CAT (QA) PYQs

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

For real $x,$ the maximum possible value of $\frac{x}{\sqrt{1+x^4}}$ is

Let k be the largest integer such that the equation $(x - 1)^2 + 2kx + 11 = 0$ has no real roots. If y is a positive real number, then the least possible value of $k/4y + 9y$ is