UPSC NDA Math Model Paper 1

For a given set of n elements:
The number of subsets with no elements =‌nC0=C0
The number of subsets with 1 element = The number of ways in which 1 element can be selected from n elements =‌nC1=C1.
The number of subsets with 2 elements = The number of ways in which 2 elements can be selected from n elements =‌−C2=C2.
And so on.
∴ The total number of subsets =C0+C1+C2+C3+......... +Cn−1+Cn=2n