CAT (QA) PYQs

Let $n$ be the least positive integer such that 168 is a factor of $1134^n$. If m is the least positive integer such that $1134^{n}$. is a factor of $168^m$, then $m + n$ equals

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

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