JEE Main202522 Jan 2025Evening ShiftMathematicsFunctionsActual

Let A = 1,2,3,4 and B = 1,4,9,16 . Then the number of many-one functions f: A B such that 1 f( ~A ) is equal to :

Options

A151
B139
C163
D127

Correct answer

A. 151

Step-by-step solution

aligned & A= 1,2,3,4 & B= 1,4,9,16 aligned Total number of functions =4^4 Total number of one-one functions =4! Total number of many one functions =4^4-4!=232 Total number of many-one functions in which 1 f(A)=3 3 3 3=81 Total number of many one functions 1 f(A) aligned & =232-81 & =151 aligned

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