CAT (QA) PYQs

For any natural number $n$, let $a_{n}$ be the largest integer not exceeding $\sqrt{n}$. Then the value of $a_{1}+a_{2}+\ldots .+a_{50}$ is

The number of integers $x$ such that $0.25 < 2^x < 200$, and $2^x + 2$ is perfectly divisible by either $3$ or $4$, is

How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7?$