 102 (c) 112 (b) 122 (a) 132 (a) 142 (a) 103 (d) 113 (d) 123 (a) 133 (a) 143 (a) 104 (c) 114 (b) 124 (a) 134 (b) 144 (d) 105 (d) 115 (c) 125 (c) 135 (a) 145 (c) 106 (a) 116 (a) 126 (c) 136 (b) 146 (c) 107 (b) 117 (b) 127 (b) 137 (b) 147 (a) 108 (a) 118 (b) 128 (a) 138 (a) 148 (b) 109 (b) 119 (b) 129 (d) 139 (d) 149 (b) 110 (d) 120 (a) 130 (d) 140 (a) 150 (d) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (b) 154. (a) 155. (b) 156. (b) 157. (b) 158. (c) 159. (a) 160. (b) 161. (a) 162. () 163. (a) 164. (a) 165. (a) 166. (b) 167. (b) 168. (a) 169. (c) 170. (a) 171. (a) 172. (c) 173. (a) 174. (b) 175. (c) 176. (a) 177. (b) 178. (a) 179. (c) 180. (a) 181. (a) 182. (b) 183. (b) 184. (a) 185. (d) 186. (c) 187. (c) 188. (b) 189. (a) 190. (b) 191. (a) 192. (a) 193. (b) 194. (b) 195. (c) 196. (c) 197. (b) 198. (b) 199. (b) 200. (b) 284 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 6 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (d) 2. (b) 3. (a) 4. (c) 5. (b) 6. (a) 7. (a) 8. (a) 9. (a) 10. (c) 11. (a) 12. (d) 13. (c) 14. (b) 15. (d) 16. (b) 17. (c) 18. (b) 19. (c) 20. (a) 21. (a) 22. (b) 23. (d) 24. (a) 25. (a) 26. (b) 27. (c) 28. (a) 29. (a) 30. (b) 31. (a) 32. (d) 33. (c) 34. (b) 35. (c) 36. (a) 37. (b) 38. (a) 39. (c) 40. (d) 41. (b) 42. (a) 43. (c) 44. (a) 45. (d) 46. (c) 47. (c) 48. (b) 49. (a) 50. (a) 51. (c) 52. (a) 53. (b) 54. (a) 55. (a) 56. (d) 57. (d) 58. (a) 59. (c) 60. (a) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (b) 62. (d) 63. (d) 64. (b) 65. (a) 66. (d) 67. (d) 68. (d) 69. (a) 70. (d) 71. (b) 72. (b) 73. (d) 74. (a) 75. (b) 76. (a) 77. (c) 78. (b) 79. (b) 80. (a) 81. (a) 82. (c) 83. (b) 84. (a) 85. (d) 86. (c) 87. (a) 88. (c) 89. (c) 90. (c) 91. (b) 92. (c) 93. (c) 94. (a) 95. (a) 96. (b) 97. (b) 98. (b) 99. (b) 100. (a) Common Proficiency Test (CPT) Volume - II 285 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 6 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (d) 111 (c) 121 (d) 131 (b) 141 (a) 102 (a) 112 (a) 122 (a) 132 (c) 142 (d) 103 (c) 113 (d) 123 (a) 133 (d) 143 (a) 104 (c) 114 (d) 124 (c) 134 (c) 144 (b) 105 (d) 115 (a) 125 (b) 135 (b) 145 (a) 106 (b) 116 (c) 126 (d) 136 (c) 146 (b) 107 (b) 117 (b) 127 (d) 137 (c) 147 (b) 108 (a) 118 (c) 128 (b) 138 (a) 148 (d) 109 (b) 119 (c) 129 (b) 139 (b) 149 (c) 110 (a) 120 (d) 130 (c) 140 (b) 150 (a) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (b) 152. (b) 153. (d) 154. (a) 155. (a) 156. (a) 157. (b) 158. (a) 159. (a) 160. (a) 161. (b) 162. (c) 163. (a) 164. () 165. (b) 166. (c) 167. (a) 168. (a) 169. (b) 170. (a) 171. (c) 172. (a) 173. (a) 174. (b) 175. (c) 176. (b) 177. (c) 178. (a) 179. (c) 180. (b) 181. (b) 182. (a) 183. (c) 184. (c) 185. (c) 186. (c) 187. (b) 188. (b) 189. (b) 190. (b) 191. (b) 192. (a) 193. (b) 194. (a) 195. (b) 196. (a) 197. (c) 198. (c) 199. (c) 200. (c) 286 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 7 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (c) 2. (b) 3. (b) 4. (d) 5. (c) 6. (c) 7. (b) 8. (c) 9. (c) 10. (a) 11. (b) 12. (a) 13. (b) 14. (d) 15. (d) 16. (c) 17. (a) 18. (d) 19. (a) 20. (b) 21. (b) 22. (b) 23. (a) 24. (c) 25. (d) 26. (a) 27. (c) 28. (d) 29. (c) 30. (d) 31. (b) 32. (d) 33. (b) 34. (a) 35. (d) 36. (a) 37. (c) 38. (d) 39. (b) 40. (b) 41. (d) 42. (c) 43. (d) 44. (b) 45. (a) 46. (c) 47. (c) 48. (a) 49. (b) 50. (c) 51. (b) 52. (c) 53. (c) 54. (d) 55. (b) 56. (b) 57. (d) 58. (a) 59. (c) 60. (b) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (c) 62. (c) 63. (d) 64. (a) 65. (c) 66. (d) 67. (d) 68. (c) 69. (b) 70. (a) 71. (b) 72. (d) 73. (c) 74. (c) 75. (c) 76. (c) 77. (b) 78. (d) 79. (c) 80. (a) 81. (d) 82. (a) 83. (c) 84. (c) 85. (a) 86. (d) 87. (d) 88. (a) 89. (a) 90. (d) 91. (c) 92. (b) 93. (b) 94. (c) 95. (b) 96. (d) 97. (a) 98. (b) 99. (d) 100. (a) Common Proficiency Test (CPT) Volume - II 287 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 7 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (d) 111 (c) 121 (a) 131 (c) 141 (b) 102 (a) 112 (b) 122 (b) 132 (c) 142 (a) 103 (b) 113 (b) 123 (d) 133 (c) 143 (c) 104 (d) 114 (c) 124 (a) 134 (d) 144 (d) 105 (a) 115 (a) 125 (a) 135 (c) 145 (d) 106 (b) 116 (b) 126 (c) 136 (b) 146 (d) 107 (c) 117 (d) 127 (a) 137 (c) 147 (a) 108 (d) 118 (b) 128 (d) 138 (a) 148 (b) 109 (c) 119 (b) 129 (d) 139 (d) 149 (a) 110 (d) 120 (d) 130 (b) 140 (a) 150 (b) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (d) 154. (a) 155. (d) 156. (a) 157. (a) 158. (a) 159. (b) 160. (c) 161. (b) 162. (c) 163. (c) 164. (b) 165. (a) 166. (c) 167. (a) 168. (b) 169. (b) 170. (c) 171. (a) 172. (a) 173. (b) 174. (c) 175. (a) 176. (b) 177. (b) 178. (a) 179. (b) 180. (a) 181. (c) 182. (a) 183. (c) 184. (b) 185. (c) 186. (a) 187. (b) 188. (c) 189. (b) 190. (a) 191. (a) 192. (a) 193. (b) 194. (a) 195. (c) 196. (a) 197. (b) 198. (b) 199. (a) 200. (c) 288 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 8 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (b) 2. (a) 3. (d) 4. (d) 5. (b) 6. (c) 7. (b) 8. (b) 9. (a) 10. (d) 11. (b) 12. (d) 13. (c) 14. (a) 15. (c) 16. (a) 17. (d) 18. (a) 19. (c) 20. (a) 21. (c) 22. (d) 23. (c) 24. (a) 25. (a) 26. (b) 27. (a) 28. (d) 29. (c) 30. (d) 31. (b) 32. (d) 33. (c) 34. (a) 35. (b) 36. (c) 37. (d) 38. (a) 39. (c) 40. (d) 41. (b) 42. (c) 43. (c) 44. (d) 45. (c) 46. (b) 47. (c) 48. (a) 49. (c) 50. (b) 51. (d) 52. (c) 53. (b) 54. (c) 55. (a) 56. (d) 57. (b) 58. (a) 59. (c) 60. (b) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (d) 62. (a) 63. (c) 64. (b) 65. (c) 66. (d) 67. (c) 68. (d) 69. (d) 70. (b) 71. (d) 72. (c) 73. (c) 74. (b) 75. (b) 76. (a) 77. (b) 78. (a) 79. (b) 80. (c) 81. (d) 82. (c) 83. (b) 84. (b) 85. (d) 86. (c) 87. (a) 88. (c) 89. (a) 90. (a) 91. (a) 92. (c) 93. (d) 94. (d) 95. (c) 96. (a) 97. (a) 98. (a) 99. (c) 100. (a) Common Proficiency Test (CPT) Volume - II 289 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 8 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (c) 121 (b) 131 (a) 141 (c) 102 (b) 112 (a) 122 (b) 132 (b) 142 (c) 103 (a) 113 (d) 123 (c) 133 (a) 143 (c) 104 (a) 114 (d) 124 (a) 134 (d) 144 (d) 105 (a) 115 (a) 125 (a) 135 (b) 145 (d) 106 (b) 116 (d) 126 (a) 136 (c) 146 (d) 107 (a) 117 (b) 127 (b) 137 (b) 147 (d) 108 (b) 118 (b) 128 (d) 138 (b) 148 (a) 109 (c) 119 (d) 129 (c) 139 (d) 149 (a) 110 (d) 120 (a) 130 (c) 140 (d) 150 (d) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (b) 152. (a) 153. (b) 154. (c) 155. (a) 156. (c) 157. (c) 158. (c) 159. (a) 160. (b) 161. (b) 162. (c) 163. (c) 164. (a) 165. (b) 166. (b) 167. (c) 168. (a) 169. (a) 170. (b) 171. (b) 172. (a) 173. (b) 174. (d) 175. (a) 176. (a) 177. (c) 178. (b) 179. (b) 180. (b) 181. (a) 182. (c) 183. (a) 184. (b) 185. (a) 186. (c) 187. (a) 188. (c) 189. (d) 190. (b) 191. (a) 192. (a) 193. (a) 194. (c) 195. (a) 196. (a) 197. (d) 198. (b) 199. (a) 200. (a) 290 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 9 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (a) 2. (c) 3. (a) 4. (a) 5. (a) 6. (b) 7. (c) 8. (b) 9. (b) 10. (c) 11. (d) 12. (c) 13. (a) 14. (b) 15. (b) 16. (d) 17. (a) 18. (b) 19. (b) 20. (c) 21. (c) 22. (a) 23. (b) 24. (a) 25. (b) 26. (c) 27. (c) 28. (a) 29. (c) 30. (d) 31. (b) 32. (b) 33. (c) 34. (d) 35. (b) 36. (c) 37. (c) 38. (a) 39. (a) 40. (b) 41. (b) 42. (b) 43. (c) 44. (d) 45. (b) 46. (d) 47. (a) 48. (b) 49. (c) 50. (c) 51. (a) 52. (d) 53. (b) 54. (d) 55. (b) 56. (a) 57. (c) 58. (a) 59. (d) 60. (c) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (b) 62. (c) 63. (d) 64. (c) 65. (c) 66. (a) 67. (d) 68. (b) 69. (c) 70. (a) 71. (c) 72. (b) 73. (b) 74. (a) 75. (c) 76. (c) 77. (d) 78. (d) 79. (b) 80. (d) 81. (d) 82. (c) 83. (c) 84. (a) 85. (b) 86. (a) 87. (a) 88. (d) 89. (d) 90. (d) 91. (b) 92. (d) 93. (d) 94. (d) 95. (d) 96. (a) 97. (b) 98. (a) 99. (a) 100. (a) Common Proficiency Test (CPT) Volume - II 291 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 9 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (b) 111 (b) 121 (b) 131 (a) 141 (a) 102 (c) 112 (a) 122 (a) 132 (c) 142 (b) 103 (b) 113 (a) 123 (c) 133 (a) 143 (c) 104 (d) 114 (c) 124 (b) 134 (d) 144 (b) 105 (c) 115 (b) 125 (c) 135 (b) 145 (d) 106 (a) 116 (c) 126 (a) 136 (b) 146 (c) 107 (a) 117 (d) 127 (a) 137 (a) 147 (a) 108 (c) 118 (d) 128 (c) 138 (d) 148 (b) 109 (a) 119 (a) 129 (d) 139 (c) 149 (d) 110 (b) 120 (a) 130 (d) 140 (d) 150 (b) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (a) 154. (b) 155. (a) 156. (a) 157. (c) 158. (a) 159. (b) 160. (c) 161. (a) 162. (b) 163. (a) 164. (b) 165. (a) 166. (a) 167. (c) 168. (b) 169. (a) 170. (c) 171. (a) 172. (c) 173. (a) 174. (b) 175. (b) 176. (a) 177. (c) 178. (a) 179. (a) 180. (a) 181. (a) 182. (b) 183. (a) 184. (a) 185. (c) 186. (b) 187. (a) 188. (b) 189. (a) 190. (b) 191. (b) 192. (a) 193. (c) 194. (b) 195. (b) 196. (a) 197. (b) 198. (b) 199. (a) 200. (b) 292 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India Answer of Model Test Papers Model Test Paper – BOS/CPT – 10 SECTION – A : FUNDAMENTALS OF ACCOUNTING 1. (a) 2. (d) 3. (b) 4. (a) 5. (b) 6. (c) 7. (b) 8. (b) 9. (b) 10. (d) 11. (a) 12. (d) 13. (d) 14. (c) 15. (a) 16. (b) 17. (c) 18. (a) 19. (c) 20. (c) 21. (a) 22. (c) 23. (c) 24. (a) 25. (d) 26. (b) 27. (a) 28. (c) 29. (a) 30. (b) 31. (c) 32. (b) 33. (c) 34. (c) 35. (b) 36. (c) 37. (c) 38. (b) 39. (c) 40. (b) 41. (d) 42. (a) 43. (a) 44. (a) 45. (b) 46. (c) 47. (c) 48. (b) 49. (a) 50. (b) 51. (a) 52. (c) 53. (a) 54. (b) 55. (b) 56. (c) 57. (a) 58. (b) 59. (a) 60. (d) SECTION – B : MERCANTILE LAWS (40 MARKS) 61. (a) 62. (a) 63. (d) 64. (a) 65. (d) 66. (d) 67. (b) 68. (b) 69. (b) 70. (a) 71. (c) 72. (c) 73. (d) 74. (b) 75. (d) 76. (c) 77. (a) 78. (a) 79. (a) 80. (b) 81. (a) 82. (d) 83. (a) 84. (d) 85. (a) 86. (a) 87. (b) 88. (c) 89. (d) 90. (d) 91. (d) 92. (d) 93. (a) 94. (a) 95. (c) 96. (d) 97. (a) 98. (d) 99. (a) 100. (c) Common Proficiency Test (CPT) Volume - II 293 © The Institute of Chartered Accountants of India ANSWERS Answer of Model Test Papers Model Test Paper – BOS/CPT – 10 SECTION – C : GENERAL ECONOMICS (50 MARKS) 101 (a) 111 (a) 121 (c) 131 (c) 141 (c) 102 (d) 112 (d) 122 (a) 132 (d) 142 (a) 103 (a) 113 (b) 123 (c) 133 (a) 143 (d) 104 (c) 114 (a) 124 (d) 134 (c) 144 (a) 105 (c) 115 (b) 125 (a) 135 (b) 145 (b) 106 (d) 116 (c) 126 (b) 136 (c) 146 (a) 107 (c) 117 (c) 127 (a) 137 (c) 147 (a) 108 (d) 118 (a) 128 (a) 138 (d) 148 (b) 109 (b) 119 (c) 129 (b) 139 (a) 149 (c) 110 (d) 120 (a) 130 (a) 140 (d) 150 (d) SECTION – D : QUANTITATIVE APTITUDE (50 MARKS) 151. (c) 152. (a) 153. (a) 154. (a) 155. (b) 156. (b) 157. (a) 158. (b) 159. (c) 160. (b) 161. (b) 162. (a) 163. (c) 164. (a) 165. (b) 166. (b) 167. (c) 168. (a) 169. (a) 170. (b) 171. (d) 172. (a) 173. (a) 174. (c) 175. (a) 176. (a) 177. (b) 178. (a) 179. (b) 180. (c) 181. (c) 182. (c) 183. (a) 184. (a) 185. (b) 186. (a) 187. (b) 188. (a) 189. (c) 190. (a) 191. (b) 192. (a) 193. (a) 194. (b) 195. (c) 196. (C) 197. (a) 198. (a) 199. (b) 200. (b) 294 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India SECTION – D : QUANTITATIVE APTITUDE Suggested Answers/ Hints Model Test Paper – BOS/CPT – 1 151. ⎜ ⎛ 1 ⎟ ⎞0 + ( 64 )−1/2 + ( −32 )5 4 = 1+ 1 + ( −1 )4( 32 )4 5 5 ⎝64⎠ 64 ( )4 1 = 1+ + 25 5 8 1 = 1+ + 24 8 1 8+1+128 137 = 1+ +16 = = 8 8 8 1 = 17 8 152. Given a2 +b2=45 → (1) ab=18 → (2) 18 (2) a= → (3) b 18 Substitute a = in (1) b ⎛18⎞2 ⎜ ⎟ +b2=45 ⎝ b ⎠ 324 +b2 = 45 b2 324+b4 =45b2 b4 −45b2+324=0 Let b2 = x x2 − 45x + 324 = 0 Common Proficiency Test (CPT) Volume - II 295 © The Institute of Chartered Accountants of India ANSWERS ( )( ) x−36 x−9 =0 x = 36, x=9 When x = 36, b = 6 When x = 9, b = 3 18 When, b = 6, (3) ⇒ a = = 3 6 18 When b = 3, (3) ⇒ a = = 6 3 When a = 3, b = 6 1 1 1 1 2+1 3 1 ∴ + = + = = = a b 3 6 6 6 2 1 1 1 1 1 When a = 6, b = 3 ⇒ + = + = a b 6 3 2 1 ∴ Ans (c) = 2 1 −1 −1 a2 +a 2 1−a 2 153. Given + 1−a 1+ a 1 1 a + 1− a a = + 1−a 1+ a a+1 a −1 = + ( ) ( ) a 1−a a 1+ a ( ) ( ) 1 ⎡( a+1 ) 1+ a + a−1 ( 1−a )⎤ = ⎢ ( ) ⎥ ( ) a ⎢⎣ 1−a 1+ a ⎥⎦ 1 ⎡ a+a a +1+ a + a −a a −1+a ⎤ = ⎢ ( ) ⎥ ( ) a ⎢⎣ 1−a 1+ a ⎥⎦ 1 ⎡ 2a+2 a ⎤ = ⎢ ( )⎥ ( ) a ⎢⎣ 1−a 1+ a ⎥⎦ ( ) 2 a a +1 = ( ) ( ) a 1−a 1+ a 296 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 2 = 1−a 154. The given equation may be written as log log54 log24 log10 2 = . log logx log10 log e e log2(4log5) or, = logx 4log2 or, log 5 = log x ∴x = 5 Ans.(b) 155. Let the total score = x. Given the condition 2 highest score = x 9 2⎛ 2 ⎞ The next highest = ⎜x− x⎟ According the third condition of the problem 9⎝ 9 ⎠ 2x 2⎛ 2 ⎞ − ⎜x− x⎟=8 9 9⎝ 9 ⎠ 2x 2 4 − x+ x = 8 9 9 81 8x81 x = =162 4 Ans. (a) 156. Let three proportionals are a, b, c b2 [ ] Then the third proportional = c = ∴b= ac a 202 400 80 ∴ c = = = 15 15 3 Ans. (a) 157. Let a, b, c be the three proportional then the mean proportional = b = ac i.e. b = 9×25 = 3 × 3 = 15 Common Proficiency Test (CPT) Volume - II 297 © The Institute of Chartered Accountants of India ANSWERS Ans. (c) 158. Let the boys Ratio 2x and the girls ratio 5x Given 2x + 5x = 280 7x = 280 280 x = =40 7 ∴ Boys Ratio = 2 × 40 = 80 Girls Ratio = 5 × 40 = 200 159. Let x be the number of coins available in a bag 1 1 Given x+ x+ x=35 2 4 4x+2x+x =35 4 7 x = 35 × 4 35×4 x = =20 7 Ans. (b) 160. Let the number be x. Then according to the given condition of the problem. x x+1 = +1 3 4 ( ) x x+1 − =1 3 4 4x−3x−3 =1 12 x − 3 = 12 x = 15 Ans. (c) − ⎛ 1 ⎞ 161. Let log ⎜ ⎟ = x 3 ⎝81⎠ 1 i.e. 3x = 81 298 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 1 = ( ) 3 4 3x = 3 −4 ∴ x = − 4 Ans. (b) ⎛ 1 ⎞ 162. Let log ⎜ ⎟ = x 2 2 ⎝256 ⎠ ( ) x 1 i.e. 2 2 = 256 ( ) x 1 2×2½ = 28 ( ) 23/2 x = 2 − 8 3 x 2 2 = 2 − 8 3 ∴ x = −8 2 −16 x = 3 Ans. (d) 1 163. Given log 3 2 = x 15 1 i.e. x15 = 3 2 1 ( )1 x15 = 2 3 Taking power 15 on both sides ⎛ 1 ⎞15 ⎛ 1 ⎞15 ⎜ ⎟ ⎜ ⎟ x15 = 23 ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ x = 25 x = 32 Ans. (b) Common Proficiency Test (CPT) Volume - II 299 © The Institute of Chartered Accountants of India ANSWERS 164. Given log[log ( log x )]= 0 3 4 2 i.e. 3° = log (log x) 4 2 1 = log (log x) 4 2 41 = log x 2 log x = 4 2 24 = x 16 = x Ans. (a) ( ) 165. Given log 0.00001 = −5 x i.e. x −5 = 0.00001 1 = 0.00001 x5 1 = x5 0.00001 i.e. x5 =100000 ( ) x5 = 10 5 ∴ x = 10 Ans. (a) 166. Suppose the x and y baskets were loaded in the first two trucks. Total number of baskets = 1230 ∴ Number of baskets initially loaded in the third basket = 1230 (x+y ) According to the question, x− 5;y−1 0;123 0− (x+y)−15 = 3:4:5 x−5 3 ∴ = 1230 −(x+y)−15 5 ⇒ 5x − 25 = 3690 − 3x − 3y − 45 ⇒ 8x + 3y = 3670 → (1) y−10 4 and = 1230 −(x+y)−15 5 ⇒ 5y − 50 = 4920 − 4x − 4y − 60 300 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India ⇒ 4x + 9y = 4910 → (2) Multiply equation (1) by 3, 24x + 9y = 11010 → (3) Subtracting equation (2) from equation (3), we get 20x = 6100 6100 ⇒ x = = 305 20 (1) ⇒ 8(305) + 3y = 3670 ⇒ 2440 + 3y = 3670 3y = 3670 − 2440 = 1230 1230 y = = 410 3 Hence number of baskets loaded in first truck = 305. Number of baskets loaded in Second Truck = 410 and the number of baskets loaded in third truck. = 1230 − (x+y) = 1230 − (305 + 410) − = 1230 715 = 515 Ans. (b) 167. The given equations are: 2x + 3y − 5z = 0 − 3x + 2y + 7z = 0 By Gross-multiplication method, we have x y x = = 21+10 15−14 4+9 x y z ⇒ = = 31 1 13 ⇒ x : y : z = 31 : 1 : 13 Ans. (c) Common Proficiency Test (CPT) Volume - II 301 © The Institute of Chartered Accountants of India ANSWERS 168. log n A = log (A1/n) a a 1 = log A a n ans. (a) log 4 log 22 169. 10 = 10 log 8 log 23 10 10 2log 2 = 10 2log 2 10 2 = 3 Ans. (c) 170. log 124.5 + log 379 = log (12.45×10) + log (3.79×100) 10 10 10 10 = log 12.45 + log 10 + log 3.79 + log 100 10 10 10 10 = 1.0952 + 0.5786 + 2 log 124.5 + log 379 = 4.6738 10 10 Ans. (b) 171. No. of ways to fill unit place = 2 No. of ways to fill to the place = 4 No. of ways to fill 100 th place = 3 ∴ Total no. of 3 digit even Nose 2 × 4 × 3 = 24 If 0 comes at 100th place then 3 digit no. 3 = 3 P 3 Total Nos. greater than 100 = 24 − (3+1) Ans. (c) 20 172. Total no. of 3 digits nos. are = 6 = 120 P 3 Nos. of 3 digit if 0 comes at hundredth place = 5 = 20 P 3 ∴ Total nos. greater than 100 and less than 1000 by using (2, 3, 4, 0, 8, 9) are = 120 − 20 = 100 Ans. (a) 100 302 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 173. No. of ways to arrange consonants = 4! 3! No. of ways to arrange vowels = 2! ∴ Total no. of words without changing order of vowels 4!×3! = =72 words. 2! Ans. (c) 72 words 4! 174. No. of ways in which vowels can be arranged = = 12 2! No. of ways in which 4 vowels taken as together 6 consonants are arranged = 7! ∴Total no. of words in which 4 vowels and 6 consonants are arranged = 7! × 12 = 60480 Ans. (a) 60480 8! 175. Total words without any restriction = 2! = 20160 6!×3! Total words if vowels comes together = 2! = 2160 ∴ Total words if vowels never Come together = 20160 −216 0 = 18000 Ans. (b) 18000 176. f(x) = ax + b 3< x < 3 f(3) = 1 ∴ a.3 + b = 1 ⇒ 3a + b = 1 f(5) = 7 a.5 + b = 7 ⇒ 5a + b = 7 ∴ a = 3, b = − 8 Ans. (a) a = 3, b = − 8 Common Proficiency Test (CPT) Volume - II 303 © The Institute of Chartered Accountants of India ANSWERS ⎡ x 9 ⎤ (x2 −9) 177. lt ⎢ − ⎥= lt x→3 ⎣x−3 x(x−3)⎦ x→3 x(x−3) x+3 3+3 = lt App lt. ⇒ = 2 x→3 x 3 Ans. (c) =2 f(2)−f(x) 0−(4−x2) x2 −4 178. lim ⇒ ⇒ x→2 x−2 x−2 x−2 lt (x+2) App lt. x→2 = 2 +2 = 4 Ans. (d) 4 d d 1+x 1−x − 1−x 1+x 179. y = 1−x ⇒ dy = dx dx 1+x dx (1+x) 1 1 1+x (−1)− 1−x − ⇒ 2 1−x 2 1+x ⇒ −1−x−1+x (1+x) 2 1−x2.(1+x) −1 ⇒ (1+x) 1−x2 −1 Ans. (b) (1+x) 1−x2 d d x (10x +logx)−(10x +logx) x 180. y = 10x +logx ⇒ dy = dx dx x dx x ⎛ 1⎞ ( ) 1 x⎜10x loge10 + ⎟− 10x +logx ⇒ ⎝ x⎠ 2 x x 10x.log10.2x+2−10x −logx 2 x ⇒ 10x(2xlog10−1)+2−logx x 2x x Ans. (a) 304 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 181. Here, considering x2 as the first function as 2x as the second function and applying the method of integration by parts, we may write x2.2x 2x ∫ 2x x2 dx = − ∫ 2x . dx log 2 log 2 = 2x x2 − 2 ∫ x2x dx log 2 log 2 = 2x x2 − 2 ⎜ ⎛ x.2x − ∫ 2x dx ⎟ ⎞ ⎜ ⎟ log 2 log 2 ⎝log 2 log 2 ⎠ = 2x x2 − 2 ⎜ ⎛ x.2x − 1 . 2x ⎟ ⎞ ⎜ ⎟ log 2 log 2 ⎝log 2 log 2 log 2⎠ 2x x2 x.2x+1 2x+1 = − + +c ( ) ( ) 2 log 2 2 log 2 3 Ans. (a) 182. let log x = z 1 log x=z 2 1 1 . dx =dz 2 x ∴ I = ∫log x dx = 2 ∫log x dx 3x 3 2x 2∫ = z dz 3 = 2⎜ ⎛ z2 ⎟ ⎞ = z2 = 1 ( log x ) 2 + c ⎜ ⎟ 3⎝ 2 ⎠ 3 3 Ans. (c) 183. ∫log x dx = ∫ log x. 1 dx x2 x2 Using Integrating by parts ⎛ 1 ⎞ (Note: here (log x) is to be taken as first function and ⎜ ⎟ as second function) ⎝x2 ⎠ Common Proficiency Test (CPT) Volume - II 305 © The Institute of Chartered Accountants of India ANSWERS ∴ ∫ log x. 1 dx =log x⎜ ⎛ − 1 ⎟ ⎞ − ∫1 ⎜ ⎛ − 1 ⎟ ⎞ dx x2 ⎝ x⎠ x ⎝ x⎠ = − 1 log x + ∫ 1 dx x x2 1 1 = − log x− +c x x 1( ) = − 1+log x +c x Ans. (b) 184. ∫ ex. x2 +1 dx.= ∫ ex⎢ ⎡ x2 −1+2 ⎥ ⎤ dx ( ) ( ) x+1 2 ⎢⎣ x+12 ⎥⎦ = ∫ ex⎢ ⎡ x2 −1 + 2 ⎥ ⎤ dx ( ) ( ) ⎢⎣ x+1 2 x+12⎥⎦ = ∫ ex ⎢ ⎢ ⎣ ⎡ ( x x + −1 1 ) + ( x+ 2 1 ) 2⎥ ⎥ ⎦ ⎤ dx = ∫ ex [ f(x) + f ′ (x) ] dx x−1 Where f (x) = x+1 ( ) = ex.f x + c ⎛x−1⎞ = ex⎜ ⎟ + c ⎝x+1⎠ Ans. (a) ∫ xex 185. Let I = dx ( ) 1+x 2 ∴ I = ∫1+x−1 ex dx ( ) 1+x 2 ⎛ ⎞ = ∫ ⎜ 1 − 1 ⎟ ex dx ⎜ ⎝1+x ( 1+x ) 2 ⎟ ⎠ 306 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India = ∫ 1 ex dx − ∫ 1 ex dx 1+x ( 1+x ) 2 ( ) = ⎢ ⎡ 1 ex − ∫( −1 )( 1+X )−2 ( 1 ) eX dx⎥ ⎤ − ∫ 1 exdx ⎣1+x ⎦ (1+x)2 = ex +∫ 1 ex dx − ∫ 1 ex dx 1+x (1+x)2 (1+x)2 ex I = + c 1+x Ans : (a) 1 186. Given y = x+ x ( ) ⎡ ( ) 1 ⎤ ⎢ x 0 −1 ⎥ dy = 1 +⎢ ( ) 2 x ⎥ dx 2 x ⎢ x 2 ⎥ ⎢ ⎥ ⎣ ⎦ 1 1 = − 2 x 2x x 1 ⎡ 1⎤ = ⎢1− ⎥ 2 x ⎣ x⎦ dy 1 ⎡x−1⎤ = ⎢ ⎥ dx 2 x ⎣ x ⎦ dy ⎡ 1 ( ) ⎤ ∴ 2 x =2x⎢ x−1⎥ dx ⎣2x x ⎦ x 1 = − x x 1 = x− x x2 +1 + x2 −1 187. Given y = x2 +1 − x2 −1 Multiply Reciprocal of R.H.S. to R.H.S. Common Proficiency Test (CPT) Volume - II 307 © The Institute of Chartered Accountants of India ANSWERS x2 +1 + x2 −1 x2 +1 + x2 −1 i.e. y = × x2 +1 − x2 −1 x2 +1 − x2 −1 ⎛ ⎞2 ⎜ x2 +1 + x2 −1⎟ [ ] ⎝ ⎠ ( )( ) = ( ) ( ) ∴ a+b a−b =a2 −b2 x2 +1 − x2 −1 ( ) ( ) x2 +1+ x2 −1+2 x2 +1 x2 −1 = 2 1⎡ ⎤ = 2x2 +2 x2 +1 x2 −1 2 ⎢⎣ ⎥⎦ ( )( ) = x2 + x2 +1 x2 −1 Differentiate on both sides. [( ) ( ) ] dy 1 ( ) ( ) =2x+ ( )( ) x2 +1 2x + x2 −1 2x dx 2 x2 +1 x2 −1 [ ] 1 = 2x + 2x3 +2x+2x3 −2x 2 x4 −1 4x3 = 2x + 2 x4 −1 dy 2x3 = 2x + dx x4 −1 Ans. (b) ⎡ 3⎤ 188. Given y = log ⎢ ⎢ ex⎜ ⎝ ⎛ x x + −2 2 ⎟ ⎠ ⎞ 4 ⎥ ⎥ ⎢⎣ ⎥⎦ ⎡ 3 ⎤ d d y x = ex⎜ ⎛x 1 −2 ⎟ ⎞ 4 3 ⎢ ⎢ ⎢ ⎣ ex 3 4 ⎜ ⎜ ⎝ ⎛ ( x x + −2 2 )⎟ ⎟ ⎠ ⎞ 4 −1 ⎜ ⎜ ⎝ ⎛( x+2 ) ( ( x 1 ) + − 2 ( ) x 2 −2 )( 1 ) ⎟ ⎟ ⎠ ⎞ ⎥ ⎥ ⎥ ⎦ ⎝x+2⎠ 3 ⎤ + ⎜ ⎛x−2 ⎟ ⎞ 4 ex ⎥ ⎝x+2⎠ ⎥ ⎥⎦ 308 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India ⎡ −1 3⎤ ex ⎢ ⎢3 4 ⎜ ⎝ ⎛ x x + −2 2 ⎟ ⎠ ⎞ 4 ⎜ ⎜ ⎝ ⎛ x+ ( x 2 + − 2 x ) 2 +2 ⎟ ⎟ ⎠ ⎞ +⎜ ⎝ ⎛ x x + −2 2 ⎟ ⎠ ⎞ 4 ⎥ ⎥ ⎢⎣ ⎥⎦ = 3 ex⎜ ⎛x−2 ⎟ ⎞ 4 ⎝x+2⎠ 1 3 3 ⎜ ⎛x−2 ⎟ ⎞ − 4 ⎢ ⎡ 4 ⎥ ⎤ + ⎜ ⎛x−2 ⎟ ⎞ 4 4⎝x+2⎠ ⎣ ( x+2 ) 2⎦ ⎝x+2⎠ = 3 ⎛x−2⎞ 4 ⎜ ⎟ ⎝x+2⎠ 1 3 − − = ( x+ 3 2 ) 2 ⎢ ⎣ ⎡ x x + −2 2 ⎥ ⎦ ⎤ 4 4 +1 3 ⎛x−2⎞ −1 = ⎜ ⎟ +1 ( x+2 ) 2 ⎝x+2⎠ 3 ⎛x+2⎞ = ⎜ ⎟ +1 ( x+2 ) 2 ⎝x−2⎠ 3 = +1 x2 −4 3+x2 −4 x2 −1 = = x2 −4 x2 −4 Ans. (a) 189. Given y = xx Taking log on both sides. ( ) log y = log xx log y = x. log x Differenciate on both sides. 1 dy 1 =x. +log x.1 y dx x dy [ ] =y 1+log x [∴ log e = 1] dx Common Proficiency Test (CPT) Volume - II 309 © The Institute of Chartered Accountants of India ANSWERS = y [log e + log x] [log m + log n = log (mn)] = y [log ex] = xx [log ex] Ans. (b) 190. Given y = xe −x2 taking log on both sides ( ) log y = log xe −x2 log y = e −x2 log x differenciate on both sides ( ) 1 dy = e −x2⎜ ⎛1 ⎟ ⎞ + logx e −x2 (−2x) y dx ⎝x⎠ = e −x2 ⎢ ⎡1 −2xlogx⎥ ⎤ ⎣x ⎦ dy = y.e −x2 ⎢ ⎡ 1−2x2logx ⎥ ⎤ dx ⎣ x ⎦ dy =xe −x2 .e −x2 ⎜ ⎜ ⎛ 1−2x2logx ⎟ ⎟ ⎞ dx ⎝ x ⎠ Ans : (a) n 191. Sn = [2a+(n−1)d] 2 n 0 = [20+(n−1)d] 2 2a 2a = (1 − n)d ⇒ d = (1−n) m Sn = [2(a+nd)+(m−1)d] 2 m⎡ 2a 2a ⎤ ⎢2a+2n. +(m−1) ⎥ 2 ⎣ 1−n 1−n⎦ ⎡1−n+2n+m−1⎤ Sm = ma ⎢ ⎥ ⎣ 1−n ⎦ 310 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India (m+n) = ma 1−n −ma(m+n) Sm = (n−1) ma(m+n) Ans. (b) − (n−1) 192. a = m d = n − m Tl = 2m 2m = m+(N−1 )d m ⇒ 2m − m = (N − 1) (n − m) ⇒ = N − 1 n−m m n+m−m ∴ N = +1+ n−m n−m n N = n−m N n ∴ s = [a + l] ⇒ [m + 2m] 2 n−m 3mn S = n−m 3mn Ans. (a) n−m 193. a = − 29 a + 4d = − 15 4d = − 15 + 29 ⇒ d = 14/4 = 7/2 Let n th term be 0 0 = a+ (n − 1) d 0 = − 29 + (n − 1) 7/2⇒ 58/7 = n − 1 ∴ n = 9.28 (not possible) ∴ 10th term will be positive ∴ Sum of remaining 31 terms. 31 ⎡ ⎛ 7⎞ 7⎤ S = ⎢2×⎜−29+9× ⎟ + (31−1) ⎥ 31 2 ⎣ ⎝ 2⎠ 2⎦ Common Proficiency Test (CPT) Volume - II 311 © The Institute of Chartered Accountants of India ANSWERS 31 = [5+105] 2 31 = ×110 =1705 2 S = 1705 (Sum of all positive nos.) 31 Ans. (b) 1705 194. Tn = a + (n − 1) d 1 ∴ = a + (m − 1)d ...(i) n 1 =a+(n−1)d ...(ii) m by solving eg. (i) and e.g. (ii) 1 1 a = , d = mn mn mn ⎡ 1 1 ⎤ ∴ S mn = ⎢2× +(mn−1) ⎥ 2 ⎣ mn mn⎦ mn ⎡ 1 ⎤ mn ⎡mn+1⎤ = × ⎢1+ ⎥ ⇒ ⎢ ⎥ 2 ⎣ mn⎦ 2 ⎣ mn ⎦ ⎡mn+1⎤ Smn = ⎢ ⎥ ⎣ 2 ⎦ 1 Ans. (c) (mn+1) 2 S n/2[12A+(n−1)D] 195. n = S ′ n n/2[2a+(n−1)d] ⎡ ⎛n−1⎞ ⎤ ⎢2(A+⎜ ⎟d⎥ 7n+1 ⎣ ⎝ 2 ⎠ ⎦ = 3n+2 ⎡ ⎛n−1⎞ ⎤ 2⎢a+⎜ ⎟d⎥ ⎣ ⎝ 2 ⎠ ⎦ Put n = 25 7×25+1 A+12D = 3×25+2 a+12d 312 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India T 176 16 ∴ 13 = = ⇒ 16:7 t 77 7 13 Ans. (b) 16:7 a+b 196. A1 = a, G , G , b 1 2 2 1 ∴ b = a(r)3 ∴ r = ⎜ ⎛b ⎟ ⎞ 3 ⎝a⎠ ∴ G3 +G3 ⇒⎢ ⎡ a ⎜ ⎛ b1/3 ⎟ ⎞ ⎥ ⎤3 +⎢ ⎡ a ⎜ ⎛ b2/3 ⎟ ⎞ ⎥ ⎤3 1 2 ⎜ ⎟ ⎜ ⎟ ⎢ ⎣ ⎝a ⎠⎥ ⎦ ⎢ ⎣ ⎝a ⎠⎥ ⎦ ⎛b⎞ ⎛b⎞2 ⎛b⎞ ⎡ b⎤ = a3.⎜ ⎟+a3⎜ ⎟ ⇒ a3⎜ ⎟ ⎢1+ ⎥ ⎝a⎠ ⎝a⎠ ⎝a ⎠ ⎣ a⎦ ⎛a+b⎞ ⎛b⎞1/3 ⎛b⎞2/3 ⎛a+b⎞ = a2b⎜ ⎟=a⎜ ⎟ .a⎜ ⎟ .2⎜ ⎟ ⎝ a ⎠ ⎝a⎠ ⎝a⎠ ⎝ 2 ⎠ = G . G . 2A = 2A G G 1 2 1 2 Ans. (b) 2A G G 1 2 197. ab = am+1+bm+1 ⇒ am+1/2.b1/2 +a1/2.bm+1/2 =am+1+bm+1 am +bm am+1−am+1/2.b1/2 =a1/2bm+1/2 −bm+1 [ ] [ ] ⇒ am+1/2 a1/2 −b1/2 =bm+1/2 a1/2 −b1/2 am+1/2 ∴ =1 ∴ m+1/2 = 0 ∴ m = − 1/2 bm+1/2 Ans. (a) −1/2 198. Ans. (c) 199. Value of 1. 4 x = 1.444... 10x = 14.444... ∴ 9x = 13.00 ∴ x = 13/9 Ans. (a) 13/9 Common Proficiency Test (CPT) Volume - II 313 © The Institute of Chartered Accountants of India ANSWERS 200. x = 0.35 6 ∴ 10x = 3.565656... 1000x = 356.5656... 353 ∴ 990x = 353.0 ⇒ x = 990 353 Ans. (c) 990 Model Test Paper – BOS/CPT – 2 151. T =2.T +1 ⇒ a + (P+ 1 − 1) d = 2 [a+qd] P+1 q ⇒ a + pd = 2a + 2qd a = d (P− 2q) ∴ T p+q+1 = a+(P+q)d = (P−2q)d+(P+q)d T a+3Pd (P−2q)d+3Pd 3p+1 (2P−q)d 1 = = ⇒ 1:2 2(2P−q)d 2 Ans. (a) 1:2 Tm a+(m−1)d d+(m−1)d 152. d = a ∴ = = Tn a+(n−1)d d+(n−1)d d+(1+m−1)d m = = ⇒ m:n d+(1+n−1)d n Ans. (b) m:n 1 1 153. =a + (m− 1)d & = a+ (n − 1)d n m 1 1 ∴ a = , d = mn mn 1 1 ∴ T = a+ (mn − 1)d ⇒ +(mn − 1) mn mn mn T = 1 mn Ans. (a) 1 314 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India 1 1 1 154. + + .....n terms 2.5 5.8 8.11 1 1 T = = n [2+(n−1)3][5+(n−1)3] (3n−1)(3n+2) 1 ⎡ 1 1 ⎤ T n = 3 ⎢ ⎣3n−1 − 3n+2 ⎥ ⎦ ∑ 1⎡1 1 ⎤ ∴ S n = (Tn) ⇒ 3 ⎢ ⎣2 − 3n+2 ⎥ ⎦ 1⎡3n+2−2⎤ ⇒ ⎢ ⎥ 3⎣2(3n+2)⎦ 1 3n n S ⇒ = n 3 2(3n+2) 2(3n+2) n Ans. ⇒ (a) 2(3n+2) 155. 0.004 + 0.02 + 0.1 + ... is 12.5 0.02 ∴ a = 0.004 r = = 5 0.004 12.500 ∴ 12.5 = 0.004 (5) n − 1 ⇒ = (5)n − 1 0.004 3125 = (5)n − 1 ⇒ 55 = 5n − 1 ∴ n − 1 = 5 ⇒ n = 6 Ans. (c) 6 [ ] ( ) 157. CI = 2000 1+0.0125 10 −1 [ ] ( ) CI = 2000 1.0125 10 −1 (Solved by taking log) CI = Rs. 260.12 ⎛ r ⎞2 158. 9P = P ⎜1+ ⎟ ⎝ 100 ⎠ ⎛ r ⎞2 r (3)2 = ⎜1+ ⎟ ⇒ 3 = 1+ ⎝ 100 ⎠ 100 ∴ r = 200% Common Proficiency Test (CPT) Volume - II 315 © The Institute of Chartered Accountants of India ANSWERS Ans. (b) 200% 159. 101.50 = P [(1+0.03)2 − 1] 101.50 P = = 1667 0.0609 P = 1667 3 ∴ SI = 1667 × ×2 = 100 (Approx) 100 Ans. (a) Rs. 100 [ ] 160. CI = P (1+0.05)2 −1 CI = 0.1025 P 5 SI = P × ×2 = 0.1P 100 CI − S I = 1.50 0.1025P − 0.10P = 1.50 ∴ 0.0025P = 1.50 ∴ P = 600 Ans. (c) Rs. 600 161. Let average is x 16(x−3)+85 ∴ x = 17 ⇒ 17x = 16x − 48 + 85 x = 37 Ans. (a) 37 d 162. Time from A to B = hrs 20 d Time from B to A = hrs. 30 d+d 2d ⇒ Average speed = = ×600 d + d 50d 20 30 Average speed = 24 km/4. Ans. (b) 24 km/4 316 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India d+d+d 163. Average speed = d d d + + 40 30 15 3d Av. Speed = ×120 =24km/H 15d Ans (b) 24 km/H 12 164. Time to cover 12 km = = 4 hrs. 3 Time to cover 18 km = 18/9 = 2 hrs. Time to cover 24 km = 24/4 = 6 hrs. 12+18+24 54 ∴ Av. speed = = = 4.5 km/H 4+2+6 12 Ans. (a) 4.5 km/H d d 3d + + 5 2 10 d 165. Av. speed = = × 30 d + d + 3d 17d 10 6 10 30 ∴ Av. speed = km/H 17 30 Ans. (b) km/H 17 Σx 166. x = n Σx = 100 × 50 = 5000 Corrected Σx = (5000 − 50 + 40) = 4990 4990 ∴ Corrected x = = 49.90 100 Ans. (b) 49.90 n x +n x +n x 167. x = 1 1 2 2 3 3 n +n +n 1 2 3 2×3+3×3+5x 3 12 = 2+3+5 120 = 15 + 5x 3 Common Proficiency Test (CPT) Volume - II 317 © The Institute of Chartered Accountants of India ANSWERS 105 ∴ x = =21 3 5 Mean of third group = 21 Ans. (b) 21 168. Made is most frequent value Ans. (c) Most Frequent Value. a+b 169. AM = 2 a+b 10 = ⇒ a + b = 20 … (i) 2 am = ab 8 = ab ⇒ ab = 64 ∴ a (20 − a) = 64 ⇒ a2 − 20a + 64 = 0 (a − 16) (a − 4) = 0 ∴ a = 16, b = 4 Ans. (b) 16, 4 170. A frequency distribution can be presented graphically by a Histogram. Ans. (b) Histogram. 171. Ans. (c) Refer Properties 172. Ans. (a) Refer Properties. 173. Since x and y are connected by the linear relation: 2x + 3y = 4 ⇒ y = − 2/3 x + 4/3 → (1) There is perfect correlation between x and y i.e. r = ± 1 (1) ⇒ x increases, y decreases Hence, there is perfect negative correlation between x and y ∴ r = − 1. Ans. (c) 174. Ans. (d) Refer Properties 175. Ans. (b) Refer Properties 176. Ans. (a) Refer Properties 318 Common Proficiency Test (CPT) Volume - II © The Institute of Chartered Accountants of India