CAT (QA) PYQs

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

Let $f(x) =$ min{$2x², 52-5x$}, where x is any positive real number. Then the maximum possible value of $f(x)$ is