CAT (QA) PYQs

What is the largest positive integer such that $\frac{n^2 + 7n + 12}{n^2 - n - 12}$ is also a positive integer?

For real $x,$ the maximum possible value of $\frac{x}{\sqrt{1+x^4}}$ is

For natural numbers $x$, $y$, and $z$, if $xy + yz = 19$ and $yz + xz = 51$, then the minimum possible value of $xyz$ is