SOLVED PAPER 2023 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

61. A pendulum swings through an angle of 9° and its end describes an arc of length 14.3 cm. What is the length of the pendulum? (take, π = 22/7)

Correct Answer: (b) 91 cm
Solution:

62. The arch of a bridge is in the form of an arc of a circle. If the span of the bridge is 40 m and height in the middle is 8 m, then what is the radius of curvature of the bridge?

Correct Answer: (c) 29 m
Solution:

63. If a, b and c are the sides of a right-angled triangle, where a > b >c, then what is the value of the expression

(a + b + c) (a + b - c) (a - b + c) (a - b - c) ?

Correct Answer: (b) - 4b²c²
Solution:

64. The cube root of x varies inversely as the square root of y. x = 8 when y = 3 What is the value of x when y = ³√3?

Correct Answer: (c) 24
Solution:

65. Three solid lead spheres of diameters 6 cm, 8 cm and 10 cm are melted together and recast as a solid sphere. What is the percentage diminution of the surface area as compared to the sum of the surface area of the three spheres ?

Correct Answer: (d) 28%
Solution:

66. A solid sphere of radius 3 cm is melted to form a hollow cylinder of height 4 cm and external diameter 10 cm. What is the thickness of the cylinder ?

Correct Answer: (d) 1.00 cm
Solution:

67. Three glasses P, Q and R have capacities in the ratio 1 : 2 : 3. All these glasses are completely filled with mixtures of milk and water. The ratio of milk to water in P is 1 : 2, in Q it is 2 : 3 and in R it is 3 : 1. If the content of all three glasses are put into a bigger container, what will be the ratio of milk to water in the container ?

Correct Answer: (b) 203 : 157
Solution:

68. Solved

Correct Answer: (c)
Solution:

69. Solved

Correct Answer: (c)
Solution:

70. If tan A + cot A = 2 where

0 < A < 90° then what is the value
of tan² A + tan³ A +tan⁴
A +.......+ tanⁿ A ?

Correct Answer: (c) n - 1
Solution: