Two finite sets have \(m\) and \(n\) elements respectively. The number of subsets of the first set is greater than the number of subsets of the second by \(56\). Then the value of \(m^2+n^2\) is equal to

None

let $m>n$

$2^m-2^n=56$

so $2^n(2^{m-n}-1)=2^3×7$

on comparison

$2^n=2^3⇒n=3$

$2^{m-n}-1=7⇒2^{m-n}=8⇒2^{m-n}=2^3$

$⇒m-n=3⇒m=6$

so $m^2+n^2=36+9=45$