Question : If $\frac{x}{4 y}=\frac{3}{4}$ then, the value of $\frac{2 x+3 y}{x–2 y}$ is:

Option 1: 7

Option 2: 9

Option 3: 6

Option 4: 8

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

Option 1: 4

Option 2: 5

Option 3: 6

Option 4: 8

Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?

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

Option 2: $\frac{3\sqrt{15}}{5}$

Option 3: $\frac{3\sqrt{15}}{8}$

Option 4: $\frac{3\sqrt{5}}{8}$

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

Option 1: 5

Option 2: 6

Option 3: 9

Option 4: 7

Question : If the 9-digit number $72 x 8431y 4$ is divisible by 36, what is the value of $(\frac{x}{y}-\frac{y}{x})$ for the smallest possible value of $y$, given that $x$ and $y$ are natural numbers?

Option 1: $1 \frac{5}{7}$

Option 2: $2 \frac{1}{10}$

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

Option 4: $2 \frac{9}{10}$