Let A and B be two finite sets with m and n elements respectively.

Question

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B$. Then the distance of the point $P(m, n)$ from the point ...

Accepted Answer

$\begin{gathered} {2}^{m}-{2}^{n}=56 \ {2}^{n}({2}^{m-n}-1)={2}^{3}	imes 7 \ {2}^{n}={2}^{3}{2}^{m-n}-1=7 \ \Rightarrow n=3{2}^{m-n}=8 \ \Rightarrow n=3m-n=3 \ \Rightarrow n=3m=6 \ P(6,3)Q(-2,-3) \ PQ=\sqrt{{8}^{2}+{6}^{2}}=\sqrt{100}=10 \end{gathered}$

Hence option (1) is correct

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