CAT (QA) PYQs

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 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