CAT (QA) PYQs

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

While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of the sum of squares of the other two numbers is