Institute of Actuaries of India Sample Questions - ACET 2016 Mathematics 1. If the range of a function is a singleton set, then it is a) b) c) d)
an identity function a one to one function a constant function a bijective function.
1mark
2. The Maclaurin series of sin x is a) b) c) d)
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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) b) c) d)
6.0 cm 7.5 cm 8.8 cm 9.0 cm
4. If and β are the roots of statements is incorrect. Which one is it?
1mark then one of the following
a) b) c) d)
2 marks
5. The roots of the quadratic polynomial a) b) c) d)
-4,-5 -4,5 9,20 4,5
are
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6. If
and
, then
is equal to
a) sin b) cos c) cot d) tan 7.
2 marks ose
is
a) 0 b) 1 c) ∞ d) 8. If a) (b) c) d)
3 marks and
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9. The curve a) b) c) d)
has a point of inflexion at
.Then
2 marks.
10. The value of a) b) c) d)
is equal to
11. The value of
is equal to
a) b) c) d)
is real, then f is increasing in the interval
1 mark
1 mark
12. The value of
; m positive integer is
a) b) c) 3 marks
d)
13. If A=
, then A2 is equal to
a) b) – c) 0 d)
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14. The inverse of the matrix
is
a) b) c) d)
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15. The angle between the vectors a) b) c) d)
450 600 900 1350
-
+
and - +
+
is
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Statistics 16. The value of a) b) c) d)
is
30 31 32 20
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17. The mean of consecutive positive integers from 2 to n is a) b) c) d)
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18. The interquartile range of the following numbers is 1, 6, 7, 3, 5, 9, 15, 12, 27, 18, 19 a) b) c) d)
9 13 11.5 18
19. If
and
a) b) c) d)
5/7 1/10 1/3 0
1 mark are independent events such that then the value of is
,
and
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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 21. The pdf of a continuous random variable X is given by
1 mark
; -
.
The value of k is a) b) 0 c) d)
2 marks
22. For a Poisson distribution, it is given that of the distribution is a) 6 b) 36 c) d) 4
. The variance
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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. X
0
0 1
3/20 7/20
1
Y 6/20 4/20
The Covariance between X and Y is a) b) c) d)
2 marks
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. 400 345
350 300 250 201
Net Profit
Crores 200
Turnover
132
150
106
100 42
30
50 1
1
28
43
65
1
0 1995-96
1996-97
1997-98
All figures in crore
1998-99
1999-00
2000-01
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 28. In which year is the cost the maximum? a) 1997-98 b) 1998-99 c) 1999-00 d) 2000-01
2 marks
1 mark
29. Cost over turnover is known as cost percentage. For which year is the cost percentage maximum?
a) b) c) d)
1997-98 1998-99 1999-00 2000-01
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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) b) c) d)
524 525 526 527
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) b) c) d)
2 3 4 5
2 marks
33. Which year witnessed the highest turnover percentage increase over the previous year? a) b) c) d)
2000-01 1999-00 1998-99 1997-98
1 mark
Questions 34 to 38 are based on the information provided in the following table.
Past Users ( Number of People)
Present and Past Users of Different Toilet Soaps Present Users ( Number of People) Lux Liril Dove Nivea No Soap Usage Lux 200 65 100 70 55 Liril 50 280 60 70 40 Dove 80 55 80 25 0 Nivea 140 40 0 50 40 No Soap Usage 200 25 0 40 190 670 465 240 255 325
490 500 240 270 455 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) b) c) d)
2.2 tonnes/month 2.25 tonnes/month 2.445 tonnes/month 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) b) c) d)
148 158 168 178
1 mark
38. Which of the following pie charts correctly represents the share of different brands amongst the present soap users surveyed? Lux Liril Dove Nivea No soap uasge
a) Lux Liril Dove Nivea No soap uasge
b) Lux Liril Dove Nivea No soap uasge
c) Lux Liril Dove Nivea No soap uasge
d)
1 mark
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) b) c) d)
by in for 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
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44. Fill the blank in the following sentence. It's a long walk tomorrow. We need to ___________ as early as possible. a) b) c) d)
set up set in set off set about
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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) b) c) d)
Compulsion Terror Provocation Force
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47. Find out the alternative whi h will repla e ‘?’ Tractor : Trailer :: Horse : ? a) b) c) d)
Stable Saddle Engine Cart
48. Choose the word which is least like the other words. a) Deck b) Quay c) Stern d) Bow
1 mark
1 mark
49. Chose the word which is not a synonym of Bliss. a) b) c) d)
Cloud nine Seventh Heaven Walking on air Walking on water
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50. Foreign investment has been simplified in India; __________ many foreign investors are planning to enter India's market. a) b) c) d)
thus even if that's why so as to
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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) b) c) d)
Apostate Profane Agnostic 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: P: Q: R: S: S6:
Many European cities have trams for local commutation. As a result, there is horrendous congestion. It was going to be technically challenging. They run down the center of the road To ease it, many cities decided to build underground railway lines. The foundation stone was laid in 1972.
The proper sequence should be a) b) c) d)
PRSQ PSQR SQRP 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) b) c) d)
PQRS SRPQ SPRQ 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) b) c) d)
JJF FIF FJJ 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) b) c) d)
FIJ JIF FJI IJF
2 marks
57. The meaning of the phrase “To take a thing lying down” is a) b) c) d)
to respect weaker people to purchase discounted item to submit without resistance 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) b) c) d)
aaab aabb abab 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) b) c) d)
Uncle Brother Grandfather 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) b) c) d)
Both A and R are true and R is the correct explanation of A. Both A and R are true but R is NOT the correct explanation of A. A is true but R is false. 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) b) c) d)
10.10:35 PM 10:23:20 PM 11:01:17 PM 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) b) c) d)
Q S R P
1 mark
68. Today is Monday. After 61 days, it will be a) b) c) d)
Wednesday Thursday Tuesday Saturday
1 mark
69. Arrange the words given below in a meaningful sequence. 1.Elephant a) b) c) d)
2. Cat
3. Tiger
4. Mosquito
5. Whale
5, 3, 1, 2, 4 4, 2, 3, 1, 5 1, 3, 5, 4, 2 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) b) c) d)
UPA NDA Either one (cannot be said) None
3 marks *****
