Question : If $x=1+\sqrt{2}+\sqrt{3}$, then the value of $(2x^4-8x^3-5x^2+26x-28)$ is:

Option 1: $2\sqrt{2}$

Option 2: $3\sqrt{3}$

Option 3: $5\sqrt{5}$

Option 4: $6\sqrt{6}$

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{5}{3}$

Question : If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$, what is the value of $x$?

Option 1: $\frac{5}{2}$

Option 2: $\frac{25}{3}$

Option 3: $4$

Option 4: $3$

Question : If $\left(x^2+\frac{1}{x^2}\right)=7$, and $0<x<1$, find the value of $x^2-\frac{1}{x^2}$.

Option 1: $3 \sqrt{5}$

Option 2: $4 \sqrt{5}$

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

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

Question : What is the value of $\sin 30^{\circ}+\cos 30^{\circ}+\tan 30^{\circ}$?

Option 1: $\frac{5+\sqrt{3}}{2 \sqrt{3}}$

Option 2: $\frac{5-\sqrt{3}}{2 \sqrt{3}}$

Option 3: $\frac{5+\sqrt{3}}{\sqrt{3}}$

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