CAT (QA) PYQs

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

The number of positive integers less than $50$, having exactly two distinct factors other than $1$ and itself, is

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