CAT (QA) PYQs

How many pairs $(m, n)$ of positive integers satisfy the equation $m^2 + 105 = n^2$?

If $a, b$ and $c$ are positive integers such that $ab = 432, bc = 96$ and $c < 9,$ then the smallest possible value of $a + b + c$ is

The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x > y \geq 3$ and $x + y < 14$ is