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SSC CGL Tier II (CGL 2019), 15 Nov 2020 question paper

100 questions · 200 marks · 120 minutes · +2 per correct answer, -0.5 per wrong one

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  1. 1
    The value of 3÷18 of 3×6+21×6÷18−3÷2+3−3÷9 of 3×93 \div 18 \text{ of } 3 \times 6 + 21 \times 6 \div 18 - 3 \div 2 + 3 - 3 \div 9 \text{ of } 3 \times 9 is:

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  2. 2
    In Δ\DeltaABC, D and E are the mid points of sides BC and AC, respectively. If AD = 10.8 cm, BE = 14.4 cm and AD and BE intersect at G at a right angle, then the area (in cm2\text{cm}^2) of Δ\DeltaABC is:

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  3. 3
    Rishu saves *x*% of her income. If her income increases by 26% and the expenditure increases by 20%, then her savings increase by 50%. What is the value of x?

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  4. 4
    If 4553=1a+1b+1c−25\frac{45}{53} = \frac{1}{a + \frac{1}{b + \frac{1}{c - \frac{2}{5}}}}, where a, b and c are positive integers, then what is the value of (4a−b+3c)(4a - b + 3c)?

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  5. 5
    A man divides a certain sum among his three sons in the ratio 3 : 4 : 5. Had he divided the sum in the ratio 13:14:15\frac{1}{3} : \frac{1}{4} : \frac{1}{5}, the son who got the least share earlier would have got ₹1,188 more. Find the sum (in ₹).

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  6. 6
    The value of sec⁡2θ(2+tan⁡2θ+cot⁡2θ)÷(sin⁡2θ−tan⁡2θ)(cosec2θ+sec⁡2θ)(1+cot⁡2θ)2\frac{\sec^2\theta(2+\tan^2\theta+\cot^2\theta)\div(\sin^2\theta-\tan^2\theta)}{(\text{cosec}^2\theta+\sec^2\theta)(1+\cot^2\theta)^2} is:

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  7. 7
    Study the given graph and answer the question that follows. The number of patients aged 10 or more years but below 40 years is what per cent less than the number of patients aged 50 or more years but below 80 years?

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  8. 8
    If (x+20)%(x + 20)\% of 250 is 25% more than x%x\% of 220, then 10% of (x+50)(x + 50) is what per cent less than 15% of xx?

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  9. 9
    Remi earns a profit of 20% on selling an article at a certain price. If she sells the articles for ₹8 more, she will gain 30%. What is the original cost price of 16 such articles?

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  10. 10
    In Δ\DeltaPQR, O is the incentre and ∠P=42∘\angle P = 42^\circ. Find the measure of ∠QOR\angle QOR.

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  11. 11
    The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be 14\frac{1}{4} that of the father. What will be the ratio of the ages of the son and father, 10 years from now?

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  12. 12
    (1cos⁡θ−1sin⁡θ)+1cosecθ−cot⁡θ−1sec⁡θ+tan⁡θ=?\left(\frac{1}{\cos\theta} - \frac{1}{\sin\theta}\right) + \frac{1}{\text{cosec}\theta - \cot\theta} - \frac{1}{\sec\theta + \tan\theta} = ?

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  13. 13
    A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes 1121\frac{1}{2} hours more than B to cover 80 km. To cover a distance of 90 km, how much time will B take travelling at his same speed?

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  14. 14
    On selling an article for ₹123.40, the gain is 20% more than the amount of loss incurred on selling it for ₹108. If the article is sold for ₹120.75, then what is the gain/loss per cent?

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  15. 15
    In Δ\DeltaPQR, ∠Q=84∘\angle Q = 84^\circ, ∠R=48∘\angle R = 48^\circ, PS ⊥\perp QR at S and the bisector of ∠P\angle P meets QR at T. What is the measure of ∠SPT\angle SPT?

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  16. 16
    In Δ\DeltaABC, ∠A=90∘\angle A = 90^\circ, AD is the bisector of ∠A\angle A meeting BC at D, and DE ⊥\perp AC at E. If AB = 10 cm and AC = 15 cm, then the length of DE, in cm, is:

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  17. 17
    The base of a right pyramid is a square of side 10 cm. If its height is 10 cm, then the area (in cm2\text{cm}^2) of its lateral surface is:

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  18. 18
    The compound interest on a sum of ₹5,500 at 15% p.a. for 2 years, when the interest is compounded 8 monthly, is:

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  19. 19
    The value of (2.4‾×0.6‾×3×0.16‾)×[0.27‾×(0.83‾÷0.16‾)](2.\overline{4} \times 0.\overline{6} \times 3 \times 0.1\overline{6}) \times [0.\overline{27} \times (0.8\overline{3} \div 0.1\overline{6})] is:

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  20. 20
    A sold a watch to B at a profit of 20%. B sold it to C at 30% profit. C sold it to D at 10% loss. If B's profit is ₹80 more than that of A, then D bought it for:

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  21. 21
    The value of [47 of 245×123−(312−216)]÷(315÷412 of 513)\left[\frac{4}{7} \text{ of } 2\frac{4}{5} \times 1\frac{2}{3} - \left(3\frac{1}{2} - 2\frac{1}{6}\right)\right] \div \left(3\frac{1}{5} \div 4\frac{1}{2} \text{ of } 5\frac{1}{3}\right) is:

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  22. 22
    The average score in Mathematics of 90 students of section A and B of class IX was 63. The number of students in A were 10 more than those in B. The average score of students in A was 30% more than that of students in B. The average score of students in B is:

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  23. 23
    The curved surface area of a right cylinder is 3696 cm2\text{cm}^2. Its height is three times its radius. What is the capacity (in litres) of the cylinder? (Take π=227\pi = \frac{22}{7})

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  24. 24
    The sides BA and DE of a regular pentagon are produced to meet at F. What is the measure of ∠EFA\angle EFA?

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  25. 25
    The expression 15(10+5)10+20+40−5−80\frac{15(\sqrt{10} + \sqrt{5})}{\sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80}} is equal to:

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  26. 26
    A person has to cover a distance of 160 km in 15 hours. If he covers 45\frac{4}{5} of the distance in 23\frac{2}{3} of the time, then what should be his speed (in km/h) to cover the remaining distance in the remaining time?

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  27. 27
    The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2\text{cm}^2) of the remaining solid?

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  28. 28
    If 9x2+y2=379x^2 + y^2 = 37 and xy=2xy = 2, x,y>0x, y > 0, then the value of (27x3+y3)(27x^3 + y^3) is:

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  29. 29
    The value of cosec230∘sin⁡245∘+sec⁡260∘tan⁡60∘cosec245∘−sec⁡260∘tan⁡45∘\frac{\text{cosec}^2 30^\circ \sin^2 45^\circ + \sec^2 60^\circ}{\tan 60^\circ \text{cosec}^2 45^\circ - \sec^2 60^\circ \tan 45^\circ} is:

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  30. 30
    Given that Δ\DeltaDEF~Δ\DeltaABC. If the area of Δ\DeltaABC is 9 cm2\text{cm}^2 and that of Δ\DeltaDEF = 12 cm2\text{cm}^2 and BC = 2.1 cm, then the length of EF is:

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  31. 31
    If a+b+c=6a + b + c = 6, a3+b3+c3−3abc=342a^3 + b^3 + c^3 - 3abc = 342, then what is the value of ab+bc+caab + bc + ca?

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  32. 32
    If 3x2−5x+1=03x^2 - 5x + 1 = 0, then the value of (x2+19x2)\left(x^2 + \frac{1}{9x^2}\right) is:

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  33. 33
    A spherical metallic shell with 6 cm external radius weighs 6688 g. What is the thickness of the shell if the density of metal is 10.5 g per cm3\text{cm}^3? (Take π=227\pi = \frac{22}{7})

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  34. 34
    Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is:

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  35. 35
    A can do a piece of work in 15 days. B is 25% more efficient than A, and C is 40% more efficient than B. A and C work together for 3 days and then C leaves. A and B together will complete the remaining work in:

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  36. 36
    The base of a right prism is a regular hexagon of side 5 cm. If its height is 12312\sqrt{3} cm, then its volume (in cm3\text{cm}^3) is:

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  37. 37
    Let x=(18753888÷1200768)×1751792x = \left(\frac{\sqrt{1875}}{\sqrt{3888}} \div \frac{\sqrt{1200}}{\sqrt{768}}\right) \times \frac{\sqrt{175}}{\sqrt{1792}}. Then x\sqrt{x} is equal to:

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  38. 38
    The area of the base of a right circular cone is 81π81\pi cm2\text{cm}^2 and its height is 12 cm. What is the curved surface area (in cm2\text{cm}^2) of the cone?

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  39. 39
    The value of 2sin⁡238∘sec⁡252∘+cos⁡64∘sin⁡26∘+sin⁡264∘tan⁡223∘+cot⁡223∘−sec⁡267∘−cosec267∘\frac{2\sin^2 38^\circ \sec^2 52^\circ + \cos 64^\circ \sin 26^\circ + \sin^2 64^\circ}{\tan^2 23^\circ + \cot^2 23^\circ - \sec^2 67^\circ - \text{cosec}^2 67^\circ} is:

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  40. 40
    Study the given graph and answer the question that follows. The total revenue in 2015 and 2017 is what per cent of the total expenditure of the company in 2016, 2018 and 2019 (correct to one decimal place)?

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  41. 41
    In Δ\DeltaABC, ∠C=90∘\angle C = 90^\circ. Points P and Q are on the sides AC and BC, respectively, such that AP : PC = BQ : QC = 1 : 2. Then, AQ2+BP2AB2\frac{AQ^2 + BP^2}{AB^2} is equal to:

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  42. 42
    The marked price of an article is 40% above its cost price. If its selling price is 7312%73\frac{1}{2}\% of the marked price, then the profit percentage is:

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  43. 43
    ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC=128∘\angle BEC = 128^\circ and ∠ECD=25∘\angle ECD = 25^\circ, then what is the measure of ∠BAC\angle BAC?

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  44. 44
    A certain sum amounts to ₹15,500 in 2 years at 12% p.a. simple interest. The same sum will amount to what in 1121\frac{1}{2} years at 10% p.a., if the interest is compounded half yearly (nearest to ₹1)?

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  45. 45
    A and B start moving towards each other from places X and Y, respectively, at the same time on the same day. The speed of A is 20% more than that of B. After meeting on the way, A and B take p hours and 7157\frac{1}{5} hours, respectively, to reach Y and X, respectively. What is the value of p?

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  46. 46
    If sec⁡θ=ab\sec\theta = \frac{a}{b}, b≠0b \ne 0, then 1−tan⁡2θ2−sin⁡2θ=?\frac{1 - \tan^2\theta}{2 - \sin^2\theta} = ?

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  47. 47
    If sin⁡3A=cos⁡(A+10∘)\sin 3A = \cos(A + 10^\circ), where 3A is an acute angle, then what is the value of 2 cosec 3A2+6sin⁡23A−32tan⁡23A2\,\text{cosec}\,\frac{3A}{2} + 6\sin^2 3A - \frac{3}{2}\tan^2 3A?

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  48. 48
    When xx is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x−2)(3x - 2) and (5x+4)(5x + 4)?

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  49. 49
    In Δ\Delta PQR, ∠Q=90∘\angle Q = 90^\circ. If cot R = 13\frac{1}{3}, then what is the value of sec⁡P(cos⁡R+sin⁡P)cosec R (sin⁡R−cosec P)\frac{\sec P(\cos R + \sin P)}{\text{cosec}\,R\,(\sin R - \text{cosec}\,P)}?

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  50. 50
    Amit sells an article for ₹369.60 after giving a discount of 12% on the marked price. Had he not given any discount, he would have made a profit of 20%. Find the cost price of the article.

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  51. 51
    When positive numbers xx, yy and zz are divided by 31, the remainders are 17, 24 and 27, respectively. When (4x−2y+3z)(4x - 2y + 3z) is divided by 31, the remainder will be:

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  52. 52
    As observed from the top of a light house, 1203120\sqrt{3} m above the sea level, the angle of depression of a ship sailing towards it changes from 30∘30^\circ to 60∘60^\circ. The distance travelled by the ship during the period of observation is:

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  53. 53
    Study the given graph and answer the question that follows. In which year was the revenue 3313%33\frac{1}{3}\% more than the average expenditure of the company during 2014 to 2019?

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  54. 54
    The value of cos⁡6θ+sin⁡6θ+3sin⁡2θcos⁡2θcosec θsec⁡θ(sin⁡θ+cos⁡θ−1)(sin⁡θ+cos⁡θ+1)\frac{\cos^6\theta + \sin^6\theta + 3\sin^2\theta\cos^2\theta}{\text{cosec}\,\theta\sec\theta(\sin\theta + \cos\theta - 1)(\sin\theta + \cos\theta + 1)} is:

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  55. 55
    A certain sum is lent at 4% p.a. for 3 years, 8% p.a. for the next 4 years, and 12% p.a. beyond 7 years. If for a period of 11 years, the simple interest obtained is ₹27,600, then the sum is (in ₹):

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  56. 56
    The areas of three adjacent faces of a cuboidal tank are 3 m2\text{m}^2, 12 m2\text{m}^2 and 16 m2\text{m}^2. The capacity of the tank, in litres, is:

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  57. 57
    A train of length 287 m, running at 80 km/h, crosses another train moving in the opposite direction at 37 km/h in 18 seconds. What is the length of the other train?

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  58. 58
    Study the given graph and answer the question that follows. The total number of employees working in departments A and C exceeds the total number of employees working in departments B and D by xx. The value of xx lies between:

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  59. 59
    Study the given graph and answer the question that follows. If 20% of the employees working in department E are transferred to department A, then the difference between the number of employees in A and 124% of the employees working in department C is:

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  60. 60
    If 14−8+3+223−22−3−223+22=a+b2\frac{1}{4 - \sqrt{8}} + \frac{3 + 2\sqrt{2}}{3 - 2\sqrt{2}} - \frac{3 - 2\sqrt{2}}{3 + 2\sqrt{2}} = a + b\sqrt{2}, then what is the value of (3a+4b)(3a + 4b)?

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  61. 61
    Study the given graph and answer the question that follows. In how many years was the profit (Revenue −- Expenditure) as a percentage of the revenue, more than 25%?

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  62. 62
    A and B are solutions of acid and water. The ratios of water and acid in A and B are 4:54 : 5 and 1:21 : 2, respectively. If xx litres of A is mixed with yy litres of B, then the ratio of water and acid in the mixture becomes 8:138 : 13. What is x:yx : y?

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  63. 63
    The numerator of a fraction is 3 more than the denominator. When 5 is added to the numerator and 2 is subtracted from the denominator, the fraction becomes 83\frac{8}{3}. When the original fraction is divided by 5125\frac{1}{2}, the fraction so obtained is:

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  64. 64
    In Δ\DeltaABC, the bisector of ∠\angleA intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, then the length of BD is:

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  65. 65
    The lengths of two sides of a parallelogram are 3 cm and 10 cm. What is the sum of the squares of the diagonals of the parallelogram?

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  66. 66
    The monthly incomes of A and B are in the ratio 3:53 : 5 and the ratio of their savings is 2:32 : 3. If the income of B is equal to three times the savings of A, then what is the ratio of the expenditures of A and B?

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  67. 67
    X and Y enter into a partnership with capital in the ratio 3:53 : 5. After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in ₹ lakhs) of X in the annual profit of ₹6.84 lakhs?

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  68. 68
    The average of three numbers a, b and c is 2 more than c. The average of a and b is 48. If d is 10 less than c, then the average of c and d is:

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  69. 69
    The radius and height of a right circular cone are in the ratio 3:43 : 4. If its curved surface area (in cm2\text{cm}^2) is 240π240\pi, then its volume (in cm3\text{cm}^3) is:

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  70. 70
    Anuja owns 6623%66\frac{2}{3}\% of a property. If 30% of the property that she owns is worth ₹1,25,000, then 45% of the value (in ₹) of the property is:

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  71. 71
    The sum of the radii of spheres A and B is 14 cm, the radius of A being larger than that of B. The difference between their surface areas is 112π112\pi. What is the ratio of the volumes of A and B?

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  72. 72
    The perimeters of Δ\DeltaABC and Δ\DeltaDEF are 43.2 cm and 28.8 cm, respectively, and Δ\DeltaABC∼\simΔ\DeltaDEF. If DE = 12 cm, then the length of AB is:

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  73. 73
    If 27(x+y)3−8(x−y)3=(x+5y)(Ax2+By2+Cxy)27(x + y)^3 - 8(x - y)^3 = (x + 5y)(Ax^2 + By^2 + Cxy), then what is the value of (A + B −- C)?

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  74. 74
    When 1062, 1134 and 1182 are divided by the greatest number xx, the remainder in each case is yy. What is the value of (x−y)(x - y)?

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  75. 75
    Pipes A and B can fill a tank in 43.2 minutes and 108 minutes, respectively. Pipe C can empty it at 3 litres/minute. When all the three pipes are opened together, they fill the tank in 54 minutes. The capacity (in litres) of the tank is:

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  76. 76
    Given that x8−34x4+1=0x^8 - 34x^4 + 1 = 0, x>0x > 0. What is the value of (x3+x−3)(x^3 + x^{-3})?

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  77. 77
    A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere and the sum of the surface areas of all the balls?

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  78. 78
    The value of 0.0203×2.920.7×0.0365×2.9÷(12.12)2−(8.12)2(0.25)2+(0.25)(19.99)\frac{0.0203 \times 2.92}{0.7 \times 0.0365 \times 2.9} \div \frac{(12.12)^2 - (8.12)^2}{(0.25)^2 + (0.25)(19.99)} is:

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  79. 79
    cos⁡A(sec⁡A−cos⁡A)(cot⁡A+tan⁡A)=?\cos A(\sec A - \cos A)(\cot A + \tan A) = ?

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  80. 80
    Study the given graph and answer the question that follows. The number of employees in department B is what per cent of the total number of employees working in departments D and E?

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  81. 81
    If the 5-digit number 535ab is divisible by 3, 7 and 11, then what is the value of (a2−b2+ab)(a^2 - b^2 + ab)?

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  82. 82
    If the radius of the base of a right circular cylinder is increased by 20% and the height is decreased by 30%, then what is the percentage increase/decrease in the volume?

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  83. 83
    The area (in sq. units) of the triangle formed by the graphs of 8x+3y=248x + 3y = 24, 2x+8=y2x + 8 = y and the xx-axis is:

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  84. 84
    A is 80% more than B and C is 4847%48\frac{4}{7}\% less than the sum of A and B. By what per cent is C less than A?

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  85. 85
    In a school, 38\frac{3}{8} of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 23\frac{2}{3} of the number of girls are also below 10 years. If the number of students of age 10 or more years is 260, then the number of boys in the school is:

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  86. 86
    A certain number of students from school X appeared in an examination and 30% students failed. 150% more students than those from school X, appeared in the same examination from school Y. If 80% of the total number of students who appeared from X and Y passed, then what is the percentage of students who failed from Y?

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  87. 87
    The radii of two right circular cylinders are in the ratio 3:23 : 2 and the ratio of their volumes is 27:1627 : 16. What is the ratio of their heights?

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  88. 88
    An article is marked 35% above its cost. If a profit of 20% is earned by selling the article, then the discount per cent offered on the marked price of the article is:

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  89. 89
    How many kg of rice costing ₹42 per kg should be mixed with 7127\frac{1}{2} kg rice costing ₹50 per kg so that by selling the mixture at ₹53.10 per kg, there is a gain of 18%?

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  90. 90
    A, B and C started a business. Twice the investment of A is equal to thrice the investment of B and also five times the investment of C. If the total profit after a year is ₹15.5 lakhs, then the share of B in the profit is (in ₹ lakhs):

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  91. 91
    In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠\angleDBC = 28∘28^\circ and BD = DC. What is the measure of ∠\angleBOC?

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  92. 92
    A can do 20% of a work in 4 days, B can do 3313%33\frac{1}{3}\% of the same work in 10 days. They worked together for 9 days. C completed the remaining work in 6 days. B and C together will complete 75% of the same work in:

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  93. 93
    Shashi sells two articles for ₹5,000 each with no loss and no profit in the overall transaction. If one article is sold at 1623%16\frac{2}{3}\% loss, then the other is sold at a profit of:

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  94. 94
    sin⁡θ[(1−tan⁡θ)tan⁡θ+sec⁡2θ](1−sin⁡θ)tan⁡θ(1+tan⁡θ)(sec⁡θ+tan⁡θ)\frac{\sin\theta[(1 - \tan\theta)\tan\theta + \sec^2\theta]}{(1 - \sin\theta)\tan\theta(1 + \tan\theta)(\sec\theta + \tan\theta)} is equal to:

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  95. 95
    In a circle with centre O, a diameter AB is produced to a point P lying outside the circle and PT is a tangent to the circle at the point C on it. If ∠\angleBPT = 36∘36^\circ, then what is the measure of ∠\angleBCP?

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  96. 96
    Surekha borrowed a sum of money and returned it in two equal annual instalments of ₹5,547 each. If the rate of interest was 712%7\frac{1}{2}\% p.a. compounded yearly, then the total interest paid by her was:

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  97. 97
    The graphs of the equations 3x−20y−2=03x - 20y - 2 = 0 and 11x−5y+61=011x - 5y + 61 = 0 intersect at P(a,b). What is the value of (a2+b2−ab)/(a2−b2+ab)(a^2 + b^2 - ab)/(a^2 - b^2 + ab)?

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  98. 98
    If (10a3+4b3):(11a3−15b3)=7:5(10a^3 + 4b^3) : (11a^3 - 15b^3) = 7 : 5, then (3a+5b):(9a−2b)=?(3a + 5b) : (9a - 2b) = ?

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  99. 99
    In Δ\DeltaABC, ∠\angleA −- ∠\angleB = 33∘33^\circ, ∠\angleB −- ∠\angleC = 18∘18^\circ. What is the sum of the smallest and the largest angles of the triangle?

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  100. 100
    Three men and 4 women can do a piece of work in 7 days, whereas 2 men and 1 woman can do it in 14 days. Seven women will complete the same work in:

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