CAT (QA) PYQs

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

If the sum of squares of two numbers is $97$, then which one of the following cannot be their product?

Let $n$ be any natural number such that $5^{n-1} < 3^{n+1}$. Then, the least integer value of m that satisfies $3^{n+1} < 2^{n+m}$ for each such $n$, is