CAT (QA) PYQs

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

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

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