ACET 2022 Question Paper (Jun)

Institute of Actuaries of India
ACET June 2022
Mathematics

1. Let 𝑓(𝑥): 𝑅 → 𝑅 be the function defined by 𝑓(𝑥) = 5𝑥 3 + 9. Then 𝑓 is
A. neither one-one nor onto.
B. one-one but not onto.
C. onto but not one-one.
D. one-one and onto.

2. The value of
1
(4 + 𝑥)2 − 2
lim
𝑥→0 𝑥
1
A. is 4.
1
B. is 2.
1
C. is 8.
D. does not exist.

3. One of the zeroes of the polynomial 2𝑥 3 + 𝑥 2 − 5𝑥 + 2 is 1. The other zeroes are
1
A. 2, .
2
1
B. 2, − .
2
1
C. −2, .
2
1
D. −2, − .
2

4. If 4 log 𝑥 3 + 2 log 𝑥 2 = 2, then the value of 𝑥 is equal to
A. 18.
B. 36.
C. 12.
D. 9.

5. The 20th and 21st terms in the expansion of (3 + 𝑎)39 are equal. Then, the value of a
is equal to

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1
A. .
3

B. 3.
19
C. .
7
7
D. .
19

6. The sum of the first 15 terms of an AP is 705 and its first term is 12. Then the 20th
term is
A. 102.
B. 107.
C. 112.
D. 117.

7. The complex conjugate of (4−3𝑖)(3+2𝑖) is
(1+3𝑖)(3−𝑖)

A. 1 + 1.5𝑖.
B. 1.16 + 1.5𝑖.
C. 1.5 + 1𝑖.
D. 1 − 1.5𝑖.

8. The value of
4
sin (cos −1 )
5
is
3
A. ± .
4
1
B. ± 5.
3
C. ± 5.
4
D. ± 5.

9. Suppose 𝑓(𝑥) is a polynomial of degree 3, and the values of 𝑦 = 𝑓(𝑥) at 𝑥 = 0, 1, 2,
3, 4 are, respectively,
𝑦0 = 0, 𝑦1 = 2, 𝑦2 = 13, 𝑦3 = 44, 𝑦4 = 85.
It is found that there is an error in the value of y2 .The correct value of 𝑦2 should be
A. 3.5.
B. 16.5.
C. 13.

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D. 9.5.
3 marks

⃗⃗ and 3𝑖⃗ − 5𝑗⃗⃗ + 2𝑘
10. If the position vectors of two points P and Q are 2𝑖⃗ + 3𝑗⃗⃗ − 4𝑘 ⃗⃗
⃗⃗⃗⃗⃗⃗ | is
respectively, then |𝑃𝑄
A. √15.
B. 15.
C. 10.
D. √101.

⃗⃗ and 𝑏⃗⃗ = 2𝑖⃗ + 𝑗⃗ + 4𝑘
11. The value of 𝑐 for which the vectors 𝑎⃗ = 3𝑖⃗ + 𝑐𝑗⃗ + 2𝑘 ⃗⃗ are
perpendicular to each other is
A. 14.
B. −14.
1
C. .
48

D. 2
.
3

12. Let 𝑦 = log √sin √𝑒 𝑥 . Then 𝑑𝑦 is equal to
𝑒 𝑑𝑥
cot √𝑒 𝑥
A.
4
√𝑒 𝑥 .
cot √𝑒 𝑥
B.
2
√𝑒 𝑥 .
C. 2√𝑒 𝑥 cot √𝑒 𝑥 .
D. 4 √𝑒 𝑥 cot √𝑒 𝑥 .

13. If 𝑦 = 2𝑥 𝑥 , 𝑥 > 0, then 𝑑𝑦 at 𝑥 = 𝑒 is
𝑑𝑥

A. 𝑒 𝑒 .
B. 2𝑒 𝑒 .
C. 3𝑒 𝑒 .
D. 4𝑒 𝑒 .

14. Let
log 𝑒 𝑥
𝑓(𝑥) = , 𝑥 > 0.
2𝑥
Then, the maximum of 𝑓(𝑥) is attained where 𝑥 is equal to
A. 𝑒.

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1
B. .
𝑒

C. 1.
D. 𝑒 2 .

15. The value of the integral
𝑒 2𝑥 + 𝑒 −2𝑥
∫ 2𝑥 𝑑𝑥
𝑒 − 𝑒 −2𝑥
is
1
A. log 𝑒 (𝑒 2𝑥 − 𝑒 −2𝑥 ) + 𝐶.
2

B. 2 log 𝑒 (𝑒 2𝑥 − 𝑒 −2𝑥 ) + 𝐶.
1
C. log 𝑒 (𝑒 2𝑥 + 𝑒 −2𝑥 ) + 𝐶.
2

D. 2 log 𝑒 (𝑒 2𝑥 + 𝑒 −2𝑥 ) + 𝐶.

16. The value of the integral
𝜋
2 sin 𝑥
∫ 𝑑𝑥
0 sin 𝑥 + cos 𝑥

is
A. 𝜋.
B. 2𝜋.
𝜋
C. .
2
𝜋
D. .
4

17. Let
1 sin 𝜃 1
𝐴 = |−sin 𝜃 1 sin 𝜃|.
−1 − sin 𝜃 1
𝜋
Then, the value of A when 𝜃 = 4 is
A. 4.
B. 3.
C. 2.
D. 1.

18. Let
sin 𝑥 tan 𝑥
𝑀=[ ].
− tan 𝑥 sin 𝑥

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𝜋
The value of 𝑥 when 0 ≤ 𝑥 ≤ 2 and 𝑀 + 𝑀𝑇 = 𝐼 is
𝜋
A. .
2
𝜋
B. .
3
𝜋
C. .
4
𝜋
D. .
6

19. If 𝐴 and 𝐵 are symmetric matrices of the same order, then 𝐴𝐵 − 𝐵𝐴 is
A. a symmetric matrix.
B. an identity matrix.
C. a scalar matrix.
D. a skew symmetric matrix.

20. The inverse of the matrix
2 1 3
𝑀 = [ 4 −1 0]
−7 2 1
is
−1 5 3
1
A. [−4 23 12 ].
3
1 −11 −6
−1 −4 1
1
B. −3[ 5 23 −11].
3 12 −6
−1 5 3
1
C. − 3 [−4 23 12 ].
1 −11 −6
−1 −4 1
1
D. [ 5 23 −11].
3
3 12 −6
3 marks

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Statistics

21. The following observations have been arranged in ascending order.
5, 7, 10, 12, 15, 𝑥, 𝑥 + 2, 23, 25, 26, 28, 𝑦
If the mean and median of the observations are 18.5 and 18 respectively, then the
values of 𝑥 and 𝑦 are
A. 17, 30.
B. 17, 35.
C. 17.5, 30.
D. 18, 32.

22. The mean and standard deviation of 𝑛 observations 𝑥1 , 𝑥2 , … , 𝑥𝑛 are 𝑥̅ and 𝑠,
respectively. Then the mean and standard deviation of 𝑎𝑥1 , 𝑎𝑥2 , … , 𝑎𝑥𝑛 , where 𝑎 is a
constant, are
A. 𝑎𝑥̅ , √|𝑎|𝑠.
B. 𝑎𝑥̅ , √𝑎𝑠.
C. |𝑎|𝑥̅ , |𝑎|𝑠.
D. 𝑎𝑥̅ , |𝑎|𝑠.

23. The daily number of road accidents in a city for 20 days are given below.
6, 5, 6, 5, 1, 2, 5, 6, 4, 1, 2, 5, 6, 5, 7, 6, 5, 9, 10, 8
Suppose highest 10% and lowest 10% of the observations are discarded. Then only
one of the following statements is true. Which one is it?
A. The mean of the remaining observations is greater than that of the original
observations.
B. The median of the new observations is same as that of the original observations.
C. The range of the new observations is 8.
D. The mode of the new observations is 6.

24. The class X of a school has two sections, A and B. Sections A and B have 48 and 52
students, respectively. The average marks of class X students in Mathematics in an
examination is 65. If the average mark of Section A is 78, then the average mark of
Section B is
A. 53.
B. 55.
C. 58.
D. 60.

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25. Which of the following statements is true?
A. If each observation is multiplied by a constant 𝑘, the inter-quartile range of the
new observations does not change.
B. For positively skewed distribution mean > median > mode.
C. For positively skewed distribution, the frequency curve has the longer tail towards
the left.
D. For negatively skewed distribution, frequency curve has longer tails toward the
right.

26. The correlation coefficient between two variables 𝑥 and 𝑦 is 𝑟 = 0.75. The means of 𝑥
and 𝑦 are 𝑥̅ = 10 and 𝑦̅ = 15, respectively. The standard deviations of 𝑥 and 𝑦 are
𝑠𝑥 = 1.5 and 𝑠𝑦 = 2.5, respectively. Then which of the following statements are true?
A. The regression line of 𝑥 on 𝑦 is 𝑥 = 3 + 0.45𝑦.

B. The regression line of 𝑥 on 𝑦 is 𝑥 = 3.25 + 1.25𝑦.

C. The regression line of 𝑦 on 𝑥 is 𝑦 = 2.5 + 1.25𝑥.

D. The regression line of 𝑦 on 𝑥 is 𝑦 = 2.5 + 0.45𝑥.

27. A bag contains 10 white and 6 black balls. Two balls are drawn at random with
replacement. The probability of getting one white and one black ball is
A. 15/64.
B. 15/32.
C. 1/4.
D. 1/2.

28. If 𝐸 and 𝐹 are independent events associated with a random experiment, then which of
the following statements is not necessarily true?
A. 𝐸̅ and 𝐹 are independent.
B. 𝐸 and 𝐹̅ are independent.
C. 𝑃(𝐸|𝐹̅ ) > 𝑃(𝐸).
D. 𝐸̅ and 𝐹̅ are independent.

29. In a factory light bulbs are produced by three machines 𝑀1 , 𝑀2 and 𝑀3 . The machines
manufacture 50%, 20% and 30% of the light bulbs. Of their outputs, 4%, 1% and 2%
are defective light bulbs. A light bulb is selected at random from the product and is
found to defective. Then the probability that it is not manufactured by machine 𝑀3 is
5
A. .
7
2
B. .
7

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3
C. .
14

D. 11
.
14

30. Consider an equilateral triangle whose common side length is 𝑋, which is uniformly
distributed over (0, 2). The expected area of the triangle is
2
A. .
√3
√3
B. .
4
1
C. .
√3
1
D. .
2√3

31. Five unbiased coins are tossed simultaneously. The probability of getting 3 heads and
2 tails is
A. 5/16.
B. 5/32.
C. 5/8.
D. 2/3.

32. A random variable 𝑋 takes values 0, 1, 2, 3 and its mean is 1.8. If 𝑃(𝑋 = 3) =
2𝑃(𝑋 = 1) and 𝑃(𝑋 = 2) = 0.2, then 𝑃(𝑋 = 0) is
A. 0.10.
B. 0.15.
C. 0.20.
D. 0.30.

33. A discrete random variable 𝑋 assume values 𝑥1 , 𝑥2 , … , 𝑥𝑚 with the respective
probabilities 𝑝1 , 𝑝2 , … , 𝑝𝑚 . Then the variance of 𝑋 is
A. ∑𝑚 2 𝑚 2
𝑖=1 𝑥𝑖 − (∑𝑖=1 𝑝𝑖 𝑥𝑖 ) .

B. ∑𝑚 2 2 𝑚 2 2
𝑖=1 𝑝𝑖 𝑥𝑖 − (∑𝑖=1 𝑝𝑖 𝑥𝑖 ) .

C. ∑𝑚 2 𝑚
𝑖=1 𝑝𝑖 𝑥𝑖 − ∑𝑖=1 𝑝𝑖 𝑥𝑖 .

D. ∑𝑚 2 𝑚 2
𝑖=1 𝑝𝑖 𝑥𝑖 − (∑𝑖=1 𝑝𝑖 𝑥𝑖 ) .

34. The 25th and 75th percentile of a normal distribution with mean 𝜇 and variance 𝜎 2 are
−1 and 1, respectively. The 25th and 75th percentile of standard normal distribution are
𝑄1 and 𝑄3 , respectively. Then 𝜇 and 𝜎 are
𝑄1 +𝑄3 1
A. and 𝑄 −𝑄 .
𝑄1 −𝑄3 3 1

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𝑄1 +𝑄3 2
B. and 𝑄 −𝑄 .
𝑄1 −𝑄3 3 1
2𝑄1 +𝑄3 2
C. and .
𝑄1 −𝑄3 𝑄3 −𝑄1
𝑄1 +0.5𝑄3 1
D. and 𝑄 −𝑄 .
𝑄3 −𝑄1 3 1

35. Let 𝑋 be a random variable with the probability mass function
𝑃(𝑋 = 𝑥) = 𝑝(1 − 𝑝)𝑥−1 , 𝑥 = 1, 2, 3, …
with 0 < 𝑝 < 1. Then for 𝑎 > 0 and 𝑏 > 0, 𝑃(𝑋 > 𝑎 + 𝑏|𝑋 > 𝑏) equals

A. 𝑃(𝑋 > 𝑎 + 𝑏).
B. 𝑃(𝑋 ≥ 𝑎 + 𝑏).
C. 𝑃(𝑋 > 𝑎).
D. 𝑃(𝑋 ≥ 𝑎).

36. Suppose 𝑋 ∼ 𝑁(𝜇, 𝜎 2 ), with 𝜇 = 2, 𝜎 2 = 3, is independent of 𝑌 ∼ 𝑈(2, 4). Then
Var(𝑋𝑌) equals
A. 88/3.
B. 30.
C. 32.
D. 80/3.

37. The number of trucks arriving on any one day at a truck depot in a certain city follows
a Poisson distribution with mean 𝜆 > 0. Suppose it is known that 𝑃(𝑋 = 5) =
2𝑃(𝑋 = 4). The probability that on a given day at most one truck will arrive at this
depot is
A. 11𝑒 −10.
B. 10𝑒 −10.
C. 11𝑒 −5.
D. 5𝑒 −5 .

38. Let 𝑋 be a random variable with probability density function 𝑓(𝑥) = 𝜆𝑒 −𝜆(𝑥−𝜃) , 𝑥 >
𝜃, 𝜆 > 0. Then which of the following statements is true?
1
A. 𝐸(𝑋) = 𝜆 + 𝜃, Var(𝑋) = 𝜆2 .
1
B. 𝐸(𝑋) = 𝜆 + 𝜃, Var(𝑋) = 𝜃 + 𝜆2 .
1 1
C. 𝐸(𝑋) = + 𝜃, Var(𝑋) = 2 .
𝜆 𝜆
1 1
D. 𝐸(𝑋) = 𝜆 + 𝜃, Var(𝑋) = 𝜃 2 + 𝜆2 .

Page 9 of 20

39. Consider two random variables 𝑋 and 𝑌 with joint probability density function given
by
𝑓(𝑥, 𝑦) = 𝑘𝑥𝑦(1 − 𝑦), for 0 < 𝑥 < 𝑦 < 1.
for some value of 𝑘. The correlation coefficient between 𝑋 and 𝑌
A. is positive.
B. is negative.
C. is zero.
D. depends on the value of 𝑘.
3 marks

40. Let 𝑋 be a random variable with the probability mass function
1
𝑃(𝑋 = ±1) = 𝑝, 𝑃(𝑋 = 0) = 1 − 2𝑝, 0<𝑝< .
2
Let 𝑌 = 𝑋 2 . Then the correlation between 𝑋 and 𝑌 is
A. 1.
B. 0.5.
C. 0.25.
D. 0.

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Data Interpretation

The following table gives the cumulative frequency distribution of sales (in Rs.) of two
outlets I & II of a restaurant chain. Answer the questions 41-44 based on your interpretation
of the table.

Sales in Rs. Number of days
Outlet I Outlet II
Less than 20000 5 8
Less than 30000 12 15
Less than 40000 18 20
Less than 50000 25 28
Less than 60000 35 32
Less than 70000 40 38
Less than 80000 42 45
Less than 90000 45 48
Less than 100000 50 50

41. The proportion of days having sales at least Rs.50000 in outlet I is
A. 0.30.
B. 0.40.
C. 0.50.
D. 0.64.

42. The percentage of days having sales less than Rs. 40000 in Outlet I is
A. 36.
B. 34.
C. 24.
D. 70.

43. The proportion of days having sales Rs.20000 or more but less than Rs.50000 in
Outlet II is
A. 0.34.
B. 0.40.
C. 0.48.
D. 0.50.

44. Which of the following is true?
A. The percentage of days having sales at least Rs. 70000 in Outlet I is more than
that in outlet II.

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B. The percentage of days having sales at least Rs. 30000 in Outlet II is more than
that in outlet I.
C. The percentage of days having sales less than Rs. 60000 in Outlet I is more than
that of Outlet II by 10%.
D. The percentage of days having sales at least Rs. 50000 but less than Rs. 80000 is
same for both Outlets I and II.

A survey was done among 170 students in a College to find out what type of music they
would like to be played in the canteen during lunch time. The survey had three choices:
movie songs (MS), classical songs (CS) and folk songs (FS). The data is summarized in the
following Venn Diagram. Answer questions 45-48 based on this diagram.

MS
65 3

3
14 12
13
8
52 CS
FS

45. The number of students indicated preference for MS is
A. 65.
B. 77.
C. 80.
D. 94.

46. The number of students who do not like CS to be played is
A. 134.
B. 131.
C. 154.
D. 157.

47. The number of students preferring only one type of music is
A. 84.
B. 36.
C. 86.
D. 130.

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48. The number of students who like both MS and CS is
A. 15.
B. 3.
C. 23.
D. 115.

Answer questions 49-51 based on the following chart, which shows monthly number of
passport applications of four age groups received in a regional passport center in 2021.

Age group wise number of passport
applications in a region in 2021
600
Number of passport applications

500
400
300
200
100
0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month

[18, 25) [25, 35) [35, 45) [45, 60)

49. The number of applications received considering all age groups together is maximum
in the month of
A. Jun.
B. Aug.
C. Sep.
D. Dec.

50. Which age group has the lowest total number of applications in the whole year?
A. [18, 25).
B. [25, 35).
C. [35, 45).
D. [45, 60).

51. Which of the following statements is true?
A. The number of applications in the age group [18, 25) does not exceed
3000.
B. The maximum number of applications is received in the age group [25, 35)
which is more than 5000.

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C. The total number of applications does not exceed 14000.
D. The number of applications received in the age group [25, 35) is maximum
in the month of Dec.
3 marks

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English

52. Select the word that correctly completes the following sentence.

I am expecting a salary ______ with my experience.

A. commensal.
B. commensurate.
C. equal.
D. similar.

53. Choose the word closest in meaning to the word “Charlatan”
A. Cleaning lady.
B. Fraud.
C. Pudding.
D. Rude person.

54. Choose the word closest in meaning to the word “Taciturn”.
A. Old man.
B. Small pot.
C. Understood.
D. Reserved.

55. Select the word that is closest in meaning to the word ‘Somnolence’.
A. Loudness.
B. Boredom.
C. Sleepiness.
D. Silence.

56. Which of the following sentences is not correct?
A. The committee comprised of older people.
B. The committee was comprised of older people.
C. The committee comprised older people.
D. Older people comprised the committee.

57. If you took an extra sheet and then found you didn’t need it, you would
A. keep it back.

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B. put it up.
C. put it back.
D. keep it up.

58. Which of these pairs has the same relationship as: “Colorful, colorless” ?
A. Torrid, frigid.
B. Torrid, horrid.
C. Smelly, fragrant.
D. Frigid, gelid.

59. Choose the pair of words that most appropriately completes the following sentence:
The granting of your application is _______ upon your clearing all the requirements
and your recommendation by a (an) _______ party.
A. contingency, uninterested.
B. contingency, disinterested.
C. contingent, uninterested.
D. contingent, disinterested.

60. The following sentences are jumbled up. Choose the correct sequence from the options
below.
I. There remain major gaps, however, in our understanding of the larger picture
of how organizational representatives describe their strategies to reach out to
and partner with men and boys.
II. The strategies literature has also most often been constructed in a toolkit
fashion for workers and agencies that may be engaging men and boys already
and shaped by the conceptual framework of the organization creating the
toolkit.
III. Current information is largely limited to some organizations' program
descriptions and evaluations, thus focusing on broader program activities and
likely omitting the subtler strategies involved in reaching out and appealing
to men.
IV. Organizations and activists throughout the world have taken up the work of
engaging men and boys in preventing violence against women and girls.
A. I, II, III, IV.
B. IV, II, I, III.
C. IV, I, III, II.
D. II, III, IV, I.

61. “Good preparation is the key to success in anything. If your foundations are weak,
anything you build on them is likely to topple over. Foresight is always better than

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hindsight, although until you acquire enough experience, hindsight is likely to be your
only teacher.”
Which of these statements can we infer from the above passage?
A. Good preparation depends on success.
B. Foresight is a substitute for experience.
C. Strong foundations are better than experience.
D. Foresight develops after hindsight.

Read the passage below and answer Question No. 62.
By the year 2050, nearly 80% of the Earth's population will live in urban centers. Applying the
most conservative estimates to current demographic trends, the human population will increase
by about three billion people by then. An estimated 10 hectares of new land (about 20% larger
than Brazil) will be needed to grow enough food to feed them if traditional farming methods
continue as they are practiced today. At present, throughout the world, over 80% of the land
that is suitable for raising crops is in use. Historically, some 15% of that has been laid waste by
poor management practices. What can be done to ensure enough food for the world's population
to live on?
The concept of indoor farming is not new, since the hothouse production of tomatoes and
other produce has been in vogue for some time. What is new is the urgent need to scale up this
technology to accommodate another three billion people. Many believe an entirely new
approach to indoor farming is required, employing cutting-edge technologies. One such
proposal is for the 'Vertical Farm'. The concept is of multi-story buildings in which food crops
are grown in environmentally controlled conditions. Situated in the heart of urban centers,
they would drastically reduce the amount of transportation required to bring food to
consumers. Vertical farms would need to be efficient, cheap to construct, and safe to operate.
If successfully implemented, proponents claim, vertical farms offer the promise of urban
renewal, sustainable production of a safe and varied food supply (through year-round
production of all crops), and the eventual repair of ecosystems that have been sacrificed for
horizontal farming.
It took humans 10,000 years to learn how to grow most of the crops we now take for granted.
Along the way, we despoiled most of the land we worked on, often turning verdant, natural
ecozones into semi-arid deserts. Within that same time frame, we evolved into an urban
species, in which 60% of the human population now lives vertically in cities. This means that,
for the majority, we humans have shelter from the elements, yet we subject our food-bearing
plants to the rigors of the great outdoors and can do no more than hope for a good weather year.
However, more often than not now, due to a rapidly changing climate, that is not what happens.
Massive floods, long droughts, hurricanes, and severe monsoons take their toll each year,
destroying millions of tons of valuable crops.
I. What is a vertical farm?
i. Multi-storied buildings.
ii. Environmentally controlled crops.
iii. Multi-story buildings in which food crops are grown in environmentally
controlled conditions.
II. Which of the following statements may be concluded from the passage?
i. 60% of the human population will live in cities by 2050.
ii. Agriculture is responsible for despoiling land.
iii. Bad management practices have despoiled land.

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III. Which of the following statements may not be concluded from the passage?
i. Climate change has made the future of agriculture uncertain.
ii. Vertical farming is a sustainable option for the future of agriculture.
iii. Vertical farming has no negative implications on agriculture.

62. The correct answers to I, II and III are
A. iii, ii, iii, respectively.
B. ii, i, i, respectively.
C. ii, ii, iii, respectively.
D. i, iii, ii, respectively.
3 marks

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Logical Reasoning

63. B said while introducing A “His brother‘s father is the only son of my grandfather.” How
is B related to A?
A. Sister.
B. Daughter.
C. Mother.
D. Niece.

64. If 1st January of 1996 was Monday, then how many Tuesdays did 1996 have?
A. 53.
B. 52.
C. 51.
D. Cannot be determined.

65. A clock shows 7 O’clock in the morning. By how much angle will the hour’s hand rotate
when the clock shows 9 O’clock in the morning.
A. 40 degrees.
B. 60 degrees.
C. 45 degrees.
D. 90 degrees.

66. From a 10 × 10 × 10 cube, which is formed by combinations of 1 × 1 × 1 cubes, a layer
of the smaller cubes is removed. What will be the number of 1 × 1 × 1 cubes present in
this new cube?
A. 488.
B. 900.
C. 512.
D. 729.

67. Zafar and Yatika skip a class if any one of Arsal and Sujatha attend it, Which of the
following inferences is correct?
A. If it is found that Sujatha skipped a class, it may be concluded that Yatika attended
it.
B. If it is found that Yatika skipped a class, it may be concluded that Zafar skipped it.
C. If it is found that Zafar attended a class, it may be concluded that Arsal skipped it.
D. If it is found that Zafar skipped a class, it may be concluded that Sujatha attended it.
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68. In a group of 85 persons, 45 play football and 37 play basketball and 8 play neither
basketball nor football. Find the number of persons who play both football and basketball.
A. 5.
B. 6.
C. 7.
D. 8.

69. There are five friends – Seema, Leena, Elly, Hemant and Omkar. They have chosen to sit
around a circular table facing center, each of them wearing a dress of unique colour –
white, blue, purple, yellow and orange. The person wearing blue is seated second place to
the right of the one wearing white. The one wearing yellow does not sit beside the one
wearing purple. Hemant is seated exactly between the one wearing yellow and the one
wearing orange. Hemant is wearing blue and seated second to the left of the Elly.
Who is wearing purple?
A. Seema.
B. Hemant.
C. Omkar.
D. Elly.

70. In the question below some statements are given, followed by some conclusions. You
have to take the given statements to be true even if they seem to be in variance with
commonly known facts. Read all the conclusions and then decide which of the given
conclusions logically follows from the given statements disregarding commonly known
facts.

Statements:
I. Only a mango can be an apple.
II. No orange is grape.
III. Some grape is guava.
IV. Some guava is mango.
Conclusions:
I. Some apple being guava is a possibility.
II. Some grape is mango.
III. Some mango being orange is a possibility.

A. Only conclusion II follows.
B. Both conclusion I and II follow.
C. Only conclusion III follows.
D. Both conclusion II and III follow.

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