Question : If $x=\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}$, then the value of $\frac{\sqrt{3}-x}{\sqrt{3}+x}$ (corrected to two decimal places) is:

Option 1: 0.25

Option 2: 0.17

Option 3: 0.19

Option 4: 0.27

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 $\cos27^{\circ}$ = $x$, then the value of $\tan 63°$ is:

Option 1: $\frac{x}{\sqrt{1–x^2}}$

Option 2: $\frac{x}{\sqrt{1+x^2}}$

Option 3: $\frac{\sqrt{1–x^2}}{x}$

Option 4: $\frac{\sqrt{1+x^2}}{x}$

Question : If $x=\frac{1}{x-3},(x>0)$, then the value of $x+\frac{1}{x}$ is:

Option 1: $\sqrt{11}$

Option 2: $\sqrt{17}$

Option 3: $\sqrt{15}$

Option 4: $\sqrt{13}$

Question : If $x=\frac{4\sqrt{ab}}{\sqrt a+ \sqrt b}$, then what is the value of $\frac{x+2\sqrt{a}}{x-2\sqrt a}+\frac{x+2\sqrt{b}}{x-2\sqrt b}$(when $a\neq b$)?

Option 1: 0

Option 2: 2

Option 3: 4

Option 4: $\frac{(\sqrt a+\sqrt b)}{(\sqrt a - \sqrt b)}$

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: $3$