ACET 2018 Answer Key (Jun)

Institute of Actuaries of India
ACET June 2018 Solutions
Mathematics

1. B. Using simplifications , and
(likewise) we get . Hence the
conclusion.

2. D. The reason is that does not exist.

3. D. Here the integrand is an odd function of .

4. A. Over , is not differentiable at , is not differentiable at
and is not differentiable at

5. B. . As
and .

6. D. The value of the coefficient determinant is . So
for a unique solution.

7. C. Let be the base of the logarithm. Then both and are strictly
increasing functions of . However, is a strictly
decreasing function. (In fact, for any is a strictly
decreasing function). So 1/3 is the only appropriate base (among the available
choices) for the given implication to hold.

8. D. implies integral values of are , , , , .

9. B.

10. A. Here , , . Hence value of the given expression is
.

11. A. From Venn diagram, it is clear that
Hence

12. B. implies that So, is a singleton set.

13. C. Since and , the given equation implies
, i.e., . This holds when is a multiple of 6. So the least value of
the positive integer is .

14. B. The given equation can be factored as , which has root
, where ω is one of the imaginary cube roots of unity. The polar
representation of the distinct roots are , and which are the
vertices of an equilateral triangle.

15. B. Clearly , . Thus . Other ordered pairs also
satisfy

16. A. , which implies that Thus

17. D. The given determinant is equal to .

18. A. , , , , ,
where , and are sets of men who received medals in Football, Basketball
and Cricket respectively.
Required number =

19. D. . This is equal to zero at . For this to be equal to
, should be . Also, , which is negative for .
Therefore, is only a maxima (not a minima).

Statistics

20. C. By using the formulae and
, we have .

21. B.

22. B. , . .

23. A. The total number of pairs of different outcomes (while distinguishing between the
two die) is 30. The favourable outcomes are , , , . Therefore, the
required probability is 2/15.

24. A. . Therefore, .

25. D.
. Since the covariance is zero, the correlation is also zero.

26. C. normal. Likewise, normal.
Thus, both and have log-normal distribution.

–
27. B. .

28. C. Regression coefficient of on , . Regression coefficient of
on , . Therefore, . Thus, .
Since both the regression coefficients are positive, we take .

29. A. . Therefore, .

30. A. Suppose is a binary variable indicating whether the ball drawn in the th draw is
white. . Therefore, the required expected value is
.

31. B. Let the mean of the distribution be . Then and ,

so that means , i.e., , i.e., .

32. C. .

Data Interpretation

33. B. Total no. of students . .
Combined pass % is (approx.).

34. D. % of girl engineers doing business management

35. B. The extremes occur in 2010 and 2008; ratio .

36. C. The steepest percentage difference occurred in 2009, when it was .

37. A. Total Indian tourists lakh. Therefore, the number of
Indian tourists in the age bracket 40-49 lakh.

38. B. lakh.

English

39. D
40. C
41. A
42. C
43. B
44. D
45. B
46. D
47. A
48. D
49. B
50. A
51. D
52. D
53. B
54. A
55. B
56. C
57. D
58. C
59. B
60. D
61. C
62. B

Logical reasoning

63. C
64. A
65. C.

Number of odd days from the year 2006 to the year 2009 days.
On 1st January 2006 it was Sunday.
Thus, on 1st Jan 2010, it is Friday.

66. B

As DAUGHTER TERDAUGH
12345678 67812345

Similarly APTITUDE UDEAPTIT
12345678 6 7812345

67. C. The correct order is

Advertisement Application Interview Selection Appointment
Probation

562341

68. B. Dodge, duck and avoid are all synonyms meaning evade. Flee means to run away
from.

69. B
Chemistry
Political
Science 18 7 9

3
5 6

12
Botany

70. D. The set of fair people contains the set of honest people, which contains the set of
politicians. Therefore, some fair people are politicians. By the same logic, some honest
persons are politicians too. The other statements do not follow.