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JEE Main20265 April 2026Morning ShiftMathematicsFunctionsActual

Let A = 1, 2, 3, 4, 5, 6 . The number of one-one functions f: A A such that f(1) 3 , f(3) 4 and f(2) + f(3) = 5 , is __________.

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Step-by-step solution

Given A = 1, 2, 3, 4, 5, 6 . Since f: A A is a one-one function, f(x) takes distinct values from A for each x A . We are given the condition f(2) + f(3) = 5 . The possible pairs for (f(2), f(3)) from the set A are: (1, 4), (2, 3), (3, 2), (4, 1) Notice that for all these pairs, the condition f(3) 4 is automatically satisfied. We also have the condition f(1) 3 . Since f is one-one, f(1) cannot take the values already assigned to f(2) and f(3) . Let us find the number of choices for f(1) in each case: Case 1: (f(2),

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