Question : If $\sqrt[3]{N}$ lies between 6 and 7, where $N$ is an integer then how many values $N$ can take?

Option 1: 126

Option 2: 127

Option 3: 128

Option 4: 125

Question : If $n= 7+4\sqrt{3}$, the value of $(\sqrt{n}+\frac{1}{\sqrt{n}})$ is:

Option 1: $2\sqrt{3}$

Option 2: $4$

Option 3: $-4$

Option 4: $-2\sqrt{3}$

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 : Find the mean proportion between $(6+\sqrt{8})$ and $(3-\sqrt{2})$.

Option 1: $2 \sqrt{12}$

Option 2: $\sqrt{14}$

Option 3: $(6-\sqrt{8})$

Option 4: $\sqrt{15}-7$

Question : The value of $\frac{7+3 \sqrt{5}}{3+\sqrt{5}}-\frac{7-3 \sqrt{5}}{3-\sqrt{5}}$ lies between:

Option 1: 3 and 3.5

Option 2: 2 and 2.5

Option 3: 1.5 and 2

Option 4: 2.5 and 3

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: $6\sqrt{6}$