Question : If $(x+\frac{1}{x})$ = 5, then the value of $\frac{5x}{x^{2}+5x+1}$ is:

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

Option 2: $\frac{1}{4}$

Option 3: $\frac{1}{2}$

Option 4: $\frac{1}{5}$

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{5}$

Question : If $2\cot x=5$, then what is $\frac{2 \cos x-\sin x}{2 \cos x+\sin x}$ equal to?

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

Option 2: $\frac{1}{3}$

Option 3: $\frac{5}{6}$

Option 4: $\frac{2}{3}$

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

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

Option 2: $\frac{4}{3}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{5}{3}$

Question : If $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ and $x^2-x y+y^2=5 \frac{1}{4}$, then one of the values of $(x-y)$ is:

Option 1: $\frac{5}{2}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{5}{4}$

Option 4: $\frac{3}{2}$