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

Total Questions: 100

41. If x = m sec A + n tan A and y = m tan A +n sec A, then what is x² - y² equal to ?

Correct Answer: (a) m² - n²
Solution:Given,

42. If for some θ lying between 0° and 90°, tan θ = 1, then what is the value of sin²θ - 2sin θ cos θ ?

Correct Answer: (d) - (½)
Solution:

43. Solve it ?

Correct Answer: (c) tanθ
Solution:

44. Solve it ?

Correct Answer: (a)
Solution:Given expression,



45. In a triangle ABC, right angle at B, AB + BC = 10 (1 + √3) cm length of the hypotenuse is 20 cm. What is the value of tan A + tan C ?

Correct Answer: (a)
Solution:In a right angled triangle ABC, it is given that,


46. (Questions 46-48) Consider the following for the next three questions that follow. A solid consisting of a right circular cone of radius x and height 2x standing on a hemisphere of radius x (Take π = ²²⁄₇)

The volume of the solid is equal to that of a

Correct Answer: (a) Sphere of radius x
Solution:Given dimensions :


47. What is the approximate total surface area of the solid

Correct Answer: (c) 13.3x²
Solution:We have,


48. The solid is placed upright in a right circular cylinder full of water such that it touches the bottom. If the internal radius of cylinder is x and height is 3x, what is the approximate volume of water left in the cylinder?

Correct Answer: (d) 5.24x²
Solution:We are given the dimensions as



49. (Questions 49 and 50) Consider the following for next two question that follow.

The chord of a circle of radius 2.1 cm is inclined the angle of 120° on the centre of circle.
[Take π = (²²⁄₇) and √3 = 1.732]

What is the approximate area of minor segment of the circle ?

Correct Answer: (a) 2.71 cm²
Solution:Given, Radius (r) of the circle


50. What is the approximate area of major segment of the circle?

Correct Answer: (d) 11.15 cm²
Solution:The approximate area of major segment of circle = Area of circle − area of minor segment of circle