JEE PYQ: Sets And Relations Question 1
Question 1 - 2021 (16 Mar Shift 2)
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:
(1) 5
(2) 6
(3) 8
(4) 7
Show Answer
Answer: (4)
Solution
$A = {2, 3, 4, 5, \ldots, 30}$
$(a, b) \simeq (c, d) \Rightarrow ad = bc$
$(4, 3) \simeq (c, d) \Rightarrow 4d = 3c$
$\Rightarrow \frac{4}{3} = \frac{c}{d}$
$\frac{c}{d} = \frac{4}{3}$ and $c, d \in {2, 3, \ldots, 30}$
$(c, d) = {(4,3), (8,6), (12,9), (16,12), (20,15), (24,18), (28,21)}$
No. of ordered pairs $= 7$
BETA
