Mathematics Questions and Answers

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Mathematics » Work and Time

A can finish a piece of the work in 16 days and B can finish it in 12 days. They worked together for 4 days and then A
left. B finished the remaining work. For how many total number of days did B work to finish the work completely?

A

8

B

6

C

4

D

9

Mathematics » Mensuration

AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ◺APC = 62°, then find the measure of the minor arc AC.

A

28º

B

31º

C

62º

D

56º

Mathematics » Mensuration

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor arc BC and ◺CBD = 40°. Find the measure of ◺BCD.

A

40º

B

30º

C

20º

D

50º

Mathematics » Trigonometry

The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60°?

A

26√ 3

B

52√ 3

C

80

D

78√ 3

Mathematics » Percentage

A

40%

B

50%

C

45%

D

55%

Mathematics » Speed Time and Distance

A motorboat whose speed is 20 km/h in still water takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. If the speed of the boat in still water is increased by 2 km/h, then how much time will it take to go 39 km downstream and 30 km upstream?

A

3h 40m

B

2h 40m

C

2h 50m

D

3h 10m

Mathematics » Mensuration

A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which
is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:

A

5

B

2

C

4

D

6

Mathematics » Average

The average weight of P and his three friends is 55 kg. If P is 4 kg more than the average weight of his three friends, what is P's weight (in kg)?

A

60

B

62

C

58

D

54

Mathematics » LCM and HCF

LCM of two numbers is 56 times their HCF, with the sum of their HCF and LCM being 1710. If one of the two numbers
is 240, then what is the other number?

A

210

B

171

C

1680

D

57

Mathematics » Simple Interest, Compound Interest

A certain sum is deposited for 4 years at a rate of 10% per annum on compound interest compounded annually. The difference between the interest at the end of 2 years and that at the end of 4 years is ₹5,082. Find the sum (in ₹).

A

10164

B

20000

C

50820

D

25500

Mathematics » Algebra

If (x + 6y) = 8, and xy = 2, where x > 0, what is the value of (x3 + 216y3)?

A

476

B

368

C

224

D

288

Mathematics » Mensuration

In a △ ABC, points P, Q and R are taken on AB, BC and CA, respectively, such that BQ = PQ and QC = QR. If ◺BAC = 75°, what is the measure of ◺PQR (in degrees)?

A

40

B

30

C

50

D

75

Mathematics » Ratio & Proportion

A

14:23

B

21:19

C

5:6

D

7:4