Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.

Option 1: $1$

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

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

Option 4: $0$

Question : In a right triangle for an acute angle $x$, if $\sin x=\frac{3}{7}$, then find the value of $\cos x$.

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

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

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

Option 4: $\frac{2\sqrt{10}}{7}$

Question : If $2 x^2-7 x+5=0$, then what is the value of $x^2+\frac{25}{4 x^2} ?$

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

Option 2: $7 \frac{1}{4}$

Option 3: $9 \frac{1}{2}$

Option 4: $9 \frac{3}{4}$

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, for a non-zero $x, 5 x^2+7 x+5=0$, then the value of $x^3+\frac{1}{x^3}$ is:

Option 1: $\frac{496}{125}$

Option 2: $\frac{532}{343}$

Option 3: $\frac{125}{532}$

Option 4: $\frac{182}{125}$