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 $(x+\frac{1}{x})=3$, then $(x^8+\frac{1}{x^8})$ is equal to:

Option 1: 2201

Option 2: 2203

Option 3: 2207

Option 4: 2213

Question : If $x+3y=-3x+y$, then $\frac{x^{2}}{2y^{2}}$ is equal to:

Option 1: $\frac{1}{8}$

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

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

Option 4: $4$

Question : If $5x+\frac{1}{x}=10$, then $x^2+\frac{1}{25x^2}$ is equal to:

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

Option 2: $3\frac{1}{5}$

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

Option 4: $2\frac{3}{5}$

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: $\frac{3}{5}$