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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Sets and Relations

BITSAT 2016 · Mathematics · Sets and Relations

Two finite sets have m and n elements. The number of subsets of the...

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

Options

  1. A4,7
  2. B7,4
  3. C4,4
  4. D7,7

Correct answer

B. 7,4

Step-by-step solution

2m−2n=112⇒2n2^{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)ComparingwegetComparing we getn=4andandm-n=3\Rightarrow n=4andandm=7
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