**SSC CGL (Tier-2) Main Examination 2017 Held on March 9, 2018**

**Quantitative Aptitude Paper-1**

1. If the unit digit of 433 × 456 × 43N is (N + 2), then what is the value of N?

(a) 1

(b) 8

(c) 3

(d) 6

2. If N = (12345)^{2} + 12345 + 12346, then what is the value of √N?

(a) 12346

(b) 12345

(c) 12344

(d) 12347

3. Which of the following statement(s) is/are true?

(I) (0.03/0.2) + (0.003/0.02) + (0.0003/0.002) + (0.00003/0.0002) = 0.6

(II) (0.01) + (0.01)^{2} + (0.001)^{2} = 0.010101

(a) Only I

(b) Only II

(c) Neither I nor II

(d) Both I and II

4. What is the value of 1/(0.1)^{2} + 1/(0.01)^{2} +1/(0.5)^{2} + 1/(0.05)^{2}?

(a) 10504

(b) 10404

(c) 10004

(d) 11400

5. Which of the following statement(s) is/are true?

(a) Only I

(b) Only II

(c) Neither I nor II

(d) Both I and II

6. Which of the following statement(s) is/are true?

(a) Only I

(b) Only II

(c) Neither I nor II

(d) Both I and II

7. If then what is the value of f(1) + f(2) + f(3) + … f(10)?

(a) 9/10

(b) 10/11

(c) 11/12

(d) 12/13

8. If N = 4^{11} + 4^{12} + 4^{13} + 4^{14}, then how many positive factors of N are there?

(a) 92

(b) 48

(c) 50

(d) 51

9. If N = 9^{9}, then Nis divisible by how many positive perfect cubes?

(a) 6

(b) 7

(c) 4

(d) 5

10. If N = 3^{14} + 3^{13} – 12, then what is the largest prime factor of N?

(a) 11

(b) 79

(c) 13

(d) 73

11. Which of the following statement(s) is/are true?

(a) Only I

(b) Only II

(c) Neither I nor II

(d) Both I and II

12. What is the value of

(a) 2

(b) 4

(c) 8

(d) 6

13. The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares?

(a) 106

(b) 196

(c) 53

(d) 68

14. What is the value of 1006^{2} – 1007 × 1005 + 1008 × 1004 – 1009 × 1003?

(a) 6

(b) 3

(c) 12

(d) 24

15. If a^{2} + b^{2} = 4b + 6a – 13, then what is the value of a + b?

(a) 3

(b) 2

(c) 5

(d) 10

16. x and y are positive integers, if x^{4} + y^{4} + x^{2}y^{2} = 481 and xy = 12, then what is the value of x^{2} – xy + y^{2}?

(a) 16

(b) 13

(c) 11

(d) 15

17. If A = 1 + 2^{P} and B = 1 + 2^{−}^{P}, then what is the value of B?

(a) (A + 1)/(A – 1)

(b) (A + 2)/(A + 1)

(c) A/(A – 1)

(d) (A – 2)/(A + 1)

18. If a and b are roots of the equation ax^{3} + bx + c = 0, then which equation will have roots (ab + a + b) and (ab – a – b)?

(a) a^{2}x^{2} + 2acx + c^{2} + b^{2} = 0

(b) a^{2}x^{2} + 2acx + c^{2} – b^{2} = 0

(c) a^{2}x^{2} – 2acx + c^{2} + b^{2} = 0

(d) a^{2}x^{2} + 2acx + c^{2} – b^{2} = 0

19. If then what is the value of

(a) 2

(b) √2

(c) 1

(d) None of these

20. If (a + b)^{2} – 2(a + b) = 80 and ab = 16, then what can be the value of 3a – 19b?

(a) −16

(b) −14

(c) −18

(d) −20

21. If x^{y + z} = 1, y^{x + z} = 1024 and z^{x + y} = 729 (x, y and z are natural numbers), then what is the value of (z + 1)^{y + x + 1}?

(a) 6561

(b) 10000

(c) 4096

(d) 14641

22. If x + y + z = 1, x^{2} + y^{2} + z^{2} = 2 and x^{3} + y^{3} + z^{3} = 3, then what is the value of xyz?

(a) 1/3

(b) 1/6

(c) 1/2

(d) 1/4

23. In triangle PQR, the internal bisector of ∠Q and ∠R meets at O, If ∠QPR = 70°, then what is the value (in degrees) of ∠QOR?

(a) 45

(b) 125

(c) 115

(d) 10

24. PQR is a triangle such that PQ = PR and QT are the median to the sides PQ and PR respectively. If the medians RS and QR intersect at right, angle, then what is the value of (PQ/QR)^{2}?

(a) 3/2

(b) 5/2

(c) 2

(d) None of these

25. PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. Which of the following is True?

(1) Triangle PST is similar to triangle PQR

(2) ST = 1/2(QR)

(3) ST is parallel to QR.

(a) I and II

(b) II and III

(c) I and III

(d) All of these

26. ABC is a triangle in which ∠ABC = 90°, BD is perpendicular to AC, which of the following is true?

(I) Triangle BAD is similar to triangle CBD.

(II) Triangle BAD is similar to triangle CAB.

(III) Triangle CBD is similar to triangle CAB.

(a) Only I

(b) II and III

(c) I and III

(d) All of these

27. Two parallel chords are one the one side of the centre of a circle. The length of the two chords is 24 cm and 32 cm. If the distance between the two chords is 8 cm, then what is the area of the circle?

(a) 724.14 cm^{2}

(b) 832.86 cm^{2}

(c) 924.12 cm^{2}

(d) 988.32 cm^{2}

28. Two circles of radius 4 cm and 6 cm touch each other Internally. What is the length of the longest chord of the outer circle, which is also a tangent to inner circle?

(a) 12√2 cm

(b) 8√2 cm

(c) 6√2 cm

(d) 4√2 cm

29. In the given figure, PT is a common tangent to three circles at points A, B and C respectively. The radius of the small, medium and large circles is 4 cm, 6 cm and 9 cm. O_{1}, O_{2} and O_{3} are the centre of the three circles. What is the value of PC?

(a) 18√6 cm

(b) 9√6 cm

(c) 24√6 cm

(d) 15√6 cm

30. PQRS is a cyclic quadrilateral, PR and QS intersect at T. If ∠SPR = 40° and ∠PQS = 80°, then what is the value of ∠PSR?

(a) 60°

(b) 40°

(c) 80°

(d) 100°

31. In the given figure, ∠PSR = 105° and PQ is the diameter of the circle. What is the value of ∠QPR?

(a) 75°

(b) 15°

(c) 30°

(d) 45°

32. There are two identical circles of radius 10 cm each. If the length of the direct common tangent is 26 cm, then what is the length of transverse common tangent?

(a) 2√69 cm

(b) 4√23 cm

(c) 4√46 cm

(d) 3√46 cm

33. PQRS is a rectangle in which side of PQ = 24 cm and OR = 16 cm. T is a point on RS. What is the area of the triangle PTQ?

(a) 192 cm^{2}

(b) 162 cm^{2}

(c) 148 cm^{2}

(d) Cannot be determined

34. In the given figure, ABCD and BEFG are squares of sides 8 cm and 6 cm respectively. What is the area (in cm^{2}) of the shaded region?

(a) 14 cm^{2}

(b) 12 cm^{2}

(c) 8 cm^{2}

(d) 16 cm^{2}

35. PQRS is a parallelogram and its area is 300 cm^{2}. Side PQ is extended to X such that PQ =QX. If XS intersects QR at Y, then what is the area of triangle SYR?

(a) 75 cm^{2}

(b) 50 cm^{2}

(c) 120 cm^{2}

(d) 100 cm^{2}

36. PQRST is a regular pentagon. If PR and QT intersects each other at X, then what is the value of ∠TXR?

(a) 98°

(b) 90°

(c) 72°

(d) 108°

37. In the given figure, ABCDEF is a regular hexagon whose side is 12 cm. What is the shaded area?

(a) 54√3 cm^{2}

(b) 36√3 cm^{2}

(c) 48√3 cm^{2}

(d) 52√3 cm^{2}

38. ABCD passes through the centres of the three circles as shown in the figure. AB = 2 cm and CD = 1. If the area of middle circle is the average of the areas of the other two circles, then what is the length of BC?

(a) (√6) – 1 cm

(b) (√6) + 1 cm

(c) (√6) – 3 cm

(d) (√6) + 3 cm

39. A = Area of the largest circle drawn Inside a square of side 1 cm.

B = Sum of areas of 4 identical (largest possible) circles drawn inside a square of side 1 cm.

C = Sum of areas of 9 identical circle (largest possible) drawn inside a square of side 1 cm.

D = Sum of area of 16 identical circles (largest possible) drawn inside a square of side 1 cm.

*Which of the following is true about A, B, C and D?*

(a) A > B > C > D

(b) A < B < C < D

(c) A > B = C > D

(d) No option is correct

40. A prism has a square base whose side is 8 cm. The height of prism is 80 cm. The prism is cut into 10 identical parts by 9 cuts which area parallel to base of prism, what is the total surface area of all the 10 parts together?

(a) 4260 cm^{2}

(b) 2560 cm^{2}

(c) 3840 cm^{2}

(d) 3220 cm^{2}

41. A cone of radius 90 cm and height 120 cm stands on its base. It is cut into 3 parts by 2 cuts parallel to its base such that the height of the three parts (from top to bottom) are in ratio of 1 : 2 : 3. What is the total surface area of the middle part?

(a) 14600 cm^{2}

(b) 16500 cm^{2}

(c) 17800 cm^{2}

(d) 18500 cm^{2}

42. The curved surface area of cylinder is 594 cm^{2} and its volume is 1336.5 cm^{3}. What is the height of the cylinder?

(a) 14 cm

(b) 21 cm

(c) 24.5 cm

(d) 10.5 cm

43. A hollow cylinder is made up of metal. The difference between outer and inner curved surface area of this cylinder is 352 cm^{2}. Height of the cylinder is 28 cm. If the total surface area of this hollow cylinder is 2640 cm^{2}, then what are the inner and outer radius (in cm)?

(a) 4, 6

(b) 10, 12

(c) 8, 10

(d) 6, 8

44. A solid metal sphere has a radius 14 cm. It is melted to form small cones of radius 1.75 cm and height 3.5 cm. How many small cones will be obtained from the sphere?

(a) 512

(b) 256

(c) 1024

(d) 2048

45. A metallic hemispherical bowl is made up of steel. The total steel used in making the bowl is 342n cm^{3}, The bowl can hold 144n cm^{3} What is the thickness (in cm) of bowl and the curved surface area (in cm^{2}) of outer side?

(a) 6, 162n

(b) 3, 162n

(c) 6, 81n

(d) 3, 81n

46. There is a box of cuboid shape. The smallest side of the box is 20 cm and largest side is 40 cm. Which of the following can be volume of the box?

(a) 18000 cm^{3}

(b) 12000 cm^{3}

(c) 36000 cm^{3}

(d) 42000 cm^{3}

47. A pyramid has a square base, whose side is 8 cm. If the height of pyramid is 16 cm, then what is the total surface area of the pyramid?

(a) 64(√17 + 1) cm^{3}

(b) 32(√13 + 1) cm^{3}

(c) 64(√3 + 1) cm^{3}

(d) 32(√5 + 1) cm^{3}

48. What is the value of

(a) sin 2θ

(b) sin^{2} θ

(c) cos^{2} θ

(d) cos 2θ

49. What is the value of

(a) 2 cot A

(b) 2tan A

(c) cot A

(d) tan A

50. What is the value of cos15° − cos 165°?

(a)

(b)

(c)

(d)

51. If P + Q + R = 60°, then what is the value of cos Q cos R (cos P – sin P) + sin Q sin R (sin P – cos P)

(a) 1/2

(b) √3/2

(c) 1/√2

(d) √2

52. What is the value of

(a) − sin 2θ

(b) − cos 2θ

(c) cos 2θ

(d) sin 2θ

53. What is the value of

(a) cos x + sin x

(b) sin x – cos x

(c) sec x + tan x

(d) sec x – tan x

54. What is the value of sin(180 – θ) sin(90 – θ) – [cot(90 – θ) /1+ tan^{2}θ]?

(a) cos^{2} θ sin θ

(b)

(c)

(d) sin^{2} θ cos θ

55. A pole is sanding on the top of a house. Height of house is 25 m. The angle of elevation of the top of house from point P is 45° and the angle of elevation of the top of pole from P is 60°. Point P is on the ground level. What is the height of pole?

(a) 10(√3 + 1)m

(b) 15(√3 + 1)m

(c) 25(√3 − 1)m

(d) 20(√3 − 1)m

56. A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 m from the wall. The angle of elevation of the top of the wall from the base of the ladder is 45°. What is the length of the ladder?

(a) 5√6 – 5√3 m

(b) 5√6 – 5√2 m

(c) 5√2 – 1m

(d) 5√3 + 5√2 m

57. An aeroplane is flying horizontally at a height of 1.8 km above the ground. The angle of elevation of plane from point X is 60° and after 20 seconds, its angle of elevation from X is become 30°. If point X is on ground, then what is the speed of aeroplane?

(a) 216√3 km/h

(b) 105√3 km/h

(c) 201√3 km/h

(d) 305√3 km/h

**Directions **(Q. Nos. 58-62) The table given below shows the production of maize by 5 different States a percentage of total production. Each State produces only maize and rice. There are three types of rice – R_{1}, R_{2} and R_{3}. The table also shows the R_{1} type of rice produced as a percentage of total rice production and the ratio of R_{2} and R_{3} type of rice. Total production by each State is 625000.

58. What is the difference between then R_{1} type of rice produced by State X and the R_{2} type of rice produced by State H?

(a) 115000

(b) 120000

(c) 55000

(d) 65000

59. What is the sum of the total production of maize by State X and T and total production of R_{2} type of Rice by State S and R?

(a) 868500

(b) 1025000

(c) 925000

(d) 892500

60. Production of R_{3} type of rice by State X is what percentage of production of R_{1} type of rice by State S?

(a) 45.45

(b) 52.52

(c) 42.5

(d) 39.5

61. A = Average of the R_{3} type of rice produced by State H, R, S and X together.

B = Difference between the R_{2} type of rice produced by State T and R_{1} type of rice produced by State R.

What is the value of B – A?

(a) 54750

(b) 56750

(c) 57500

(d) 57000

62. F = Total production of R_{2} types of rice by all the States.

K = Average of the total production of R_{1} type of rice by all the States.

What is the value of K/F?

(a) 0.875

(b) 0.802

(c) 0.08

(d) 0.702

63. If x beakers of 100 ml containing 1 : 4 acid-water solution are mixed with y beakers of 200 ml containing 3 : 17 acid-water solution then the ratio of acid to water in the resulting mixture becomes 19 : 91. Find x : y.

(a) 5 : 3

(b) 3 : 5

(c) 7 : 13

(d) 13 : 7

64. In what ratio should 20% ethanol solution be mixed with 40% ethanol solution to obtain a 28% ethanol solution?

(a) 2 : 3

(b) 8 : 5

(c) 3 : 2

(d) 5 : 8

65. A and B start a business by investing equal amounts. Four months later, C joins them by investing Rs 3.5 lakh. By withdrawing his investment in the business B leaves the business 4 months after C joined. At the end of the year the business makes Rs 62400 profit out of which A collects Rs 24000 as his share of profit. How much should be paid to C as his share of profit?

(a) Rs 16000

(b) Rs 32000

(c) Rs 22400

(d) Rs 27800

66. A and B invest in a business in the ratio 3 : 7. The business makes a profit of Rs 60000 in 1 year. They decide to distribute the profit remaining after reinvesting 40% of the profit. How much will A get?

(a) Rs 25200

(b) Rs 15600

(c) Rs 10800

(d) Rs 20400

67. A can do a work in 72 days and B in 90 days. If they work on it together for 10 days, then what fraction of work is left?

(a) 3/4

(b) 1/4

(c) 4/5

(d) 5/6

68. A is thrice as a good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for B alone to paint the house?

(a) 32

(b) 64

(c) 96

(d) 72

69. C is 5 times as productive as B, A takes 60 days to complete a task. If A, B and C work together they can complete the task in 12 days. In how many days can B complete the task if the worked alone?

(a) 18

(b) 27

(c) 90

(d) 72

70. A can complete 50% of a job in 9 days and B can complete 25% of the job in 9 days if they worked alone. If they worked together how much of the job can they complete in 9 days?

(a) 80%

(b) 90%

(c) 75%

(d) 100%

71. Giving two successive discounts of 60% is equal to giving one discount of

(a) 90%

(b) 72%

(c) 96%

(d) 84%

72. If an item marked at Rs 480 is being sold at Rs 400, then what is the effective discount on the item?

(a) 20%

(b) 16.67%

(c) 25%

(d) 15%

73. On an item there is cash 5% discount on the marked price of Rs 25000. After giving an additional season’s discount the item is sold at Rs 20900. How much was the season’s discount?

(a) 11%

(b) 10%

(c) 12%

(d) 9%

74. A retailer marks up his goods by 20% and then offers 25% discount. What will be the selling price on an item that he sells if its cost price is Rs 2500?

(a) Rs 2400

(b) Rs 3000

(c) Rs 2750

(d) Rs 2250

75. Find two numbers such that their mean proportional is 18 and the third proportional to them is 144.

(a) 6 and 42

(b) 9 and 36

(c) 3 and 18

(d) 6 and 12

76. If 6A = 4B = 9C; find A : B : C

(a) 6 : 4 : 9

(b) 6 : 9 : 4

(c) 4 : 9 : 6

(d) 9 : 6 : 4

77. Find the third proportional to 10 and 25.

(a) 2.5

(b) 62.5

(c) 40

(d) 100

78. A purse has Rs 34.5 in the form of Rs 1, 50 paise and 10 paise coins in the ratio 6 : 9 : 10. Find the number of 10 paise coins.

(a) 10

(b) 30

(c) 20

(d) 40

79. What number should be added to each of numbers 103, 135, 110 and 144 so, that the resulting numbers are in proportion?

(a) 12

(b) 15

(c) 9

(d) 6

80. When ticket prices to a water park are increased in the ratio 11 : 12 then the number of daily visitors to the park fall in the ratio 8 : 7. If the dally revenues before the increase in ticket price was Rs 176000 then find the daily revenues after the increase in ticket price.

(a) Rs 264000

(b) Rs 112000

(c) Rs 192000

(d) Rs 168000

81. The average weight of X, Y and Z is 745 kg. In the average weight of X and Y be 68 kg and that and Z be 78 kg, then the weight of Y is.

(a) 72 kg

(b) 70 kg

(c) 68 kg

(d) 66 kg

82. Of the 3 numbers whose average is 126, the first is 2/11 times the sum of other two. The first number is

(a) 16

(b) 13

(c) 11

(d) 12

83. The average weight of a class of 50 students is 48.6 kg. If the average weight of the 20 boys is 54 kg, then find the average weight of the girls in the class.

(a) 40 kg

(b) 46 kg

(c) 45 kg

(d) 42 kg

84. The average of all odd numbers from 113 to 159 to

(a) 135

(b) 134

(c) 133

(d) 136

85. A trader buys jowar at Rs 30 per kg. 20% of the grain gets wasted. He plans to sell the remaining grain to that he makes 40% overall profit. At what price should he shell the grain?

(a) Rs 48 per kg

(b) Rs 50 per kg

(c) Rs 52.5 per kg

(d) Rs 47.5 per kg

86. If a vendor sells a watermelon at Rs 69 he makes 8% loss. If he wants to make 16% profit then at what price should he sell?

(a) Rs 91

(b) Rs 83

(c) Rs 87

(d) Rs 79

87. The cost of 25 items is the same as the revenue earned by selling x items. Find x, if the profit made in the transaction is 25%.

(a) 25

(b) 16.67

(c) 20

(d) 32

88. An item is sold for Rs 7130 making a 15% profit. What is the cost price of this item?

(a) Rs 6000

(b) Rs 6125

(c) Rs 6250

(d) Rs 6200

89. 0.02% of 150% of 600 is

(a) 0.18

(b) 1.8

(c) 18

(d) 0.018

90. When a number is increased by 40, it becomes 125% of itself, what is the number?

(a) 200

(b) 60

(c) 160

(d) 100

91. In an exam of 300 marks a students gets 75 marks. If she had scored 6 more she would have attained passing percentage. What is the passing percentage?

(a) 25%

(b) 30%

(c) 35%

(d) 27%

92. A man’s annual income has increased by Rs 7 lakh, but the tax on income that he has to pay has reduced from 20% to 16%. He now pays the same amount of tax as before. What is his increased income?

(a) Rs 8 lakh

(b) Rs 10 lakh

(c) Rs 12 lakh

(d) Rs 6 lakh

93. A car covers 630 km in 20 hours. Calculate its average speed in meters/second?

(a) 8.25

(b) 7.25

(c) 8.75

(d) 7.25

94. A jet ski goes upstream at a speed of 48 km/h and comes back the same distance at 80 km/h. Find the average speed for the total journey.

(a) 64 km/h

(b) 62 km/h

(c) 66 km/h

(d) 60 km/h

95. A bullet fired from a rifle travels at an average speed of 2520 km/hr. It hits the target after 0.2 seconds. How far is the target from the rifle?

(a) 70 m

(b) 140 m

(c) 100 m

(d) 200 m

96. Train A and B start at the same time. Train A travels at 55 km/h from station X to station Y and train B travels at 80 km/h from station Y to station X. They cross each other after 1 hour and 36 minutes. What is the distance between station X and Y?

(a) 196 km

(b) 232 km

(c) 240 km

(d) 216 km

97. If in 2 years at simple interest the principal increases by 16%, what will be the compound interest earned on Rs 25000 in 2 years at the same rate?

(a) Rs 4000

(b) Rs 2160

(c) Rs 2000

(d) Rs 4160

98. If compound interest received on a certain amount in the 2nd year is Rs 250. What will be the compound interest for the 3rd year on the same amount at 12% rate of interest?

(a) Rs 250

(b) Rs 300

(c) Rs 280

(d) Rs 270

99. What is the difference between the compound interest on Rs 12500 for 1 year at 8% per annum compounded yearly and half-yearly?

(a) Rs 16

(b) Rs 25

(c) Rs 20

(d) Rs 40

100. The amount received at 8% per annum compound interest after 2 years is Rs 72900. What was the principle?

(a) Rs 65000

(b) Rs 67500

(c) Rs 60000

(d) Rs 62500

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