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Class 12 Relations And Functions · Mcq Single Correct1 Markscounting_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #100

For functions from \(A=\{1,2,\ldots,12\}\) to \(B=\{1,2,\ldots,11\}\), choose the most complete correct option.

✅ Step-by-Step Solution

Final Answer: Option (D): All of these
  1. An onto map from 12 inputs to 11 outputs has exactly one two-element fibre. Choose that pair in \(\binom{12}{2}\) ways, then assign the 11 resulting blocks bijectively to the outputs in \(11!\) ways. The count is \(\binom{12}{2}11!=12!\,11/2\). Total functions number \(11^{12}\); subtracting gives the non-onto count. All three displayed statements are true.

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