SSC CGL 2017 Tier II — Quantitative Abilities — 21 February 2018

Quantitative Abilities

1. 1. If A = 1 – 10 + 3 – 12 + 5 – 14 + 7 + … upto 60 terms, then what is the value of A?

   • (a) – 360
   • (b) – 310
   • (c) – 240
   • (d) – 270
   उत्तर देखें

   उत्तर: (d)

2. 2. How many natural numbers are there between 1000 to 2000, which when divided by 341 leaves remainder 5?

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

   उत्तर: (a)

3. 3. Which of the following statement(s) is/are TRUE? I. √(64) + √(0.0064) + √(0.81) + √(0.0081) = 9.07 II. √(0.010201) + √(98.01) + √(0.25) = 11.51

   • (a) Only I
   • (b) Only II
   • (c) Both I and II
   • (d) Neither I nor II
   उत्तर देखें

   उत्तर: (a)

4. 4. Which of the following statement(s) is/are TRUE? I. (0.7)2 + (0.07)2 + (11.1)2 > 123.8 II. (1.12)2 + (10.3)2 + (1.05)2 > 108.3 II. (1.12) + (10.3) + (1.05) > 108.3

   • (a) Only I
   • (b) Only II
   • (c) Both I and II
   • (d) Neither I nor II
   उत्तर देखें

   उत्तर: (b)

5. 6. Which of the following statement(s) is/are TRUE? I. 3/71 < 5/91 < 7/99 II. 11/135 > 12/157 > 13/181

   • (a) Only I
   • (b) Only II
   • (c) Both I and II
   • (d) Neither I nor II
   उत्तर देखें

   उत्तर: (c)

6. 7. If 1 + (1/2) + (1/3) + … + (1/20) = k, then what is the value of (1/4) + (1/6) + (1/8) + … + (1/40)?

   • (a) k/2
   • (b) 2k
   • (c) (k – 1)/2
   • (d) (k + 1)/2
   उत्तर देखें

   उत्तर: (c)

7. 9. If x + y = 10 and xy = 4, then what is the value of x4 + y4? 4

   • (a) 8464
   • (b) 8432
   • (c) 7478
   • (d) 6218
   उत्तर देखें

   उत्तर: (b)

8. 10. M is the largest three digit number which when divided by 6 and 5 leaves remainder 5 and 3 respectively. What will be the remainder when M is divided by 11?

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

   उत्तर: (d)

9. 11. Which of the following statement(s) is/are TRUE? I. √5 + √5 > √7 + √3 II. √6 + √7 > √8 + √5 III. √3 + √9 > √6 + √6

   • (a) Only I
   • (b) Only I and II
   • (c) Only II and III
   • (d) Only I and III
   उत्तर देखें

   उत्तर: (b)

10. 16. If x2 – 16x – 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]? 2

    • (a) 14
    • (b) 18
    • (c) 16
    • (d) 20
    उत्तर देखें

    उत्तर: (b)

11. 18. If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc? 3

    • (a) 48
    • (b) 24
    • (c) 36
    • (d) 42
    उत्तर देखें

    उत्तर: (b)

12. 19. If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + (1/x – 4)]?

    • (a) 3
    • (b) 5
    • (c) 6
    • (d) 8
    उत्तर देखें

    उत्तर: (c)

13. 20. Cost of 8 pencils, 5 pens and 3 erasers is Rs 111. Cost of 9 pencils, 6 pens and 5 erasers is Rs 130. Cost of 16 pencils, 11 pens and 3 erasers is Rs 221. What is the cost (in Rs) of 39 pencils, 26 pens and 13 erasers?

    • (a) 316
    • (b) 546
    • (c) 624
    • (d) 482
    उत्तर देखें

    उत्तर: (b)

14. 21. If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?

    • (a) 32
    • (b) 52
    • (c) 64
    • (d) 46
    उत्तर देखें

    उत्तर: (b)

15. 22. PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?

    • (a) 5/√3
    • (b) 10√3
    • (c) 10/√3
    • (d) 5√2
    उत्तर देखें

    उत्तर: (a)

16. 23. What is the area (in cm ) of the circumcircle of a triangle whose sides are 6 cm, 8 cm and 10 cm respectively?

    • (a) 275/7
    • (b) 550/7
    • (c) 2200/7
    • (d) 1100/7
    उत्तर देखें

    उत्तर: (b)

17. 25. ABCD is a trapezium in which AB is parallel to CD and AB = 4(CD). The diagonals of the trapezium intersects at O. What is the ratio of area of triangle DCO to the area of the triangle ABO?

    • (a) 1 : 4
    • (b) 1 : 2
    • (c) 1 : 8
    • (d) 1 : 16
    उत्तर देखें

    उत्तर: (d)

18. 28. PAB and PCD are two secants to a circle. If PA = 10 cm, AB = 12 cm and PC = 11 cm, then what is the value (in cm) of PD?

    • (a) 18
    • (b) 9
    • (c) 20
    • (d) 12
    उत्तर देखें

    उत्तर: (c)

19. 29. Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ∠PQR = 40°, then what is the value (in degrees) of ∠QPR?

    • (a) 40
    • (b) 45
    • (c) 50
    • (d) 55
    उत्तर देखें

    उत्तर: (c)

20. 31. दो गैर-प्रतिच्छेदी वृत्तों से अधिकतम कितनी अनुस्पर्श रेखा खींची जा सकती है?

    • (a) 2
    • (b) 4
    • (c) 3
    • (d) 6
    उत्तर देखें

    उत्तर: (b)

21. 32. Triangle PQR is inscribed in the circle whose radius is 14 cm. If PQ is the diameter of the circle and PR = 10 cm, then what is the area of the triangle PQR?

    • (a) 196
    • (b) 30√19
    • (c) 40√17
    • (d) 35√21
    उत्तर देखें

    उत्तर: (b)

22. 33. PQR is a right angled triangle in which PQ = QR. If the hypotenuse of the triangle is 20 cm, then what is the area (in cm2) of the triangle PQR?

    • (a) 100√2
    • (b) 100
    • (c) 50√2
    • (d) 50
    उत्तर देखें

    उत्तर: (b)

23. 34. PQRS is a square whose side is 20 cm. By joining opposite vertices of PQRS are get four triangles. What is the sum of the perimeters of the four triangles?

    • (a) 40√2
    • (b) 80√2 + 80
    • (c) 40√2 + 40
    • (d) 40√2 + 80
    उत्तर देखें

    उत्तर: (b)

24. 35. If ABCDEF is a regular hexagon, then what is the value (in degrees) of ∠ADB?

    • (a) 15
    • (b) 30
    • (c) 45
    • (d) 60
    उत्तर देखें

    उत्तर: (b)

25. 36. ABCD is square and CDE is an equilateral triangle outside the square. What is the value (in degrees) of ∠BEC?

    • (a) 15
    • (b) 30
    • (c) 25
    • (d) 10
    उत्तर देखें

    उत्तर: (a)

26. 40. The height of a cone is 24 cm and the area of the base is 154 cm . What is the curved surface area (in cm ) of the cone? 2

    • (a) 484
    • (b) 550
    • (c) 525
    • (d) 515
    उत्तर देखें

    उत्तर: (b)

27. 42. A right circular cylinder is formed. A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?

    • (a) 154
    • (b) 308
    • (c) 462
    • (d) 616
    उत्तर देखें

    उत्तर: (b)

28. 47. {(sin 4x + sin 4y) [(tan 2x — 2y)]}/(sin 4x - sin 4y) का मान क्या है?

    • (a) tan 2 (2x + 2y)
    • (b) tan2
    • (c) cot (x – y)
    • (d) tan (2x + 2y)
    उत्तर देखें

    उत्तर: (d)

29. 48. What is the value of (32 cos6 x – 48 cos4 x + 18 cos2 x – 1)/[4 sin x cos x sin (60 – x) cos (60 – x) sin (60 + x) cos (60 + x)]? 6 (32 cos x – 48 cos 4 2

    • (a) 4 tan 6x
    • (b) 4 cot 6x
    • (c) 8 cot 6x
    • (d) 8 tan 6x
    उत्तर देखें

    उत्तर: (c)

30. 49. What is the value of [2 cot × (p – A)/2]/[1 + tan2 × (2p – A)/2]?

    • (a) 2 sin2 A/2
    • (b) cos A
    • (c) sin A
    • (d) 2 cos2 A/2
    उत्तर देखें

    उत्तर: (c)

31. 51. What is the value of (cos 40° – cos 140°)/(sin 80° + sin 20°)?

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

    उत्तर: (b)

32. 52. What is the value of [1 – tan (90 – θ) + sec (90 – θ)]/[tan (90 – θ) + sec (90 – θ) + 1]?

    • (a) cot (θ/2)
    • (b) tan (θ/2)
    • (c) sin θ
    • (d) cos θ
    उत्तर देखें

    उत्तर: (b)

33. 53. What is the value of [sin (90 – A) + cos (180 – 2A)]/[cos (90 – 2A) + sin (180 – A)]?

    • (a) sin (A/2) cos A
    • (b) cot (A/2)
    • (c) tan (A/2)
    • (d) sin A cos (A/2)
    उत्तर देखें

    उत्तर: (c)

34. 54. The distance between the tops of two building 38 metres and 58 metres high is 52 metres. What will be the distance (in metres) between two buildings?

    • (a) 46
    • (b) 42
    • (c) 44
    • (d) 48
    उत्तर देखें

    उत्तर: (d)

35. 55. 220 मीटर ऊँचे एक वृक्ष के दो बिन्दुओं का समान तल पर उन्नयन कोण 30° तथा 45° हैं। दो बिन्दुओं के मध्य दूरी (मीटर में) क्या है?

    • (a) 193.22
    • (b) 144.04
    • (c) 176.12
    • (d) 161.05
    उत्तर देखें

    उत्तर: (d)

36. 56. The angles of elevation of the top of a tower 72 metre high from the top and bottom of a building are 30° and 60° respectively. What is the height (in metres) of building?

    • (a) 42
    • (b) 20√3
    • (c) 24√3
    • (d) 48
    उत्तर देखें

    उत्तर: (d)

37. 57. What is the difference between the number of students who were present in Physics and Biology examination from school N?

    • (a) 21150
    • (b) 14352
    • (c) 22594
    • (d) 24250
    उत्तर देखें

    उत्तर: (c)

38. 61. If the number of students who were present in the Physics examination from school A is 250% of the difference of the number of the students who were present in Physics and Biology examination, from school K, then what is the ratio of the number of students who were present from school L to number of students who were present in Physics examination from school A?

    • (a) 5079 : 4631
    • (b) 1692 : 1547
    • (c) 1547 : 4631
    • (d) 1692 : 2345
    उत्तर देखें

    उत्तर: (b)

39. 62. A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?

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

    उत्तर: (a)

40. 63. एक मिश्र धातु में तांबे और टिन का अनुपात 3 : 2 है। यदि इस मिश्र धातु में 250 ग्राम तांबा मिला दिया जाता है तो इसमें उपस्थित तांबा इसमें उपस्थित टिन की मात्रा का दोगुना हो जाता है। इस मिश्र धातु में टिन कितनी मात्रा (ग्राम में) में है?

    • (a) 250
    • (b) 750
    • (c) 1000
    • (d) 500
    उत्तर देखें

    उत्तर: (d)

41. 64. A starts a cement trading business by investing Rs 5 lakhs. After 2 months, B joins the business by investing Rs 10 lakhs and then 4 months after B joined C too joins them by investing Rs 20 lakhs. 1 year after A started the business they make Rs 3,50,000 in profit. What is B's share of the profit (in Rs)?

    • (a) 75000
    • (b) 1,25,000
    • (c) 1,50,000
    • (d) 1,00,000
    उत्तर देखें

    उत्तर: (b)

42. 65. A, B and C invest in a business in the ratio 3 : 6 : 5. A and C are working partners. Only B is a sleeping partner hence his share will be 3/4th of what it would have been if he were a working partner. If they make Rs 50,000 profit, half of which is reinvested in the business and the other half is distributed between the partners, then how much does C get (in Rs)?

    • (a) 20000
    • (b) 6000
    • (c) 10000
    • (d) 9000
    उत्तर देखें

    उत्तर: (c)

43. 66. A can do a work in 21 days and B in 42 days. If they work on it together for 7 days, then what fraction of work is left?

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

    उत्तर: (d)

44. 67. A can paint a house in 55 days and B can do it in 66 days. Along with C, they did the job in 12 days only. Then, C alone can do the job in how many days?

    • (a) 24
    • (b) 44
    • (c) 33
    • (d) 20
    उत्तर देखें

    उत्तर: (d)

45. 68. A, B and C together can finish a task in 12 days. A is twice as productive as B and C alone can do the task in 36 days. In how many days can A and B do the task if C goes on leave?

    • (a) 10
    • (b) 20
    • (c) 15
    • (d) 18
    उत्तर देखें

    उत्तर: (d)

46. 69. A, B and C can together do a job in 9 days. C alone can do the job in 36 days. In how many days can A and B do 50% of the job working together?

    • (a) 6
    • (b) 12
    • (c) 9
    • (d) 15
    उत्तर देखें

    उत्तर: (a)

47. 70. 25% की दो लगातार छूट ___% की एक छूट के बराबर होती है।

    • (a) 43.75
    • (b) 56.25
    • (c) 50
    • (d) 45
    उत्तर देखें

    उत्तर: (a)

48. 71. यदि कोई घड़ी जिसकी अंकित कीमत 8,500 रूपये है 7,225 रुपयों में बेची जाती है तो घड़ी पर कितनी छूट (% में) दी गयी?

    • (a) 24
    • (b) 15
    • (c) 25
    • (d) 20
    उत्तर देखें

    उत्तर: (b)

49. 72. On a machine there is 10% trade discount on the marked price of Rs 2,50,000. But the machine is sold at Rs 2,16,000 after giving a cash discount. How much is this cash discount (in %)?

    • (a) 5
    • (b) 4
    • (c) 6
    • (d) 7
    उत्तर देखें

    उत्तर: (b)

50. 73. A trader marks up his goods by 120% and offers 30% discount. What will be the selling price (in Rs) if the cost price is Rs 750?

    • (a) 1225
    • (b) 1080
    • (c) 1280
    • (d) 1155
    उत्तर देखें

    उत्तर: (d)

51. 74. Sanjay's test marks in two subjects, English and Hindi are in the ratio 7 : 11. If he got 20 marks more in Hindi than in English, what are his marks in English?

    • (a) 35
    • (b) 55
    • (c) 45
    • (d) 65
    उत्तर देखें

    उत्तर: (a)

52. 75. सिमी और सीमा की वर्तमान आयु का अनुपात 5 : 4 है। 9 वर्षों बाद उनकी आयु का अनुपात 8 : 7 हो जाएगा। सिमी की वर्तमान आयु क्या है (वर्षों में)?

    • (a) 12
    • (b) 15
    • (c) 24
    • (d) 21
    उत्तर देखें

    उत्तर: (b)

53. 76. Find the third proportional to 6 and 12.

    • (a) 18
    • (b) 9
    • (c) 24
    • (d) 15
    उत्तर देखें

    उत्तर: (c)

54. 77. According to the will the wealth of Rs 21,25,000 was to be divided between the son and the daughter in the ratio 7/6 : 5/3. How much did the son get (in Rs)?

    • (a) 875000
    • (b) 12,50,000
    • (c) 10,00,000
    • (d) 11,25,000
    उत्तर देखें

    उत्तर: (a)

55. 78. If Rs 25,000 is to be divided between A, B and C in the ratio 1/10 : 1/6 : 1/15, then how much will C get (in Rs)?

    • (a) 5000
    • (b) 7500
    • (c) 10000
    • (d) 12500
    उत्तर देखें

    उत्तर: (a)

56. 79. Rizwan has a box in which he kept red and blue marbles. The red marbles and blue marbles were in the ratio 5 : 4. After he lost 5 red marbles the ratio became 10 : 9. How many marbles does he have now?

    • (a) 81
    • (b) 86
    • (c) 76
    • (d) 91
    उत्तर देखें

    उत्तर: (c)

57. 80. The average weight of L, M and N is 93 kg. If the average weight of L and M be 89 kg and that of M and N be 96.5 kg, then the weight (in kg) of M is ________.

    • (a) 92
    • (b) 86
    • (c) 101
    • (d) 95
    उत्तर देखें

    उत्तर: (a)

58. 81. Mahesh buys 3 shirts at an average price of Rs 1250. If he buys 2 more shirts at an average price of Rs 1450 what will be the average price (in Rs) of all the 5 shirts he buys?

    • (a) 1370
    • (b) 1330
    • (c) 1310
    • (d) 1390
    उत्तर देखें

    उत्तर: (b)

59. 82. In a one day match of 50 overs in an innings the Team A had a run rate of 6.1 runs per over. Team B is playing and 10 overs are left and the required run rate to tie the match is 6.5 per over. What is Team B's score now?

    • (a) 235
    • (b) 230
    • (c) 240
    • (d) 225
    उत्तर देखें

    उत्तर: (c)

60. 83. 222 और 250 के बीच की सभी सम संख्याओं का औसत ____ है।

    • (a) 234
    • (b) 232
    • (c) 236
    • (d) 230
    उत्तर देखें

    उत्तर: (c)

61. 84. A vendor buys bananas at 7 for Rs 6 and sells at 6 for Rs 7. What will be the result?

    • (a) 36.1% loss
    • (b) 26.5% profit
    • (c) 36.1% profit
    • (d) 26.5% loss
    उत्तर देखें

    उत्तर: (c)

62. 85. एक खनिक किसी व्यापारी को 40% के लाभ पर एक हीरा बेचता है और व्यापारी इसे 25% के लाभ पर ग्राहक को बेचता है। यदि ग्राहक ने इस हीरे को खरीदने के लिए 56 लाख रुपयों का भुगतान किया है तो खनिक को यह हीरा कितने रुपयों (लाख रुपयों में) में मिला?

    • (a) 30
    • (b) 28
    • (c) 25
    • (d) 32
    उत्तर देखें

    उत्तर: (d)

63. 86. A grocer had 1600 kgs of wheat. He sold a part of it at 20% profit and the rest at 12% profit, so that he made a total profit of 17%. How much wheat (in kg) did he sell at 20% profit?

    • (a) 600
    • (b) 1000
    • (c) 800
    • (d) 1200
    उत्तर देखें

    उत्तर: (b)

64. 87. पुराने टू-व्हीलर के विक्रेता ने एक स्कूटर 46,000 रुपयों में बेचा और उसे कुछ नुकसान हुआ। यदि उसने इसे 58,000 रूपयों में बेचा होता तो उसका लाभ उसके नुकसान से दोगुना होता। स्कूटर का लागत मूल्य (रुपयों में) क्या था?

    • (a) 52000
    • (b) 54000
    • (c) 48000
    • (d) 50000
    उत्तर देखें

    उत्तर: (d)

65. 88. 0.08% of 120% of 50,000 is equal to __________.

    • (a) 480
    • (b) 48
    • (c) 4800
    • (d) 4.8
    उत्तर देखें

    उत्तर: (b)

66. 89. When a number is increased by 24, it becomes 115% of itself. What is the number?

    • (a) 160
    • (b) 250
    • (c) 100
    • (d) 200
    उत्तर देखें

    उत्तर: (a)

67. 90. दो संख्याएं किसी तीसरी संख्या से 40% और 80% कम हैं। दूसरी संख्या को कितने प्रतिशत तक बढ़ाया जाए कि यह पहली संख्या के बराबर हो जाए?

    • (a) 100
    • (b) 33.3
    • (c) 66.6
    • (d) 200
    उत्तर देखें

    उत्तर: (d)

68. 91. डीज़ल की कीमत 45 रूपये प्रति लीटर से बढ़कर 50 रूपये प्रति लीटर हो जाती है। डीज़ल की खपत को कितना कम (% में) किया जाए कि व्यय केवल 5% तक ही बढ़े?

    • (a) 5.5
    • (b) 5
    • (c) 4
    • (d) 4.5
    उत्तर देखें

    उत्तर: (a)

69. 92. A plane flies a distance of 1800 km in 5 hours. What is its average speed in meters/second?

    • (a) 200
    • (b) 10
    • (c) 20
    • (d) 100
    उत्तर देखें

    उत्तर: (d)

70. 93. If a boat goes upstream at a speed of 24 km/hr and comes back the same distance at 40 km/hr. What is the average speed (in km/hr) for the total journey.

    • (a) 32
    • (b) 30
    • (c) 31
    • (d) 33
    उत्तर देखें

    उत्तर: (b)

71. 94. Two bikers A and B start and ride at 75 km/hr and 60 km/hr respectively towards each other. They meet after 20 minutes. How far (in km) were they from each other when they started?

    • (a) 60
    • (b) 45
    • (c) 30
    • (d) 15
    उत्तर देखें

    उत्तर: (b)

72. 95. विरामों को छोड़ दिया जाए तो बस की गति 80 कि.मी./घंटा और विरामों को मिलाकर बस की गति 60 कि.मी./घंटा है। बस प्रति घंटा कितने मिनट रुकती है?

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

    उत्तर: (b)

73. 96. In 2 years at simple interest the principal increases by 8%. What will be the compound interest earned (in Rs) on Rs 10 lakhs in 2 years at the same rate?

    • (a) 86000
    • (b) 81600
    • (c) 90000
    • (d) 94000
    उत्तर देखें

    उत्तर: (b)

74. 97. If the compound interest for the 3rd and 4th year on a certain principal is Rs 125 and Rs 135 respectively, what is the rate of interest (in %)?

    • (a) 9
    • (b) 10
    • (c) 8
    • (d) 12
    उत्तर देखें

    उत्तर: (c)

75. 98. A certain bank offers 8% rate of interest on the 1st year and 9% on the 2nd year in a certain fixed deposit scheme. If Rs 17,658 are received after investing for 2 years in this scheme, then what was the amount (in Rs) invested?

    • (a) 16000
    • (b) 15000
    • (c) 15500
    • (d) 16500
    उत्तर देखें

    उत्तर: (b)

76. 99. What is the difference (in Rs) in Compound interest earned in 1 year on a sum of Rs 25,000 at 20% per annum compounded semi-annually and annually?

    • (a) 125
    • (b) 250
    • (c) 500
    • (d) 375
    उत्तर देखें

    उत्तर: (b)