JEE Mains · Maths · STD 12 - 1. relation and function
Let \(S=\{1,2,3,4\}\). Then the number of elements in the set \(\{f: S \times S \rightarrow S: f\) is onto and \(f(a, b)=f(b, a)\) \(\geq a; \forall(a, b) \in S \times S\}\) is
- A \(37\)
- B \(378\)
- C \(97\)
- D \(30\)
Answer & Solution
Correct Answer
(A) \(37\)
Step-by-step Solution
Detailed explanation
\((1,1),(1,4),(4,1),(2,4),(4,2),(3,4),(4,3)\), \((4,4)-\) all have one choice for image. \((2,1),(1,2),(2,2)\) - all have three choices for image \((3,2),(2,3),(3,1),(1,3),(3,3)-\) all have two choices for image. So the total functions…
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