CAT (QA) PYQs

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

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