SOLVED PAPER 2022 (CDS) (I) (Elementary Mathematics)

Total Questions: 100

71. An equilateral triangular sheet is formed by joining 9 equilateral triangular sheets each of area 9√3 cm². What is the height of the bigger triangular sheet?

Correct Answer: (a) 9√3 cm

72. A farmland is in the shape of a rhombus. The perimeter of the land is 100 m and the length of one of the diagonals is 40 m. The land is divided into four equal parts. What is the area of each part?

Correct Answer: (b) 225m²

73. ABCD is a trapezium in which AB is parallel to DC. Let E and F be the mid-points on AD and BC respectively. If EF = 10cm and AB - DC = 4cm then what is the value of AB × DC ?

Correct Answer: (b) 96 cm²

74. ABCD is a parallelogram with AB = 15cm and AD = 8cm. If θ is the acute angle between AB and AD, then what is the area of the parallelogram (in sq cm) ?

Correct Answer: (b) 120sin θ

75. If the perimeter of an isosceles right angled triangle is 4(2 + √2)cm, then what is its area in square cm?

Correct Answer: (a) 8

76. The diagonal of a square is 12√2 cm and the area of an equilateral triangle is 64√3 square cm. Which of the following statements is/are correct?

1. The square and the triangle have the same perimeter.
2. Four times the area of the square is equal to 3√3 times the area of the triangle.

Select the correct answer using the code given below.

Correct Answer: (c) Both 1 and 2

77. Consider the following statements:

1. The sum of any two sides of a triangle is less than twice the median drawn to the third side.
2. The perimeter of a triangle is greater than the sum of the three medians.

Which of the above statements is/are correct?

Correct Answer: (b) Only 2

78. Let D, E and F be the mid-points of the sides BC, CA and AB respectively of a triangle ABC. Triangle DEF is congruent to which of the following triangles?

1. AEF
2. FBD
3. EDC

Select the correct answer using the code given below.

Correct Answer: (d) 1, 2 and 3

79. In a triangle ABC, AB = AC and BC is produced to D such that ∠ACD = x, then what is ∠BAC equal to?

Correct Answer: (b) 2x - 180°

80. ABC is a triangle right angled at B with AC = 2BC If ∠A = x then what is ∠C equal to ?

Correct Answer: (b) 2x