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

Total Questions: 100

71. A cloth of 3 m width is used to make a conical tent 12 m in diameter with a slant height of 7 m. What is the length of the cloth? (Take π = ²²⁄₇)

Correct Answer: (c) 44 m
Solution:

72. A sphere of diameter 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 6 cm. If the sphere is completely submerged in water, then by how much will the surface level of water be raised?

Correct Answer: (b) 1 cm
Solution:

73. A sector is cut from a circle of radius 21 cm. If the length of the arc of the sector is 55 cm, then what is the area of the sector?

Correct Answer: (a) 577.5 cm²
Solution:

74. A wire is in the form of a circle of radius 70 cm. If it is bent in the form of a rhombus, then what is its side length? (Take π = ²²⁄₇)

Correct Answer: (d) 110 cm
Solution:

75. If the perimeter of a semi-circular park is 360 m, then what is its area ? (Take π = ²²⁄₇)

Correct Answer: (b) 7700 m²
Solution:

76. In a trapezium ABCD, AB is parallel to DC. The diagonals AC and BD intersect at P.

If AP : PC = 4 : (4x - 4) and BP : PD = (2x - 1) /: (2x + 4), then what is the value of x ?

Correct Answer: (b) 3
Solution:

77. ΔABC is similar to ΔDEF. The perimeters of ΔABC and ΔDEF are 40 cm and 30 cm respectively. What is the ratio of (BC + CA) to (EF + FD) equal to ?

Correct Answer: (b) 4 : 3
Solution:

78. Two isosceles triangles have equal vertical angles and their areas are in the ratio 4.84 : 5.29. What is the ratio of their corresponding heights ?

Correct Answer: (c) 22 : 23
Solution:

Let ABC and DEF are the isosceles
triangles whose vertical angles are equal.

79. ABC is a triangle right angled at A and AD is perpendicular to ВС. If BD = 8 cm and DC = 125cm, then what is AD equal to?

Correct Answer: (d) 10 cm
Solution:

80. The surface area of a cube is equal to that of a sphere. If x is the volume of the cube and y is the volume of the sphere, then what is (x²) : (y²) equal to?

Correct Answer: (a) π : 6
Solution: