CAT (QA) PYQs

If $a, b$ and $c$ are positive integers such that $ab = 432, bc = 96$ and $c < 9,$ then the smallest possible value of $a + b + c$ is

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

How many different pairs $(a, b)$ of positive integers are there such that $a ≤ b$ and $\frac{1}{a} + \frac{1}{b} = \frac{1}{9}$