Institute of Actuaries of IndiaSample 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) 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) 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 1 mark 10. then f is increasing in the interval 1 mark 1 mark . If a) (b) c) d) 3 marks and 3 marks 9.Then 2 marks. The value of a) b) c) d) is equal to 11. If and . 2 marks ose is a) 0 b) 1 c) ∞ d) 8. The value of is equal to a) b) c) d) is real. then is equal to a) sin b) cos c) cot d) tan 7. The curve a) b) c) d) has a point of inflexion at .6. The value of .12. The inverse of the matrix is a) b) c) d) 1 mark 15. If A= . m positive integer is a) b) c) 3 marks d) 13. then A2 is equal to a) b) – c) 0 d) 1 mark 14.+ + is 2 marks . The angle between the vectors a) b) c) d) 450 600 900 1350 - + and . 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 . 5. The interquartile range of the following numbers is 1. 18. 15. 0 1 2 3 The mean of X is a) 1 b) 31/30 c) 6/5 d) 3/2 21. 9. 19 a) b) c) d) 9 13 11. The value of a) b) c) d) is 30 31 32 20 1 mark 17. The pdf of a continuous random variable X is given by 1 mark .Statistics 16. 7. 12. The mean of consecutive positive integers from 2 to n is a) b) c) d) 1 mark 18. A random variable X has the following discrete probability distribution. 6.5 18 19. and 1 mark 20. 3. 27. Each driver drives only one vehicle. For a Poisson distribution. What is the probability that the vehicle was a car? a) b) c) d) 1mark 25. - .. it is given that of the distribution is a) 6 b) 36 c) d) 4 . 4000 car drivers and 6000 truck drivers. The company has learnt that one of these insured drivers has crashed against a wall and that the vehicle involved was not a truck. The joint probability mass function of X and Y is given in the following table. 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. and has the same chance of making an accident. The value of k is a) b) 0 c) d) 2 marks 22. The variance 2 marks 23. 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 . An insurance company has insured 2000 scooter drivers. 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. 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? . 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. While fitting a regression line Y on X and also of X on Y.26. 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. then what will be the cost in 2001-02? a) b) c) d) 524 525 526 527 1 mark 31.a) b) c) d) 1997-98 1998-99 1999-00 2000-01 1 mark 30. what percentage of the turnover is the cost in 2001-02? a) 88% b) 89% c) 90% d) 91% 1 mark 32. 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. 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. . Using the data given in the above question. 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. 8% b) 42.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. the total soap usage increases by 20% and Lux users increase by 25%.15% c) No change d) 2. and the brand shift to Palmolive from the present users is Lux 10%.5 kgs of soap a month on the average. Liril 10%.10% b) 2.8% d) 44.25 tonnes/month 2. what is the present soap usage amongst the soap-users surveyed? a) b) c) d) 2. Dove 8% and Nivea 6%. If a new brand Palmolive is introduced into the market. What is the decrease in the usage of Liril as a percentage of the total present soap users from the sample population? a) 2.20% 2 marks 37. If from the present users.445 tonnes/month Cannot be determined 1 mark 36.8% c) 43. how many users will Palmolive have? .8% 1 mark 35. approximately what percent of the soap using market would be Lux users? a) 41. If a soap user uses 1.2 tonnes/month 2. 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 . a) b) c) d) by in for from 1 mark 42. The politician has been told he will have to pay the fine _____ his influential position. Find out the part which contains an error. The scientist had copied the paper word _______ word. Fill the blank in the following sentence. A synonym for Congenital is a) Unhygienic b) Indigenous c) Suitable d) Unsuitable 1 mark . One word for “Without payment” is a) Gratis b) Hedonist c) Stoic d) Precious 1 mark 43.English 39. a) even if b) although c) against d) despite 1 mark 40. 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. a) sheer b) simple c) deep d) plain 1 mark 46. a) b) c) d) set up set in set off set about 1 mark 45. Fill the blank in the following sentence. a cup of tea with a friend or seeing a good film at the cinema. Often. we don't enjoy the ________ pleasures of life such as a beautiful sky.44. 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. We need to ___________ as early as possible. It's a long walk tomorrow. Fill the blank in the following sentence. Find out the alternative whi h will repla e ‘?’ Fear : Threat :: Anger : ? a) b) c) d) Compulsion Terror Provocation Force 1 mark 47. a) Deck b) Quay c) Stern d) Bow 1 mark 1 mark . Foreign investment has been simplified in India. __________ many foreign investors are planning to enter India's market. they are also the major contributor to traffic. One word for a person who abandons his religious faith is a) b) c) d) Apostate Profane Agnostic Atheist 1 mark . a) b) c) d) thus even if that's why so as to 1 mark 51. a) Whenever b) Whereas c) On the other hand 1 mark d) As long as 52. a) b) c) d) Cloud nine Seventh Heaven Walking on air Walking on water 1 mark 50.49. Chose the word which is not a synonym of Bliss. _____________ cars are the most convenient way of transport. R: Another problem is air pollution due to traffic. These are labelled as P. Q: Government is building some flyovers to ease the traffic congestion. Find out the proper order for the four sentences.53. The foundation stone was laid in 1972. Q. R and S. The middle four sentences have been jumbled up. These are labelled as P. S1: Traffic is a big issue in Mumbai. The first and sixth sentences of a passage are given in the beginning and in the end. Find out the proper order for the four sentences. The middle four sentences have been jumbled up. S6: Some new roads are also being planned. there is horrendous congestion. They run down the center of the road To ease it. It was going to be technically challenging. The proper sequence should be a) b) c) d) PRSQ PSQR SQRP RPSQ 2 marks 54. S1: P: Q: R: S: S6: Many European cities have trams for local commutation. P: So many vehicles on road are the source of air pollution. many cities decided to build underground railway lines. respectively. S: Daily commuting has become very difficult. The first and sixth sentences of a passage are given in the beginning and in the end. The proper sequence should be a) b) c) d) PQRS SRPQ SPRQ QRPS 2 marks . Q. respectively. As a result. R and S. Inference (I). III. Judgment (J). Classify each of the statements given below as Fact (F). a) b) c) d) FIJ JIF FJI IJF 2 marks 57. I. Judgment (J). satisfied with the government. Increasing air pollution is the biggest problem in Delhi. a) b) c) d) JJF FIF FJJ FIJ 2 marks 56. The odd-even formula reduced the traffic but not the air pollution. 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. Classify each of the statements given below as Fact (F). Inference (I). Choose the correct sentence. There are many other factors that contribute to air pollution along with traffic. a) It is probable that the new smartphone by Orange might be ready for testing around the end of next year. II. II. A recently conducted survey says that people are. . I. The government is doing a good job. c) It is probable that the new smartphone by Orange may be ready for testing about the end of next year. III. Government has announced a new scheme for unemployed people.55. in general. b) It is probable that the new smartphone by Orange will be ready for testing toward the end of next year. b) The main business of the corner shops is newspaper distribution and food items represent a small part of their turnover. It is strange that outside the Hotel Megastar. a) Being deserted by our friends is the cause of great sorrow for us. if true. 2 marks 60. Which of the following. we feel great sorrow. and is open 24-hours. Choose the correct sentence. d) The secretary smelled a rat when he put the office on fire. d) The corner shops are willing to make home deliveries. 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. 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. 2 marks 61. c) We feel great sorrow when our friends desert us. d) Being deserted by our friends.d) It is probable that the new smartphone by Orange might be ready for testing toward next year’s end. 2 marks 59. the hotel also has a big restaurant which sells food at cheaper prices. there are so many corner shops selling food items. 2 marks . c) The minister smelled a rat when his office caught fire and all the files were destroyed. b) Tom smells a rat every time he plans a vacation. b) Our being deserted by our friends is the cause of great sorrow. Choose the correct sentence. a) Jack smelled a rat when he scrambled out of the dirty ditch. After all. Now these machines have given way to new form of information technology. storage and dissemination of vocal. Information has become accessible from anywhere. development of machinery in general iii. The correct answers to I. computers have become smaller ii. I. Computing systems are taking the form of clouds means: i. Nowadays. processing. II and III are: a) iii. advances in computing systems ii. Humans were the first "computers". ii. both i and ii above 62. Information technology is changing principally because of: i. textual and numerical information by a microelectronics-based combination of computing and telecommunications. Thanks to the continuous development of computers. government policies ii. i ii respectively c) i.Read the passage below and answer Question No 62: If you want a brief history of information technology. Information technology deals with the acquisition. becoming accessible more easily whenever needed. both i and ii above II. the original computing systems became minicomputers and later personal computers took the lead. both i and ii above III. i. ii respectively b) ii. Information technology in this sense has transformed people and companies and has allowed digital technology to influence society and economy alike. pictorial. ii respectively d) iii. here is one. i respectively 3 marks . computing power will be disembodied. iii. Then machines were invented to carry out the computational tasks. mobile phones are dethroning the personal computer and computing is evolving faster to become disembodied more like a cloud. new technological advances iii. Development of information technology is the result of: i. ii. What time will it show at 10 PM on the same day? a) b) c) d) 10. A watch gains 5 seconds in 3 minutes and was set right at 8 AM. a) b) c) d) Both A and R are true and R is the correct explanation of A. Which alternative is appropriate? aa _ ab _ _ aaa _ a a) b) c) d) aaab aabb abab baaa 1 mark 64. Both A and R are true but R is NOT the correct explanation of A. Assertion (A) : We feel colder on mountains than on plains.10:35 PM 10:23:20 PM 11:01:17 PM 10:31:20 PM 1 mark . 1 mark 66. Reason (R) : Temperature decreases with altitude. so that the series contains a repeated pattern. Please read the following Assertion and Reason. 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. A is true but R is false. In the following letter series. Sa hin’s mother is the only daughter of Priyanka’s father.Logical Reasoning 63. A is false but R is true. the missing letters have to be filled from one of the given alternatives in the given order. 5. Cat 3. Who wins the elections? a) b) c) d) UPA NDA Either one (cannot be said) None 3 marks ***** . 3. 1. 1. 4.Elephant a) b) c) d) 2. Whale 5. 3 1 mark 70. 1. Z says neither NDA nor UPA wins the elections. Study the following diagram and answer the following question. Arrange the words given below in a meaningful sequence. Tiger 4. it will be a) b) c) d) Wednesday Thursday Tuesday Saturday 1 mark 69. 4. Mosquito 5. X says either NDA or UPA wins the elections. After 61 days. 2. Three persons give three statements. 2.67. 4 4. 5. Today is Monday. 3. Y says NDA wins. the married teachers who do not live in joint family are represented? a) b) c) d) Q S R P 1 mark 68. 3. By which letter. Of these statements only one is wrong. 2 2. 5 1. 1.