**SSC CGL – MATHS**

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**Tier-2 (13 Sept 2019)**

Instructions For the following questions answer them individually

Q.1 N solid metallic spherical balls are melted and recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is:

A 30

B 27

C 24

D 36

Answer: B

Q.2 If x is the remainder when 3^{61284} is divided by 5 and y is the remainder when 4^{96} is divided by 6, then what is the value of (2x – y)?

A -4

B 4

C -2

D 2

Answer: C

Q.3 What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12 and the x-axis?

A 2

B 3

C 4

D 6

Answer: B

Q.4 The value of √(28+10√3) – √(7-4√3)is closest to:

A 7.2

B 6.1

C 6.5

D 5.8

Answer: C

Q.5 If secθ + tanθ = p, ( p > 1 ) then ^{cosecθ+1}/_{cosecθ-1} =?

A ^{p+1}/_{p-1}

B P^{2}

C ^{p-1}/_{p+1}

D 2p^{2}

Answer: B

Q.6 The value cosec(67^{0} + θ) − sec(23^{0} − θ) + cos15^{0} cos35^{0} cos55^{0} cos60^{0} cos75^{0} is:

A 2

B 0

C 1

D ½

Answer: D

Q.7 35% of goods were sold at a profit of 65%, while the remaining were sold at x% loss. If the overall loss is 12%, then what is the value of x ? (correct to one decimal place)

A 51.8

B 50.6

C 53.5

D 52.4

Answer: C

Q.8 In a circle with centre O, ABCD is cyclic quadrilateral and AC is the diameter. Chords AB and CD are produced to meet at E. If ∠CAE = 34^{0} and ∠E = 30^{0}, then ∠CBD is equal to:

A 36^{0}

B 26^{0}

C 24^{0}

D 34^{0}

Answer: B

Q.9 ab(a − b) + bc(b − c) + ca(c − a) is equal to:

A (a + b)(b − c)(c − a)

B (a − b)(b + c)(c − a)

C (a − b)(b − c)(c − a)

D (b − a)(b − c)(c − a)

Answer: D

Q.10 The radius of the base of a right circular cylinder is increased by 20%. By what percent should its height be reduced so that its volume remains the same as before?

A 25

B 30 ^{2}/_{9}

C 30 ^{5}/_{9}

D 28

Answer: C

Q.11 A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in:

A 110 days

B 88 days

C 84 days

D 90 days

Answer: A

Q.12 If 2cos^{2} θ + 3sinθ = 3 , where 0^{0} < θ < 90^{∘} , then what is the value of sin^{2} 2θ + cos^{2} θ + tan^{2} 2θ + cosec^{2} 2θ ?

A 35/12

B 29/3

C 35/6

D 29 6

Answer: C

Q.13 The radius and the height of a right circular cone are in the ratio 5 : 12. Its curved surface area is 816.4 cm². What is the volume (in cm³ ) of the cone? (Take π = 3.14)

A 2512

B 1256

C 3140

D 628

Answer: A

Q.14 Given that (5x − 3)^{3} + (2x + 5)^{3} + 27(4 − 3x)^{3} = 9(3 − 5x)(2x + 5)(3x − 4), then the value of (2x + 1) is:

A -13

B 15

C -15

D 13

Answer: B

Q.15 The sides of a triangle are 12 cm, 35 cm and 37 cm. What is the circumradius of the triangle

A 19 cm

B 17.5 cm

C 17 cm

D 18.5 cm

Answer: D

Q.16 The base of a right pyramid is an equilateral triangle with area 163cm^{2}. If the area of one of its lateral faces is 30 cm^{2}, then its height (in cm) is:

A √(^{739}/_{12})

B √(^{209}/_{12})

C √(^{611}/_{12})

D √(^{643}/_{12})

Answer: C

Q.17 A vessel contains a 32 litre solution of acid and water in which the ratio of acid and water is 5 : 3. If 12 litres of the solution are taken out and 7½ litres of water are added to it, then what is the ratio of acid and water in the resulting solution?

A 4 : 7

B 5 : 6

C 4 : 9

D 8 : 11

Answer: B

Q.18 A sphere of maximum volume is cut out from a solid hemisphere. What is the ratio of the volume of the sphere to that of the remaining solid?

A 1 : 4

B 1 : 2

C 1 : 3

D 1 : 1

Answer: C

Q.19 If √5x^{3}+2√2y^{3 }= (Ax+√2y)(Bx^{2}+2y^{2}+Cxy), then the value of (A^{2} + B^{2} − C^{2}) is:

A 15

B 20

C 30

D 40

Answer: B

Q.20 The value of (1 + cotθ − cosecθ )(1 + cosθ + sinθ)secθ =?

A -2

B 2

C sec θ cosec θ

D sin θ cos θ

Answer: B

Q.21 S is the incenter △PQR of ∠PSR = 125^{0}. If , then the measure of ∠PQR is:

A 75^{0}

B 55^{0}

C 80^{0}

D 70^{0}

Answer: D

Q.22 The value of 0.4 7 + 0.5 03 − 0.3 9 × 0.8 is:

A 0.615

B 0.615

C 0.625

D 0.625

Answer: D

Q.23 If △ABC in , D and are the points on AB and BC respectively such that DE ∥ BC, and AD : AB = 3: 8, then (area of △BDE) : ( area of quadrilateral DECA) = ?

A 9 : 55

B 9 : 64

C 8 : 13

D 25 : 39

Answer: D

Q.24 Monika spends 72% of her income. If her income increases by 20% and savings increase by 15%, then her expenditure increases by: (correct to 1 decimal place)

A 20.8%

B 20.2%

C 21.9%

D 19.8%

Answer: C

Q.25 A. B and C started a business with their capitals in the ratio 2 : 3 : 5. A increased his capital by 50% after 4 months, B increased his capital by 33⅓% after 6 months and C withdrew 50% of his capital after 8 months, from the start of the business. If the total profit at the end of a year was ₹86,800,then the difference between the shares of A and C in the profit was:

A ₹12,600

B ₹7,000

C ₹9,800

D ₹8,400

Answer: A

Q.26 The graph of the equations 5x − 2y + 1 = 0 and 4y − 3x + 5 = 0, interest at the point P(α,β), What is the value of (2α − 3β)?

A 4

B 6

C -4

D -3

Answer: A

Q.27 An article was sold at a profit of 14%. Hadit been sold for ₹121 less, a loss of 8% would have been incurred. If the same article would have been sold for ₹536.25, then the profit/loss per cent would have been:

A Profit, 5%

B Loss, 5%

C Loss, 2.5%

D Profit, 2.5%

Answer: C

Q.28 A shopkeeper allows 18% discount on the marked price of an article and still makes a profit of 23%. If he gains ₹18.40 on the sale of the article, then what is the marked price of the article?

A ₹140

B ₹125

C ₹120

D ₹146

Answer: C

Q.29 The value of (sec^{2}θ/cosec^{2}θ)+ (cosec^{2}θ/sec^{2}θ) – (sec^{2}θ+cosec^{2}θ)is:

A 0

B -2

C 2

D 1

Answer: B

Q.30 The given graph shows the weights of students in a school on a particular day.

The number of students weighing less than 50 kg is what percent less than the number of students weighing 55 kg or more?

A 44

B 40

C 55

D 30

Answer: A

Q.31 A right prism has height 18 cm and its base is a triangle with sides 5 cm, 8 cm and 12 cm. What is its lateral surface area (in cm^{2}) ?

A 450

B 468

C 432

D 486

Answer: A

Q.32 A can do one-third of a work in 15 days, B can do 75% of the same work in 18 days and C can do the same work in 36 days. B and C work together for 8 days. In how many days will A alone complete the remaining work?

A 24 days

B 18 days

C 20 days

D 16 days

Answer: C

Q.33 A person buys 80 kg of rice and sells it at a profit of as much money as he paid for 30 kg. His profit per cent is:

A 27 ³/₁₁

B 35

C 40

D 37½

Answer: D

Q.34 To cover a distance of 416 km, a train A takes 2⅔ hours more than train B. If the speed of A is doubled, it would take 1⅓ hours less than B, What is the speed (in km/h) of train A?

A 56

B 54

C 52

D 65

Answer: C

Q.35 The value of (2√10) / (√5+√2-√7) – √(√5-2/√5+2) – (3/√7-2)is:

A 2+√2

B 2√5

C √2

D √7

Answer: C

Q.36 The price of oil has increased by 20%. However, its consumption decreased by 8⅓%. What is the percentage increase or decrease in the expenditure on it?

A Increase by 10%

B Increase by 5%

C Decrease by 10%

D Decrease by 5%

Answer: A

Q.37 The average age of 120 students in a group is 13.56 years. 35% of the number of students are girls and the rest are boys. If the ratio of the average age of boys and girls is 6 : 5, then what is the average age (in years)of the girls?

A 12

B 11.6

C 10

D 14.4

Answer: A

Q.38 The marked price of an article is ₹1500. If two successive discounts, each of x% . on the marked price is equal to a single discount of ₹587.40, then what will be the selling price of the article if a single discount of x% is given on the marked price?

A ₹1,025

B ₹1,155

C ₹1,170

D ₹1,200

Answer: C

Q.39 Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is 5√13cm. What is the distance (in cm) between the chords?

A 2

B 3

C 2.5

D 1.5

Answer: A

Q.40 Study the following bar graph and answer the question given.

The ratio of the total demand of motorcycles of companies A, C and E to the total production of motorcycles of B and C is:

A 1 : 1

B 2 : 1

C 11 : 10

D 3 : 2

Answer: D

Q.41 A circle touches the side BC of ABC at D and AB and AC are produced to E and F, respectively. If AB = 10 em, AC = 8.6 cm and BC = 6.4 cm, then BE =?

A 3.2 cm

B 3.5 cm

C 2.2 cm

D 2.5 cm

Answer: D

Q.42 If the measure of each exterior angle of a regular polygon is 51^{3}/_{7}^{0} then the ratio of the number of its diagonals to the number of its sides is:

A 5 : 2

B 13 : 6

C 3 : 1

D 2 : 1

Answer: D

Q.43 Two numbers are in the ratio 3 : 5. If 13 is subtracted from each, the new numbers are in the ratio 10 : 21, If 15 is added to each of the original numbers, then the ratio becomes:

A 5 : 7

B 23 : 33

C 4 : 5

D 24 : 35

Answer: D

Q.44 Pipes A and B are filling pipes while pipe C is an emptying pipe. A and B can fill a tank in 72 and 90 minutes respectively. When all the three pipes are opened together, the tank gets filled in 2 hours. A and B are opened together for 12 minutes, then closed and C is opened, The tank will be empty after:

A 15 minutes

B 18 minutes

C 12 minutes

D 16 minutes

Answer: B

Q.45 The LCM of two numbers x and y is 204 times their HCF. If their HCF is 12 and the difference between the numbers is 60, then x + y = ?

A 660

B 426

C 852

D 348

Answer: D

Q.46 In △ABC,BE ⊥ AC,CD ⊥ AB and BE and CD intersect each other at O. The bisectors of ∠OBC and ∠OCB meet at P. If ∠BPC = 148^{∘}, then what is the measure of ∠A?

A 56^{0}

B 28^{0}

C 32^{0}

D 64^{0}

Answer: D

Q.47 The value of is:

A -1

B -2

C 2

D 1

Answer: D

Q.48 The value of 24 × 2 ÷ 12 + 12 ÷ 6 of 2 ÷ (15 ÷ 8 × 4) of (28 ÷ 7 of 5) is:

A 4⅙

B 4 ^{8}/_{75}

C 4⅔

D 4 ^{32}/_{75}

Answer: A

Q.49 A person covers 40% of the distance from A to B at 8 km/h, 40% of the remaining distance at 9 km/h and the rest at 12 km/h. His average speed (in km/h) for the journey is:

A 9⅝

B 9⅔

C 9⅜

D 9⅓

Answer: C

Q.50 A 15 m deep well with radius 2.8 m is dug and the earth taken out from it is spread evenly to form platform of breadth 8 m and height 1.5 m. What will be the length of the platform? (Take π = 22/7)

A 28.4 m

B 28.8 m

C 30.2 m

D 30.8 m

Answer: D

Q.51 In △PQR,∠Q > ∠R,PS is the bisectors of ∠P and PT ⊥ PQ. If ∠SPT = 28^{∘} and ∠ R = 23^{∘}, then the measure of ∠Q is:

A 74^{∘}

B 79^{∘}

C 82^{∘}

D 89^{∘}

Answer: B

Q.52 25 persons can complete a work in 60 days. They started the work. 10 persons left the work after x days. If the whole work was completed in 80 days, then whatis the value of x ?

A 9

B 8

C 12

D 15

Answer: C

Q.53 The value of sin^{2}64^{∘} + cos64^{∘} sin26^{∘} + 2cos43^{∘} cosec47^{∘} is:

A 4

B 1

C 2

D 3

Answer: D

Q.54 A tank is in the form of a cuboid with length 12 m. If 18 kilolitre of water is removed from it, the water level goes down by 30cm. What is the width (in m) of the tank?

A 4

B 5

C 5.5

D 4.5

Answer: B

Q.55 In finding the HCF of two numbers by division method, the last divisor is 17 and the quotients are 1. 11 and 2, respectively. What is the sum of the two numbers?

A 833

B 867

C 816

D 901

Answer: C

Q.56 A person invested one-fourth of the sum of ₹25,000 at a certain rate of simple interest and the rest at 4% p.a. higher rate. If the total interest received for 2 years is ₹4,125, what is the rate at which the second sum was invested?

A 9.5%

B 9.25%

C 5.25%

D 7.5%

Answer: B

Q.57 The radius of the base of a right circular cylinder is 3 cm and its curved surface area is 60πcm^{2}, The volume of the cylinder (in cm^{3}) is:

A 90π

B 72π

C 60π

D 81π

Answer: A

Q.58 If [3(x^{2}+1)-7x] / 3x = 6, x ≠ 0, then the value of √x+ ^{1}/_{√x} is:

A √^{25}/_{3}

B √^{11}/_{3}

C √^{35}/_{3}

D √^{31}/_{3}

Answer: D

Q.59 Basir’s working hours per day were increased by 15% and his wages per hour were increased by 20%. By how much percent did his daily earnings increase?

A 40

B 38

C 35

D 36

Answer: B

Q.60 A student was asked to find the value of 9⁴/_{9} ÷ 11⅓ of ⅙ +(1⅓×1⅘÷⅗)×2⅙ of ⅔÷⁴/_{3}of ⅔.His answer was 19¼What is the difference between his answer and the correct answer

A 7¾

B 6⅔

C 7½

D 6⅓

Answer: A

Q.61 If a 10-digit number 5 4 3 2 y 1 7 4 9 x is divisible by 72, then what is the value of (5x – 4y)?

A 14

B 15

C 10

D 9

Answer: A

Q.62 What is the remainder when (12797+9797) is divided by 32?

A 4

B 2

C 7

D 0

Answer: D

Q.63 The value of [(sinθ-cosθ)(1+tanθ+cotθ)]/1+sinθcosθ= ?

A secθ − cosecθ

B cosecθ − secθ

C sinθ + cosθ

D tanθ − cotθ

Answer: A

Q.64 A, B and C spend 80%, 85% and 75% of their incomes, respectively. If their savings are in the ratio 8 : 9 : 20 and the difference between the incomes of A and C is ₹18,000, then the income of B is:

A ₹24,000

B ₹27,000

C ₹30,000

D ₹36,000

Answer: B

Q.65 If 25% of half of x is equal to 2.5 times the value of 30% of one-fourth of y. then x is what percent more or Less than y?

A 33⅓% more

B 50% more

C 33⅓% less

D 50% less

Answer: B

Q.66 The value of (sinθ+cosθ-1)/(sinθ-cosθ+1)×[tan^{2}θ(cosec^{2}θ-1)]/(secθ-tanθ) is:

A 0

B -1

C 1

D 1

Answer: C

Q.67 In an examination, A obtained 10% more marks than B, B obtained 20% more marks than C and C obtained 32% less marks than D. If A obtained 272 more marks than C, then the marks obtained by B is:

A 850

B 816

C 1020

D 952

Answer: C

Q.68 In quadrilateral ABCD,∠C = 72^{∘} and ∠D = 28^{∘} . The bisectors of ∠A and ∠B meet in O. What is the measure of ∠AOB ?

A 48∘

B 54∘

C 50∘

D 36∘

Answer: C

Q.69 a, b and c are three fractions such that a < b < c. If c is divided by a, the result is 9/2, which exceeds b by 23/6. The sum of a, b and c is 19/12, What is the value of (2a + b – c)?

A ½

B ⅓

C 1/12

D ¼

Answer: D

Q.70 How many kg of salt costing ₹28 per kg must be mixed with 39.6 kg of salt costing ₹16 per kg, so that selling the mixture at ₹29.90, there is a gain of 15%?

A 33

B 31

C 35

D 32

Answer: A

Q.71 Study the following bar graph and answer the question given.

The total production of motorcycles of companies C, D and E is what percent less than the total demand of motorcycles of all the companies during five years?

A 43

B 32

C 38

D 47

Answer: B

Q.72 A, B and C started a business, Thrice the investment of A is equal to twice the investment of B and also equal to four times the investment of C, If C’s share out of the total profit is ₹4,863,then the share ofA in the profit is:

A ₹7,272

B ₹6,484

C ₹9,726

D ₹8,105

Answer: B

Q.73 Two positive numbers differ by 2001. When the larger number is divided by the smaller number, the quotient is 9 and the remainder is 41. The sum of the digits of the larger number is:

A 15

B 11

C 10

D 14

Answer: D

Q.74 Let , then the value of x^{2}+y^{2} is:

A 223/36

B 221/36

C 221/9

D 227/9

Answer: A

Q.75 If (5x + 2y) : (10x + 3y) = 5 : 9 , then (2x^{2} + 3y^{2} ) : (4x^{2} + 9y^{2} ) = ?

A 31 : 87

B 10 : 27

C 16 : 47

D 1 : 3

Answer: A

Q.76 The average of 18 numbers is 37.5. If six numbers of average X are added to them, then the average of all the numbers increases by one, The value of x is:

A 40

B 41.5

C 42

D 38.5

Answer: B

Q.77 In an office, ⅝ of the total number of employees are males and the rest are females. ⅖ of the number of males are non technical workers while ⅔ of the number of females are technical workers, What fraction of the total number of employees are technical workers?

A ⅝

B ⅖

C ½

D ⅜

Answer: A

Q.78 A solid cylinder of base radius 12 cm and height 15 cm is melted and recast into m toys each in the shape of a right circular cone of height 9 cm mounted on a hemisphere of radius 3 cm. The value of n is:

A 27

B 64

C 48

D 54

Answer: C

Q.79 In △ABC,D and E are the points on AB and AC respectively such that AD × AC = AB × AE. If ∠ADE = ∠ACB + 30^{∘} and ∠ABC = 78^{∘} , then ∠A =?

A 56∘

B 54∘

C 68∘

D 48∘

Answer: B

Q.80 P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are 60^{∘} and 30^{∘}, respectively and the distance between them is 84√3m. What is the height (in m) of the pole?

A 63

B 73.5

C 52.5

D 60

Answer: A

Q.81 If in △PQR,∠P = 120^{∘} ,PS ⊥ QR at S and PQ + QS = SR . then the measure of ∠Q is:

A 20^{∘}

B 50^{∘}

C 40^{∘}

D 30^{∘}

Answer: C

Q.82 The given pie-chart shows the break-up of total marks obtained by a student in five subjects A, B, C, D and E. The maximum marks in each subject is 150 and he obtained a total of 600 marks.

In how many subjects did the student obtain more than his average score?

A 3

B 2

C 4

D 1

Answer: B

Q.83 Walking at 60% of his usual speed, a man reaches his destination 1 hour 40 minutes late, His usual time (in hours) to reach the destination is:

A 2½

B 2¼

C 3⅛

D 3¼

Answer: A

Q.84 A man can row a distance of 900 metres against the stream in 12 minutes and returns to the starting point in 9 minutes. What is the speed (in km/h) of the man in still water?

A 4½

B 6

C 5¼

D 5

Answer: C

Q.85 If x + y + z = 6,xyz = −10 and x^{2} + y^{2} + 2^{2} = 30, then what is the value of (x^{3} + y^{3} + z^{3} )?

A 132

B 135

C 130

D 127

Answer: A

Q.86 The value of is:

A 24.42

B 24.24

C 25.42

D 25.48

Answer: D

Q.87 If ,0^{∘ }< θ <90^{∘},then the value of (tanθ +secθ)^{-1} is:

A 2-√3

B 3-√2

C 2+√3

D 3+√2

Answer: A

Q.88 Sudha bought 80 articles at the same price. She sold some of them at 8% profit and the remaining at 12% loss resulting in an overall profit of 6%. The number of items sold at 8% profit is:

A 64

B 60

C 72

D 70

Answer: C

Q.89 The given pie-chart shows the break-up of total marks obtained by a student in five subjects A, B, C, D and E. The maximum marks in each subject is 150 and he obtained a total of 600 marks.

The total marks obtained by the student in subjects C and E is approximately how much per cent more than what he obtained in A and D together?

A 9.09%

B 10.25%

C 8.33%

D 7.26%

Answer: A

Q.90 If the selling price of an article is 32% more than its cost price and the discount offered on its marked price is 12%, then what is the ratio of its cost price to the marked price?

A 4 : 5

B 3 : 8

C 2 : 3

D 1 : 2

Answer: C

Q.91 Study the following bar graph and answer the question given.

The number of companies whose production of motorcycles is equal to or more than the average demand of motorcycles (per year) over five years is:

A 4

B 2

C 1

D 3

Answer: D

Q.92 The internal diameter of a hollow hemispherical vessel is 24 cm. It is made of a steel sheet which is 0.5 cm thick. What is the total surface area (in cm^{2}) of the vessel?

A 612.75 π

B 468.75 π

C 600.2 π

D 600.5 π

Answer: A

Q.93 The bisector of in ∠A △ABC meets BC in D. If AB = 15cm,AC = 13cm and BC = 14cm , then DC =?

A 8.5 cm

B 7.5 cm

C 6.5 cm

D 8 cm

Answer: C

Q.94 A certain loan was returned in two equal half yearly instalments each of ₹6,760. If the rate of interest was 8% p.a., compounded yearly, how much was the interest paid on the loan?

A ₹750

B ₹810

C ₹790

D ₹770

Answer: D

Q.95 A sum is divided among A, B, C and D such that the ratio of the shares of A and is 2 : 3, that of B and C is 1 : 2 and that of C and D is 3 : 4. If the difference between the shares of A and is ₹648,then the sum of their shares is:

A ₹2,052

B ₹2,160

C ₹2,484

D ₹1,944

Answer: A

Q.96 The given pie-chart shows the break-up of total marks obtained by a student in five subjects A, B, C, D and E. The maximum marks in each subject is 150 and he obtained a total of 600 marks.

What is the difference between the marks obtained by the student in subjects B and D?

A 20

B 27

C 30

D 12

Answer: A

Q.97 A sector of radius 10.5 cm with the central angle 120^{0} is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in cm^{3}) of the cone so formed?

A (343√2)π /6

B (343√3)π /6

C (343√3)π /12

D (343√2)π /12

Answer: D

Q.98 A certain sum amounts to ₹4,205.55 at 15% p.a. in years, interest compounded yearly. The sum is:

A ₹3,200

B ₹3,500

C ₹2,700

D ₹3,000

Answer: D

Q.99 In △ABD,C is the midpoint of BD. If AB = 10cm,AD = 12cm and AC = 9cm, then BD =?

A 2√14 cm

B 2√10 cm

C √41 cm

D √10 cm

Answer: A

Q.100 A sum of ₹10,500 amounts to ₹13,825 in years at a certain rate per cent per annum simple interest. What will be the simple interest on the same sum for 5 years at double the earlier rate?

A ₹8,470

B ₹8,750

C ₹8,670

D ₹8,560

Answer: B

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