1
###
Let a vertical tower AB have its end A on the level ground

Let a vertical tower AB have its end A on the level ground. Let C be the midpoint of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to:

- 6/7
- 1/4
- 2/9
- 4/9

2
###
If 5(tan^2 x – cos^2x) = 2 cos 2x + 9, then the value of cos 4x is

If 5(tan^{2} x – cos^{2}x) = 2 cos 2x + 9, then the value of cos 4x is

- -3/5
- 1/3
- 2/9
- -7/9

3
###
If 0 ≤ x the number of real values of x

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation

cos x + cos 2x + cos 3x + cos 4x = 0 is

- 3
- 5
- 7
- 9

4
###
The sum of the radii of inscribed and circumscribed circles

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

- a/2 cot(π/2n)
- a/4 cot(π/2n)
- a cot(π/n)
- a cot(π/2n)

5
###
Let cos(a + b) = 4/5 and let sin(a - b) = 5/13

Let cos(a + b) = 4/5 and let sin(a - b) = 5/13 where 0 ≤ a,b ≤ π/4. Then tan 2a is

- 20/17
- 25/16
- 56/33
- 19/12

6
###
In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1

In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

- π/4
- 3π/4
- 5π/6
- π/6

7
###
If A = sin^2 x + cos^4 x, then for all real x

If A = sin^{2} x + cos^{4} x, then for all real x

- 3/4 ≤ A ≤ 1
- 1 ≤ A ≤ 2
- 3/4 ≤ A ≤ 13/16
- 13/16 ≤ A ≤ 1

8
###
Let fk(x) = 1/k(sin^k x + cos^k x) where x ∈ R and k ≥ 1

Let f_{k}(x) = 1/k(sin^{k} x + cos^{k} x) where x ∈ R and k ≥ 1. Then f_{4}(x) - f_{6}(x) equals

- 1/12
- 1/6
- 1/4
- 1/3

9
###
The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

- 0
- 1
- 2
- 3

10
###
The number of real values of x, which satisfy the equation cosx + cos2x + cos3x + cos4x = 0

If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation

cosx + cos2x + cos3x + cos4x = 0 is:

- 5
- 7
- 9
- 3