IPMAT Indore (SA) PYQs

The sum of the squares of all the roots of the equation $x^{2}+|x+4|+|x-4|-35=0$ is

If $a, b, c$ are three distinct natural numbers, all less than $100$, such that $|a - b| + |b - c| = |c - a|$, then the maximum possible value of $b$ is ______

For $a > b > c > 0$, the minimum value of the function $f(x) = |x - a| + |x - b| + |x - c|$ is