CAT (QA) PYQs

Consider the pair of equations: $x^{2}-x y-x=22$ and $y^{2}-x y+y=34$. If $x>y$, then $x-y$ equals

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