Mathematics - Sets and Relations Question with Solution | TestHub

MathematicsSets and RelationsQuestions on number of relations and setsMedium2 minPYQ_2020

MathematicsMediumnumerical

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 $m \cdot n$ is___.

Answer:

28.00

Solution:

$2^{m} = 2^{n} + 112$
$\Rightarrow 2^{m} - 2^{n} = 112$
$\Rightarrow 2^{n} \cdot (2^{m - n} - 1) = 2^{4} \cdot (2^{3} - 1)$
$\Rightarrow n = 4, m = 7$

Stream:JEESubject:MathematicsTopic:Sets and RelationsSubtopic:Questions on number of relations and sets

⏱ 2mℹ️ Source: PYQ_2020

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