Question : If $2x=\sqrt{a}+\frac{1}{\sqrt{a}}, a>0$, then the value of $\frac{\sqrt{x^{2}-1}}{x-\sqrt{x^{2}-1}}$ is:

Option 1: $a+1$

Option 2: $\frac{1}{2}(a+1)$

Option 3: $\frac{1}{2}(a–1)$

Option 4: $a–1$

Question : If $\frac{\sqrt{38-5 \sqrt{3}}}{\sqrt{26+7 \sqrt{3}}}=\frac{a+b \sqrt{3}}{23}, b>0$, then the value of $(b-a)$ is:

Option 1: 7

Option 2: 18

Option 3: 29

Option 4: 11

Question : Which of the following is TRUE?
I. $\frac{1}{\sqrt[3]{12}}>\frac{1}{\sqrt[4]{29}}>\frac{1}{\sqrt5}$
II. $\frac{1}{\sqrt[4]{29}}>\frac{1}{\sqrt[3]{12}}>\frac{1}{\sqrt5}$
III. $\frac{1}{\sqrt5}>\frac{1}{\sqrt[3]{12}}>\frac{1}{\sqrt[4]{29}}$
IV. $\frac{1}{\sqrt5}>\frac{1}{\sqrt[4]{29}}>\frac{1}{\sqrt[3]{12}}$

Option 1: Only I

Option 2: Only II

Option 3: Only III

Option 4: Only IV

Question : If $\frac{\sqrt{26-7 \sqrt{3}}}{\sqrt{14+5 \sqrt{3}}}=\frac{b+a \sqrt{3}}{11}, b>0$, then what is the value of $\sqrt{(\mathrm{b}-\mathrm{a})}$?

Option 1: 5

Option 2: 25

Option 3: 12

Option 4: 9

Question : If $\frac{22 \sqrt{2}}{4 \sqrt{2}-\sqrt{3+\sqrt{5}}}=a+\sqrt{5} b$, with $a, b>0$, then what is the value of $(a b):(a+b)$?

Option 1: 7 : 8

Option 2: 7 : 4

Option 3: 4 : 7

Option 4: 8 : 7