MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (01 to 50)

Total Questions: 50

21. What is the maximum value of n such that 5ⁿ divides (30! + 35!) where n is a natural number?

Correct Answer: (c) 7
Solution:

22. What is the value of

2(2 × 1) + 3(3 × 2 × 1) + 4(4 × 3 × 2 × 1) +
5(5 × 4 × 3 × 2 × 1) +________+9(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) + 2?

Correct Answer: (b) 10!
Solution:

23. A = {(1, 2, 3)}, then how many elements are there in the power set of A?

Correct Answer: (b) 2
Solution:A = {(1,2,3)}
n(A) = 1
Number of element in P(A) = 2¹ = 2

24. If a, b, c are in GP where a > 0, b > 0, c > 0 then which of the following are correct?

1. a² b² c² in GP
2 1/a, 1/b, 1/c are in GP
3. √a, √b, √c are in GP
Select the correct answer using the code given below:

Correct Answer: (d) 1, 2 and 3
Solution:

25. If (a + b)/2, b, (b + c)/2 are in HP, then which one of the following is correct?

Correct Answer: (b) a, b, c are in GP
Solution:

26. What is value of cot²15° + tan²15°?

Correct Answer: (b) 14
Solution:

27. What is angle B equal to?

In a triangle ABC, sin A - cos B - cos C = 0.

Correct Answer: (d) π/2
Solution:

28. If α+ β = π/4 and 2tanα = 1, then what is tan 2β equal to?

Correct Answer: (c) 3/4
Solution:

29. If tan(45° + θ) = 1 + sin2θ, where -π/4 < θ < π/4 , then what is the value of cos2θ?

Correct Answer: (c) 1
Solution:

30. Let sin2θ = cos3θ, where θ is acute angle. What is the value of 1 + 4sinθ?

Correct Answer: (c) √5
Solution: