Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

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

Option 4: $2$

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

Option 1: $\frac{14}{13}$

Option 2: 1

Option 3: $\frac{13}{15}$

Option 4: $\frac{15}{13}$

Question : If $x-\frac{1}{x}=5, x \neq 0$, then what is the value of $\frac{x^6+3 x^3-1}{x^6-8 x^3-1} ?$

Option 1: $\frac{3}{8}$

Option 2: $\frac{13}{12}$

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

Option 4: $\frac{11}{13}$

Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?

Option 1: –$10$

Option 2: $\frac{9}{8}$

Option 3: $10$

Option 4: $–\frac{9}{8}$

Question : The value of $\left(2 \frac{6}{7}\right.$ of $\left.4 \frac{1}{5} \div \frac{2}{3}\right) \times 5 \frac{1}{9} \div\left(\frac{3}{4} \times 2 \frac{2}{3}\right.$ of $\left.\frac{1}{2} \div \frac{1}{4}\right)$ is:

Option 1: 25

Option 2: 19

Option 3: 23

Option 4: 21