Institute of Actuaries of India Sample Questions - …

1 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) cm b) cm c) cm d) cm 1mark 4.

2 If and 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.

3 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.

4 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) 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.

5 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?

6 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.

7 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.

8 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.

9 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.

10 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) b) c) d) 1 mark 35. If a soap user uses kgs of soap a month on the average, what is the present soap usage amongst the soap-users surveyed? a) tonnes/month b) tonnes/month c) tonnes/month d) Cannot be determined 1 mark 36.