Question : $\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=?$

Option 1: 5

Option 2: 4

Option 3: 3

Option 4: 2

Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:

Option 1: $5 \sqrt{5}$

Option 2: $4 \sqrt{5}$

Option 3: $2 \sqrt{5}$

Option 4: $3 \sqrt{5}$

Question : If $\left (\sqrt{5} \right)^{7}\div \left (\sqrt{5} \right)^{5}=5^{p},$ then the value of $p$ is:

Option 1: $5$

Option 2: $2$

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

Option 4: $1$

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

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

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$

Question : Which is the largest among the numbers $\sqrt{5},\ 3\sqrt{7}$ and $4\sqrt{13}$.

Option 1: $\sqrt{5}$

Option 2: $3\sqrt{7}$

Option 3: $4\sqrt{13}$

Option 4: All are equal