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 : 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 : 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 $x+\left [\frac{1}{(x+7)}\right]=0$, what is the value of $x-\left [\frac{1}{(x+7)}\right]$?

Option 1: $3\sqrt{5}$

Option 2: $3\sqrt{5}-7$

Option 3: $3\sqrt{5}+7$

Option 4: $8$

Question : If $\frac{10x}{3}+\frac{5}{2}(2-\frac{x}{3})=\frac{7}{2}$, then the value of $x$ is:

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

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

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

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