CAT 2017 [slot 1] Question with solution 28

For the value of given expression to be minimum, the values of $a, b, c$ and $d$ should be as close as possible. 30/4 = 7.5. Since each one of these are integers so values must be 8, 8, 7, 7. On putting these values in the given expression, we get
$(8 - 8)^{2} + (8 - 7)^{2} + (8 - 7)^{2}$
=> 1 + 1 = 2