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

Total Questions: 100

81. A circle is inscribed in a triangle ABC. It touches the sides AB and AC at M and N respectively. If O is the centre of the circle and ∠A = 70°, then what is ∠MON equal to?

Correct Answer: (c) 110°
Solution:Given, A circle inscribed in a triangle ABC.

82. The sum of the squares of sides of a right-angled triangle is 8450 square units. What is the length of its hypotenuse?

Correct Answer: (d) 65 units
Solution:

83. A triangle and a parallelogram have equal areas and equal bases. If the altitude of the triangle is k times the altitude of the parallelogram, then what is the value of k ?

Correct Answer: (b) 2
Solution:

84. Areas of two squares are in the ratio m² : n⁴ What is the ratio of their perimeters?

Correct Answer: (c) m : n²
Solution:

85. AD is the median of the triangle ABC. If P is any point on AD, then which one of the following is correct?

Correct Answer: (b) Area of triangle PAB is equal to area of triangle PAC.
Solution:We have, AD is median of the ∆ABC. P is any point on AD.

86. What is the area of a segment of a circle of radius r subtending an angle θ at the centre ?

Correct Answer: (b)
Solution:


87. ABC is a triangle right-angled at C. Let P be any point on AC and Q be any point on BC. Which of the following statements is/are correct?

1. AQ² + BP² = AB² + PQ²
2. AB = 2PQ

Select the correct answer using the code given below :

Correct Answer: (a) only 1
Solution:


88. Four circular coins of equal radius are placed with their centres coinciding with four vertices of a square. Each coin touches two other coins. If the uncovered area of the square is 42 cm² then what is the radius of each coin? (Assume π = ²²⁄₇)

Correct Answer: (b) 7 cm
Solution:Let radius of coins = r

89. The radii of the flat circular faces of a bucket are x and 2x. If the height of the bucket is 3x, what is the capacity of the bucket ? (Assume π = ²²⁄₇)

Correct Answer: (b) 22x³
Solution:Given,

90. If p, q, r, s and t represent length, breadth, height, surface area and volume of a cuboid respectively, then

Correct Answer: (c)
Solution: