NDA/NA SOLVED PAPER 2016-I (MATHEMATICS)

Total Questions: 120

1. Suppose w is a cube root of unity with ω ≠ 1. Suppose P and Q are the points on the complex plane defined by w and ω² . If O is the origin, then what is the angle between OP and OQ?

Correct Answer: (a) 60°
Solution:


2. Suppose there is a relation * between the positive numbers x and y given by xy if and only if x ≤ y². Then which one of the following is correct?

Correct Answer: (a) * is reflexive but not transitive and symmetric
Solution:

3. x² + px + 4 > 0 for all real values ofx, then which one of the following is correct?

Correct Answer: (b) |p| ≤ 4
Solution:

4. Solve the following equation

Correct Answer: (a) π
Solution:


5. Solve the following equation

Correct Answer: (a) In (1 - x)/(1 + x)
Solution:


6. What is the range of the function y = (x²)/(1 + x²), where x in R ?

Correct Answer: (a) [0, 1)
Solution:

7. A straight line intersects x and y axes at P and Q respectively. If (3, 5) is the middle point of PQ, then what is the area of the triangle OPQ?

Correct Answer: (d) 30 square units
Solution:

8. If a circle of radius b units with centre at (0, b) touches the line y = x - √2 then what is the value of b?

Correct Answer: (a) 2 + √2
Solution:

9. What is the maximum value of the function f(θ)?

Consider the function f(θ) = 4(sin²θ + cos⁴θ)

Correct Answer: (d) 4
Solution:


10. What is the minimum value of the function f(θ)?

Consider the function f(θ) = 4(sin²θ + cos⁴θ)

Correct Answer: (d) 3
Solution: