CAT (QA) PYQs

If $p^{2}+q^{2}-29=2 p q-20=52-2 p q$, then the difference between the maximum and minimum possible value of $\left(p^{3}-q^{3}\right)$ is

If $x$ is a positive real number such that $x^8 + \frac{1}{x^8} = 47$, then the value of $x^9 + \frac{1}{x^9}$ is

If $(a + b\sqrt{3})^2 = 52 + 30\sqrt{3}$, where $a$ and $b$ are natural numbers, then $a + b$ equals