SOLVED PAPER 2021 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

61. A cone and a hemisphere have equal bases and equal volumes. What is the ratio of the height of the cone to the radius of the hemisphere?

Correct Answer: (b) 2 : 1
Solution:

62. A solid sphere of diameter 60 mm is melted to stretch into a wire of length 144 cm. What is the diameter of the wire?

Correct Answer: (b) 1 cm
Solution:

63. The ratio of the radius of base to the height of a cylinder is 2 : 3. If the volume of the cylinder is 1617c m³ then what is the curved surfaced area of the cylinder? (Take π = ²²⁄₇)

Correct Answer: (c) 462 cm²
Solution:


64. The difference between the outside and the inside surface area of a cylindrical pipe 14 cm long is 44 cm². The pipe is made of 99 cm³ of metal. If R is the outer radius and r is the inner radius of the pipe, then what is (R + r) equal to? (Take π = ²²⁄₇)

Correct Answer: (d) 4.5 cm
Solution:

65. A metal solid cube of edge 24 cm is melted and made into three small cubes. If the edges of two small cubes are 12 cm and 16 cm, then what is the surface area of the third small cube?

Correct Answer: (c) 2400 cm²
Solution:

66. A conical vessel whose internal radius is 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. What is the height to which the water rises?

Correct Answer: (b) 2 cm
Solution:

67. A metal solid cube of side 22 cm is melted to make a cone of height 21 cm. What is the radius of the base of the cone? (Take π = ²²⁄₇)

Correct Answer: (c) 22 cm
Solution:

68. A cone of height 24 cm has a curved surface area 550 cm². What is the ratio of its radius to slant height? (Take π = ²²⁄₇)

Correct Answer: (c) ⁷⁄₂₅
Solution:

69. A rectangular paper is 44 cm long and 22 cm wide. Let x be the volume of the largest cylinder formed by rolling the paper along its length and y be the volume of the largest cylinder formed by rolling the paper along its width. What is the ratio of x to y? (Take π = ²²⁄₇)

Correct Answer: (b) 2 : 1
Solution:


70. A hollow spherical shell is made up of a metal of density 3 g /cm³. If the internal and external radii are 5 cm and 6 cm respectively, then what is the mass of the shell ? (Take π = ²²⁄₇)

Correct Answer: (a) 1144 g
Solution: