Question : If $\left(2^2+4\right)^2 \times(3-5)+20 \%$ of $400+x \%$ of $30=30 \%$ of $30$, find the value of $x$.

Option 1: 150

Option 2: 120

Option 3: 190

Option 4: 160

Question : If $\small p^{3}-q^{3}=\left (p-q \right )\left \{ \left (p-q \right)^{2}-xpq \right \}$, then find the value of $x$.

Option 1: 3

Option 2:  –3

Option 3: 1

Option 4:  –1

Question : If $x^{2}+x=19,$ then what is the value of $(x+5)^{2}+\left [ \frac{1}{(x+5)^{2}} \right ]\;?$

Option 1: 77

Option 2: 79

Option 3: 81

Option 4: 83

Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:

Option 1: $\frac{2 \sqrt{6}-6}{5}$

Option 2: $\frac{4 \sqrt{6}-6}{5}$

Option 3: $\frac{4 \sqrt{6}-6}{3}$

Option 4: $\frac{4 \sqrt{3}-6}{5}$

Question : If $x+\frac{1}{x}=2$, then find the value of $x^5+\frac{1}{x^5}$.

Option 1: 1

Option 2: 3

Option 3: 4

Option 4: 2

Question : If $\alpha +\beta =90^{0}$, then value of $\left (1-\sin^{2}\alpha \right)\left (1-\cos^{2}\alpha \right)\times \left (1+\cot^{2}\beta \right)\left (1+\tan^{2}\beta \right)$ is:

Option 1: 1

Option 2:  –1

Option 3: 0

Option 4: 2