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Institute of Actuaries of India
Sample Questions - ACET
Mathematics
- 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
- The Maclaurin series of sin x is
a) b) c) d) 1mark
- 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
- 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
- The roots of the quadratic polynomial are
a) -4,- b) -4, c) 9, d) 4,5 1 mark
- If and , then is equal to
a) sin b) cos c) cot d) tan 2 marks
- ose is a) 0 b) 1 c) ∞ d) 3 marks
- If and is real, then f is increasing in the interval a) (- b) c) d) 3 marks
- The curve has a point of inflexion at .Then a) b) c) d) 2 marks.
- The value of is equal to a) b) c) d) 1 mark
- The value of is equal to
a) b) c) d) 1 mark
Statistics
- The value of is
a) 30 b) 31 c) 32 d) 20 1 mark
- The mean of consecutive positive integers from 2 to n is
a) b) c) d) 1 mark
- 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. d) 18 1 mark
- If and are independent events such that , and then the value of is
a) 5/ b) 1/ c) 1/ d) 0 1 mark
- A random variable X has the following discrete probability distribution.
0 1 2 3
The mean of X is a) 1 b) 31/ c) 6/ d) 3/2 1 mark
- The pdf of a continuous random variable X is given by
The value of k is a) b) 0 c) d) 2 marks
- For a Poisson distribution, it is given that. The variance of the distribution is a) 6 b) 36 c) d) 4 2 marks
- 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
- 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
- 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
a) 1997- b) 1998- c) 1999- d) 2000-01 1 mark
- 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
- 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
- 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
- Which year witnessed the highest turnover percentage increase over the previous year?
a) 2000- b) 1999- c) 1998- 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
- 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
- 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
- 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
- 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?
English
- 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
- 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
- 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
- One word for “Without payment” is a) Gratis b) Hedonist c) Stoic d) Precious 1 mark
- A synonym for Congenital is a) Unhygienic b) Indigenous c) Suitable d) Unsuitable 1 mark
- 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
- 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
- Find out the alternative whi h will repla e ‘?’
Fear : Threat :: Anger :?
a) Compulsion b) Terror c) Provocation d) Force 1 mark
- Find out the alternative whi h will repla e ‘?’
Tractor : Trailer :: Horse :?
a) Stable b) Saddle c) Engine d) Cart 1 mark
- Choose the word which is least like the other words. a) Deck b) Quay c) Stern d) Bow 1 mark
- 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
- 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
- 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
- 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
- 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
- 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.
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
- 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
- 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
- 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
- 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
- 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
