SOLVED PAPER 2024 (CDS) (II) (Mathematics)

Total Questions: 100

91. What is the HCF of 2³⁶-1 and 2⁴⁵-1?

Correct Answer: (c) 511
Solution:

92. The section of a solid right circular cone by a plane containing vertex and perpendicular to base is an equilateral triangle of side 14 cm. What is the volume of the cone? (π = 22/7)

Correct Answer: (b) 1078/√3 cubic cm
Solution:In ΔAOB,

93. Three identical cones each with base radius 3 cm are placed on their bases, so that each is touching the other two. There will be one and only circle that would pass through each of the vertices of the cones. What is the area of the circle?

Correct Answer: (d) 12π square cm
Solution:Area of circle
= π(2√3)²
= 12π
∴ (d) is the correct option

94. A circle is inscribed in a triangle ABC right-angled at B. If AB = 5 cm and BC = 12cm then what is the radius of the circle?

Correct Answer: (c) 2 cm
Solution:

95. The ratio of sum of interior angles to sum of exterior angles of a regular polygon of n sides is 7/2 . What is the measure of an interior angle of polygon?

Correct Answer: (d) 140°
Solution:

96. The number 199 can be written as m² - n² where m n are natural numbers (m > n) What is the value of mn?

Correct Answer: (a) 9900
Solution:m, n are natural numbers and (m > n)
m² - n² = 199
(m + n)(m - n) = 199 × 1
m + n = 199
m - n = 1
⇒ m = 100
⇒ n = 99
mn =100 × 99 ⇒ 9900
(a) is the correct option.

97. How many numbers of the form 2ⁿ-1 and less than 2000 are prime ?

Correct Answer: (b) 4
Solution:

98. In a class of 160 students, each of them opt at least one language from among English, Hindi and Sanskrit. It is found that 130 students opt English, 120 students Hindi and 110 Sanskrit. If the students opt either only one language or all three languages, then what is the number of students who study all three languages?

Correct Answer: (d) 100
Solution:Let all languages = x
Only English = (130-x)
Only Hindi (120-x)
Only Sanskrit = (110-x)
All three languages
= (130 - x) + (120 - x) + (110 - x) + x
⇒ 160 = 360 - 2x
2x = 200
x = 100

99. Let S = 5ᵃ + 7ᵇ + 11ᶜ + 13ᵈ where a, b, c and d are natural numbers. What is the number of distinct remainders of S when it is divided by 10?

Correct Answer: (c) 5
Solution:S = 5ᵃ + 7ᵇ + 11ᶜ + 13ᵈ
Here, 5 is even and the unit digit of even number is 0, 2, 4, 8
Number of distinct remainder of S when, it is divided by 10 is 5.

100. In a right triangle ABC, ∠A = 90° and AD is perpendicular to BC. If ∠CAD = 60° and BC = 6cm then what is AB equal to

Correct Answer: (a) 3 cm
Solution: