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

Total Questions: 100

71. Two circles touch internally. The sum of their areas is 136π cm² and distance between their centres is 4 cm. What are the radii of the circles?

Correct Answer: (b) 10 cm, 6 cm
Solution:


72. If area of a circle and a square are same, then what is the ratio of their perimeters?

Correct Answer: (c)
Solution:Let radius of circle be r and side of square be x.

73. A circle of diameter 8 cm is placed in such a manner that it touches two perpendicular lines. Then another smaller circle is placed in the gap such that it touches the lines and the circle. What is the diameter of the smaller circle?

Correct Answer: (d) 8(3 - 2√2) cm
Solution:


74. The thickness of a cylinder is 1 foot, the inner radius of the cylinder is 3 feet and height is 7 feet. To paint the inner surface it requires one litre of a particular colour. How much quantity of the same colour is required to paint all the surfaces of the cylinder?

Correct Answer: (c)
Solution:Given, thickness of a cylinder is 1 feet and inner radius of the cylinde r₂=3feet


75. A square and a rectangle have equal areas. If one side of the rectangle is of length numerically equal to the square of the length of the side of the square, then the other side of the rectangle is

Correct Answer: (c) of unit length
Solution:Let side of square be x, then one side of rectangle be x² and let other side of rectangle be y.

Then, according to the question, x² = x² × y area of square = area of rectangle) ⇒ y = 1

76. The length and breadth of a rectangle are in the ratio 4 : 3. Then, what is the ratio of the area of the triangle formed by the parts of the diagonals with a long side to the area of the triangle formed by the parts of diagonals with a short side?

Correct Answer: (d) 1 : 1
Solution:Let length of rectangle be 4x and breadth of rectangle be 3x.

77. Suppose a region is formed by removing a sector of 20° from a circular region of radius 30 feet. What is the area of this new region?

Correct Answer: (d) 850π square feet
Solution:Area of new region,

78. ABCD is a parallelogram where AC and BD are the diagonals. If ∠BAD = 60°, ∠ADB = 90°, then what is BD² equal to?

Correct Answer: (b)
Solution:


79. A line through the vertex A of a parallelogram ABCD meets DC in P and BC produced in Q. If P is the mid-point of DC, then which of the following is/are correct?

1. Area of ΔPDA is equal to that of ΔPCQ.
2. Area of ΔQAB is equal to twice that of ΔPCQ.

Select the correct answer using the code given below:

Correct Answer: (a) Only 1
Solution:Since, BC ll AD


80. How many cubic metre of earth is to be dug out to dig a well of radius 1.4 m and depth 5 m?

Correct Answer: (d) 30.8m³
Solution:

Volume of well with radius 1.4 m
and depth 5 m.