CAT (QA) PYQs

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

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

The number of divisors of $(2^6 \times 3^5 \times 5^3 \times 7^2)$, which are of the form $(3r+1)$, where $r$ is a non-negative integer, is