Mathematics NDA/NA SOLVED PAPER 2018 (I) (01 to 50)

Total Questions: 50

1. Simplify the equation?

Correct Answer: (b) 2000
Solution:

2. Simplify the equation?

Correct Answer: (b) 1
Solution:

3. In the expansion of (1 + x)⁴³, if the coefficients of (2r + 1) th and (r + 2) th terms are equal, then what is the values of r (r≠ 1)?

Correct Answer: (b) 14
Solution:

4. What is the principal argument of (-1 -i), where i = √-1?

Correct Answer: (c) − 3π/4
Solution:

5. Let α and β be real number and z be a complex number. If z² + αz + β = 0 has two distinct non-real roots with Re (z) = 1, then it is necessary that:

Correct Answer: (c) β ∈ (1, ∞)
Solution:

6. Let A and B be subsets of X and C = ( A ∩ B′) ∪ ( A ′∩ B), where A' and B' are complements of A and B respectively in X. What is C equal to?

Correct Answer: (c) (A ∪ B) - (A ∩ B)
Solution:

7. How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed?

Correct Answer: (d) 60
Solution:

Number lying between 100 and 1000 are of three digit. Since the numbers are to be formed with 5, 6, 7, 8, 9 and repetition is not allowed, so total number of numbers
= 5 × 4 × 3 = 60

8. The number of non-zero integral solution of the equation |1 - 2i|ˣ = 5ˣ is:

Correct Answer: (a) Zero (no solution)
Solution:

9. If the ratio of AM of GM of two positive numbers a and b is 5 : 3, then a : b is equal to?

Correct Answer: (c) 9 : 1
Solution:

Let a and b be two numbers.

10. If the coefficients of aᵐ and aⁿ is the expansion of (1 + a)ᵐ ⁺ ⁿ are α and β, then which one of the following is correct?

Correct Answer: (c) 2α = β
Solution: