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 : $\frac{1}{\sqrt a}-\frac{1}{\sqrt b}=0$, 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 $n= 7+4\sqrt{3}$, the value of $(\sqrt{n}+\frac{1}{\sqrt{n}})$ is:

Option 1: $2\sqrt{3}$

Option 2: $4$

Option 3: $-4$

Option 4: $-2\sqrt{3}$

Question : If $\sin(\theta+30^{\circ})=\frac{3}{\sqrt{12}}$, then the value of $\cos^{2}\theta$ is:

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

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

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

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

Question : The value of $\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{8}}$ is:

Option 1: $2-2 \sqrt{2}$

Option 2: $4+2 \sqrt{2}$

Option 3: $4-2 \sqrt{2}$

Option 4: $2+2 \sqrt{2}$