SOLVED PAPER 2023 (CDS) (II) (Elementary Mathematics)

Total Questions: 100

81. A sphere of radius 5 cm is dropped in a right circular cylindrical vessel partly filled with water. The radius of the cylindrical vessel is 10 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel ?

Correct Answer: (a) ⁵⁄₃ cm
Solution:

82. Consider the following statements

I. The angle in a sector greater than a semi-circle is less than a right angle.

II. If two sides of a pair of opposite sides of a cyclic quadrilateral are equal, then its diagonals are also equal.

Which of the statements given above is/are correct?

Correct Answer: (c) Both I and II
Solution:



83. If a, b, c, x, y, z are real numbers such that

(a + b + c)² - 3(ab + bc + ca)
+ 3(x² + y² + z²) = 0 then
which one of the following is correct?

Correct Answer: (c) a = b = c, x = y = z = 0
Solution:



84. In a triangle ABC, angle B = 90° and p is the length of the perpendicular from B to AC. If BC = 10 cm and AC = 12cm, then what is the value of p ?

Correct Answer: (a)
Solution:


85. The mean of p, q, r, s and t is 280. If the mean of p, r and t is 240, what is the mean of q and s ?

Correct Answer: (d) 340
Solution:

86. (Questions 86-90) Consider the following for the next five items that follow.

A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B as G to E and E to D. The average age of D and G is 16 yrs; the average age of A and E is 11 yr, the average age of B and C is also 11 yr. B and C have equal weight. A's weight is 10 kg less than that of B, D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight ratio of 9 : 20, where age is in years and weight in kg; A has age-weight ratio of 2 : 5. Moreover, none of them is more than 40 kg.

What is D's age (in yr)?

Correct Answer: (d) 18
Solution:

D's age is 18 yr.

87. What is the average age (in yr) of B, C, D, E and G?

Correct Answer: (c) 14
Solution:Required average age
= (12 + 10 + 18 + 16 + 14) ÷ 5
= 70 ÷ 5 = 14

88. What is the difference between the weights (in kg) of G and C?

Correct Answer: (b) 3
Solution:Difference between weights of G and C = 28 - 25 = 3

89. What is the average weight (in kg) of A, B, C, D, E, F and G?

Correct Answer: (a) 201÷7
Solution:Required average weight
= (15 + 25 + 25 + 40 + 36 + 32 + 28) ÷ 7
= 201 ÷  7

90. Consider the following statements.

1. The age of F cannot be determined due to insufficient data.
2. The average weight of D and F is equal to weight of E.
3. The weight difference is maximum for D and A.

Which of the statements given above are correct?

Correct Answer: (d) 1, 2 and 3
Solution:All are correct.