SSC CGL 2017 Tier II — Quantitative Abilities — 18 February 2018

Quantitative Abilities

1. 1. How many three digit numbers are there in which all the digits are odd?

   • (a) 100
   • (b) 125
   • (c) 500
   • (d) 250
   उत्तर देखें

   उत्तर: (b)

2. 2. If the sum of ten different positive integers is 100, then what is the greatest possible number among these 10 numbers?

   • (a) 45
   • (b) 91
   • (c) 55
   • (d) 64
   उत्तर देखें

   उत्तर: (c)

3. 6. If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?

   • (a) 6
   • (b) 8
   • (c) 12
   • (d) 10
   उत्तर देखें

   उत्तर: (b)

4. 8. What is the sum of all natural numbers between 100 and 400 which are divisible by 13?

   • (a) 5681
   • (b) 5334
   • (c) 5434
   • (d) 5761
   उत्तर देखें

   उत्तर: (a)

5. 10. If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?

   • (a) 34
   • (b) 35
   • (c) 33
   • (d) 33.5
   उत्तर देखें

   उत्तर: (a)

6. 11. Which of the following statement(s) is/are true? I. (65)1/6 > (17)1/4 > (12)1/3 II. (17)1/4 > (65)1/6 > (12)1/3 III. (12)1/3 > (17)1/4 > (65)1/6

   • (a) Only I
   • (b) Only III
   • (c) Only II
   • (d) None of these
   उत्तर देखें

   उत्तर: (b)

7. 12. If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?

   • (a) 148
   • (b) 189
   • (c) 194
   • (d) 204
   उत्तर देखें

   उत्तर: (c)

8. 13. If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?

   • (a) 31
   • (b) 23√5
   • (c) 27√5
   • (d) 25
   उत्तर देखें

   उत्तर: (d)

9. 14. If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?

   • (a) 25
   • (b) 22
   • (c) 17
   • (d) 43
   उत्तर देखें

   उत्तर: (a)

10. 15. A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2 )/(a + b + c)?

    • (a) 35/3
    • (b) 37/3
    • (c) – 105/11
    • (d) – 105/13
    उत्तर देखें

    उत्तर: (c)

11. 16. If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?

    • (a) – 4
    • (b) 2
    • (c) – 1
    • (d) – 6
    उत्तर देखें

    उत्तर: (a)

12. 17. If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?

    • (a) – 8 + √3
    • (b) – 8 – √3
    • (c) – 8 + √5
    • (d) None of these
    उत्तर देखें

    उत्तर: (d)

13. 19. If x + y = 3, then what is the value of x3 + y3 + 9xy?

    • (a) 15
    • (b) 81
    • (c) 27
    • (d) 9
    उत्तर देखें

    उत्तर: (c)

14. 20. A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value of A2 + 2AB + AB2?

    • (a) 96475
    • (b) 98625
    • (c) 92425
    • (d) 89125
    उत्तर देखें

    उत्तर: (b)

15. 21. यदि x - 4y = 0 तथा x + 2y = 24 हैं, तो (2x + 3y)/(2x - 3y) का मान है?

    • (a) 9/5
    • (b) 11/5
    • (c) 13/7
    • (d) 9/7
    उत्तर देखें

    उत्तर: (b)

16. 24. In a triangle PQR, ∠PQR = 90o, PQ = 10 cm and PR = 26 cm, then what is the value (in cm) of inradius of incircle?

    • (a) 9
    • (b) 4
    • (c) 8
    • (d) 6
    उत्तर देखें

    उत्तर: (b)

17. 26. In a triangle PQR, PX, QY and RZ be altitudes intersecting at O. If PO = 6 cm, PX = 8 cm and QO = 4 cm, then what is the value (in cm) of QY?

    • (a) 6.3
    • (b) 5.8
    • (c) 6
    • (d) 7
    उत्तर देखें

    उत्तर: (d)

18. 27. A line cuts two concentric circles. The lengths of chords formed by that line on the two circles are 4 cm and 16 cm. What is the difference (in cm2) in squares of radii of two circles?

    • (a) 240
    • (b) 120
    • (c) 60
    • (d) 90
    उत्तर देखें

    उत्तर: (c)

19. 38. एक 20 किमी/घंटा की गति से दौड़ रहा है। एक वृत्ताकार बगीचा जिसकी 350 मीटर है, को पार करने में द्वारा कितना समय (सेकंड में) लिया जायेगा?

    • (a) 412
    • (b) 336
    • (c) 396
    • (d) 376
    उत्तर देखें

    उत्तर: (c)

20. 40. A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?

    • (a) 54(3 + √3)
    • (b) 36(3 + √3)
    • (c) 48(4 + √3)
    • (d) 24(4 + √3)
    उत्तर देखें

    उत्तर: (c)

21. 41. A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?

    • (a) 5
    • (b) 6
    • (c) 8
    • (d) 9
    उत्तर देखें

    उत्तर: (c)

22. 42. A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?

    • (a) 5
    • (b) 6
    • (c) 15
    • (d) 7.5
    उत्तर देखें

    उत्तर: (d)

23. 43. A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in cm2) of the remaining part?

    • (a) 3842
    • (b) 4312
    • (c) 3296
    • (d) 4436
    उत्तर देखें

    उत्तर: (b)

24. 44. Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?

    • (a) 1077.31
    • (b) 905.14
    • (c) 966.07
    • (d) 1007.24
    उत्तर देखें

    उत्तर: (b)

25. 45. Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is 2√2 cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?

    • (a) 4 : 3 : [(√2) + 1]
    • (b) 4 : 3 : [2 + (√2)]
    • (c) 4 : 3 : 2√2
    • (d) 2 : 1 : (1 + √2)
    उत्तर देखें

    उत्तर: (a)

26. 46. एक ठोस घन को 27 समरूप घनों में काटा जाता है। कुल पृष्ठीय क्षेत्रफल में कितने प्रतिशत की वृद्धि हुई है?

    • (a) 150
    • (b) 200
    • (c) 300
    • (d) 250
    उत्तर देखें

    उत्तर: (b)

27. 48. What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

    • (a) 1
    • (b) 2 tan
    • (c) tan 2
    • (d) tan (3 /2) x
    उत्तर देखें

    उत्तर: (b)

28. 49. What is the value of [(cos3 2θ + 3 cos 2θ)÷(cos6 θ – sin6 θ)]?

    • (a) 0
    • (b) 1
    • (c) 4
    • (d) 2
    उत्तर देखें

    उत्तर: (c)

29. 52. What is the value of sin (630o + A) + cos A?

    • (a) √3/2
    • (b) 1/2
    • (c) 0
    • (d) 2/√3
    उत्तर देखें

    उत्तर: (c)

30. 53. What is the value of [(sin 59o cos 31o + cos 59o sin 31o)÷(cos 20o cos 25o – sin 20o sin 25o)]?

    • (a) 1/√2
    • (b) 2√2
    • (c) √3
    • (d) √2
    उत्तर देखें

    उत्तर: (d)

31. 54. cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) — sin (90 – C) cos (A + B) का मान है?

    • (a) 1
    • (b) sin ( +
    • (c) cos ( +
    • (d) 0 A B – C) B C – A)
    उत्तर देखें

    उत्तर: (d)

32. 55. Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45o and 60o. If the height of the tree which makes 45o angle is 200 metres, then what will be the height (in metres) of the other tree?

    • (a) 200
    • (b) 200√3
    • (c) 100√3
    • (d) 250
    उत्तर देखें

    उत्तर: (b)

33. 56. A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60o and 45o respectively. What is the height (in metres) of tower?

    • (a) 20√3
    • (b) 30(√3 + 1)
    • (c) 40(√3 – 1)
    • (d) 50(√3 – 1)
    उत्तर देखें

    उत्तर: (c)

34. 57. From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?

    • (a) 720
    • (b) 960
    • (c) 840
    • (d) 1030
    उत्तर देखें

    उत्तर: (b)

35. 63. A beaker contains acid and water in the ratio 1 : x. When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid and water becomes 2 : 5. What is the value of x?

    • (a) 2
    • (b) 1
    • (c) 3
    • (d) 4
    उत्तर देखें

    उत्तर: (a)

36. 64. A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?

    • (a) 110
    • (b) 55
    • (c) 220
    • (d) 70
    उत्तर देखें

    उत्तर: (a)

37. 66. A, B and C invest in a business in the ratio 4 : 5 : 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?

    • (a) 7560
    • (b) 10800
    • (c) 8640
    • (d) 9200
    उत्तर देखें

    उत्तर: (b)

38. 67. A can do a work in 36 days and B in 12 days. If they work on it together for 3 days, then what fraction of work is left?

    • (a) 2/3
    • (b) 1/3
    • (c) 1/4
    • (d) 1/5
    उत्तर देखें

    उत्तर: (a)

39. 69. A,B and C together can finish a task in 7.5 days. C is thrice as productive as A and B alone can do the task in 15 days. In how many days can A and C do the job if B goes on leave?

    • (a) 30
    • (b) 10
    • (c) 20
    • (d) 15
    उत्तर देखें

    उत्तर: (d)

40. 70. A, B and C can do job in 9, 12 and 36 days respectively if they worked alone. A leaves after they have worked together for 3 days. In how many days can B and C do the rest of the job?

    • (a) 3
    • (b) 4
    • (c) 5
    • (d) 6
    उत्तर देखें

    उत्तर: (a)

41. 72. If a website is selling smartphone at Rs 18,000 which is marked at Rs 25,000, then what is the discount (in %) at which the smartphone is being sold?

    • (a) 25
    • (b) 22
    • (c) 28
    • (d) 20
    उत्तर देखें

    उत्तर: (c)

42. 73. If on an item there is 12% discount on the marked price of Rs 10,000 but the item is sold at Rs 8,360 only then what additional discount (in %) did the customer get? 10,000

    • (a) 6
    • (b) 7
    • (c) 5
    • (d) 8
    उत्तर देखें

    उत्तर: (c)

43. 74. A shopkeeper marks up his wares by 125% and offers 25% discount. What will be the selling price if the cost price (in Rs) is Rs 640?

    • (a) 1080
    • (b) 1000
    • (c) 920
    • (d) 860
    उत्तर देखें

    उत्तर: (a)

44. 75. Priya's marks in History and Geography are in the ratio 5 : 7. If she got 14 marks more in Geography than in History, what are her History marks?

    • (a) 49
    • (b) 42
    • (c) 56
    • (d) 35
    उत्तर देखें

    उत्तर: (d)

45. 76. The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13:19. What is Rahul's present age (in years)?

    • (a) 36
    • (b) 48
    • (c) 42
    • (d) 54
    उत्तर देखें

    उत्तर: (a)

46. 77. What is the third proportional to 9 and 15?

    • (a) 30
    • (b) 27
    • (c) 36
    • (d) 25
    उत्तर देखें

    उत्तर: (d)

47. 79. If Rs 7,800 is to be divided between A, B and C in the ratio 1/2 : 1/3 : 1/4, then how much share will B get (in Rs)?

    • (a) 3600
    • (b) 1800
    • (c) 2400
    • (d) 1200
    उत्तर देखें

    उत्तर: (c)

48. 80. Bunty had candies and chewing gums in his sweet box in the ratio 7 : 13. After he has eaten 8 candies and 11 chewing gums the ratio became 1 : 2. How many candies does he have now?

    • (a) 65
    • (b) 35
    • (c) 54
    • (d) 27
    उत्तर देखें

    उत्तर: (d)

49. 81. The average weight of P, Q and R is 71 kg. If the average weight of P and Q be 66 kg and that of Q and R be 76.5 kg, then the weight (in kg) of Q is.

    • (a) 60
    • (b) 72
    • (c) 81
    • (d) 75
    उत्तर देखें

    उत्तर: (b)

50. 82. रीता ने 2250 रुपये के औसत मूल्य से 5 साड़ियां खरीदी। यदि उसने तीन और साड़ियां 2750 के औसत मूल्य से खरीदी तो सभी साड़ियों का औसत मूल्य (रुपयों में) होगा?

    • (a) 2437.5
    • (b) 2500
    • (c) 2450
    • (d) 2332.5
    उत्तर देखें

    उत्तर: (a)

51. 83. In a one day match of 50 overs in an innings the team A had a run rate of 5.3 runs per over. Team B is playing and 5 overs are left and the required run rate to tie the match is 7.2 per over to match the score of Team A. What is team B's score?

    • (a) 265
    • (b) 238
    • (c) 254
    • (d) 229
    उत्तर देखें

    उत्तर: (d)

52. 84. Average of all even numbers between 104 and 148 is __________.

    • (a) 128
    • (b) 130
    • (c) 124
    • (d) 126
    उत्तर देखें

    उत्तर: (d)

53. 85. एक विक्रेता 3 में 4 केले खरीदता है और 4 में 3 केले बेचता है। परिणाम होगा?

    • (a) 43.75% लाभ
    • (b) 77.7% हानि
    • (c) 77.7% लाभ
    • (d) 43.75% हानि
    उत्तर देखें

    उत्तर: (c)

54. 86. A wholesaler sells a watch to a retailer at a profit of 8% and the retailer sells it to a customer at a profit of 12%. If the customer pays Rs. 8,448 what had it cost (approximately) to the wholesaler (in Rs)?

    • (a) 6984
    • (b) 6082
    • (c) 7120
    • (d) 7022
    उत्तर देखें

    उत्तर: (a)

55. 87. A trader had 2000 kgs of rice. He sold a part of it at 10% profit and the rest at 16% profit, so that he made a total profit of 14.2%. How much rice (in kg) did he sell at 10% profit?

    • (a) 1400
    • (b) 600
    • (c) 800
    • (d) 1000
    उत्तर देखें

    उत्तर: (b)

56. 88. एक यूज्ड कार डीलर किसी कार को 7.6 लाख मूल्य क्या था? (लाख रु में) में बेचता है और उसे कुछ नुकसान होता है। यदि वह इसे 9.2 लाख में बेचता तो उसका लाभ उसकी हानि का तीन गुना होता। कार का

    • (a) 8.5
    • (b) 8.75
    • (c) 8.25
    • (d) 8
    उत्तर देखें

    उत्तर: (d)

57. 89. 0.09% of 25% of 1200 is equal to____________.

    • (a) 0.27
    • (b) 2.7
    • (c) 27
    • (d) 270
    उत्तर देखें

    उत्तर: (a)

58. 90. When a number is increased by 20, it becomes 116% of itself. What is the number?

    • (a) 100
    • (b) 250
    • (c) 125
    • (d) 400
    उत्तर देखें

    उत्तर: (c)

59. 91. Two numbers are 50% and 75% lesser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number?

    • (a) 50
    • (b) 25
    • (c) 75
    • (d) 100
    उत्तर देखें

    उत्तर: (d)

60. 92. Price of petrol increased from Rs 60/liter to Rs 75/liter. How much should the consumption of petrol be reduced (in %) so as to increase expenditure by only 10%?

    • (a) 12
    • (b) 20
    • (c) 15
    • (d) 18
    उत्तर देखें

    उत्तर: (a)

61. 93. एक ट्रेन को 900 किमी. की दूरी 25 घंटे में तय करनी है तो उसकी औसत गति मीटर/सेकंड में होनी चाहिए?

    • (a) 20
    • (b) 10
    • (c) 18
    • (d) 36
    उत्तर देखें

    उत्तर: (b)

62. 95. Two cyclists A and B start cycling at 21 km/hr and 24 km/hr towards each other. They meet after 1 hour and 12 minutes. How far (in km) were they from each other when they started?

    • (a) 48
    • (b) 42
    • (c) 54
    • (d) 36
    उत्तर देखें

    उत्तर: (c)

63. 96. यदि विराम को निकाल दिया जाए तो बस की चाल 60 कि.मी./घंटा है और यदि विराम को शामिल किया जाए तो बस की चाल 45 कि.मी./घंटा है। बस प्रति घंटा कितने मिनट के लिए रुकती है ?

    • (a) 12
    • (b) 9
    • (c) 15
    • (d) 10
    उत्तर देखें

    उत्तर: (c)

64. 98. If the amount received at the end of 2nd and 3rd year at compound Interest on a certain Principal is Rs 9,600 and Rs 10,272 respectively, what is the rate of interest (in %)?

    • (a) 7
    • (b) 8
    • (c) 6
    • (d) 5
    उत्तर देखें

    उत्तर: (a)

65. 99. A invested an amount of x rupees in a bank for 2 years which gave 5% interest in year 1 and 6% interest in year 2. The amount received after 2 years is Rs 24,486. What is the value of x?

    • (a) 23000
    • (b) 22500
    • (c) 22000
    • (d) 21500
    उत्तर देखें

    उत्तर: (c)

66. 100. What is the difference (in Rs) in Compound interest earned in 1 year on a sum of Rs 10,000 at 40% per annum compounded quarterly and annually?

    • (a) 461
    • (b) 346
    • (c) 463
    • (d) 641
    उत्तर देखें

    उत्तर: (d)