JEE MAIN - Mathematics (2021 - 16th March Evening Shift - No. 10)
Let A = {2, 3, 4, 5, ....., 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 :
5
6
8
7
Explanation
ad = bc
(a, b) R (4, 3) $$ \Rightarrow $$ 3a = 4b
a = $${4 \over 3}$$b
b must be multiple of 3
b = {3, 6, 9 ..... 30}
(a, b) = {(4, 3), (8, 16), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)}
$$ \Rightarrow $$ 7 ordered pair
(a, b) R (4, 3) $$ \Rightarrow $$ 3a = 4b
a = $${4 \over 3}$$b
b must be multiple of 3
b = {3, 6, 9 ..... 30}
(a, b) = {(4, 3), (8, 16), (12, 9), (16, 12), (20, 15), (24, 18), (28, 21)}
$$ \Rightarrow $$ 7 ordered pair
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