Mathematics (NDA/NA SOLVED PAPER 2021-I) (01 to 50)

Total Questions: 50

1. The smallest positive integer n for which

Correct Answer: (a) 2
Solution:

2. The value of x, satisfying the equation logcₒₛₓ sin x = 1, where 0 < x < π/2, is

Correct Answer: (c) π/4
Solution:

3. Find the value?

Correct Answer: (d) pqΔ
Solution:

4. If C₀, C₁, C₂,_____,Cₙ are the coefficients in the expansion of (1 + x)ⁿ, then what is the value of C₁ + C₂+ C₃+_____+Cₙ?

Correct Answer: (b) 2ⁿ- 1
Solution:

5. If a + b + c = 4 and ab + bc + ca = 0, then what is the value of the following determinant?

Correct Answer: (b) -64
Solution:

6. The number of integer values of k, for which the equation 2sin x = 2k + 1 has a solution, is

Correct Answer: (c) two
Solution:Hence, number of integer values of k that satisfy are 2 and that are (-1 and 0)

7. If a₁, a₂, a₃,______,a₉ are in GP, then what is the value of the following determinant?

Correct Answer: (a) 0
Solution:

8. If the roots of the quadratic equation x² + 2x + k = 0 are real, then

Correct Answer: (d)
Solution:

9. If n = 100!, then what is the value of the following?

Correct Answer: (b) 1
Solution:

10. If z = 1 + i, where i = √-1, then what is the modulus of z + 2/z?

Correct Answer: (b) 2
Solution: