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 positive integers less than $50$, having exactly two distinct factors other than $1$ and 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