CAT (QA) PYQs

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

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

If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is