NDA/NA SOLVED PAPER 2016-II (MATHEMATICS)

Total Questions: 120

1. Let S be a set of all distinct numbers of the form P/Q, where p, q ∈ {1, 2, 3, 4, 5, 6} . What is the cardinality of the set S?

Correct Answer: (b) 23
Solution:



2. If c > 0 and 4a + c < 2b then ax² - bx + c = 0 has a root in which one of the following intervals?

Correct Answer: (a) (0, 2)
Solution:Let f(x) = ax² - bx + c
f(2) = 4a - 2b + c < 0 (given)
f(0) = c > 0 (given)
So, we can see that sign of f(x) changes, when x changes from 0 to 2, so it has a root in the interval (0, 2).

3. If A = {x ∈ R : x² + 6x - 7 0} , then which of the following is/are correct?

1. A cap B = {X ∈ R : - 2 < x < 1}
2. A backslash B = {x ∈ R : - 7 < x < - 2}

Select the correct answer using the code given below:

Correct Answer: (c) Both 1 and 2
Solution:

4. IfA is semy square matrix of order 3 and det A = 5 then what is det[(2A)⁻¹] equal to?

Correct Answer: (d) 1/40
Solution:

5. What is ω¹⁰⁰ + ω²⁰⁰ + ω³⁰⁰ equal to, where is the cube root of unity?

Correct Answer: (d) 0
Solution:

6. If Re (z - 1)/(z + 1) = 0 where z = x + iy is a complex number, then which one of the following is correct?

Correct Answer: (d) |z| = 1
Solution:

7. Solve the following equation

Correct Answer: (d)
Solution:

8. Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n?

Correct Answer: (c) 5
Solution:

9. Solve the following equation

Correct Answer: (a) 0
Solution:

10. If both the roots of the equation x² - 2kx + k² - 4 = 0 lie between -3 and 5, then which one of the following is correct?

Correct Answer: (d) - 1 < k < 3
Solution: