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JEE Main202228 Jun 2022Evening ShiftMathematicsFunctionsActual

The probability that a randomly chosen one-one function from the set a , b , c , d to the set 1 , 2 , 3 , 4 , 5 satisfied f a + 2 f b - f c = f d is

Options

  1. A1 24
  2. B1 40
  3. C1 30
  4. D1 20

Correct answer

D. 1 20

Step-by-step solution

Total cases will be 5 C 4 × 4 ! Now favourable cases for 2 f b = f c + f d - f a will be, Case (I) if f b = 1 then f c ,   f d ,   f a can take the value 3 , 4 , 5 & 4 , 3 , 5 respectively Case (II) if f b = 2 then f c ,   f d ,   f a can take value 3 , 5 , 4   &   5 , 3 , 4 respectively Case (III) if f b = 3 then f c ,   f d ,   f a can take value 2 , 5 , 1   &   5 , 2 , 1 respectively So total favourable case will be 6 So probability = favourable &#16

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