CAT (QA) PYQs

The minimum possible value of the sum of the squares of the roots of the equation $x^{2}+(a+3) x-(a+5)=0$ is

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

The minimum possible value of $\frac{x^2-6x+10}{3-x}$, for $x < 3$, is