ACET 2016 Answer Key (May)

Institute of Actuaries of India
Solutions for ACET MAY 2016

Mathematics
1. D. .

2. A. =
3. C. Interpolation possible by solving linear equations for unknown
coefficients.
4. C. For the function to be defined the value inside the root must be non-negative. That is,
implies the domain is .

5. B. +1. When x=3.
6. D. by definition.

7. D. implies

Putting we have and by putting we have . Hence,
.

8. A. The roots of are given by . Identifying the
coefficients and constant in we have .

9. B. by definition.

10.B. . Then + ,

since .
11. D. so . In order that decreasing in in an
interval Hence implies which is valid if .

12. C. For , = follows by properties definite integrals.

13. D. Put . Then Further , when and when
, . Hence,

14. B. The eight square matrices A of order 3 satisfying are

. The matrix given in option B is one of these eight choices (plus or minus

sign can be used in any of the three places).
15. C. If A = [2 0 1] then = 5. Hence the rank is 1.

16. C. implies mm.

17. B. and .

By adding, we have

18. D. The repayments are in AP. .
The nth instalment is .
Here, . Therefore, .

Statistics
19. A. If = , then n must be 10. So = =66.
20. C. The shoe sizes of 20 students, after decoding the dot plot are (in ascending order)

The mode is 6; the median (middle most number) is 7, and the mean is certainly larger
than 7. This last fact the apparent from the dot plot, as the centroid of the data has to be to
the right of 7.
21. C. The mean is zero. The standard deviation is the square root of the sum of squares of
the items divided by the number of items.
22. D. Let be the event that the electric relay is defective. Let be the event that
the electric relay is manufactured in plant i.

Hence, , ,
So,
= = 0.027.
23. C. and P( . So,
Hence, .

24. B. implies . So, .

25. B. The mean and variance of the exponential distribution are and , respectively.

26. C. is Poisson and implies . Hence variance is .
27. D. Follows from the properties of the correlation coefficient.

28. A. .

Data Interpretation
29. D. September.
30. B. August and November.
31. B. Trade balance = Exports – Imports. The aggregate for the year is about –10 million.
32. B. .
33. C. August (deficit is ).
34. B. .
35. C. 11% + 2% = 13% ( 11% for NRI and 2% for National Banks).
36. C. .
37. C. .
38. A. .

English
39. C.
40. B.
41. A.
42. B.
43. B.
44. C.
45. A.
46. C.
47. C.
48. D.
49. A.
50. C.

51. B.
52. D.
53. C.
54. C.
55. B.
56. C.
57. C.
58. D.
59. C.
60. A.
61. D.
62. A.
63. C.

Logical Reasoning
64. A. The man in the photograph is son of Mitali's grandfather's son i.e., the son of Mitali's
father. Hence, the man is Mitali’s brother.
65. D. Explanation: First Letter as it is. Second and Third Letter interchanged. Fourth and
Fifth letter interchanged. Sixth and Seventh letter interchanged. Eighth letter as it is.
66. A.
67. B. The watch gains 5 seconds in 3 minutes, which is 100 seconds in 1 hour (3600
seconds), or 1 minute in 36 minutes. From 7 AM to 4:15 PM on the same day, the clock
has passed 9 hours and 15 min, i.e., 555 min ( min). The actual time that has
passed must be min. Thus, the correct time should be 4:00 PM.
68. B. This is a leap year. So, none of the next 3 years will be leap years. Each year will give
one odd day so the day of the week will be 3 odd days beyond Monday i.e. it will be
Thursday.
69. D.
70. C. We solve this problem by assuming that one of them is the robber and then check
whose statement is true of false. We summarize the findings in a table.
Robber → Salman Aamir Saif Shahrukh
Statement ↓
Salman F T F F
Aamir F F F T
Saif T T F T
Shahrukh T T T F
Only column with a single T
Therefore, it must be Saif who did it.