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

Total Questions: 100

51. What is the value of

(cos² 32° + cos² 58°)
÷ (sec² 50° - sec² 40°)
4 tan13° tan37° tan53° tan77° ?

Correct Answer: (d) 5
Solution:

52. What is the value of

(l + cot² θ)(l + cos θ)(l - cos θ)
- (l + tan²θ)  (l + sin θ)(l - sin θ)

Correct Answer: (b) 0
Solution:

53. If 2cos² θ + sin θ - 2 = 0, 0 < θ ≤ π/2 then what is the value of θ ?

Correct Answer: (a) π/2
Solution:

54. A person on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 min for the angle of depression to change from 30° to 45°, and further t min to reach the tower, which one of the following is correct

Correct Answer: (b) 8 < t < 8.3
Solution:

55. A woman is standing on the deck of a ship, which is h (in metres) above water level. she observes the angle of elevation of the top of a tower as 60° and the angle of depression of the base of the tower as 30°. What is the height of the tower?

Correct Answer: (c) 4h
Solution:

56. Let ABC be a right-angled triangle with sides 5 cm, 12 cm and 13 cm. If p is the length of the perpendicular drawn from vertex A on the hypotenuse BC, then what is the value of 13p?

Correct Answer: (c) 60
Solution:

57. OABC is a rhombus whose three vertices lie on a circle with centre at O. If the area of the rhombus is 32√3cm² then what is the radius of the circle?

Correct Answer: (c) 8 cm
Solution:

58. The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which one of the following is correct?

Correct Answer: (d) 10 < p < 12
Solution:

59. A solid cube is cut into two cuboids of equal volume. What is the ratio of total surface area of the given cube to that of one of the cuboids?

Correct Answer: (b) 3 : 2
Solution:

60. The length of a diagonal of a cuboid is 11 cm. The surface area is 240 square cm. What is the sum of its length, breadth and height?

Correct Answer: (d) 19 cm
Solution: