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?

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

The number of real-valued solutions of the equation $2^x + 2^{-x} = 2 - (x - 2)^2$ is