JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{a, b, c\}\) and \(B=\{1,2,3,4\}\) Then the number of elements in the set \(C =\{ f : A \rightarrow B \mid 2 \in f ( A )\) and \(f\) is not one-one \(\}\) is
- A \(18\)
- B \(19\)
- C \(17\)
- D \(20\)
Answer & Solution
Correct Answer
(B) \(19\)
Step-by-step Solution
Detailed explanation
\(C =\{ f : A \rightarrow B \mid 2 \in f ( A )\) and \(f\) is not one-one \(\}\) Case-I : \(\quad\) If \(f(x)=2 \forall x \in A\) then number of function \(=1\) Case-II : \(\quad\) If \(f(x)=2\) for exactly two elements then total number of many-one function…
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