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 $x+3y=-3x+y$, 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 : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

Option 4: $\frac{8}{7}$

Question : If $2x+\frac{2}{x}=3$, then the value of $x^{3}+\frac{1}{x^{3}}+2$ is:

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

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

Option 3: $\frac{5}{8}$

Option 4: $\frac{7}{8}$

Question : If $2x-\frac{2}{x}=1(x \neq 0)$, then the the value of $(x^3-\frac{1}{x^3})$ is:

Option 1: $\frac{13}{4}$

Option 2: $\frac{13}{8}$

Option 3: $\frac {17}{4}$

Option 4: $\frac{17}{8}$