JEE Main20264 April 2026Morning ShiftMathematicsFunctionsActual

The number of functions f: 1, 2, 3, 4 a, b, c , which are not onto, is:

Options

Correct answer

B. 45

Step-by-step solution

Total number of functions from a set of 4 elements to a set of 3 elements is 3^4 = 81 . The number of onto functions is given by the inclusion-exclusion principle: 3^4 - ³C₁ 2^4 + ³C₂ 1^4 = 81 - 3 16 + 3 1 = 81 - 48 + 3 = 36 The number of functions which are not onto is the total number of functions minus the number of onto functions: 81 - 36 = 45 Answer: 45

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