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1.Relation and Function
easy
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