CAT (QA) PYQs

If $a, b, c,$ and $d$ are integers such that $a + b + c + d = 30$, then the minimum possible value of $(a - b)^2 + (a - c)^2 + (a - d)^2$ is

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

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