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

Total Questions: 100

31. (Questions 31 and 32) Consider the following for the next two items that follow.

A flagstaff stands on the top of a vertical tower. The angle of elevation of the top of the flagstaff from a certain place on the same horizontal level with the base of the tower is found to be a. Advancing a distance d towards the tower in the same horizontal plane; the angle of elevation of the top of the flagstaff is observed to be ẞ and that of the top of the tower is observed to be y. Let H be the height of the top of the flagstaff from the base of the tower and h be the height of the tower.

Which one of the following is correct?

Correct Answer: (a) H tanϒ-htanẞ = 0
Solution:

32. Which one of the following is correct?

Correct Answer: (c)
Solution:

33. (Questions 33 and 34) Consider the following for the next two items that follow.

AB is a straight road leading to the foot P of a tower of height h. Q is at distance x from P and R is at a distance y from Q(R is farther from P than Q; R, Q are on the same side). The angle of elevation of the top of the tower at Q is twice of that at R.
use the formula, tan 2θ = (2tan θ) ÷ (1 - tan² θ)

Which one of the following is correct?

Correct Answer: (b) x < y
Solution:

34. Which one of the following is correct?

Correct Answer: (d) h² = y² - x²
Solution:Also, h² = y² - x²

35. (Questions 35 and 36) Consider the following for the next two items that follow.

Two parallel chords AB and CD of a circle are of lengths 60cm and 80cm respectively. They are on the same side of the centre O and 10 cm a part.

What is the diameter of the circle?

Correct Answer: (c) 100 cm
Solution:

36. If the chord AB subtends an angle a and chord CD subtends an angle beta at the centre O, then what is the value of tan(β/2) - tan(α/2) ?

Correct Answer: (d) 7/12
Solution:

37. (Questions 37 and 38) Consider the following for the next two items that follow.

Let p = x⁴ - y² z², q = y⁴ - z² x²,  r = z⁴ - x² y²

What is px² + qy² + rz² equal to ?

Correct Answer: (a) (x² + y² + z²) (p + q + r)
Solution:

38. What is x² (px² + qy² + rz²) + qr - p² equal to?

Correct Answer: (a) 0
Solution:

39. (Questions 39 and 40) Consider the following for the next two items that follow.

A right conical cap just covers two spheres placed one above the other on a table such that it touches both the spheres. Let r be the radius of the smaller sphere and R be the radius of the bigger sphere. Let 20 be the vertical angle of the cone.

What is the height of the cone ?

Correct Answer: (b)
Solution:

40. What is the radius of the base of the cone?

Correct Answer: (b)
Solution: