Question : $2\sqrt[3]{40}-4\sqrt[3]{320}+3\sqrt[3]{625}-3\sqrt[3]{5}$ is equal to:

Option 1: $-2\sqrt[3]{340}$

Option 2: $0$

Option 3: $\sqrt[3]{340}$

Option 4: $\sqrt[3]{660}$

Question : If $x=\sqrt{–\sqrt{3}+\sqrt{3+8 \sqrt{7+4 \sqrt{3}}}}$ where $x > 0$, then the value of $x$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 1

Option 4: 2

Question : If $x^{2} + \frac{1}{x^{2}} = 18$ and $x > 0$, what is the value of $x^{3} + \frac{1}{x^{3}}?$

Option 1: $36 \sqrt{5}$

Option 2: $40 \sqrt{5}$

Option 3: $46 \sqrt{5}$

Option 4: $34 \sqrt{5}$

Question : If $\left(x^2+\frac{1}{x^2}\right)=7$, and $0<x<1$, find the value of $x^2-\frac{1}{x^2}$.

Option 1: $3 \sqrt{5}$

Option 2: $4 \sqrt{5}$

Option 3: $-4\sqrt{3}$

Option 4: $-3\sqrt{5}$

Question : If $m=\sqrt{5+\sqrt{5+\sqrt{5+........}}}$ and $n=\sqrt{5-\sqrt{5-\sqrt{5...........}}}$ then among the following, the relation between m and n is:

Option 1: $m - n + 1 = 0$

Option 2: $m + n - 1 = 0$

Option 3: $m + n + 1 = 0$

Option 4: $m - n - 1 = 0$

Question : If $x^2-7 x+1=0$ and $0<x<1$, what is the value of $x^2-\frac{1}{x^2}?$

Option 1: $21\sqrt{5}$

Option 2: $-21\sqrt{5}$

Option 3: $28\sqrt{5}$

Option 4: $-28\sqrt{5}$