Question : If $x=1+\sqrt{2}+\sqrt{3}$, then the value of $(2x^4-8x^3-5x^2+26x-28)$ is:

Option 1: $2\sqrt{2}$

Option 2: $3\sqrt{3}$

Option 3: $5\sqrt{5}$

Option 4: $6\sqrt{6}$

Question : If $\sqrt{11-3 \sqrt{8}}=a+b \sqrt{2}$, then what is the value of (2a + 3b) ?

Option 1: 7

Option 2: 9

Option 3: 3

Option 4: 5

Question : If $x^2-\frac{1}{x^2}=4 \sqrt{2}$, what is the value of $x^4-\frac{1}{x^4}?$

Option 1: $16 \sqrt{2}$

Option 2: $8\sqrt{2}$

Option 3: $24 \sqrt{2}$

Option 4: $32 \sqrt{2}$

Question : Which of the following given value is greater than $\sqrt[3]{12}$?

Option 1: $\sqrt[6]{121}$

Option 2: $\sqrt[12]{33214}$

Option 3: $\sqrt[5]{60}$

Option 4: $\sqrt[9]{1500}$

Question : Simplify the expression $\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}$, where $x=2$ and $y=3$.

Option 1: $2\sqrt{6}-6$

Option 2: $\sqrt{6}-5$

Option 3: $5-2\sqrt{6}$

Option 4: $2\sqrt{6}-5$