JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{1,2,3,4,5\}\) and \(B=\{1,2,3,4,5,6\}\). Then the number of functions \(f: A \rightarrow B\) satisfying \(f(1)+f(2)=f(4)-1\) is equal to
- A \(360\)
- B \(361\)
- C \(362\)
- D \(363\)
Answer & Solution
Correct Answer
(A) \(360\)
Step-by-step Solution
Detailed explanation
\(f(1)+f(2)+1=f(4) \leq 6\) \(f(1)+f(2) \leq 5\) Case \((i)\) \(f(1)=1 \Rightarrow f(2)=1,2,3,4 \Rightarrow 4\) mappings Case \((ii)\) \(f(1)=2 \Rightarrow f(2)=1,2,3 \Rightarrow 3\) mappings Case \((iii)\) \(f(1)=3 \Rightarrow f(2)=1,2 \Rightarrow 2\) mappings Case \((iv)\)…
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