CAT (QA) PYQs

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

The smallest integer $n$ such that $n^3 - 11n^2 + 32n - 28 > 0$ is

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