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JEE Main 202522 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2025 · 22 January · Evening Shift · Mathematics · Functions

Let A=\ 1,2,3,4\ and B=\ 1,4,9,16\ . Then the number of many-one...

Let A={1,2,3,4}\mathrm{A}=\{1,2,3,4\} and B={1,4,9,16}\mathrm{B}=\{1,4,9,16\}. Then the number of many-one functions f:A→Bf: \mathrm{A} \rightarrow \mathrm{B} such that 1∈f( A)1 \in f(\mathrm{~A}) is equal to :

Options

  1. A151
  2. B139
  3. C163
  4. D127

Correct answer

A. 151

Step-by-step solution

A={1,2,3,4}B={1,4,9,16}\begin{aligned} & A=\{1,2,3,4\} \\ & B=\{1,4,9,16\} \end{aligned} Total number of functions =44=4^4 Total number of one-one functions =4!=4! Total number of many one functions =44−4!=232=4^4-4!=232 Total number of many-one functions in which 1∉f(A)=3×3×3×3=81∴1 \notin f(A)=3 \times 3 \times 3 \times 3=81 \therefore Total number of many one functions 1∉f(A)1 \notin f(A)=232−81=151\begin{aligned} & =232-81 \\ & =151 \end{aligned}$$
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