Let A={1,2,3, ldots ldots .100} . Let R be a relation on A defined by (x, y) ∈ R if and only if 2

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1.Relation and Function

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Let $A=\{1,2,3, \ldots \ldots .100\}$. Let $R$ be a relation on A defined by $(x, y) \in R$ if and only if $2 x=3 y$. Let $R_1$ be a symmetric relation on $A$ such that $\mathrm{R} \subset \mathrm{R}_1$ and the number of elements in $\mathrm{R}_1$ is $\mathrm{n}$. Then, the minimum value of $n$ is..........................

A

$60$

B

$66$

C

$50$

D

$40$

(JEE MAIN-2024)

Solution

$ \mathrm{R}=\{(3,2),(6,4),(9,6),(12,8), \ldots \ldots \ldots .(99,66)\} $

$\mathrm{n}(\mathrm{R})=33 $

$ \therefore 66$

Standard 12

Mathematics

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