JEE Mains · Maths · STD 12 - 1. relation and function
The number of functions \(f: \{1, 2, 3, 4\} \rightarrow \{a, b, c\}\), which are not onto, is:
- A \(48\)
- B \(45\)
- C \(51\)
- D \(35\)
Answer & Solution
Correct Answer
(B) \(45\)
Step-by-step Solution
Detailed explanation
Total number of functions from a set of \(4\) elements to a set of \(3\) elements is \(3^4 = 81\). The number of onto functions is given by the inclusion-exclusion principle: \(3^4 - ^{3}C_{1} 2^4 + ^{3}C_{2} 1^4\) \(= 81 - 3 \times 16 + 3 \times 1\) \(= 81 - 48 + 3 = 36\) The…
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