CAT (QA) PYQs

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

Suppose $a,b,c$ are three distinct natural numbers, such that $3ac = 8(a+b)$. Then, the smallest possible value of $3a+2b+c$ is

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