CAT (QA) PYQs

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

The number of pairs of integers ( $x, y$ ) satisfy $x \geq y \geq-20$ and $2 x+5 y=99$ is

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