JEE Mains · Maths · STD 12 - 1. relation and function
Let \(R =\{ a , b , c , d , e \}\) and \(S =\{1,2,3,4\}\). Total number of onto function \(f: R \rightarrow S\) such that \(f(a) \neq\) 1 , is equal to \(.............\).
- A \(180\)
- B \(170\)
- C \(160\)
- D \(150\)
Answer & Solution
Correct Answer
(A) \(180\)
Step-by-step Solution
Detailed explanation
Total onto function \(\frac{[5}{\left\lfloor{3}\lfloor 2\right.} \times\lfloor 4=240\) Now when \(f(a)=1\) \(\lfloor 4+\frac{\lfloor 4}{\lfloor 2\lfloor 2} \times\lfloor 3=24+36=60\) so required \(f ^{ n }=240-60=180\)
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