(Mathematics) NDA/NA SOLVED PAPER 2024 – I (01 to 50)

Total Questions: 50

21. What is the number of different matrices, each having 4 entries that can be formed using 1, 2, 3, 4 (repetition is allowed)?

Correct Answer: (d) 768
Solution:Possible order of matrices with 4 entries

1 × 4,  2 × 2,  4 × 1

Total number of matrices = 4 × 4 × 4 × 4 × 3 = 768

22. Let A = {x ∈ R : - 1 < x < 1}. Which of the following is/are bijective functions from A to itself?

(A) f(x) = x|x|

(B) g(x) = cos(πx)

Select the correct answer using the code given below:

Correct Answer: (a) A only
Solution:

23. Let R be a relation on the open interval (-1, 1) and is given by

R = {(x, y) : |x + y| < 2}. Then which of the following is correct?

Correct Answer: (d) R is an equivalence relation
Solution:

24. For any three non-empty sets A, B, C, what is

(A ∪ B) - {(A - B) ∪ (B - A) ∪ (A ∩ B)} is equal to?

Correct Answer: (a) Null set
Solution:

25. If a, b, c are the sides of triangle ABC, then what is

Correct Answer: (a) Zero
Solution:

26. If a, b, c are in AP; b, c, d are in GP; c, d, e are in HP, then which of the following is/are correct?

(A) a, c and e are in GP

(B) 1/a,  1/c,  1/e are in GP

Select the correct answer using the code given below:

Correct Answer: (a) A only
Solution:

27. What is the number of solutions of

log₄ (x - 1) = log₂ (x - 3)?

Correct Answer: (b) One
Solution:

28. Then the value of k can never be equal to?

Correct Answer: (d) 1
Solution:

29. which of the following statements is/ are correct?

(A) A⁻¹ = adjA

(B) A is skew-symmetric matrix

(C) A⁻¹ = Aᵀ

Select the correct answer using the code given below:

Correct Answer: (c) A and C
Solution:

30. What is the coefficient of x¹⁰ in the expansion of

Correct Answer: (a) -1
Solution: