INDIAN INSTITUTE OF FOREIGN TRADE (IIFT) 2006

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Solutions : INDIAN INSTITUTE OF FOREIGN TRADE (IIFT) 2006 l. [2] 2. [4] Hermaphrodite: having both male and female qualities. 3. [4] Yoke-burden. 4. [3] 5. [1] 6. [3] coeval contemporary 7. [1] 8.

[4] grapple of is wrong, Since all the choices have III, we tick [4]. 12. [1] 13. [4] opposite of adept is unskillful, there is no word that matches. 14. [2] 15. [1] 16. [3] 17.

1 Solutions : INDIAN INSTITUTE OF FOREIGN TRADE (IIFT) 2006 l. [2] 2. [4] Hermaphrodite: having both male and female qualities. 3. [4] Yoke-burden. 4. [3] 5. [1] 6. [3] coeval contemporary 7. [1] 8. [4] The fourth option is correct but there is no such choice. 9. [4] 'indicate to is wrong. But all the choices have I in it, hence [4]. 10. [3] Except I, all others are correct. 11. [4] grapple of is wrong, Since all the choices have III, we tick [4]. 12. [1] 13. [4] opposite of adept is unskillful, there is no word that matches. 14. [2] 15. [1] 16. [3] 17. [3] degauss - to remove magnetism 18. [1] culvert - a channel 19. [2] plumose - having many fine branches 20. [3] maraud - loot 21. [2] halcyon idyllic 22. [1] shard - a broken piece 23. [4] all are correctly spelt 24. [1] the word is scrimmage and scribbling. CAT\Test\Various Exam.s\IIFT-2006\Page.1

2 25. [3] proselytize. 26. [3] all the words except IV are spelt wrong. 27. [4] all the words are spelt correctly. 28. [1] I and III are wrong: bourgeois and boutique. 29. [1] 30. [2] 31. [3] 32. [1] 33. [4] should be merge or blend 34. [3] French - rotten pot 35. [2] splissen: Dutch extra 36. [3] Greek-margaron: pearl 37. [2] Latin - mamma: breast 38. [1] Chinese sampan - small boat. 39. [1] shock at the news because they had predicted something else. 40. [1] mastery over unruly; disrupt means chaos 41. [3] a prime source of publicity. 42. [4] The answer should be the less developed ASEAN countries: it started to cast a large shadow on the less developed ASEAN economies, many of which were competing head on with China to attract FDI... CAT\Test\Various Exam.s\IIFT-2006\Page.2

3 43. [4] The answer should be integration of East Asian economies: Over the longer run, the economic rise of China can be seen not only as a new engine for the region's economic growth, but also as a powerful force for integrating the East Asian economies. 44. [3] Many small and mid-size American manufacturers see China's as a company killer and a job killer, largely repressible for the disappearance of 2.7 million United States factory jobs since [3] Directly mentioned: the Chinese Government is currently much concerned over economic overheating, having taken a number of vigorous administrative and macroeconomic control measures to cool down overheated economic activities. 46. [4] All the choices are mentioned in the passage. 47. [4] According to the author, the play's ironic nuances are deliberate social commentaries. None of the given choices. comes close to this description. 48. [4] The author says, has led some critics to interpret the play's thematic conflicts as mere confusion, contradiction, or eclecticism which implies the critics have not been able to see through her irony. Hence we cannot agree with any of the given choices. 49. [4] All the choices are mentioned in the first paragraph. Precious management time, concentrating on core competencies, enjoy significant economies of scale, all have been mentioned. 50. [3] Directly mentioned: The heads somehow take care of the aggregate trade in services but not in details of all kinds BPOs. 51. [4] If BPOs become commodities, it will be to the benefit of companies in the developed world. All the consequences would follow. 52. [4] Evaluation parameters and sector trading data are not mentioned in the passage. Developed countries are not skeptical about India, hence [4]. 53. [1] While I and II are mentioned, III and IV are not mentioned in the passage, hence [1]. 54. [1] Note that I and III are a quality of psychohistory. Traditional history, on the other hand, gives an individuality to the past. 55. [4] All the given choices are part of the passage. 56. [1] Psychohistory applies psychology laws to the people of the past, hence [1]. CAT\Test\Various Exam.s\IIFT-2006\Page.3

4 57. [3] Psycho historians, convinced of the absolute rightness of their own theories, are also convinced that theirs is the deepest explanation of any event, that other explanations fall sort of the truth. 58. [1] The passage describes the aims of psychohistory and mentions certain shortcomings in the method. 59. [4] The passage clearly mentions that Becker's model predicts the effect on profit, also that men and women are not perfect substitutes. 60. [1] For males, it is mentioned that potential = actual work experience. 61. [2] The passage concludes that black players were paid less than their marginal product [4] The mid point of the diagonal must lie on BD, hence substitute (3, 4) in the given equations to get the answer. 63. [3] Let S = 2, then M = 3 and R = 6. Time taken to do the work is given by 1/2 + 1/3 + 1/6 = 1. Since the job is completed in 4 days, each factor should be multiplied by 4, hence 24, 12 and 8 days respectively. 64. [3] s = (20 + 2l + 29)/2 = 35. Area = [3] Refer to the following diagram: O x If O is the centre of the circle, radius r is given by r 2 = x Also from the second triangle, r 2 = (x + 1) Equating the two, we get 2x + l = 7, or : x = 3. Substituting this in the first equation we get r = 5. Hence diameter = [1] log(9/14 16/15 35/24) = log l = 0. r 67. [1] Notice that = 923, which is divisible by 71, hence [1]. CAT\Test\Various Exam.s\IIFT-2006\Page.4

5 68. [3] We can do this sum by alligation. 2/3 4/5 3/4 1/20 1/12 Required ratio = 1/20 : 1/12 = 3 : [2] Let R's capital be used for x months. Then, 5 8:6 x = 5:9. On solving the ratio, we get x = [2] Reconcile the ratio as follows : 3 : 4 7 : 5 Resolving the ratio, we get the ratio = 2 1 : 28 : [3] Atleast one event will happen = l none = l 5/7 5/11 = 1 25/77 = 52/ [1] The hands are in the straight line at two time during an hour. Hence 22 times during 12 hours, or 44 times in 24 hours. 73. [1] Let the speed of the water be x. Then speed upstream = 10 + x and speed downstream = 10 x. Hence 91/ (10 + x) 91/(10 x) = 20. On solving, we get x = [3] The minimum value of 1 1 x or y will be when both x and y are equal or both are x y equal to 1/2. In this case 2 2 and 2 2. Thus x y y 2 x y [4] No of shares he has = 5508/102 = 54. He sells them for = No of shares he gets for 126 = 5670/126 = 45. Change in income = % % = = [1] Work from the choices. If the sides are 4 and 8, then interior angles in the first case = 90 and second case = (2 8 4) 90 = 1080/8 = 135, since these are in the ratio of 2 : 3, hence answer is [1]. 77. [2] Since we need an odd number, second place can be filled by 3 ways. First place can be filled by any 5 ways, hence total = 5 3 = 15, 2 2 CAT\Test\Various Exam.s\IIFT-2006\Page.5

6 78. [1] Since the glasses are equal, we should take the LCM of their capacities, i.e. 7, 9 and 11, which is 693. Tabulating the quantities in the glasses we get ( ) : ( ) = 920: [4] Time taken to fill with out leak= 1/14 + 1/16= 15/112 or 448 min or 7 hrs, 28 min. Time taken with the leak = 7 hr 28 min + 32 min = 8 hrs. If the leak takes x hrs, then 1/14 + 1/16 1/x= 1/8. On solving, we get x = 112 hrs. 80. [1] tan θ = 6/2 3 = 3. Since tan 60 = 3, hence = [2] There are three expressions for f(x, y) and these are as follows: (i) f(0, y) = y + l (ii) f(x+ l, 0) = f(x, l) and (iii) f(x + 1, y + 1) = f{x, f(x + 1, y)} thus f(1, 2) = f{0 + 1, 1 + 1} = f{0, f(1, 1)} = f(1, 1) + 1. Since f(1, 1) is seen as y in the function of f{0, f(1, 1)} is seen as f(0, y). Now f(1, 1) + 1 = f(0 + 1) + 1 = f{0, f(1, 0)} + 1 = f(1, 0) = f(0 + 1) = f(0, 1) since f(0 + 1, 0) is seen as f(x + 1, 0) and this is f(x + 1, 1) in above. Now f(0, l) is a, case of f(0, y) = y + 1 = 2; thus f(l, 2) = f(0, 1) + l + l = 2 + l + l = [1] Vol. of the wood = outer box inner box = = [3] 84. [2] x + 1/x = 3 x 3 + 1/x 3 + 3x 1/x (x + 1/x) = 27 x 3 + 1/x 3 = [4] A = (x + 5) 2 (x + l) 3 (x 3). B = (x + l) (x 3) 2 (x + 5). L.C.M. of A and B = (x + 5) 2 (x + 1) 3 (x 3) [1] + = b/a, = c/a, = ( + ) 2. Substituting; we get the answer. 87. [3] As they are in AP, 2y = x + z. Also, as they are in HP, y = 2xz/(x + z). Eliminating y, we get x = z. Also y = 2xz/2y i.e. y 2 = xz. Hence x, y and z are in GP. 88. [1] By definition of continuity, Lim (x' /4) f( /4). On solving we get f( /4) = 1/ [2] Since A 2 is symmetric, (I + A 2 ) is also symmetric. Hence A 2 (I + A 2 ) is also symmetric, [Product of 2 symmetric matrices is also a symmetric matrix.] CAT\Test\Various Exam.s\IIFT-2006\Page.6

7 90. [1] If the series is in GP, then ar = 2, S = 25/2. Hence a/(l r) = 25/2. Since ar = 2, r = a/2. Substitute in the equation to get a = 10, r = 1/5. Hence 4 th term =ar 3 = 2/ [2] The equations have a unique solution is the determinant 0. Solve the matrix: 1 r 1 hence r 3/ [3] cos x(1 sin x) (cos x)/(l sin x) (l + sin x)/(l + sin x) = 0.6, hence (l + sin x)/cos x = 0.6 = 2 cos x 0.6/1. Applying componendo, we get (l + sin x + cos x)/cos x = (0.6 + l)/l = 8/ [4] 94. [1] P(A B) = P(A) + P(B) P(A B). If A and B are independent variables, then P(A B) = P(A).P(B) hence 0.4 = P(B) 0.3 P(B). From both the equations, we get P(B) = 1/ [4] By theorem 96. [1] If the function achieves max or min value, dy/dx = 0, hence [1]. 97. [2] The constant is n!. It is always divisible by (n 1). 98. [3] LCM (2, 3, 4, 5) = 60. The number is 61, which is prime. 99. [1] x 2 y 2 = 20 hence y = y ± 20/x. If x is positive, y is ±; if x is negative, y is ± [1] z 2 4 z 2 = i. Hence (x + iy) 2 4(x iy) 2 =9+20i. Equating real and imaginary parts we get x + l and y = 2. Hence z z = x 2 + y 2 = = [2] The greatest value of sin x is l and least value is [1] We see that production of watches is highest in 2000: = 6660 (000), which is the highest [2] Income from gold jewellery in 2002 = = The figure in 2001 is = 20110; the increase is 6800, which is the highest. CAT\Test\Various Exam.s\IIFT-2006\Page.7

8 104. [1] The figure of silver jewellery in 2002 is = 216. In 2001 the figure was = 186. The reduction is about 30,000, which is the least. Note that the figures in all the other choices are quite large [3] Watches sold in 4 years = Total items sold in 4years = Percentage required = 24710/ = 85%approx [4] All the given statements are true [1] Visual question: we see that prices of sunglasses do not show a consistent trend [4] 109. [1] We can get the answer from the first statement itself. The scale is not required since only the gradient is required [4] We cannot get the statement even by using both the statements [2] Since each would have 11 balls, it follows that d = 22 and a + b + c = 22. Now, working from the choices, we see that if a = 2, b = 6, c = 14 which does not satisfy C's condition. If a = 3, then b = 7 and c = 12. If C has 3 less he has 9, which is treble that of A, hence [2] [4] The clocks gain 3 min in l hr. They will be correct time after 12 hrs (since they are analog watches). 12 hrs are gained in 12 60/3 = 240 hrs, or 10 days. Hence they will be correct time at 10 August [2] If the sample is not representative, we will get wrong results, hence III is correct [2] In (C), Brian = 5, and in (A), C > D, hence both are wrong. Only condition (B) satisfies all the conditions [3] Both the statements are correct but R is unconnected to why people treat IQ that way [2] Tabulate the scores of each house to get score house 11 as = = 82, which is the highest [3] The least preferred houses are: (9) with a score of 50; (4) with a score of 24; and (6) with a score of [3] In scheme 2, X gets the highest score (36) and S gets the second highest score (13). CAT\Test\Various Exam.s\IIFT-2006\Page.8

9 119. [4] In scheme l, Z gets the highest score of [4] In scheme l, the lowest scores are: Q (10), P(13) and X(26) [1] R gets 27 in scheme l and 8 in scheme 2, hence scheme l is preferred [1] P gets 13 in scheme l and 5 in scheme [4] All the given statements are false [2] the series is abbcccdddd [4] 126. [1] Since the average is 2, the middle term is 2 and common difference is given in choices. For first choice, we get the temperatures as 6, 2, 2, 6 and 10, hence total is l0 and product is less than [2] The letters move + l, 1 consecutively [1] = Average = 15. Converting the base of 15, we get [2] HCF of l010, 1111 and l0010 i.e. 10, 15 and 18, is 1. Hence the answer is & [1] LCM of 1100, and 110 i.e. 12, 18 and 6 is 36. Converting 36 to base 2 we get [4] None of the given choices are factors of [3] David to Akshay = DGMAA, which is the longest [3] Sunny can send the message to Amrita. It cannot reach Shilpa [2] We see that for paraxylene, the shortage is (000) = 160, which is the highest after benzene [3] For maleic anhydride, we see that demand is less and capacity is more, hence it can be exported. CAT\Test\Various Exam.s\IIFT-2006\Page.9

10 136. [3] Only for these products are the demand less than capacity, hence III [3] For propylene oxide, it goes up from 17 to 115, which is the largest increase [4] We see that III is wrong, but I and II are correct [1] 140. [1] Passed at least one subject = Total failed in all = = [3] 142. [3] 143. [4] 144. [2] 145. [4] 146. [1] 147. [4] 148. [4] 149. [3] 150. [4] 151. [3] 152. [4] 153. [3] 154. [4] 155. [1] 156. [1] 157. [1] 158. [2] 159. [4] 160. [3] 161. [2] 162. [2] 163. [3] 164. [1] 165. [2] 166. [2] 167. [2] 168. [2] 169. [3] 170. [2] 171. [3] 172. [2] 173. [2] 174. [3] 175. [3] CAT\Test\Various Exam.s\IIFT-2006\Page.10

PGT Mathematics. 1. The domain of f(x) = is:-

PGT Mathematics. 1. The domain of f(x) = is:- PGT Mathematics 1. The domain of f(x) = is:- a. (-2, + ) b. R-{-1, -2, -3} c. (-3, + )-{-1, -2} d. R-{-1, -2} 2. If f is a function such that f(0) = 2, f(1) = 3 & f(x+2) = 2f(x)-f(x + 1) for every real