UPSC NDA Math Model Paper 8

Total number of subsets of the first is 2m while total number of subsets of the second is 2n.

Now it is given that
2m=2n+56
⇒2m−2n=56
⇒23(2m−3−2n−3)=56
⇒(2m−3−2n−3)=7
⇒(2m−3−2n−3)=8−1
⇒(2m−3−2n−3)=23−20
Hence compare the terms,
m−3=3 thus m=6 and
n−3=0 giving n=3
Hence, (m,n)=(6,3)