JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{0,1,2,3,4,5,6,7\} .\) Then the number of bijective functions \(f: A \rightarrow A\)such that \(f(1)+f(2)=3-f(3)\) is equal to \(.....\)
- A \(500\)
- B \(620\)
- C \(720\)
- D \(885\)
Answer & Solution
Correct Answer
(C) \(720\)
Step-by-step Solution
Detailed explanation
\(f(1)+f(2)=3-f(3)\) \(\Rightarrow f(1)+f(2)+f(3)=3\) The only possibility is: \(0+1+2=3\) \(\Rightarrow\) Elements \(1,2,3\) in the domain can be mapped with \(0,1,2\) only. So number of bijective functions. \(=\lfloor 3 \times\lfloor 5=720\)
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