CAT (QA) PYQs

$f(x) = \frac{x^2+2x-15}{x^2-7x-18}$ is negative if and only if

For how many integers $n$, will the inequality $(n - 5) (n - 10) - 3(n − 2) \leq 0$ be satisfied?

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?