IPMAT Indore (SA) PYQs

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 ______

The length of the line segment joining the two intersection points of the curves $y = 4970 - |x|$ and $y = x ^ 2$ is

Given that $f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|, x \in(-\infty, \infty)$ the minimum value of $f(x)$ is _________.