Question : If $x^{4}+\frac{1}{x^{4}}=16$, then what is the value of $x^{2}+\frac{1}{x^{2}}$?

Option 1: $3 \sqrt{2}$

Option 2: $2 \sqrt{2}$

Option 3: $5 \sqrt{2 }$

Option 4: $4 \sqrt{2}$

Question : If $x^2+y^2=427$ and $xy=202$, then find the value of $\frac{x+y}{x-y}$.

Option 1: $\sqrt{\frac{835}{23}}$

Option 2: $\sqrt{\frac{830}{29}}$

Option 3: $\sqrt{\frac{831}{23}}$

Option 4: $\sqrt{\frac{830}{23}}$

Question : If $\sin (x - y) = \frac{1}2$ and $\cos (x + y) = \frac{1}2$, then what is the value of $\sin x \cos x + 2\sin^2x + cos^3x \sec x$?

Option 1: $2$

Option 2: $\sqrt{2}+1$

Option 3: $1$

Option 4: $\frac{3}{4}$

Question : If $x+y=4, x^{2}+y^{2}=14$ and $x>y$, then the correct value of $x$ and $y$ is:

Option 1: $2+\sqrt{3} \text{ and } 2-\sqrt{3}$

Option 2: $2-\sqrt{2} \text{ and } \sqrt{3}$

Option 3: $3 \text{ and } 1$

Option 4: $2+\sqrt{3} \text{ and } 2\sqrt{2}$

Question : If $\sqrt{y}=4x$, then $\frac{x^{2}}{y}$ is:

Option 1: $2$

Option 2: $\frac{1}{16}$

Option 3: $\frac{1}{4}$

Option 4: $4$