SSC CGL COMBINED GRADUATE LEVEL

TIER-II

2019-2021 SOLVED PAPERS 08 SETS

QUANTITATIVE ABILITIES

08 SETS

ENGLISH LANGUAGE & COMPREHENSION

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Contents Solved Papers (2019) SOLVED PAPER–01 ✦

SSC CGL TIER-II (CBE) EXAM, 11.09.2019 Quantitative Abilities ......................................................................... CGL/II/2019/E-5

SOLVED PAPER–02 ✦

SSC CGL TIER-II (CBE) EXAM, 11. 09.2019 English Language & Comprehension ................................................. CGL/II/2019/E-22

SOLVED PAPER–03 ✦

SSC CGL TIER-II (CBE) EXAM, 12.09.2019 Quantitative Abilities .................................................................... CGL/II/2019/E-45

SOLVED PAPER–04 ✦

SSC CGL TIER-II (CBE) EXAM, 12. 09.2019 English Language & Comprehension ................................................ CGL/II/2019/E-62

SOLVED PAPER–05 ✦

SSC CGL TIER-II (CBE) EXAM, 13.09.2019 Quantitative Abilities ...................................................................... CGL/II/2019/E-84

SOLVED PAPER–06 ✦ ✦

SSC CGL TIER-II (CBE) EXAM, 13. 09.2019 English Language & Comprehension .............................................. CGL/II/2019/E-101 Important Questions based on Quantitative Abilities .................... CGL/II/2019/E-125

Solved Papers (2020) SOLVED PAPER–07 ✦

SSC CGL TIER-II (CBE) EXAM, 15.11.2020 Quantitative Abilities .................................................................... CGL/II/2019/E-129

SOLVED PAPER–08 SSC CGL TIER-II (CBE) EXAM, 15. 11.2020

CGL/II/2019/E-3

✦

English Language & Comprehension .............................................. CGL/II/2019/E-151

SOLVED PAPER–09 SSC CGL TIER-II (CBE) EXAM, 16.11.2020

✦

Quantitative Abilities .................................................................. CGL/II/2019/E-175

SOLVED PAPER–10 SSC CGL TIER-II (CBE) EXAM, 16.11.2020

✦

English Language & Comprehension .............................................. CGL/II/2019/E-197

SOLVED PAPER–11 SSC CGL TIER-II (CBE) EXAM, 18.11.2020

✦

Quantitative Abilities .................................................................... CGL/II/2019/E-221

SOLVED PAPER–12 SSC CGL TIER-II (CBE) EXAM-2021, (29.01.2022)

✦

English Language & Comprehension .............................................. CGL/II/2019/E-241

Solved Papers [2021(22)] SOLVED PAPER–13 SSC CGL TIER-II (CBE) EXAM-2021, (29.01.2022)

✦

Quantitative Abilities .................................................................. CGL/II/2019/E-265

SOLVED PAPER–14 SSC CGL TIER-II (CBE) EXAM-2021, (29.01.2022)

✦

English Language & Comprehension .............................................. CGL/II/2019/E-289

SOLVED PAPER–15 SSC CGL TIER-II (CBE) EXAM-2021, (03.02.2022)

✦

Quantitative Abilities .................................................................... CGL/II/2019/E-314

SOLVED PAPER–16 SSC CGL TIER-II (CBE) EXAM-2021, (03.02.2022)

✦

English Language & Comprehension ...................................... CGL/II/2019/E-337-360

CGL/II/2019/E-4

SOLVED PAPER–01

S E T

SOLVED PAPER–01

SOLVED PAPER

1

SSC CGL TIER-II (CBE) EXAM, 2018 Held on : 11.09.2019

QUANTITATIVE ABILITIES 1. The value of

150

275

first three numbers is 39 and that of next seven numbers is 49. The 11th number is two times the 12th number and 12th number is 3 less than the 13th number. What is the average of 11th and 13th number? (1) 54.5 (2) 57 (3) 56 (4) 55.5 6. If sinθ = 3 cosθ, 0° < θ < 90°, then the value of (2sin2θ + sec2θ + sinθ secθ + cosecθ) is : (1)

33 +10 3 6

(2)

19 +10 3 6

(3)

33 +10 3 3

175

200

200

150

250

250

300

Type-B 275

Type-A

200 225

Exports (in ` millions)

350

300 325

7 + 8 × 8 ÷ 8 of 8 + 8 ÷ 8 × 4 of 4 4 ÷ 4 of 4 + 4 × 4 ÷ 4 – 4 ÷ 4 of 2 is : (1) 7.8 (2) 4.6 (3) 8.7 (4) 6.4 Directions (2–4) : The bar graph shows the exports of cars of types A and B (in ` millions). Study the graph and answer the questions.

100 50 0

2014 2015 2016 2017 2018 Years

2. In which year, the exports of cars of type A was 10% more than the average exports (per year) of cars of type A over the given five years? (1) 2015 (2) 2017 (3) 2014 (4) 2016 3. What is the ratio of the total exports of cars of type A in 2014 and 2018 to the total exports of cars of type B in 2015 and 2016 ? (1) 11 : 10 (2) 10 : 9 (3) 5 : 4 (4) 3 : 2 4. The total exports of cars of type A from 2014 to 2017 is approximately what percentage less than the total exports of cars of type B from 2015 to 2018? (1) 31.3 (2) 30.4 (3) 14.3 (4) 23.8 5. The average of thirteen numbers is 47. The average of the

19 +10 3 3 7. If x8 –1442x4 + 1 = 0, then a (4)

possible value of

FG x – 1 IJ H xK

is :

(1) 5 (2) 8 (3) 4 (4) 6 8. The graphs of the equations 3x + y – 5 = 0 and 2x – y – 5 = 0 intersect at the point P (α, β). What is the value of (3α + β) ? (1) 4 (2) – 4 (3) 3 (4) 5 9. If

86 – 60 2 = a – b 2 , then what will be the value of a 2 + b 2 , correct to one decimal

place? (1) 8.4 (2) 8.2 (3) 7.8 (4) 7.2 10. The sides AB and AC of ∆ ABC are produced to P and Q respectively. The bisectors of ∠CBP and ∠BCQ meet at R. If

CGL/II/2019/E-5

the measure of ∠A is 44°, then what is the measure of

1 ∠BRC? 2 (1) 33° (2) 38° (3) 34° (4) 32° 11. In ∆ ABC, D is a point on side BC such that ∠ ADC = ∠ BAC. If CA = 12 cm, CB = 8 cm, then CD is equal to : (1) 12 cm. (2) 15 cm. (3) 18 cm. (4) 16 cm. 12. A person marks his goods x % above the cost price and allows a discount of 30% on the marked price. If his profit is 5%, then the value of x will be : (1) 50 (2) 60 (3) 45 (4) 35 13. If a2 + b2 + c2 + 96 = 8(a + b – 2c), then

ab – bc + ca is equal to :

(1) 6

(2) 2 2

(3) 4 (4) 2 3 14. A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube? (1) 19 (2) 28 (3) 23 (4) 21 15. The ratio of the volumes of two cylinders is x : y and the ratio of their diameters is a : b. What is the ratio of their heights? (1) xb : ya (2) xa : yb (3) xb2 : ya2 (4) xa2 : yb2 16. The value of the expression (cos6θ + sin6θ – 1) (tan2θ + cot2θ + 2) is : (1) 0 (2) – 1 (3) – 3 (4) 1 17. If A is 28% more than B and C is 25% less than the sum of A and B, then by what percent will C be more than A (correct to one decimal place)?

SOLVED PAPER–01 (1) 32.2% (2) 28% (3) 43% (4) 33.6% 18. A shopkeeper bought 120 quintals of wheat, 20% of it was sold at 25% loss. At what percent gain should he sell the rest to gain 25% on the whole transaction? (1) 36

1 2

(2) 40

SOLVED PAPER–01 23. A and B can do a piece of work in 6 days and 8 days, respectively. With the help of C, they completed the work in 3 days and earned 1,848. What was the share of C? (1) 231 (2) 924 (3) 462 (4) 693 24. If x + y + z = 11, x2 + y2 + z2 = 133, and x3 + y3 + z3 = 881, then the value of

1 (3) 37 2

(4) 35

19. The value of 22. 4 + 11.567 – 33.59 is : (1) 0. 32

(2) 0. 412

(3) 0.31 (4) 0.412 20. Anu sold an article for ` 480 at some profit. Had she sold it for ` 400, then there would have been a loss equal to onethird of the initial profit. What was the cost price of the article? (1) ` 450 (2) ` 430 (3) ` 425 (4) ` 420

4 21. In a school, of the number 9 of students are girls and the 3 of the num5 ber of boys are below 12 years rest are boys.

5 of the number 12 of girls are 12 years or above 12 years of age. If the number of students below 12 years of age is 480, then of age and

5 of the total number of stu18 dents in the school will be equal to : (1) 270 (2) 315 (3) 225 (4) 240

22.

(2sin A )(1 + sin A ) is equal to : 1 + sin A + cos A (1) 1 + sin A – cos A (2) 1 – sin A cos A (3) 1 + cos A – sin A (4) 1 + sin A cos A

3

xyz is :

(1) –6 (2) 6 (3) –8 (4) 8 Directions (25–27) : The given pie chart shows the breakup of total number of the employees of a company working in different offices (A, B, C, D and E). Study the pie chart and answer the questions. Total number of employees = 2400

E 72°

A 126°

D 90° C 54°

B 18°

25. What is the number of offices in which the number of employees of the company is between 350 and 650 ? (1) 1 (2) 4 (3) 2 (4) 3 26. If the percentage of male employees in office C is 20% and that of female employees in E is 40%, then what is the ratio of the number of female employees in C to that of female employees in E? (1) 3 : 2 (2) 5 : 4 (3) 2 : 3 (4) 3 : 8 27. If 40% of the number of employees in office A are shifted equally to office B and E, then what is the difference between the number of employees in B and that in C? (1) 72 (2) 120 (3) 82 (4) 130

CGL/II/2019/E-6

28. The number of students in a class is 75, out of which

1 % are boys and the rest 3 are girls. The average score in mathematics of the boys is 33

2 % more than that of the 3 girls. If the average score of all the students is 66, then the average score of the girls is : (1) 52 (2) 55 (3) 54 (4) 58 29. A shopkeeper allows 28% discount on the marked price of an article and still makes a profit of 20%. If he gains 30.80 on the sale of one article, then what will be the cost price of the article? (2) 145 (1) 164 (3) 160 (4) 154 30. In ∆ABC, ∠ A = 52° and 0 is the orthocentre of the triangle (BO and CO meet AC and AB at E and F respectively when produced). If the bisectors of ∠OBC and ∠OCB meet at P, then the measure of ∠BPC is : (1) 124° (2) 132° (3) 138° (4) 154° 31. Let a, b and c be the fractions such that a < b < c. If c is di66

vided by a, the result is

5 , 2

7 . 4

which exceeds b by

11 , then (c – a) 12 will be equal to : If a + b + c = 1

(1)

1 3

1 6 32. The value of (3)

(2)

2 3

(4)

1 2

b253g + b247g 3

3

25.3 × 25.3 – 624.91 + 24.7 × 24.7 is 50 × 10k, then the value of k is : (1) 3 (2) 4 (3) 2 (4) – 3

SOLVED PAPER–01

SOLVED PAPER–01

33. Travelling at 60 km/h, a person reaches his destination in a certain time. He covers 60%

2 of his journey in th of the 5 time. At what speed (in km/h) should he travel to cover the remaining journey so that he reaches the destination right on time? (1) 40 (2) 48 (3) 42 (4) 36 34. Study the graph and answer the question that follows. 70

65 60

Number of Workers

60

55

50

45

40

35 30

30 20 10

0 400450500550600650 700 Daily wages (in ) What is the ratio of the total number of workers whose daily wages are less than 500 to the total number of workers whose daily wages are 600 and above ? (1) 5 : 6 (2) 6 : 7 (3) 3 : 4 (4) 15 : 11 35. The value of

bcos9°+sin81°gbsec 9°+cosec81°g sin 56° sec34°+cos25° cosec65° is : 1 2

(1) 4

(2)

(3) 2

1 (4) 4

36. If

e

j

2 + 5 – 3 × k = – 12,

then what will be the value of k? (1) (2)

(3)

e

2 + 5 – 3 2+ 5

je

j

(4)

e

2+ 5+ 3 2– 5

je

j

37. If θ lies in the first quadrant

1 , then the 2 2 value of (tan 2θ + sin23θ) is : (1)

7 2

(2) 3

(3) 4

(4)

4 3

38. A sum of 18,000 is lent at 10% p.a. compound interest, compounded annually. What is the difference between the compound interest for 3rd year and 4th year ? (1) 220.60 (2) 217.80 (3) 221.80 (4) 215.40 39. What is the value of cosec (65° + θ) – sec (25° – θ) + tan220° – cosec270°? (1) 0 (2) 1 (3) 2 (4) – 1 40. The ratio of the income of A to that of B is 5 : 7. A and B save 4,000 and 5,000 respectively. If the expenditure of A

2 % of the ex3 penditure of B, then the total income of A and B is : (1) 25,200 (2) 24,000 (3) 26,400 (4) 28,800 41. In ∆ ABC, AB = 6 cm, AC = 8 cm, and BC = 9 cm. The length of median AD is : is equal to 66

(1)

317 cm 2

(2)

119 cm 2

(3)

313 cm 2

je

2 + 5 + 3 2 – 10

j

(4)

115 cm 2

CGL/II/2019/E-7

the value of

6 x + 7y will be :

(1) 6

(2)

(3)

and cos2θ – sin2θ =

2+ 5+ 3

e

42. If a nine-digit number 389x 6378y is divisible by 72, then

(4) 8

46

b1 + cos θg + sin ecosec θ – 1j sin 2

43.

13

2

2

θ

2

θ

=?

(1) cosθ(1 + sinθ) (2) 2cosθ(1 + secθ) (3) secθ(1 + sinθ) (4) 2secθ(1 + secθ) 44. When 12, 16, 18, 20 and 25 divide the least number x, the remainder in each case is 4 but x is divisible by 7. What is the digit at the thousand’s place in x ? (1) 5 (2) 8 (3) 4 (4) 3 45. If (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 27, then what will be the value

1 1 1 : : ? a b c (1) 3 : 6 : 4 (2) 3 : 2 : 4 (3) 4 : 3 : 6 (4) 3 : 4 : 2 46. PQRS is a cyclic quadrilateral in which PQ = 14.4 cm. QR = 12.8 cm and SR = 9.6 cm. If PR bisects QS, what is the length of PS? (1) 15.8 cm (2) 16.4 cm (3) 13.6 cm (4) 19.2 cm 47. In what ratio, sugar costing 60 per kg be mixed with sugar costing 42 per kg such that by selling the mixture at 56 per kg there is a gain of 12%? (1) 5 : 6 (2) 8 : 9 (3) 4 : 5 (4) 5 : 7 48. When an article is sold for 355, there is a loss of 29%. To gain 21%, it should be sold for : (1) 629.20 (2) 580.80 (3) 605 (4) 635 of

49.

FG 1 – tan θ IJ H 1 – cot θ K (1) cosec2θ (3) sin2θ

2

+1 = ? (2) sec2θ (4) cos2θ

SOLVED PAPER–01 50.

SOLVED PAPER–01

cot θ + cos θ is equal to : cot θ – cos θ

(1) secθ + tanθ (2) 1 + secθ tanθ (3) 1 – secθ tanθ (4) secθ – tanθ 51. If 5 sinθ – 4 cosθ = 0, 0° < θ < 90°, then the value of 5 sin θ – 2 cos θ is : 5 sin θ + 3 cos θ

(1)

3 8

(2)

3 7

2 5 (4) 7 8 52. If the radius of the base of a cone is doubled, and the volume of the new cone is three times the volume of the original cone, then what will be the ratio of the height of the original cone to that of the new cone? (1) 1 : 3 (2) 4 : 3 (3) 2 : 9 (4) 9 : 4 53. Abhi rows upstream a distance of 28 km in 4 hours and rows downstream a distance of 50 km in 2 hours. To row a distance of 44.8 km in still water, he will take : (1) 2.8 hours (2) 3.2 hours (3) 2.4 hours (4) 2.2 hours 54. A sum of 8,400 amounts to 11,046 at 8.75% per annum simple interest in certain time. What is the simple interest on the sum of 9,600 at the same rate for the same time? (1) 2,990 (2) 3,012 (3) 2,686 (4) 3,024 55. If the diameter of the base of a cone is 42 cm and its curved surface area is 2310 cm2, then what will be its volume (in cm3)? (1) 25872 (2) 19404 (3) 12936 (4) 38808 56. If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes? (3)

(1) 65 : 72 (2) 37 : 48 (3) 24 : 35 (4) 32 : 39 57. When x is added to each of 2, 3, 30 and 35, then the numbers obtained in this order, are in proportion. What is the mean proportional between (x + 7) and (x – 2)? (1) 7 (2) 4 (3) 6 (4) 5 58. The ratio of investment by A to that by B in a business is 14 : 15 and the ratio of their respective profits at the end of a year is 2 : 5. If A invested the money for 3 months, then for how much time (in months) B invested his money? (1) 7 (2) 6 (3) 5 (4) 9 59. In ∆ABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then BD is equal to : (1)

16 cm 3

(2)

15 cm 4

14 17 cm (4) cm 3 4 60. The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1731.6 cm3, then the height (in cm) of the prism will be : (1) 15.6 (2) 15.2 (3) 14.8 (4) 14.2 61. Raghav spends 80% of his income. If his income increases by 12% and the savings decrease by 10%, then what will be the percentage increase in his expenditure? (1) 20.5 (2) 16 (3) 17.5 (4) 22 62. The lateral surface area of a cylinder is 352 cm2. If its height is 7 cm, then its volume (in cm3) is : (3)

FG Take π = 22 IJ H 7 K (1) 1408 (3) 1243

63. What will be the compound interest on a sum of 31,250 for 2 years at 12% p.a., if the interest is compounded 8monthly? (1) 8,106 (2) 8,116 (3) 8,016 (4) 8,156 64. When 7897, 8110 and 8536 are divided by the greatest number x, then the remainder, in each case is the same. The sum of the digits of x is : (1) 14 (2) 5 (3) 9 (4) 6 65. The ratios of copper to zinc in alloys A and B are 3 : 4 and 5 : 9 respectively. A and B are taken in the ratio 2 : 3 and melted to form a new alloy C. What is the ratio of copper to zinc in C? (1) 8 : 13 (2) 3 : 5 (3) 9 : 11 (4) 27 : 43 66. In ∆ABC, D and E are the points on sides AB and BC respectively such that DE || AC. If AD : DB = 5 : 3, then what is the ratio of the area of ∆BDE to that of the trapezium ACED? (1) 4 : 25 (2) 9 : 55 (3) 9 : 64 (4) 1 : 6 67. One year ago, the ratio of the age (in years) of A to that of B was 4 : 3. The ratio of their respective ages, 3 years from now, will be 6 : 5. What will be the ratio of respective ages of A and B, 9 years from now? (1) 7 : 6 (2) 10 : 9 (3) 9 : 8 (4) 8 : 7 68. The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the radius of the circle circumscribing the triangle? (1) 31.5 cm (2) 31 cm (3) 30 cm (4) 30.5 cm 5,000 is divided 69. A sum of into two parts such that the simple interest on the first part

1 2 years at 6 % p.a. is 5 3 double the simple interest on

for 4

3 years 4 at 40% p.a. What is the difference between the two parts? the second part for 2

(2) 1078 (4) 891

CGL/II/2019/E-8

SOLVED PAPER–01 (1) (3) 70. If x =

680 560

1+

SOLVED PAPER–01

(2) (4)

600 620

3 3 , then – 1– 2 2

the value of

2–x 2+x

will be

closest to : (1) 0.17 (2) 0.12 (3) 1.4 (4) 1.2 71. Pipes A, B and C can fill a tank in 30 hours, 40 hours and 60 hours respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m. and 10 a.m. respectively on the same day. When will the tank be full? (1) 10.00 p.m. (2) 10.20 p.m. (3) 9.20 p.m. (4) 9.40 p.m. 72. In a trapezium ABCD, DC || AB, AB = 12 cm and DC = 7.2 cm. What is the length of the line segment joining the midpoints of its diagonals? (1) 2.6 cm (2) 4.8 cm (3) 2.4 cm (4) 3.6 cm 73. A number is first increased by 16% and then increased by 14%. The number, so obtained, is now decreased by 30%. What is the net increase or decrease percent in the original number (nearest to an integer)? (1) 6% increase (2) 7% decrease (3) No increase or decrease (4) 9% decrease 74. Radha marks her goods 25% above the cost price. She sells 35% of goods at the marked price, 40% at 15% discount and the remaining at 20% discount. What is her overall percentage gain? (1) 11.25 (2) 10 (3) 11.75 (4) 12.75 75. Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. If PC = 18 cm, and BP = 15 cm, then AB is equal to :

(1) 5.8 cm (2) 6.2 cm (3) 6.6 cm (4) 8.5 cm 76. One of the factors of (82k + 52k), where k is an odd number, is : (1) 86 (2) 88 (3) 84 (4) 89 77. The internal and external radii of a hollow hemispherical vessel are 6 cm and 7 cm respectively. What is the total surface area (in cm2) of the vessel? (1) 183 π (2) 189 π (3) 177 π (4) 174 π 78. When the price of an item was reduced by 25%, then its sale was increased by x%. If there is an increase of 20% in the receipt of the revenue, then the value of x will be : (1) 50 (2) 60 (3) 45 (4) 75 79. In a constituency, 55% of the total number of voters are males and the rest are females. If 40% of the males are illiterate and 40% of the females are literate, then by what percent is the number of literate males more than that of illiterate females? (1) 22

8 11

(2) 18

2 9

2 2 (4) 18 9 11 80. From the top of a tower, the angles of depression of two objects on the ground on the same side of it, are observed to be 60° and 30° respectively and the distance between the (3) 22

objects is 400 3 metre. The height (in metre) of the tower is : (1) 800

(2) 800 3

(3) 600

(4) 600 3 81. A train travelling at the speed of x km/h crossed a 200 metre long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x ?

CGL/II/2019/E-9

(1) 50 (2) 54 (3) 56 (4) 60 82. Let x = (633) 24 – (277) 38 + (266)54. What is the unit’s digit of x ? (1) 7 (2) 6 (3) 4 (4) 8 83. Three solid metallic spheres whose radii are 1 cm, x cm and 8 cm, are melted and recast into a single solid sphere of diameter 18 cm. The surface area (in cm2) of the sphere with radius x cm is : (1) 144 π (2) 72 π (3) 64 π (4) 100 π

FG H

84. The value of 2

1

1 ÷ 9

6 1 2 of 4 ÷ 7 5 3

FG 3 × 2 2 of 1 ÷ 1 IJ H 4 3 2 4K

(1) 5

IJ × K

is :

(2) 8

1 1 (4) (3) 8 5 85. An article is sold at a certain 1 % of 3 this price, there is a loss of price. If it is sold at 33

1 % . What is the percent3 age profit when it is sold at 60% of the original selling price? (1) 20 (2) 30 33

1 1 (4) 17 3 3 86. If a3 + b3 = 218 and a + b = 2, then the value of ab is : (1) 34 (2) – 35 (3) – 31 (4) 32 87. In ∆ABC, ∠A = 58°. If I is the incentre of the triangle, then the measure of ∠BIC is : (1) 109° (2) 123° (3) 112° (4) 119° (3) 33

e

88. If 2 2 x 3 – 3 3y 3

e Ax

2

2 x – 3y

j

j

+ By 2 + Cxy , then the

value of (1) 11 (3) 19

(A2

+

B2

– C2) is : (2) 7 (4) 10

SOLVED PAPER–01

SOLVED PAPER–01

89. A circle is inscribed in ∆ABC, touching AB, BC and AC at the points P, Q and R respectively. If AB – BC = 4 cm, AB – AC = 2 cm and the perimeter of ∆ABC = 32 cm, then (PB + AR) is equal to : (1) 12 cm (2) 13 cm

33 38 cm (4) cm 5 3 90. If each interior angle of a reg(3)

FG H

ular polygon is 128

IJ K

4 ° , then 7

what is the sum of the number of its diagonals and the number of its sides? (1) 15 (2) 19 (3) 17 (4) 21 91. If the radius of a sphere is increased by 4 cm, its surface area is increased by 464 π cm2. What is the volume (in cm3) of the original sphere? (1) (2)

15625 π 6

11979 π (3) 2 15625 π 8 92. The sum of the digits of a two(4)

1 of the num7 ber. The unit’s digit is 4 less than the ten’s digit. If the number obtained on reversing its digits is divided by 7, the remainder will be : (1) 4 (2) 5 (3) 1 (4) 6 93. The graph of the equation x – 7y = – 42, intersects the y-axis at P (α, β) and the graph of 6x + y – 15 = 0, intersects the x-axis at Q (γ, δ). What is the value of (α + β + γ + δ) ? digit number is

(3)

9 2

1 hours and 8 hours 8 respectively. If the speed of B is 28 km/h, then the speed (in km/h) of A is : (1) 40 (2) 42 (3) 32 (4) 36 97. If the radius of a right circular cylinder is decreased by 20% while its height is increased by 40%, then the percentage change in its volume will be : (1) 1.04% increase (2) 10.4% decrease (3) No increase or decrease (4) 10.4% increase 98. The volume of a right pyramid neys in 6

35937 π 8

17 (1) 2

94. In quadrilateral ABCD, the bisectors of ∠A and ∠B meet at O and ∠AOB = 64°. (∠C + ∠D) is equal to : (1) 136° (2) 128° (3) 116° (4) 148° 95. ‘A’ started a business with a capital of 54,000 and admitted ‘B’ and ‘C’ after 4 months and 6 months, respectively. At the end of the year, the profit was divided in the ratio 1 : 4 : 5. What is the difference between the capitals invested by ‘B’ and ‘C’? (1) 1,08,000 (2) 1,62,000 (3) 2,16,000 (4) 3,24,000 96. A and B started their journeys from X to Y and Y to X, respectively. After crossing each other, A and B completed the remaining parts of their jour-

(2) 6 (4) 5

is 45 3 cm3 and its base is an equilateral triangle with side 6 cm. What is the height (in cm) of the pyramid? (1) 15 (2) 18 (3) 12 (4) 20 99. A certain number of persons can complete a work in 34 days working 9 hours a day. If the number of persons is decreased by 40%, then how many hours a day should the remaining persons work to complete the work in 51 days?

CGL/II/2019/E-10

(1) 9 (2) 8 (3) 12 (4) 10 100. To do a certain work, the ratio of efficiency of A to that of B is 3 : 7. Working together, they

1 2 days. They work together for 8 days. 60% of the remaining work will be completed by A alone in : can complete the work in 10

(1) 5

1 days (2) 5 days 2

(3) 6

1 days (4) 4 days 2

1. (4)

2. (4)

3. (2)

4. (4)

5. (2)

6. (1)

7. (4)

8. (4)

9. (3) 10. (3)

11. (3)

12. (1)

13. (3) 14. (4)

15. (3)

16. (3)

17. (4) 18. (3)

19. (4)

20. (4)

21. (3) 22. (1)

23. (1)

24. (1)

25. (4) 26. (1)

27. (1)

28. (3)

29. (4) 30. (4)

31. (4)

32. (1)

33. (1) 34. (1)

35. (3)

36. (2)

37. (3) 38. (2)

39. (4)

40. (2)

41. (2) 42. (4)

43. (4)

44. (2)

45. (3) 46. (4)

47. (3)

48. (3)

49. (2) 50. (1)

51. (3)

52. (2)

53. (1) 54. (4)

55. (3)

56. (1)

57. (3) 58. (1)

59. (3)

60. (3)

61. (3) 62. (1)

63. (2)

64. (4)

65. (4) 66. (2)

67. (3)

68. (4)

69. (2) 70. (1)

71. (3)

72. (3)

73. (2) 74. (1)

75. (3)

76. (4)

77. (1) 78. (2)

79. (3)

80. (3)

81. (4) 82. (4)

83. (1)

84. (1)

85. (1) 86. (2)

87. (4)

88. (2)

89. (4) 90. (4)

91. (1)

92. (4)

93. (1) 94. (2)

95. (3)

96. (3)

97. (2) 98. (1)

99. (4) 100. (2)

SOLVED PAPER–01

SOLVED PAPER–01

1. (4) Expression =

7 + 8 × 8 ÷ (8 × 8) + 8 ÷ 8 × (4 × 4) 1 4 ÷ ( 4 × 4) + 4 × 4 × – 4 ÷ ( 4 × 2) 4 [By BODMAS rule] 8×8 1 + 8 × × 16 8×8 8 1 4 ÷ 16 + 4 − 4 × 8

7+

=

=

7 + 1 + 16 24 = 1 1 1 + 16 − 2 +4− 4 2 4

24 × 4 32 = 15 5 = 6.4 2. (4) Average exports of type-A cars

=

= Rs. FG 200 + 150 + 275 + 175 + 300 IJ millions

H

5

K

= Rs. 1100 millions 5 = 220 millions ∴ 110% of Rs. 220 millions 220 × 110 = Rs.242 millions 100 Exports of type –A cars in 2016 = Rs. 275 millions 3. (2) Required ratio = (200 + 300) : (250 + 200) = 500 : 450 = 10 : 9 4. (4) Total exports of type-A cars from 2014 to 2017 = Rs.(200 + 150 + 275 + 175) millions = Rs. 800 millions Total exports of type –B cars from 2015 to 2018 = Rs.(250 + 200 + 275 + 325) millions = Rs.1050 millions ∴ Required per cent

2x + x + x + 3 = 13 × 47 – 3 × 39 – 7 × 49 ⇒ 4x + 3 = 611 – 117 – 343 = 151 ⇒ 4x = 151 – 3 = 148

=

FG 1050 – 800 IJ × 100 H 1050 K

2500 = 23.8% 105 5. (2) 12th number = x ∴ 11th number = 2x 13th number = x + 3 According to the question,

=

3

3 = tan 60° ⇒ θ = 60° ∴ 2sin2θ + sec2θ + sinθ.secθ + cosecθ = 2sin260° + sec260° + sin60°. sec60° + cosec60°

=

=

=

=

2

⇒

1 x

IJ K

2

+ 2.x.

= 38 –2 = 36

86 – 2 × 30 2 = a – b 2 86 – 2 × 6 × 5 2 = a – b 2

36 + 50 – 2 × 6 × 5 2 = a – b 2 (6)2 + (5 2 )2 − 2 × 6 × 5 2

=a–b 2

10 3 + 33 = 6

⇒

7. (4) x8 –1442x4 + 1 = 0 ⇒ x8 + 1 = 1442x4 Dividing both sides by x4,

FG H

FG H

⇒

10 3 + 11 3 × 3 6

2 ⇒ x +

IJ K

⇒

3

2 3× 3

1

1 x

⇒

2 3

x4

FG H

2

⇒ x−

1444 = 38

86 – 60 2 = a – b 2

3 3 +8 3 +2×3+4

x4 +

=

10 =2 5 From equation (i), 3×2+β–5=0 ⇒ β + 1 = 0 ⇒ β = –1 ∴ 3α + β = 3 × 2 –1 = 5 9. (3) Here,

3 2 +4+ 3+ 2 3

e10 + 11 3 j ×

1

⇒α=

2 3 ×2+ 3 2

+ (2)2 +

= 1442 + 2 = 1444

1 = 36 = ±6 x 8. (4) The graphs of equations 3x + y – 5 = 0 and 2x – y – 5 = 0 intersect at point P (α, β). ∴ 3α + β – 5 = 0 ......(i) 2α – β – 5 = 0 .....(ii) By adding equations (i) and (ii), 3α + 2α – 10 = 0 ⇒ 5α = 10

⇒ tanθ =

F 3I GH 2 JK

2

⇒x–

6. (1) sinθ = 3 cosθ

=2×

IJ K

x2

⇒ x−

3 × 37 + 3 114 = = = 57 2 2

sin θ = cos θ

x

2

1 = 38 x 2 2 2 [ Q a + b = (a – b) + 2ab]

2x + x + 3 3x + 3 = 2 2

⇒

1

⇒ x2 +

148 ⇒x= = 37 4 ∴ Average of 11th and 13th number

=

=

FG H

2 ⇒ x +

2

e6 − 5 2 j [Q

a2

+

b2

e

= a −b 2 – 2ab = (a – b)2]

j

⇒ ± 6 −5 2 = a −b 2 ⇒ a = ± 6, b = ± 5

= 1442 ∴ 1 x

2

IJ K

2

− 2 × x2 ×

1 x2

= 1442

CGL/II/2019/E-11

a 2 + b2 =

= 62 + 52 = =

61 = 7.8

b –a g + b –b g 2

36 + 25

2

SOLVED PAPER–01

SOLVED PAPER–01 ⇒ a – 4 = 0; b – 4 = 0; c + 8 = 0 [If x2 + y2 + z2 = 0, then x = y = z = 0] ⇒ a = 4; b = 4; c = –8

10. (3) A

B

C

R

P

∠BRC = 90° –

Q

∠A 2

44° = 90° – = 90° – 22° = 68° 2 1 ∠BRC = 68° ÷ 2 = 34° 2

∴

A

11. (3)

∴

ab − bc + ca

=

4 × 4 – 4 × (–8) + (–8) × 4

= 16 + 32 − 32 = 16 = 4 14. (4) Let the edge of cube be a units. ∴ Radius of the base of cylinder of maximum volume a units 2 Height of cylinder = a units Volume of cube = a3 cu.units Volume of cylinder

=

Fπ × a × aI GH 4 JK F 22 × a IJ = GH K 7×4

11a 3 cu.units 14 Volume of rest material 3 = a −

12 CD = 8 12

=

30 x = 5, 100 where y = –30 ⇒ x – 0.3x = 35 ⇒ 0.7x = 35

∴ x – 30 –

35 350 = = 50 0.7 7 2 2 2 13. (3) a + b + c + 96 = 8a + 8b – 16c ⇒ a2 + b2 + c2 + 96 – 8a – 8b + 16c = 0 ⇒ a2 – 8a + 16 + b2 – 8b + 16 + c2 + 16c + 64 = 0 ⇒ (a – 4)2 + (b – 4)2 + (c + 8)2 = 0

⇒x=

=–

3a 3 14a 3

× 100

150 ≈ 21 7

V1 πr 2h = 12 1 15. (3) V2 πr2 h 2

⇒

r12h1

=

r22h 2

FG a IJ h H 2K ⇒ FG b IJ h H 2K

x y

2

1

2

=

x y

2

⇒

⇒

a 2h1 2

b h2

=

2

F sin θ + cos θ I GH cos θ. sin θ JK 2

= –3 sin2θ.cos2θ

2

2

2

3sin 2θ.cos 2 θ

= –3 cos 2θ. sin 2θ [ Q sin2θ + cos2θ = 1] 17. (4) Let, B = 100 ∴ A = 128

=

11a 3 3 3 = a cu. units 14 14

⇒

FG x + y + xy IJ % H 100 K

2

75 100

228 × 3 = 171 4 ∴ Required percent

=

Required percent =

=

FG 1 + 1 IJ H cos θ sin θ K

=

cu.units

AC CD = CB AC

12 × 12 = 18 cm. 8 12. (1) Percentage effect

= (1–3sin2θ.cos2θ–1)

and, C = (100 + 128) ×

cu.units

∴

⇒ CD =

= + sin2θ)3 –3cos2θ.sin2θ (cos2θ + sin2θ) –1} (sec2θ + cosec2θ) [ Q a3 + b3 = (a + b)3 – 3ab (a + b); sec2θ – tan2θ = cosec2θ – cot2θ = 1]

2

=

3

B D C In ∆ABC and ∆ACD, ∠BAC = ∠ADC. ∠C is common. By AA-similarity theorem, ∆DAC ~ ∆ACB

{(cos2θ

43 × 100 1075 = = 33.59 128 32 ≈ 33.6% 18. (3) C.P. of 120 quintals of wheat = Rs. 120 (let). S.P. of 20% of 120 i.e. 24 quintals of wheat

=

= 24 ×

h1 xb 2 = h 2 ya 2

16. (3) Expression = (cos6θ + sin6θ–1) (tan2θ + 1 + cot2θ + 1)

CGL/II/2019/E-12

75 = Rs.18 100

Total S.P. =

120 × 125 100

= Rs.150 ∴ S.P. of (150–24) = 96 quintals of wheat = 150 – 18 = Rs.132 Required profit per cent =

x y

FG 171 − 128 IJ × 100 H 128 K

FG 132 − 96 IJ ×100 = 36 × 100 H 96 K 96

75 1 % = 37 % 2 2 19. (4) Expression

=

= 22. 4 + 11.567 − 33.59 = 22 + 0. 4 + 11 + 0.567 − 33 − 0.59 = (22 + 11 − 33) + 0. 4 + 0.567 – 0.59

SOLVED PAPER–01 =

4 567 − 5 59 − 5 + − 9 990 90

=

4 562 54 + − 9 990 90

=

440 + 562 − 594 408 = 990 990

=

SOLVED PAPER–01 7 4x 7x × = 12 9 27 According to the question,

=

x 7x + = 480 3 27

412 − 4 = 0.412 990

⇒

9x + 7 x = 480 27

⇒

16 x = 480 27

OR ⇒x=

Expression . = 22. 4 + 11567 − 33.59

= 22.444 + 11.567 − 33.599 = 0.444 + 0.567 − 0.599 = 0.412 [Maximum recurring places = 2; non-recurring place = 1] 20. (4) Case I, Let the profit be Rs. x. ∴ C.P. of article = Rs. (480–x) Case II, x 3 ∴ C.P. of article

5x 5 × 810 = = 225 18 18 22. (1) Expression 2sinA(1 + sinA) 1 + sinA + cosA Rationalising the denominator,

2sinA(1 + sinA)(1 + sinA - cosA) = (1 + sinA + cosA)(1 + sinA - cosA) 2sinA(1 + sinA)(1+ sinA - cosA)

x = Rs.(400 + ) 3

=

⇒x+

x = 480 − 400 3

4x 80 × 3 = 80 ⇒ x = 3 4 = Rs.60 ∴ C.P. of article = Rs. (480 – 60) = Rs. 420 21. (3) Let total students in the school be x.

⇒

∴ Girls =

4x 9

5x 9 Boys of age less than 12 years

Boys =

x 3 5x × = 3 5 9 Girls of age less than 12 years.

=

F 5 IJ × 4x = GH1 − 12 K 9

=

= =

(1 + sinA)2 − (cosA)2 2sinA(1 + sinA)(1 + sinA – cosA) 1 + sin 2 A + 2sinA – cos 2 A 2sinA(1 + sinA)(1 + sinA – cosA) sin 2 A + sin 2 A + 2sinA ( Q 1 – cos2A = sin2A) 2sinA(1 + sinA)(1 + sinA − cosA) 2sinA + 2sin 2 A

= 1 + sinA – cosA 23. (1) (A + B)’s 1 day’s work 1 1 4 +3 7 + = = 6 8 24 24

(A + B + C)’s 1 day’s work = ∴ C’s 1 day’s work 1 7 8−7 1 − = = 3 24 24 24 ∴ Ratio of their shares

=

1 1 1 : : = =4:3:1 6 8 24 Sum of the terms of ratio =4+3+1=8

CGL/II/2019/E-13

⇒ xyz =

−648 = –216 3

∴ 3 xyz = 3 −216 = –6 25. (4) When employees are 350, corresponding angle 360 × 350 = 52.5 2400 When employees are 650, corresponding angle

=

360 × 650 = 97.5 2400 ∴ Required offices ⇒ C, D and E 26. (1) Total employees in office C

=

2400 × 54 = 360 360 ∴ Female employees

=

2sinA(1 + sinA)(1 + sinA − cosA) 2sinA (1 + sinA)

=

FG 1 × 1848IJ H8 K

= Rs. 231 24. (1) x3 + y3 + z3 –3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)....(i) Here, x + y + z = 11; x2 + y2 + z2 = 133 ∴ (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx ⇒ (11)2 = 133 + 2 (xy + yz + zx) ⇒ 121 = 133 + 2 (xy + yz + zx) ⇒ 2 (xy + yz + zx) = 121 – 133 = –12 ⇒ xy + yz + zx = –6 From equation (i), 881 – 3xyz = 11(133 – (–6)) ⇒ 881 – 3xyz = 11 × 139 = 1529 ⇒ 3xyz = 881 – 1529 = –648

=

=

x = 480 − x 3

480 × 27 = 810 16

∴

Loss = Rs.

∴ 400 +

∴ C’s share = Rs.

4 = 288 5 Total employees in office E

= 360 ×

2400 × 72 = 480 360 ∴ Female employees

= 1 3

480 × 40 = 192 100 Required ratio = 288 : 192 =3:2 27. (1) Total employees in office A

=

=

2400 × 126 = 840 360

40% of 840 =

840 × 40 100

SOLVED PAPER–01

SOLVED PAPER–01

= 336 2400 × 18 Office B ⇒ 360 = 120

Office C ⇒

2400 × 54 360

= 360 Required difference

F 336 + 120IJ = 360 – GH K 2 = 360 – (168 + 120) = 360 – 288 = 72 28. (3) Number of students in the 100 = 25 300 Number of girls = 75 – 25 = 50 Average marks of girls = x ∴ Average marks of boys

In ∆PBC, ∠BPC = 180° – ∠PBC – ∠PCB = 180° – 26° = 154° 31. (4) Here, a < b < c. 5 c = Again, a 2 ⇒c:a=5:2

∴a+b+c=

3 23 + 5x = 4 12

⇒ 7x =

23 3 23 − 9 − = 12 4 12

FG H

= 100 +

IJ K

200 % of x 3

500 5x = 3 300 According to the question,

= x×

50x +

5x ×25 = 66 × 75 3

150x + 125x = 66 × 75 3 ⇒ 275x = 66 × 75 × 3

=

66 × 75 × 3 ⇒x= = 54 275 29. (4) 20% of C.P. = Rs. 30.80

∴ C.P. =

7 1 = 6×7 6 ∴ c – a = 5x – 2x = 3x 1 1 = 6 2 32. (1) Let, 25.3 = x ∴ 253 = 10x and 24.7 = y ∴ 247 = 10y ∴ Expression

= 3×

=

F

E O P C

The point of intersection of the three altitudes of the triangle is called the orthocentre. ∠BOC = 180° – ∠A = 180° – 52° = 128° In ∆OBC, ∴ ∠OBC + ∠OCB = 180° – 128° = 52° 52 ∴ ∠PBC + ∠PCB = = 26° 2

=

Distance Time

bcos 9°+ cos 9°gbsec 9°+ sec 9°g sin 56° . cosec 56°+ cos 25° .sec 25°

=

3

x × x – xy + y × y

[ Q 25.3 × 24.7 = 624.91]

=

A

B

=

6 hours 5

= 40 kmph 34. (1) Required ratio = (30 + 45) : (55 + 35) = 75 : 90 = 5 : 6 35. (3) sin81° = cos (90° – 81°) = cos9° cosec 81° = sec(90° – 81°) = sec9° sec 34° = cosec (90°–34°) = cosec 56° cosec 65° = sec (90° – 65°) = sec 25° ∴ Expression

b10x g + b10y g 3

30.80 × 100 = Rs. 154 20

30. (4)

14 7 = 12 6

⇒x=

⇒

=

hours

F 48 I G J = G 6 J kmph GH 5 JK F 48 × 5 IJ kmph = G H 6 K

23 12

⇒ 2x +

class = 75 ×

FG 3 × 2IJ H5 K

∴ Required speed =

5 7 10 − 7 3 − = = 2 4 4 4

and, b =

=

1000 (x 3 + y3)

4 =2 2 [ Q cosθ.secθ = 1; sinθ.cosecθ = 1]

=

36. (2)

x 2 − xy + y2 1000( x + y )( x 2 − xy + y 2 )

= 1000 (25.3 + 24.7) = 50000 = 50 × 103 ∴ 50 × 103 = 50 × 10k ⇒k=3 33. (1) Let, total distance = 120 km. 120 60

CGL/II/2019/E-14

j

2 + 5 − 3 × k = –12 −12 2+ 5− 3

e

−12 2 + 5 + 3 =

e

2+ 5− 3

je

j

2+ 5+ 3

j

Rationalising the denominator,

e

−12 2 + 5 + 3 =

= 2 hours Again, 60% of 120km 120 × 60 = = 72 km. 100 Remaining distance = 120 – 72 = 48 km. Remaining time

e

⇒k=

x 2 − xy + y 2

∴ Required time =

2 cos 9° .2 sec 9° 1 +1

e

2+ 5

e

−12

=

j

2

j − e 3j

2+ 5+ 3

j

2 + 5 + 2 10 − 3

e

−12

=

2

2+ 5+ 3 4 + 2 10

j

SOLVED PAPER–01

=

SOLVED PAPER–01

e

−12 2 + 5 + 3

e

2 2 + 10 −6 =

e

j

j je

2 + 5 + 3 2 − 10

e2 +

je

10 2 − 10

j

j

Rationalising the denominator,

−6 = =

e

je

2 + 5 + 3 2 − 10

j

4 − 10

e

je

2 + 5 + 3 2 − 10

j

1 37. (3) cos2θ – sin2θ = 2

⇒ cos2θ – (1–cos2θ) = ⇒ 2cos2θ – 1 = ⇒

2cos2θ

1 2

1 2

1 3 =1+ = 2 2 3 4

⇒ cosθ =

3 = cos30° [ Q 0°< θ 2