CAT (QA) PYQs

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

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

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