CAT (QA) PYQs

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

The number of solutions $(x, y, z)$ to the equation $x - y - z = 25$, where $x, y$, and $z$ are positive integers such that $x \le 40, y \le 12$, and $z \le 12$ is

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