Question

Let $A=\{2,3,4,5,\dots ,,30\}$ 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 :

• A. 5
• B. 6
• C. 8
• D. 7

Answer 1

Answer: (D)

$A=\{2,3,4,5,\dots ,,30\}$
$(a,b)\simeq (c,d)\Rightarrow ad=bc$
$(4,3)\simeq (c,d)\Rightarrow 4d=3c$
$\Rightarrow \frac{4}{3}=\frac{c}{d}$
$\frac{c}{d}=\frac{4}{3}\&c,d\in \{2,3,\dots \dots ,30\}$
$(c,d)=\{(4,3),(8,6),(12,9),(16,12),(20,,15),(24,18),(28,21)\}$
No. of ordered pair $=7$