SOLVED PAPER 2020 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

61. In a quadrilateral ABCD, ∠B = 90° and AB² + BC² + CD² - AD² = 0, then what is ∠ACD equal to ?

Correct Answer: (c) 90°
Solution:Given, in quadrilateral ABCD

62. In a ∆ABC, AC = 12cm, AB = 16cm and AD is the bisector of ∠A. If BD = 4cm, then what is DC equal to ?

Correct Answer: (b) 3 cm
Solution:Given, in ∆ABC

63. ABCD is a cyclic quadrilateral. The bisectors of the angles A, B, C and D cut the circle at P, Q, R and S respectively. What is a ∠PQR + ∠RSP equal to?

Correct Answer: (c) 180°
Solution:

64. ABC is an equilateral triangle. The side BC is trisected at D such that BC = 3 BD. What is the ratio of AD² to AB² ?

Correct Answer: (a) 7 : 9
Solution:Here, ABC is an equilateral triangle.


65. Consider the following statements:

1. The diagonals of a trapezium divide each proportionally. other
2. Any line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:1. Diagonals of a trapezium divide each other proportionally are true


66. If H, C and V are respectively the height, curved surface area and volume of a cone, then what is 3πVH³ + 9V² equal to ?

Correct Answer: (a) C² H²
Solution:Here, H C, and V are respectively the height, curved surface area and volume of a cone.

67. How many solid lead balls each of diameter 2 mm can be made from a solid lead ball of radius 8 cm ?

Correct Answer: (d) 512000
Solution:Here, R = 8 cm, r = 01. cm

68. The two sides of a triangle are 40 cm and 41 cm. If the perimeter of the triangle is 90 cm, what is its area ?

Correct Answer: (d) 180 cm²
Solution:ere, sides of triangle are 40 cm, 41 cm and perimeter of triangle is 90 cm.

69. The diagonals of a rhombus differ by 2 units and its perimeter exceeds the sum of the diagonals by 6 units. What is the area of the rhombus ?

Correct Answer: (c) 24 sq units
Solution:Let the diagonal of rhombus.


70. What is the area of a right-angled triangle, if the radius of the circumcircle is 5 cm and altitude drawn to the hypotenuse is 4 cm ?

Correct Answer: (a) 20 cm²
Solution:ABC is a right angle triangle.