Question : If $\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}=c$, then the value of $\mathrm{c}$ is:

Option 1: 1

Option 2: 4

Option 3: 3

Option 4: 2

Question : If $x+\frac{1}{x}=\sqrt{3}$, then the value of $x^{3}+\frac{1}{x^{3}}$ is equal to:

Option 1: $1$

Option 2: $3\sqrt{3}$

Option 3: $0$

Option 4: $3$

Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

Question : $\frac{1}{\sqrt a}-\frac{1}{\sqrt b}=0$, then the value of $\frac{1}{a}+\frac{1}{ b}$ is:

Option 1: $\frac{1}{\sqrt{ab}}$

Option 2: $\sqrt{ab}$

Option 3: $\frac{2}{\sqrt{ab}}$

Option 4: $\frac{1}{2\sqrt{ab}}$

Question : If $x+\frac{1}{x}=2$, then the value of $x^{2}+\frac{1}{x^{6}}$ is equal to:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3