JEE Main 2021 (Online) 16th March Evening ShiftQuestion 1
Let $A=\{2,3,4,5,\ldots,30\}$ and '$\simeq$' be an equivalence relation on $A\times A$, defined by $(a,b)\simeq(c,d)$, if and only if $ad=bc$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :
Sets, Relations and Function
Solution
$(a,b)\simeq(4,3)\iff 3a=4b\iff a/b=4/3$. Pairs in $\{2..30\}$: $(4,3),(8,6),(12,9),(16,12),(20,15),(24,18),(28,21)$ = 7. Option (C).