CAT (QA) PYQs

If $a,b,c$ and $d$ are integers such that their sum is 46, then the minimum possible value of $(a-b)^2 + (a-c)^2 + (a-d)^2$ is

If $x$ and $y$ are positive real numbers satisfying $x + y = 102$, then the minimum possible value of $2601(1+\frac{1}{x})(1+\frac{1}{y})$ 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