CAT (QA) PYQs

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

The number of integers n that satisfy the inequalities $|n -60| < |n-100| <| n-20|$ is

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