AP EAMCET Engineering 26 Apr 2017 Shift 1 Paper

The coefficient of xr in the expansion of (1+x)n is given by nCr.
Therefore, the coefficient of x5 in the given expansion is calculated as,
Coeff x5=21C5+22C5+......+‌30C5
=21C6+21C5+22C5+....+30C5)−21C6
=(22C6+22C5+....+‌30C5)−21C6
Expanding in the similar pattern further,
cocff‌x5=(31C6+30C5)−21C6
=31C6−21C6