CAT (QA) PYQs

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

For natural numbers $x$, $y$, and $z$, if $xy + yz = 19$ and $yz + xz = 51$, then the minimum possible value of $xyz$ is

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