JEE Mains · Maths · STD 12 - 1. relation and function
Let \(\mathrm{A}=\{1,2,3,4\}\) and \(\mathrm{B}=\{1,4,9,16\}\). Then the number of many-one functions \(f: \mathrm{A} \rightarrow \mathrm{B}\) such that \(1 \in f(\mathrm{~A})\) is equal to :
- A 151
- B 139
- C 163
- D 127
Answer & Solution
Correct Answer
(A) 151
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & A=\{1,2,3,4\} \\ & B=\{1,4,9,16\} \end{aligned}\) 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…
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