JEE Main 2024 (Online) 6th April Morning ShiftQuestion 1
Let the relations $R_1$ and $R_2$ on the set $X=\{1,2,3,\ldots,20\}$ be given by $R_1=\{(x,y):2x-3y=2\}$ and $R_2=\{(x,y):-5x+4y=0\}$. If $M$ and $N$ be the minimum number of elements required to be added in $R_1$ and $R_2$, respectively, in order to make the relations symmetric, then $M+N$ equals
Sets, Relations and Function
Solution
$R_1$: $y=(2x-2)/3$ gives $(4,2),(7,4),(10,6),(13,8),(16,10),(19,12)$, none has its reverse in $R_1$, so $M=6$. $R_2$: $5x=4y$: $(4,5),(8,10),(12,15),(16,20)$, none symmetric, so $N=4$. $M+N=10$. Option (B).