CAT (QA) PYQs

How many pairs $(a, b)$ of positive integers are there such that $a \le b$ and $ab =$ $4^{2017}$?

The sum of the first two natural numbers, each having $15$ factors (including $1$ and the number itself), is

How many factors of $2^4 \times 3^5 \times 10^4$ are perfect squares which are greater than $1?$