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

Total Questions: 100

71. The total population of an area is 10000 put of which males and females are equal in number. Out of the total population 30% are Newspaper readers. Out of the total newspaper readers, one-third read English Newspaper. Out of the total English Newspaper readers, 20% are females. What is the number of males who do not read English Newspaper?

Correct Answer: (c) 4200
Solution:

72. What is the maximum area of a rectangle, in square cm, whose perimeter is 400 cm?

Correct Answer: (d) 10000
Solution:

73. What is the remainder if we divide 3¹⁰ by 7?

Correct Answer: (d) 4
Solution:

74. What is the square root of 64%?

Correct Answer: (d) 80%
Solution:

75. The difference of 10³¹- 5 and 10³⁰+ p is divisible by 3 where p is a digit. How many values of p are possible?

Correct Answer: (b) 3
Solution:

76. Consider the following statements

I. 61 divides 107¹⁰⁰ - 76¹⁰⁰

II. 100 divides 67⁵ + 33⁵

Which of the statements given above is/are correct?

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

77. The average of the temperatures recorded at noontime from Monday to Sunday is 31°C If the lowest temperature recorded is 30°C then what is the maximum of temperature that is possible to record at noontime on any one of the days

Correct Answer: (d) 37°C
Solution:7 days (sum) = 31° × 7 = 217°C
(6 day)ₘᵢₙ = 6 × 30° × C = 180°C
The maximum of temperature any one of the days
= 217 - 180 = 37°C
∴ (d) is the correct answer.

78. Solved ?

Correct Answer: (b) -1
Solution:

79. Consider the following statements in respect of

p = n(n + 1)(n + 2)(n + 3) + 1
where n is a natural number.
I. p is always odd
II. p is a perfect square.
Which of the statements given above is/are correct?

Correct Answer: (c) Both I and II
Solution:P = n(n + 1)(n + 2)(n + 3) + 1
Here, n, (n + 1) (n + 2) (n + 3) are 4 consecutive natural number.
So n(n + 1)(n + 2)(n + 3) is an even number.
⇒ P is always odd.
So, Statement I is correct.
P = n(n + 1)(n + 2)(n + 3) + 1
= (n² + n)(n² + 5n + 6) + 1
= n⁴ + 5n³ + 6n² + n³ + 5n² + 6n + 1
= n⁴ + 6n³ + 11n² + 6n + 1
P = (n² + 3n + 1)²
So, P is always perfect square.
∴ (c) is the correct option.

80. What is the difference between the average of first 50 even natural numbers and the average of first 50 odd natural numbers?

Correct Answer: (c) 1
Solution: