CUET · MATHS · PYQ PAPER 2023
The number of all onto functions from the set \(\{1,2, \ldots, n\}\) to itself is
- A \(2^n\)
- B \(n^2\)
- C \(n!\)
- D \((2 n)!\)
Answer & Solution
Correct Answer
(C) \(n!\)
Step-by-step Solution
Detailed explanation
For a function from {1,2,…,n} to itself to be onto, every element must have exactly one pre-image.Since domain and codomain have equal size, onto ⇒ one-to-one (bijection).Number of such functions = permutations of n elements = n!. (C) n!
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