Maths Questions (English)

Set 2 : Maths Questions

Q.1: A solid metallic hemisphere of radius 6.3 cm is melted and recast into a right circular cylinder of radius 9 cm. What is the height (in cm, correct to one decimal place) of the cylinder?
(A) 1.9
(B) 2.7
(C) 2.5
(D) 2.1

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Ans : (D) 2.1

Q.2: If $cos\theta =\frac{4x}{1+4x^2}$ , then what is the value of $sin\theta$ ?
(A) $\frac{1+4x^2}{1-4x^2}$
(B) $\frac{1+4x^2}{4x^2}$
(C) $\frac{1-4x^2}{1+4x^2}$
(D) $\frac{1-4x^2}{4x}$

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Ans : (C) $\frac{1-4x^2}{1+4x^2}$

Q.3: In a triangle ABC, $\angle\text{BAC}=90^o$ and AD is perpendicular to BC. If AD = 8.4 cm and BD = 4.8 cm, then the length of BC is:
(A) 19.5 cm
(B) 15 cm
(C) 18 cm
(D) 18.5 cm

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Ans : (A) 19.5 cm

Q.4: Tap P can fill a cistern in 6 hours and tap Q can empty the full cistern in 10 hours. If both taps P and Q are kept open simultaneously, then in how many hours will the empty cistern be completely full ?
(A) 15
(B) 18
(C) 16
(D) 12

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Ans : (A) 15

Q.5: One dozen notebooks quoted at ₹125 are available at 20% discount. How many notebooks can be bought for ₹75 ?
(A) 10
(B) 6
(C) 9
(D) 8

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Ans : (C) 9

Q.6: A man invests ₹7,000 at 8% per annum simple interest for 2 years and ₹10,000 at compound interest at the sane rate for the same period, compounded annually. What will be the total interest and the total interest and the total amount (in ₹) respectively, on maturity ?
(A) 19,748 and 2,874
(B) 2,748 and 19,784
(C) 19,784 and 2,784
(D) 2,784 and 19,784

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Ans : (D) 2,784 and 19,784

Q.7: If (sin A-cos A) =0, then what is the value of cot A ?
(A) $\frac\pi6$
(B) 0
(C) 1
(D) $\frac\pi4$

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Ans : (C) 1

Q.8: A boat can travel with a speed of 19 km/h in still water. If the speed of the stream is 3 km/h, then what will be the total time ( in hours) taken by the boat to go 88 km downstream and 24 km upstream ?
(A) 4.5
(B) 5
(C) 4
(D) 5.5

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Ans : (D) 5.5

Q.9: A is 150% of B and B is 40% of C. If A+B+C=20, then the value of 2B+3C-4A is equal to:
(A) 16
(B) 14
(C) 20
(D) 15

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Ans : (B) 14

Q.10: The following histogram represents the distribution of household expenditure (in ₹) of 200 manual workers in a city.

The ratio of the number of workers whose household expenditure is less than ₹200 to the number of workers whose household expenditure is ₹300 and above is:

(A) 3 : 5
(B) 2 : 5
(C) 4 : 5
(D) 3 : 4

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Ans : (A) 3 : 5

Q.11: Using algebraic identities, simplify the following expression.
$\frac{(x^4+x^2+1)}{x^2+x+1)}$
(A) (x² – 2x + 1)
(B) (x² + x + 1)
(C) (x² + 2x + 1)
(D) (x² – x + 1)

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Ans : (D) (x² – x + 1)

Q.12: Students of Primary, Middle, Secondary and Sr. Secondary classes collected donation for a Relief Fund as shown in the pie chart. If the donation collected from Middle classes was ₹6,750 then how much money was collected by the Primary classes ?

(A) ₹4,050
(B) ₹4,005
(C) ₹4,500
(D) ₹3,960

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Ans : (A) ₹4,050

Q.13: One quarter of a circular pizza of diameter 28 cm was removed from the whole pizza. What is the perimeter (in cm) of the remaining pizza ? (take $\pi=\frac{22}{7})$
(A) 88
(B) 94
(C) 80
(D) 66

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Ans : (B) 94

Q.14: The inner and outer radii of two concentric circles are 6.7 cm and 9.5 cm, respectively. What is the difference between their circumferences (in cm) ? Take $\pi=\frac{22}{7}$
(A) 20.5
(B) 10.5
(C) 6.5
(D) 17.6

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Ans : (D) 17.6

Q.15: Study the given graph and answer the question that follows.

The average production of paper by company B in 2014, 2017 and 2018 was $13\frac13$ % less than the production of paper by company A in the year’.

13\frac13 — The average production of paper by company B in 2014, 2017 and 2018 was $13\frac13$ % less than the production of paper by company A in the year’.

(A) 2016
(B) 2018
(C) 2017
(D) 2019

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Ans : (D) 2019

Q.16: What is the perimeter (in cm) of an equilateral triangle whose height is 3.46 cm? take $\sqrt3=1.73$ .
(A) 10.4
(B) 9
(C) 6
(D) 12

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Ans : (D) 12

Q.17: The value of $[(232\div29 of 2)+ 77\times10\div18] -\frac{18\times8\div4 of 3-4}{2\times(8-6)+1-2\times3\div4 of\frac12}$ is:
(A) 39
(B) 44
(C) 33
(D) 47

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Ans : (A) 39

Q.18: The string of a kite is 158 m long and it makes an angle of 30^o with the horizontal. What is height (in m) of the kite? Assume there is no slack in the string.
(A) 100
(B) 99
(C) 79
(D) 80

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Ans : (C) 79

Q.19: If $(x+\frac1x)^3=27$ , then what is the value of $(x^2+\frac{1}{x^2})$ ? Given that x is real.
(A) 11
(B) 25
(C) 7
(D) 9

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Ans : (C) 7

Q.20: What is the area (in cm², correct to one decimal place) of a triangle whose base is 214 cm and height is 15.5 cm?
(A) 165.9
(B) 156.6
(C) 165.6
(D) 156.9

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Ans : (A) 165.9

Q.21: One-fifth of a journey is covered at a speed of km/h, one-fourth of the journey at a speed of 25 km/h and the rest at 60 km/h. What is the average speed (in km/h, correct to one decimal place) for the whole journey?
(A) 38.7
(B) 30.6
(C) 40.5
(D) 25.4

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Ans : (A) 38.7

Q.22: If a + b = p, ab = q, then (a⁴ + b⁴) is equal to:
(A) p⁴ – 2p²q² + q²
(B) p⁴ – 4p²q² + 2q²
(C) p⁴ – 4p²q + q²
(D) p⁴ – 4p²q + 2q²

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Ans : (D) p⁴ – 4p²q + 2q²

Q.23: What is the greatest five-digit number that is completely divisible by 8, 15, 16, 21 and 5 ?
(A) 92680
(B) 99120
(C) 95760
(D) 98320

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Ans : (B) 99120

Q.24: By selling an article for 1,170, Elisa suffers as much loss as she would have gained by selling it at a profit of 22%. If she sells it for 1,450, then her profit/loss per cent (correct up to one decimal place) is:
(A) Profit, 3.3
(B) Loss, 3.3
(C) Loss, 26.2
(D) Profit, 26.2

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Ans : (B) Loss, 3.3

Q.25: If A : B = 11 : 7 and B : C = 5 : 19, then what is A : B : C ?
(A) 55 : 35 : 133
(B) 35 : 55 : 133
(C) 35 : 133 : 55
(D) 55 : 133 : 35

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Ans : (A) 55 : 35 : 133

Maths Questions for SSC CHSL

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