UPSC CAPF Assistant Commandant Model Paper 1

Given,3737+37
=(38)37+37
=−(1−38)2+37
(1−x)n=1−nx+n(n−1)x /2......
Thus, (1–38)37 = 1 – 37 × 38 …. All other term will contain 38.
= - (1 – terms containing 38 as a factor) + 37
= terms containing 38 as a factor + 36
Thus when the above number is divided by 38, remainder will be 36.