Question : If $\sqrt{3^{n}} = 2187$, then the value of $n$ is:

Option 1: 13

Option 2: 14

Option 3: 15

Option 4: 16

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: $2+2 \sqrt{2}$

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 $y+\frac{1}{y}=11$, then the value of $y^3-\frac{1}{y^3}$ is:

Option 1: $345 \sqrt{13}$

Option 2: $360 \sqrt{13}$

Option 3: $352 \sqrt{13}$

Option 4: $368 \sqrt{13}$

Question : If $2=x+\frac{1}{1+\frac{1}{5+\frac{1}{2}}}$, then the value of $x$ is equal to:

Option 1: $\frac{14}{13}$

Option 2: 1

Option 3: $\frac{13}{15}$

Option 4: $\frac{15}{13}$

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: $\sqrt{13}$