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

If $C$ = $\frac{16x}{y} + \frac{49y}{x}$ for some non-zero real numbers $x$ and $y$, then $c$ cannot take the value

Let p, q and r be three natural numbers such that their sum is 900, and r is a perfect square whose value lies between 150 and 500. If p is not less than 0.3q and not more than 0.7q, then the sum of the maximum and minimum possible values of p is