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JEE Main202225 Jul 2022Morning ShiftMathematicsFunctionsActual

The total number of functions, f : 1 , 2 , 3 , 4 → 1 , 2 , 3 , 4 , 5 , 6 such that f 1 + f 2 = f 3 , is equal to

Options

  1. A60
  2. B90
  3. C108
  4. D126

Correct answer

B. 90

Step-by-step solution

Given, f 1 + f 2 = f 3 Now possible values of f 3 are 2 , 3 , 4 , 5 and 6 (it cannot be 1 as minimum value f 1   &   f 2 is 1 , so 1 + 1 = 2 ) For each k , if f 3 = k then there will be k - 1 set of values for f 1 and f 2 For example if f 3 = 3 then possible value of f 1   &   f 2 will be 1 , 2   or   2 , 1 ⇒ 2 values Similarly for f 3 = 4 , possible values will be 1 , 3 , 3 , 1 , 2 , 2 ⇒ 3 values. And so on. So number of possible combinations of f 1 ,   f 2 an

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