Question : If $k$ is the largest possible real number such that $p^{4}+q^{4}=(p^{2}+kpq+q^{2})(p^{2}-kpq+q^{2})$, then the value of $k$ is:

Option 1: $1$

Option 2: $–\sqrt{2}$

Option 3: $2$

Option 4: $\sqrt{2}$

Question : $x$ is a negative number such that $k+k^{-1}=-2$, then what is the value of $\frac{k^2+4 k-2}{k^2+k-5}$?

Option 1: 7

Option 2: 1

Option 3: –7

Option 4: –1

Question : The value of $\sqrt{–\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}$ is:

Option 1: 2

Option 2: 4

Option 3: $\pm 2$

Option 4: –2

Question : If $p^{3}-q^{3}=(p-q)[(p+q)^{2}-xpq$, then the value of $x$ is:

Option 1: 1

Option 2: –1

Option 3: 2

Option 4: –2

Question : If $a = 64$ and $b = 289$, then the value of $\sqrt{\sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}}}$ is:

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

Option 2: $2$

Option 3: $4$

Option 4: $–1$

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