CAT (QA) PYQs

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

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