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JEE Main202116 Mar 2021Evening ShiftMathematicsSets and RelationsActual

Let A = 2 , 3 , 4 , 5 , … . , 30 and ' ≃ ' be an equivalence relation on A × A , defined by a , b ≃ 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 :

Options

  1. A5
  2. B6
  3. C8
  4. D7

Correct answer

D. 7

Step-by-step solution

A = 2 , 3 , 4 , 5 , … , , 30 a , b = c , d ⇒ a d = b c 4 , 3 = c , d   ⇒   4 d = 3 c ⇒ 4 3 = c d c d = 4 3   &   c , d ∈ 2 , 3 , … … , 30 c ,   d   = 4 , 3 , 8 , 6 , 12 , 9 , 16 , 12 , 20 , 15 , 24 , 18 , 28 , 21 No. of ordered pair = 7

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