Let $\mathrm{A}=\{2,3,4,5, \ldots ., 30\}$ and ' $\simeq$ ' be an equivalence relation on $\mathrm{A} \times \mathrm{A}$, defined by $(a, b) \simeq(c, d)$, if and only if $a d=b c$. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4,3)$ is equal to :
Correct Option: , 4
$A=\{2,3,4,5, \ldots ., 30\}$
$(a, b) \simeq(c, d) \quad \Rightarrow \quad a d=b c$
$(4,3) \simeq(\mathrm{c}, \mathrm{d}) \quad \Rightarrow \quad 4 \mathrm{~d}=3 \mathrm{c}$
$\Rightarrow \frac{4}{3}=\frac{\mathrm{c}}{\mathrm{d}}$
$\frac{\mathrm{c}}{\mathrm{d}}=\frac{4}{3} \quad \& \mathrm{c}, \mathrm{d} \in\{2,3, \ldots \ldots, 30\}$
$(\mathrm{c}, \mathrm{d})=\{(4,3),(8,6),(12,9),(16,12),(20,$,
$15),(24,18),(28,21)\}$
No. of ordered pair $=7$
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