CAT (QA) PYQs

The number of real-valued solutions of the equation $2^x + 2^{-x} = 2 - (x - 2)^2$ 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

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