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

Total Questions: 100

81. If the diagonals of a rhombus are x and y, then what is its area?

Correct Answer: (a)
Solution:

Area of rhombus,

82. The lengths of sides of a triangle

Correct Answer: (c) 1, 1, 1
Solution:

Lengths of sides of a triangle are

83. What is the maximum number of circumcircles that a triangle can have?

Correct Answer: (a) 1
Solution:A triangle has maximum one circumcircles since it touches all the vertex of the triangle.

84. If an arc of a circle of radius 6 cm subtends a central angle measuring 30°, then which one of the following is an approximate length of the arc?

Correct Answer: (a) 3.14 cm
Solution:


85. A ladder 5 m long is placed in a room so as to reach a point 4.8 m high on a wall and on turning the ladder over to the opposite side of the wall without moving the base, it reaches a point 1.4 m high. What is the breadth of the room?

Correct Answer: (c) 6.2 m
Solution:Here, AC and AE are portion of ladder.


86. What is the area of the largest square plate cut from a circular disk of radius one unit?

Correct Answer: (d) 2 square units
Solution:For largest square plate cut from a circular disk,

87. Out of 4 identical balls of radius r, 3 balls are placed on a plane such that each ball touches the other two balls. The 4th ball is placed on them such that this ball touches all the three balls. What is the distance of centre of 4th ball from the plane?

Correct Answer: (a)
Solution:Let Q be the mid-point of BC and since ∆ABC is an equilateral triangle.



88. A right circular cylinder just encloses a sphere. If p is the surface area of the sphere and q is the curved surface area of the cylinder, then which one of the following is correct?

Correct Answer: (a) p = q
Solution:Let radius of sphere be r.

89. ABCD is a quadrilateral such that AD = DC = CA = 20 units, BC = 12 units and ∠ABC = 90° . What is the approximate area of the quadrilateral ABCD?

Correct Answer: (a) 269 square units
Solution:In right angled triangle ABCD,


90. Let PQRS be the diameter of a circle of radius 9 cm. The length PQ, QR and RS are equal. Semi-circle is drawn with QS as diameter (as shown in the given figure). What is the ratio of the shaded region to that of the unshaded region?

Correct Answer: (b) 5 : 13
Solution:We have, PS = 2 × 9 = 18cm