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

If $N$ and $x$ are positive integers such that $N^{N}=2^{160}$ and $N^{2}+2 ^N$ is an integral multiple of $2^x$, then the largest possible $x$ is

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is