CAT (QA) PYQs

How many pairs $(a, b)$ of positive integers are there such that $a \le b$ and $ab =$ $4^{2017}$?

The sum of the first two natural numbers, each having $15$ factors (including $1$ and the number itself), is

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