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 $(2+\sqrt{3})a=(2-\sqrt{3})b=1$, then the value of $\frac{1}{a}+\frac{1}{b}$ is:

Option 1: $1$

Option 2: $2$

Option 3: $2\sqrt{3}$

Option 4: $4$

Question : If $\text{a}= {\sqrt{2}+1}$ and $\text{b} = {\sqrt{2}–1}$, then the value of $\frac{1}{a+1}+\frac{1}{b+1}$ will be:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

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 : The value of $5–\frac{8+2\sqrt{15}}{4}–\frac{1}{8+2\sqrt{15}}$ is equal to:

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

Option 2: $1$

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

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