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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2020 · 6 September · Morning Shift · Mathematics · Sets and Relations

Set A has m elements and set B has n elements. If the total number...

Set AA has mmelements and set BB has nnelements. If the total number of subsets of AA is 112112 more than the total number of subsets of BB, then the value of m⋅nm \cdot n is___.

Correct answer

0

Step-by-step solution

2m=2n+112{2}^{m} = {2}^{n} + 112
⇒2m−2n=112⇒ {2}^{m} - {2}^{n} = 112
⇒2n⋅(2m−n−1)=24⋅(23−1)⇒ {2}^{n} \cdot \left({2}^{m - n} - 1\right) = {2}^{4} \cdot \left({2}^{3} - 1\right)
⇒n=4,m=7⇒ n = 4, m = 7
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