Institute of Actuaries of India Solutions for Sample Questions - ACET 2016
Mathematics 1. c. It is by definition. 2. a. It is by definition. 3. d. Height of the plant in 15 days (by linear interpolation) is
4.
Su
of the roots α+β =
and product of the roots αβ = . The other options are
true on simple algebra. 5. a. The roots are given by x =
6. d.
=
7. a.
and
. a =1 ;b=9 and c = 20. Hence, x= -4 or -5.
=
is in ∞-∞ for
. Hence
.
To have form we write . Appling L Hospitals rule twice we get the value as
0. 8. b. interval
, which is positive only in the
9. c. Differentiating y wrt to x twice and putting x=1 we get the answer. 10.
10.a.
dx =
Since log x for x
is not defined, put t = - x, so that
. 11. c.
=
12. d.
= 1 By integration by parts. is to be treated as a gamma function which is
!
13. b.
14. d. The matrix formed by the co factors is . Hence Inverse of A = 15. c. ( - + angle is
)( - +
. Therefore AdjA= .
+
.Therefore the
Statistics 16. b.
= 5+10+10 +5+1=31
17. a. Make use the formula for sum of
positive integers from 1 to n.
18. b. There are 11 numbers. When arranged in increasing order 9 is the middle most number. The median of the numbers below 9 is 5. Hence, Q 1=5. Similarly Q3=18. Thus the interquartile range is: Q3 - Q1= 18-5=13. 19. c. This implies k=1/3. 20. c. The Mean of X is (0× 1/6)+( 1× 1/2)+(2× 3/10)+(3× 1/30) = 6/5. 21. a. = 1 implies
, since Thus
22. a. X is Poisson such that This implies
and =
. . That is
.
=36. Thus, the positive root of 36 is 6. The variance
is 6.
23. c. The number of claims is a discrete variable, and the normal distribution is the only one meant for a continuous variable. 24. c. Let ,
and
be the events that the vehicle involved was a scooter, a car and a truck,
respectively. These events are disjoint. Further,
,
and
. The required probability is
25. a.
. Thus
26. d. The correlation coefficient is
= -1/2 (since the regression
coefficients are negative.)
Data Interpretation 27. c. 43/201 from 1999-00 is the highest ratio. 28. d. 180 = 345-65 from 2000-01 is the maximum cost. 29. a. 105/106= 99.06% for the year 1997-98 is the highest cost percentage. 30. d. 345 * ( 345/201) – 65 = 527 31. b. 345 * (345/201) = 592; 527/592 = 89% 32. b. For years 1995-96, 1996-97 and 1997-98 33. d. is the highest turnover increase percentage in 1997-98 over the previous year 1996-97. 34. b. 42.8% = 837.5/ 1956, where 1956= 1630*1.2 and 837.5 = 670*1.25, where 1630 is the number of total present soap users and 670 is the number of present Lux users. 35. c. 2.445 = 1630 *1.5 /1000 36. b. Percentage of past Liril users of present total soap users is 500/1630 = 30.67%.
Percentage of present Liril users of present total soap users = 465/1630 = 28.53%. The decrease in percentage is
.
37. a. Shift from present Lux users = 10% * 670= 67 Shift from present Liril users= 10% * 465 = 46.5 Shift from present Dove users= 8% * 240= 19.2 Shift from present Nivea users= 6% * 255= 15.3 Number of Palmolive users answer is an integer).
(no rounding needed;
39. a. Lux has the largest share, so option b is wrong. Nivea has the second largest share, so c is eliminated. Options a and d are consistent with these two facts. The number of users of Dove and Nivea are comparable, while these two numbers are smaller than the number of non-users of soap. Only option a correctly represents this fact.
English 39. d. 40. b. 41. c. 42. a. 43. b. 44. c. 45. b. 46. c. 47. d. 48. b. 49. d. 50. c. 51. b. 52. a. 53. d.
54. b. 55. a. 56. b. 57. c. 58. b. 59. c. 60. c. 61. d. 62. b.
Logical Reasoning 63. a. The pattern aaaaba is repeated. 64. d. The only daughter of Priyanka's father is Priyanka herself. So, Sachin's mother is Priyanka. Thus, Priyanka's husband is the father of Sachin. 65. a. 66. b. The watch gains 5 seconds in 3 minutes => 100 seconds in 1 hour. From 8 AM to 10 PM on the same day, time passed is 14 hours. In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds. So, when the correct time is 10 PM, the watch would show 10:23:20 PM. 67. c. 68. d. Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday. After 61 days, it will be Saturday. 69. b. The correct order is Mosquito Cat Tiger Elephant Whale 4
2
3
1
5
70. b. As only one statement is wrong, other two statements will be true.
If you assume UPA wins the election. Now Statements of Y and Z are becoming false which is against our condition. If you assume that neither wins the collection, then Statements of X and Y become wrong, which goes against our condition. Assume NDA wins the election. Now Statements of X and Y are true. This satisfies our condition that two of them tell the truth. So NDA wins the election. *****
