• Q1:

If $x + y = 2$, then the value of $x^4 + y^4 - x^3y^2 - x^2y^3 + 16xy$ is equal to

1. (A)16
2. (B)32
3. (C)4
4. (D)2

• Q2:

If the roots of the equation $ax^2 + 2bx + c = 0$ are $\alpha \text{ and } \beta$ is equal to

1. (A)$\frac{2b}{ac}$
2. (B)$-\frac{2b}{\sqrt ac}$
3. (C)$\frac{2b}{\sqrt ac}$
4. (D)$\frac{-b}{\sqrt ac}$

• Q3:

If $2^x = 4^y = 8^z$ and $xyz = 288$, then $\frac{1}{2x} + \frac{1}{4y} + \frac{1}{8z}$ is equal to

1. (A)$\frac{11}{8}$
2. (B)$\frac{11}{24}$
3. (C)$\frac{11}{48}$
4. (D)$\frac{11}{96}$

• Q4:

if  $\Big(\frac{a}{b} \Big)^{x-1} = \Big(\frac{b}{a}\Big)^{x-3}$, then the value of x is

1. (A)1
2. (B)2
3. (C)3
4. (D)4
The solution of the equation $2^{x-7} = 256$ is