CAT (QA) PYQs

A value of $c$ for which the minimum value of $f(x) = x^2 - 4cx + 8c$ is greater than the maximum value of $g(x) = -x^2 + 3cx - 2c$, is

An elevator has a weight limit of $630$ kg. It is carrying a group of people of whom the heaviest weighs $57$ kg and the lightest weighs $53$ kg. What is the maximum possible number of people in the group?

If $a$ and $b$ are non-negative real numbers such that $a + 2b = 6$, then the average of the maximum and minimum possible values of $(a + b)$ is