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

Total Questions: 100

21. The arithmetic mean of n numbers is M. If the sum of first (n - 1) terms is k, then what is the nth number?

Correct Answer: (b) nM - k
Solution:

22. What is the geometric mean of 3, 9, 27, 81, 243, 729, 2187?

Correct Answer: (a) 81
Solution:3, 9, 27, 81, 243, 729, 2187 ?
If a₁, a₂, ..... aₙ are in GP,

23. A person purchases one kg of tea powder from each of the four places A, B, C, D at the rate of ₹1000 per 1 kg, 2 kg, 4 kg, 5 kg. If on an average he purchased x kg of tea powder per ₹1000, then what is the approximate value of x ?

Correct Answer: (c) 2.05
Solution:

24. What is the sum of the largest and the smallest 4-digit numbers made by using single digit prime numbers (without repetition)?

Correct Answer: (d) 9889
Solution:Single digit prime number are 2, 3, 5, 7.
Now largest four digit = 7532
and smallest four digit number = 2357
Now sum of largest and smallest four digit
number = 7532 + 2357 = 9889
∴ (d) is the correct option.

25. What is the remainder when 3²⁵⁵ is divided by 28?

Correct Answer: (d) 27
Solution:

26. What is the value of x(0 ≤ x ≤ 8) if (100⁹⁷ + 100⁵⁴ + x + 1) leaves a remainder 0 when divided by 9?

Correct Answer: (b) 6
Solution:

27. In a triangle ABC, D is a point on BC. If AB ⋅ DC = AC ⋅ BD angle ∠BAD = α and ∠CAD = β then which one of the following is correct?

Correct Answer: (a) α = β
Solution:

28. Let N = 12345678AB be a 10 digit number, where A, B are digits. If N is divisible by 9, then which of the following statements is/are correct?

I. (A + B) is divisible by 9.
II. If A is odd, then B is odd.

Select the answer using the code given below.

Correct Answer: (a) Only I
Solution:

29. .

Correct Answer: (b) 6
Solution:

30. If 11x + 5y is a prime number where x, y are natural numbers, then what is the minimum value of (x + y) ?

Correct Answer: (c) 5
Solution:11x + 5y is a prime number,
x, y ∈ N
Applying hit and trial method
Take, x = 1, y = 1
11+5= 16 is not prime number
Now, x = 1, y = 4
11+20= 31 is prime number.
So, x + y = 5