Institute of Actuaries of India Sample Questions - ACET

Mathematics

1. If the range of a function is a singleton set, then it is a) an identity function b) a one to one function c) a constant function d) a bijective function. 1mark

2. The Maclaurin series of sin x is

a)

b)

c)

d)

1mark

3. A plant reaches the height of 5 cm in 7 days and 10 cm in 17 days. By using linear interpolation, the approximate height of the plant in 15 days is a) 6.0 cm b) 7.5 cm c) 8.8 cm d) 9.0 cm 1mark

4. If and β are the roots of then one of the following

statements is incorrect. Which one is it?

a)

b)

c)

d)

2 marks

5. The roots of the quadratic polynomial are

a) -4,-5 b) -4,5 c) 9,20 d) 4,5 1 mark

6. If and , then

is equal to

a) sin

b) cos

c) cot

d) tan

2 marks

7. ose

is

a) 0 b) 1 c) ∞

d)

3 marks

8. If and is real, then f is increasing in the interval

a) (- b) c) d) 3 marks

9. The curve has a point of inflexion at .Then

a) b) c) d) 2 marks.

10. The value of

is equal to

a) b) c) d) 1 mark

11. The value of

is equal to

a) b) c) d) 1 mark

12. The value of

; m positive integer is

a)

b)

c)

d)

3 marks

13. If A=

, then A2 is equal to

a)

b) – c) 0 d) 1 mark

14. The inverse of the matrix

is

a)

b)

c)

d)

1 mark

15. The angle between the vectors - + and - + + is

a) 450

b) 600

c) 900

d) 1350 2 marks

Statistics

16. The value of

is a) 30 b) 31 c) 32 d) 20 1 mark

17. The mean of consecutive positive integers from 2 to n is

a)

b)

c)

d)

1 mark

18. The interquartile range of the following numbers is

1, 6, 7, 3, 5, 9, 15, 12, 27, 18, 19

a) 9 b) 13 c) 11.5 d) 18 1 mark

19. If and are independent events such that , and

then the value of is

a) 5/7 b) 1/10 c) 1/3 d) 0 1 mark

20. A random variable X has the following discrete probability distribution.

0 1 2 3

The mean of X is

a) 1 b) 31/30 c) 6/5 d) 3/2 1 mark

21. The pdf of a continuous random variable X is given by

; - .

The value of k is

a) b) 0 c) d) 2 marks

22. For a Poisson distribution, it is given that . The variance of the distribution is

a) 6 b) 36

c) d) 4 2 marks

23. Which of the following distributions is certainly not appropriate for modeling the

annual number of claims arising from a group insurance policy of ten workers? a) Binomial distribution b) Poisson distribution c) Normal distribution d) Geometric distribution 1 mark

24. An insurance company has insured 2000 scooter drivers, 4000 car drivers and

6000 truck drivers. Each driver drives only one vehicle, and has the same chance of making an accident. The company has learnt that one of these insured drivers has crashed against a wall and that the vehicle involved was not a truck. What is the probability that the vehicle was a car? a) b) c) d) 1mark

25. The joint probability mass function of X and Y is given in the following table.

The Covariance between X and Y is

a) b) c) d) 2 marks

X Y

0 1

0 3/20 6/20

1 7/20 4/20

26. While fitting a regression line Y on X and also of X on Y, a student computed

and

The sample correlation coefficient between X and Y is

a) b) c) d) 2 marks

Data Interpretation

Questions 27 to 33 are based on the Chart given below.

All figures in crore Cost = Turnover – Net profit

27. In which year is the ratio of net profit to turn over the maximum?

a) 1997-98

b) 1998-99

c) 1999-00

d) 2000-01 2 marks

28. In which year is the cost the maximum?

a) 1997-98 b) 1998-99 c) 1999-00 d) 2000-01 1 mark

29. Cost over turnover is known as cost percentage. For which year is the cost

percentage maximum?

1 1 1 28

43 65

30 42

106 132

201

345

0

50

100

150

200

250

300

350

400

1995-96 1996-97 1997-98 1998-99 1999-00 2000-01

Crores Net Profit

Turnover

a) 1997-98 b) 1998-99 c) 1999-00 d) 2000-01 1 mark

30. If the percentage rise in turnover in 2001-02 over 2000-01 is the same as the

percentage rise in 2000-01 over 1999-00 with the net profit in 2001-02 being the

same as in 2000-01, then what will be the cost in 2001-02?

a) 524

b) 525

c) 526

d) 527 1 mark

31. Using the data given in the above question, what percentage of the turnover is

the cost in 2001-02?

a) 88%

b) 89%

c) 90%

d) 91% 1 mark

32. For how many years is the turnover as a percentage of net profit more than 700

per cent?

a) 2

b) 3

c) 4

d) 5 2 marks

33. Which year witnessed the highest turnover percentage increase over the

previous year?

a) 2000-01

b) 1999-00

c) 1998-99

d) 1997-98 1 mark

Questions 34 to 38 are based on the information provided in the following table.

Present and Past Users of Different Toilet Soaps

Present Users ( Number of People)

Lux Liril Dove Nivea No Soap Usage

Past Users ( Number of People)

Lux 200 65 100 70 55 490

Liril 50 280 60 70 40 500

Dove 80 55 80 25 0 240

Nivea 140 40 0 50 40 270

No Soap Usage 200 25 0 40 190 455

670 465 240 255 325 1955

34. If from the present users, the total soap usage increases by 20% and Lux users

increase by 25%, approximately what percent of the soap using market would be

Lux users?

a) 41.8%

b) 42.8%

c) 43.8%

d) 44.8% 1 mark

35. If a soap user uses 1.5 kgs of soap a month on the average, what is the present

soap usage amongst the soap-users surveyed?

a) 2.2 tonnes/month

b) 2.25 tonnes/month

c) 2.445 tonnes/month

d) Cannot be determined 1 mark

36. What is the decrease in the usage of Liril as a percentage of the total present

soap users from the sample population?

a) 2.10%

b) 2.15%

c) No change

d) 2.20% 2 marks

37. If a new brand Palmolive is introduced into the market, and the brand shift to

Palmolive from the present users is Lux 10%, Liril 10%, Dove 8% and Nivea 6%,

how many users will Palmolive have?

a) 148

b) 158

c) 168

d) 178 1 mark

38. Which of the following pie charts correctly represents the share of different

brands amongst the present soap users surveyed?

a)

b)

c)

d) 1 mark

Lux

Liril

Dove

Nivea

No soap uasge

Lux

Liril

Dove

Nivea

No soap uasge

Lux

Liril

Dove

Nivea

No soap uasge

Lux

Liril

Dove

Nivea

No soap uasge

English

39. The politician has been told he will have to pay the fine _____ his influential

position.

a) even if

b) although

c) against

d) despite 1 mark

40. Find out the part which contains an error.

a) hardly had we settled down

b) startled on the loud noise being made outside the house

c) for the night's rest when we were

d) one hour ought to be enough time

1 mark

41. Fill the blank in the following sentence.

The scientist had copied the paper word _______ word.

a) by

b) in

c) for

d) from 1 mark

42. One word for “Without payment” is

a) Gratis

b) Hedonist

c) Stoic

d) Precious 1 mark

43. A synonym for Congenital is

a) Unhygienic

b) Indigenous

c) Suitable

d) Unsuitable 1 mark

44. Fill the blank in the following sentence.

It's a long walk tomorrow. We need to ___________ as early as possible.

a) set up

b) set in

c) set off

d) set about 1 mark

45. Fill the blank in the following sentence.

Often, we don't enjoy the ________ pleasures of life such as a beautiful sky, a cup of tea with a friend or seeing a good film at the cinema. a) sheer

b) simple

c) deep

d) plain 1 mark

46. Find out the alternative whi h will repla e ‘?’

Fear : Threat :: Anger : ?

a) Compulsion

b) Terror

c) Provocation

d) Force 1 mark

47. Find out the alternative whi h will repla e ‘?’

Tractor : Trailer :: Horse : ?

a) Stable

b) Saddle

c) Engine

d) Cart 1 mark

48. Choose the word which is least like the other words.

a) Deck

b) Quay

c) Stern

d) Bow 1 mark

49. Chose the word which is not a synonym of Bliss.

a) Cloud nine

b) Seventh Heaven

c) Walking on air

d) Walking on water 1 mark

50. Foreign investment has been simplified in India; __________ many foreign

investors are planning to enter India's market.

a) thus

b) even if

c) that's why

d) so as to 1 mark

51. _____________ cars are the most convenient way of transport, they are also the

major contributor to traffic.

a) Whenever

b) Whereas

c) On the other hand

1 mark

d) As long as

52. One word for a person who abandons his religious faith is

a) Apostate

b) Profane

c) Agnostic

d) Atheist 1 mark

53. The first and sixth sentences of a passage are given in the beginning and in the

end, respectively. The middle four sentences have been jumbled up. These are

labelled as P, Q, R and S. Find out the proper order for the four sentences.

S1: Many European cities have trams for local commutation. P: As a result, there is horrendous congestion. Q: It was going to be technically challenging. R: They run down the center of the road S: To ease it, many cities decided to build underground railway lines. S6: The foundation stone was laid in 1972.

The proper sequence should be

a) PRSQ

b) PSQR

c) SQRP

d) RPSQ 2 marks

54. The first and sixth sentences of a passage are given in the beginning and in the

end, respectively. The middle four sentences have been jumbled up. These are

labelled as P, Q, R and S. Find out the proper order for the four sentences.

S1: Traffic is a big issue in Mumbai. P: So many vehicles on road are the source of air pollution. Q: Government is building some flyovers to ease the traffic congestion. R: Another problem is air pollution due to traffic. S: Daily commuting has become very difficult. S6: Some new roads are also being planned.

The proper sequence should be

a) PQRS

b) SRPQ

c) SPRQ

d) QRPS 2 marks

55. Classify each of the statements given below as Fact (F), Inference (I), Judgment

(J).

I. Increasing air pollution is the biggest problem in Delhi.

II. The odd-even formula reduced the traffic but not the air pollution.

III. There are many other factors that contribute to air pollution along with

traffic.

a) JJF

b) FIF

c) FJJ

d) FIJ 2 marks

56. Classify each of the statements given below as Fact (F), Inference (I), Judgment

(J).

I. The government is doing a good job.

II. A recently conducted survey says that people are, in general, satisfied with

the government.

III. Government has announced a new scheme for unemployed people.

a) FIJ

b) JIF

c) FJI

d) IJF 2 marks

57. The meaning of the phrase “To take a thing lying down” is

a) to respect weaker people

b) to purchase discounted item

c) to submit without resistance

d) to avoid 2 marks

58. Choose the correct sentence.

a) It is probable that the new smartphone by Orange might be ready for testing

around the end of next year.

b) It is probable that the new smartphone by Orange will be ready for testing

toward the end of next year.

c) It is probable that the new smartphone by Orange may be ready for testing

about the end of next year.

d) It is probable that the new smartphone by Orange might be ready for testing

toward next year’s end. 2 marks

59. Choose the correct sentence.

a) Being deserted by our friends is the cause of great sorrow for us.

b) Our being deserted by our friends is the cause of great sorrow.

c) We feel great sorrow when our friends desert us.

d) Being deserted by our friends, we feel great sorrow. 2 marks

60. Choose the correct sentence.

a) Jack smelled a rat when he scrambled out of the dirty ditch.

b) Tom smells a rat every time he plans a vacation.

c) The minister smelled a rat when his office caught fire and all the files were

destroyed.

d) The secretary smelled a rat when he put the office on fire. 2 marks

61. It is strange that outside the Hotel Megastar, there are so many corner shops

selling food items. After all, the hotel also has a big restaurant which sells food at

cheaper prices, and is open 24-hours.

Which of the following, if true, would be of least help in explaining the paradoxical observation in the given passage? a) The corner shops are selling specialist food items not available in the hotel

restaurant.

b) The main business of the corner shops is newspaper distribution and food

items represent a small part of their turnover.

c) The corner shops are mainly family-owned businesses and have been there

for much longer than the hotel restaurant and are perceived as an important

feature of the community.

d) The corner shops are willing to make home deliveries. 2 marks

Read the passage below and answer Question No 62: If you want a brief history of information technology, here is one. Humans were the first "computers". Then machines were invented to carry out the computational tasks. Now these machines have given way to new form of information technology. Information has become accessible from anywhere. Information technology deals with the acquisition, processing, storage and dissemination of vocal, pictorial, textual and numerical information by a microelectronics-based combination of computing and telecommunications. Thanks to the continuous development of computers, the original computing systems became minicomputers and later personal computers took the lead. Nowadays, mobile phones are dethroning the personal computer and computing is evolving faster to become disembodied more like a cloud, becoming accessible more easily whenever needed. Information technology in this sense has transformed people and companies and has allowed digital technology to influence society and economy alike.

I. Information technology is changing principally because of: i. government policies ii. new technological advances iii. both i and ii above

II. Development of information technology is the result of:

i. advances in computing systems ii. development of machinery in general iii. both i and ii above

III. Computing systems are taking the form of clouds means:

i. computers have become smaller ii. computing power will be disembodied. iii. both i and ii above

62. The correct answers to I, II and III are:

a) iii, ii, ii respectively

b) ii, i ii respectively

c) i, ii, ii respectively

d) iii, i, i respectively 3 marks

Logical Reasoning

63. In the following letter series, the missing letters have to be filled from one of the

given alternatives in the given order, so that the series contains a repeated

pattern. Which alternative is appropriate?

aa _ ab _ _ aaa _ a

a) aaab b) aabb c) abab d) baaa 1 mark

64. Sa hin’s mother is the only daughter of Priyanka’s father. If Priyanka had married

only on e, what is Priyanka`s husband’s likely relationship with Sa hin?

a) Uncle b) Brother c) Grandfather d) Father 1 mark

65. Please read the following Assertion and Reason.

Assertion (A) : We feel colder on mountains than on plains.

Reason (R) : Temperature decreases with altitude.

a) Both A and R are true and R is the correct explanation of A.

b) Both A and R are true but R is NOT the correct explanation of A.

c) A is true but R is false.

d) A is false but R is true. 1 mark

66. A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day?

a) 10.10:35 PM b) 10:23:20 PM c) 11:01:17 PM d) 10:31:20 PM 1 mark

67. Study the following diagram and answer the following question.

By which letter, the married teachers who do not live in joint family are

represented?

a) Q

b) S

c) R

d) P 1 mark

68. Today is Monday. After 61 days, it will be

a) Wednesday b) Thursday c) Tuesday d) Saturday 1 mark

69. Arrange the words given below in a meaningful sequence.

1.Elephant 2. Cat 3. Tiger 4. Mosquito 5. Whale

a) 5, 3, 1, 2, 4 b) 4, 2, 3, 1, 5 c) 1, 3, 5, 4, 2 d) 2, 5, 1, 4, 3 1 mark

70. Three persons give three statements.

X says either NDA or UPA wins the elections. Y says NDA wins. Z says neither NDA nor UPA wins the elections. Of these statements only one is wrong. Who wins the elections?

a) UPA b) NDA c) Either one (cannot be said) d) None 3 marks

*****