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 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

If $m$ and $n$ are natural numbers such that $n > 1$, and $m^{n}=2^{25} \times 3^{40}$, then $m-n$ equals