Mathematics NDA/NA SOLVED PAPER 2021-II (51 to 100)

Total Questions: 50

1. For what values of k is the system of equations 2k²x + 3y - 1 = 0, 7x - 2y + 3 = 0, 6kx + y + 1 = 0 consistent?

Correct Answer: (b)
Solution:

2. The inverse of a matrix A is given by

What is A equal to?

Correct Answer: (a)
Solution:

3. What is the period of the function f(x) =ln(2+sin²) ?

Correct Answer: (b) π
Solution:

4. If sin(A + B) = 1 and 2sin(A - B) = 1, where 0 < A, B <π/2 then what is tan A : tan B equal to?

Correct Answer: (d) 3 : 1
Solution:

5. Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

Correct Answer: (b) 50
Solution:

6. Consider all the real roots of the equation x⁴ - 10x² + 9 = 0. What is the sum of the absolute values of the roots?

Correct Answer: (c) 8
Solution:

7. Consider the expansion of (1 + x)ⁿ. Let p, q, r and s be the coefficients of first, second ,nᵗʰ and (n + 1)ᵗʰ terms respectively. What is (ps + qr) equal to?

Correct Answer: (c) 1 + n²
Solution:

8. Find the value?

Correct Answer: (c) 3
Solution:

9. Let sin x + sin y = cos x + cos y for all x, y ∈ R. What is tan (x/2 + y/2) equal to?

Correct Answer: (a) 1
Solution:

10. Where m, n are positive real numbers and I is the identity matrix. what is (m + n) equal to?

Correct Answer: (d) 3/2
Solution: