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1.Set Theory
medium
Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of $m \times n$ is
A
$7$
B
$4$
C
$28$
D
$24$
(JEE MAIN-2020)
Solution
$2^m -2^{ n }=112$
$m =7, n =4$
$\left(2^{7}-2^{4}=112\right)$
$m \times n =7 \times 4=28$
Standard 11
Mathematics