JEE Mains · Maths · STD 12 - 1. relation and function
Let \(S=\{1,2,3,4,5,6,7\} .\) Then the number of possible functions \(f: S \rightarrow S\) such that \(f(m \cdot n)=f(m) \cdot f(n)\) for every \(m, n \in S\) and \(m . n \in S\) is equal to \(......\)
- A \(500\)
- B \(600\)
- C \(570\)
- D \(490\)
Answer & Solution
Correct Answer
(D) \(490\)
Step-by-step Solution
Detailed explanation
\(f(m n)=f(m) \cdot f(n)\) Put \(m=1 f(n)=f(1) \cdot f(n) \Rightarrow f(1)=1\) Put \(m=n=2\) \(f(4)=f(2) \cdot f(2)\) \(f(2)=1 \Rightarrow f(4)=1 \text { or } f(2)=2 \Rightarrow f(4)=4\) Put \(m=2, n=3\) \(f(6)=f(2) \cdot f(3)\)…
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