NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

1. Let θ be a positive angle. If the number of degrees in θ is divided by the number of radians in θ, then an irrational number 180/π results. If the number of degrees in theta is multiplied by the number of radians in θ, then an irrational number 125π/9 results. The angle θ must be equal to

Correct Answer: (c) 50°
Solution:



2. In a triangle ABC, a = (1 + √3) cm, b = 2 cm and angle C = 60°. Then the other two angles are

Correct Answer: (a) 45° and 75°
Solution:


3. What is tan α equal to?

Let α be the root of the equation 2cos² θ + 5cos θ - 12 = 0, where π/2 < α < π.

Correct Answer: (a) - 3/4
Solution:


4. What is sin 2 α equal to?

Let α be the root of the equation 2cos² θ + 5cos θ - 12 = 0, where π/2 < α < π.

Correct Answer: (b) - 24/25
Solution:

5. The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?

Correct Answer: (b) 20m
Solution:

6. The equation tan⁻¹(1 + x) + tan⁻¹(1 - x) = π/2 is satisfied by

Correct Answer: (c) x = 0
Solution:

7. The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43° and 47° respectively. What is the height of the tower?

Correct Answer: (b) 42m
Solution:


8. (1 - sin A + cos A) ^ 2 is equal to

Correct Answer: (b) 2(1 - sin A)(1 + cos A)
Solution:(1 - sin A + cos A)² = 1 + sin² A + cos² A - 2sin A - 2sin A cos A + 2cos A
= 2 - 2sin A - 2sin A cos A + 2cos A
= 2(1 - sin A) + 2cos A (1 - sin A)
= 2(1 + cos A)(1 - sin A)
∴ Option (b) is correct.

9. Solve the following equation

Correct Answer: (b) sin θ + cos θ
Solution:

10. What is x equal to?

Consider x = 4 tan⁻¹(1/5), y = tan⁻¹(1/70) and z = tan⁻¹(1/99)

Correct Answer: (b) tan⁻¹(120 / 119)
Solution: