Question : The simplified value of $(\sqrt{3}+1)( 10+\sqrt{12})(\sqrt{12}-2)(5-\sqrt{3})$ is:

Option 1: 16

Option 2: 88

Option 3: 176

Option 4: 132

Question : If $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then the value of $x^{3} + y^{3}$ is:

Option 1: 950

Option 2: 730

Option 3: 650

Option 4: 970

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 $a= \frac{\sqrt{x+2}+\sqrt{x-2}}{\sqrt{x+2}-\sqrt{x-2}}$, then the value of $(a^{2}-ax)$ is:

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : What is the value of the positive square root of $(69+28\sqrt{5})$?

Option 1: $(7+2\sqrt{5})$

Option 2: $(7-2\sqrt{5})$

Option 3: $(2+7\sqrt{5})$

Option 4: $(2-7\sqrt{5})$