Let A = {2, 3, 4, 5, …….., 30} and $≃$ be an equivalence relation on $A \times A$
, defined by $(a, b) ≃ (c, d)$ , 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

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answer is B.

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Detailed Solution

ad = bc
$\frac{a}{b} = \frac{c}{d}$ $\Rightarrow \frac{4}{3} = \frac{c}{d}$

$\Rightarrow c = \frac{4 d}{3} s o, d = 3 k d = 3, 6, 9 .......21.$
The number of pairs equivalent to (4, 3) is 7

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