(Papers) : IIT Madras HSEE Papers-2020
(Analytical & Quantitative Ability)

37. Consider a right angled triangle, in which, p represents the height, b, the base and h , the hypotenuse.The ratio h/b is known as
(a) Cosine
(b) Sine
(c) Tangent
(d) Secant
38. The maximum and minimum values the Sine function (in trigonometry) can have are
(a) 1 and 0
(b) 1 and -1
(c) 0 and -1
(d) 2 and 1
39. Consider a ratio 20/40 that changes to 22/50. Then the percentage change in the ratio is
(a) 12%
(b) 6%
(c) 8%
(d) 10%
40. The sum of the two integers is 10 and sum of their reciprocals is 5/12. One of the integers must be
(a) 5
(b) 7
(c) 3
(d) 6
41. The third lowest prime number is
(a) 7
(b) 3
(c) 5
(d) 11
42. The total number of factors of number 40 are
(a) 4
(b) 8
(c) 10
(d) 6
43. Petrol price has gone up by 40%. How much percentage (approx.) reduction in consumption is required to keep the budget unchanged?
(a) 28%
(b) 32%
(c) 20%
(d) 25%
44. A 25% rise in the price of atta leads to 20 kg reduction in purchase for Rs. 400. The original price (per kg) of atta was
(a) 6
(b) 4
(c) 8
(d) 2
45. A shopkeeper uses a 900 gm weight for 1 kg. The profit in percentage he makes is
(a) 9.6
(b) 10.5
(c) 11.1
(d) 12.5
46. A sum of money doubles in 10 years. The percentage rate of interest is
(a) 12
(b) 14
(c) 10
(d) 8
47. A certain principal amount is charged at a rate of 10% compound interest for two years and the amount becomes Rs. 605. The principal amount is
(a) Rs. 450
(b) Rs. 500
(c) Rs. 550
(d) Rs. 530
48. Rs. 10000 has to be divided among Amar, Akbar and Anthony in such a way that if Rs. 200, 300 and 500 are deducted from their respective shares, their money will be in the ratio of 3, 5 and 7. Find Akbar’s share (in Rs. 10000)
(a) Rs. 3000
(b) Rs. 2800
(c) Rs. 3300
(d) Rs. 3500
49. Three containers have capacities in the ratio of 2: 3: 5.  Container A has milk mixed with water in the ratio of 2: 3, container B 1:2 and container C 3:2. When all the milk and water from three containers are mixed together , the final ratio of milk and water will be
(a) 5 by 8
(b) 7 by 9
(c) 1 by 3
(d) 12 by 13
50. A contractor engages 100 persons to complete a  work. They finish 2/3 of the work in 8 weeks. At this stage, 50 persons left the work. How much more time the contractor will take to finish the work with remaining 50 persons
(a) 8 weeks
(b) 10 weeks
(c) 12 weeks
(d) 14 weeks
51. Donald can do a work in 8 days and Mike can do in 12 days. How many days (approx.) will it take to finish the work if they work on alternate days
(a) 8 days
(b) 10 days
(c) 12 days
(d) 7 days​​​​​​​
52. Ritu is twice as efficient as Titu. If they work together and complete a work in 30 days, then the time required by each to complete the work individually are
(a) 30 and 60 days
(b) 50 and 100 days
(c) 45 and 90 days
(d) 25 and 50 days​​​​​​​
53. How many numbers of 3 digits can be formed with the digits 1, 2, 3, 4 and 5 (without any repetition of digits).
(a) 40
(b) 60
(c) 80
(d) 120
54. Consider the number of ways the letters in the word LUCKNOW can be arranged. What is the probability that 3 letters N, O and W will always come together
(a) 5! / 7!
(b) 3! / 5!
(c) 4! / 6!
(d) 2! / 3!
55. On a certain road 3 consecutive traffic lights change  after 36, 42 and 72 seconds respectively. If the lights are first switched on exactly at 6 am (06:00:00), then they will again change simultaneously at
(a) 06:10:14
(b) 06:12:46
(c) 06:14:36
(d) 06:08:24
56. The highest common factor (HCF) of (234 - 1) and (285 - 1) is
(a) 2³⁴ - 1
(b) 2¹⁹ - 1
(c) 2⁷⁷ - 1
(d) 217 - 1
57. The least common multiple (LCM) and highest common factor (HCF) of two numbers are 120 and 20. If one of the numbers is 30, then the other number is
(a) 80
(b) 70
(c) 60
(d) 50
58. A batsman has an average of 48 runs in 20 innings. How much should he score in 21st innings so that the average increases to 50?
(a) 48
(b) 80
(c) 90
(d) 50
59. The mean temperature at a place from Sunday to Tuesday was 25 °C and that from Monday to Wednesday was 27 °C. If the temperature on Sunday was 4/5 of the temperature on Wednesday, what
was the temperature on  Wednesday?
(a) 25 °C
(b) 27 °C
(c) 28 °C
(d) 30 °C
60. The average age of 80 students of a certain batch in IIT Madras is 20 years. When the age of 20 faculty members are also counted, the overall average age increases to 25. The average age of the 20 faculty
members are
(a) 40
(b) 45
(c) 25
(d) 30
61. What day of the week was 15 August 1947?
(a) Saturday
(b) Monday
(c) Sunday
(d) Friday
62. The calendar for 2020 will be​​​​​​​ repeated in
(a) 2022
(b) 2025
(c) 2030
(d) 2048
63. The ages of Boris and Johnson are in the ratio of 4:5. Fifteen years ago their ages were in the ratio of 2:3. The present age of Boris is
(a) 30
(b) 45
(c) 35
(d) 40
64. My sister is 4 years elder  to me. My father was 29 years when by brother was born and mother was 27 years when I was born. If my brother was 3 years of age when my sister was born, what were the ages of my father and mother respectively when my sister was born?
(a) 30 years and 28 years
(b) 32 years and 29 years
(c) 32 years and 23 years
(d) 30 years and 25 years
65. In statistics, the percentage distribution of any data is represented as
(a) Barchart
(b) Histogram
(c) Frequency polygon
(d) Pie chart
66. The digit at the unit place in (264)102 + (264)103 will be
(a) 0
(b) 6
(c) 4
(d) 2
67. If (x + y) = 10 - z and y (x + z) +  xz = 20 , then the value of (x2 + y2 + z2) will be
(a) 10
(b) 60
(c) 40
(d) 20
68. Find the odd number in the series 284, 331, 383, 263, 133, 242
(a) 284
(b) 383
(c) 263
(d) 133
69. In algebra, if B represents "bracket" operation, O represents "of" , D represents division, M represents multiplication, A represents addition and S represents subtraction. Then the correct sequence of mathematical operation is
(a) B-O-D-M-A-S
(b) A-M-S-B-O-D
(c) D-B-O-M-A-S
(d) D-O-B-M-A-S
70. An importer pays 10% customs  duty on an item priced at Rs. 5000 (price at abroad in equivalent Indian rupees). How much price should be marked on the item if the importer wishes to earn a profit of 20% even after giving a discount of 40% on the marked price?
(a) 8500
(b) 9500
(c) 10000
(d) 11000
71. If the word CHENNAI is represented by EKISTHQ then MUMBAI can be represented as
(a) PMNAIR
(b) MNOPQR
(c) OXQGGP
(d) LKZIXP
72. If the equation y = k x (k is constant) is plotted between x and y, the resultant graph will be a
(a) Circle
(b) Straight line
(c) Parabola
(d) Ellipse

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