CAT (QA) PYQs

Any non-zero real numbers $x, y$ such that $y \neq 3$ and $\frac{x}{y}<\frac{x+3}{y-3}$, Will satisfy the condition.

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

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