# 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

Ans : (D) 2.1

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

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

Q.3: In a triangle ABC, $latex \angle\text{BAC}=90^o$ 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

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

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

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

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

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

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

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

Ans : (B) 14

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

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

Ans : (A) 3 : 5

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

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

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 $latex \pi=\frac{22}{7})$
(A) 88
(B) 94
(C) 80
(D) 66

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 $latex \pi=\frac{22}{7}$
(A) 20.5
(B) 10.5
(C) 6.5
(D) 17.6

Ans : (D) 17.6

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

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

Ans : (D) 2019

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

Ans : (D) 12

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

Ans : (A) 39

Q.18: The string of a kite is 158 m long and it makes an angle of 30o 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

Ans : (C) 79

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

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

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

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

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

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

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