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

If $x$ and $y$ are positive real numbers satisfying $x + y = 102$, then the minimum possible value of $2601(1+\frac{1}{x})(1+\frac{1}{y})$ is