SOLVED PAPER 2022 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

61. Consider the following statements:

1. If two chords AB and AC of a circle are equal, then the centre of the circle lies on the angle bisector of angle CAB.
2. If two concentric circles are intersected by a line at A, B, C and D respectively, then AC = BD

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2

62. A circle of radius 25 cm has a chord of length 48 cm. What is the length of the perpendicular drawn from the centre of the circle to the chord?

Correct Answer: (d) 7 cm

63. The surface area of a cube of length x is equal to the surface area of a sphere of radius y.

Consider the following statements

Statements
1. 2x > 3y
2. The volume of the cube is greater than the volume of the sphere.

Which of the above statements is/are correct?

Correct Answer: (d) Neither 1 nor 2

64. The radius and height of a right circular cone are in the ratio 3 : 7. If the volume of the cone is 528 cm³, then what is the height of the cone? (Take π = ²²⁄₇)

Correct Answer: (d) 14.0 cm

65. A cylindrical pipe has inner diameter of 14 cm. Water flows through it at a rate of 154 litres per minute. What is the speed of water (in km / h)? (Take π = ²²⁄₇)

Correct Answer: (b) 0.6

66. A spherical ball of lead 6 cm in diameter is melted and recast into three spherical balls. The diameters of the balls are 2 cm, 4 cm and x cm. Which one of the following is correct?

Correct Answer: (b) 5.2 cm < x cm < 5.4 cm

67. A rectangle of length 10 units and breadth 8 units is split into two squares each of area x square units and two rectangles each of area y square units.

Consider the following statements:

1. y is always greater than x.
2. y can be 15 square units.

Which of the above statements is/are correct?

Correct Answer: (b) Only 2

68. A square sheet is formed by joining n identical square sheets of same size. If the length of the diagonal of the bigger square sheet so formed is m, then what is the side length of a smaller square sheet?

Correct Answer: (c)

69. A rectangular sheet is of length x and breadth y. If p is the volume of the cylinder formed by rolling the sheet along its breadth and q is the volume of the cylinder formed by rolling the sheet along its length, and q = 2p, then which one of the following is correct?

Correct Answer: (c) x = 2y

70. A tall cylindrical container with circular base of radius 18 cm contains a good quantity of water. Metal balls each of radius 0.9 cm are immersed in it. How many balls are required to raise the water level by 3 cm?

Correct Answer: (c) 1000