CAT (QA) PYQs

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

If $a$ and $b$ are integers such that $2x^2 - ax + 2 > 0$ and $x^2 −bx + 8 \geq 0$ for all real numbers $x,$ then the largest possible value of $2a-6b$ is

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