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 $a=\frac{1}{a - 5}(a>0)$, then the value of $a+\frac{1}{a}$ is:

Option 1: $\sqrt{29}$

Option 2: $–\sqrt{27}$

Option 3: $-\sqrt{29}$

Option 4: $\sqrt{27}$

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

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 $x^2+y^2=29$ and $xy=10$, where $x>0,y>0$ and $x>y$. Then the value of $\frac{x+y}{x-y}$ is:

Option 1: $- \frac{7}{3}$

Option 2: $\frac{7}{3}$

Option 3: $\frac{3}{7}$

Option 4: $-\frac{3}{7}$