Let \(A=\{1,2,3,4\}\) and \(B=\{1,4,9,16\}\). Then the number of many-one functions \(f: A \rightarrow B\) such that \(1…
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Let \(A=\{1,2,3,4\}\) and \(B=\{1,4,9,16\}\). Then the number of many-one functions \(f: A \rightarrow B\) such that \(1 \in f(A)\) is equal to :
[JEE Main 2025, 22 Jan (Shift 2)]
✓ Correct answer: b)
151
Explanation
Total number of functions = \({4}^{4}=256\)
One-one functions = \(4!\)
Many-one functions = 256-24 = 232
Many-one functions in which \(1\notin \mathrm{f}(\mathrm{A})\)
\(=3.3.3.3=81\)
Required number of functions =
\(232-81=151\)
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