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

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

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?