• Q1:

The value of $\frac{\text{sin } 45^\circ + \text{ sin } 105^\circ + \text{ cos } 105^\circ \text{ cos } 45^\circ} { \text{sin } 75^\circ + \text{ cos } 75^\circ }$ is euqal to

1. (A)$\frac{1}{\sqrt6}$
2. (B)$\frac{1}{\sqrt3}$
3. (C)$\frac{1}{2\sqrt3}$
4. (D)$\frac{1}{3\sqrt2}$

• Q2:

If $\text{ tan}x + \text{cot}x = 3, \text{then sec}^2x + \text{cosec}^2x$ is equal to

1. (A)3
2. (B)9
3. (C)12
4. (D)15

• Q3:

Two boys are on opposite sides of a tower of 100 meter height. If they measure the elevation of the top of the tower as $30^\circ$ and $45^\circ$ respectively, the distance between the tower is 200 metres, then the distance between the boys is

1. (A)$100\sqrt3 \text{ metres}$
2. (B)$100(\sqrt3 + 1) \text{ metres}$
3. (C)$100(\sqrt3 - 1) \text{ metres}$
4. (D)$100\sqrt3 + 1 \text{ metres}$

• Q4:

For $\lambda \ne 0$, the angle between the lines given by the equation $\lambda y^2 + (1 - \lambda^2) \; xy - \lambda x^2 = 0$ is

1. (A)$30^\circ$
2. (B)$45^\circ$
3. (C)$60^\circ$
4. (D)$90^\circ$
If $\text{cos } \alpha + \text{sec } \alpha = 2$, then the value of $\text{cos}^8 \alpha + \text{sec}^8 \alpha$ is equal to
1. (A)$2$
2. (B)$2^2$
3. (C)$2^4$
4. (D)$2^8$