CAT (QA) PYQs

How many three-digit numbers are greater than $100$ and increase by $198$ when the three digits are arranged in the reverse order?

For a $4$-digit number, the sum of its digits in the thousands, hundreds and tens places is $14$, the sum of its digits in the hundreds, tens and units places is $15$, and the tens place digit is $4$ more than the units place digit. Then the highest possible $4$-digit number satisfying the above conditions is

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