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?

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

The minimum possible value of $\frac{x^2-6x+10}{3-x}$, for $x < 3$, is

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

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

Among $100$ students, $x_{1}$ have birthdays in January, $x_{2}$ have birthday in February, and so on.

If $x_{0}=\max \left(x_{1}, x_{2}, \ldots , x_{12}\right)$, then the smallest possible value of $x_{0}$ is

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