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 $x$ and $y$ are real numbers such that $x^2 + (x - 2y − 1)^2 = - 4y(x + y)$, then the value $x - 2y$ is

The product of two positive numbers is $616$. If the ratio of the difference of their cubes to the cube of their difference is $157: 3$, then the sum of the two numbers is