Q42 / 125 · BITSAT 2016 · Mathematics

Two finite sets have $m$ and $n$ elements. The number of subsets of the first set is 112 more than that of the second set. The values of $m$ and $n$ respectively are,

  • A
    4,7
  • Correct answer
    B
    7,4
  • C
    4,4
  • D
    7,7

Solution

$2^{m}-2^{n}=112 \Rightarrow 2^{n}\left(2^{m-n}-1\right)=16.7$ $\quad \therefore \quad 2^{n}\left(2^{m-n}-1\right)=2^{4}\left(2^{3}-1\right)$ Comparing we get $n=4$ and $m-n=3$ $\Rightarrow n=4$ and $m=7$

Hence, the correct answer is option: 'B'.

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