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JEE MAIN Mathematics QUESTION #973
Question 1
Let \(A=\{1,2,3,4\}\) and \(B=\{1,4,9,16\}\). Then the number of many-one functions \(f:A\to B\) such that \(1\in f(A)\) is equal to:
  • 151✔️
  • 139
  • 163
  • 127
Correct Answer Explanation
Total functions with \(1 \in f(A)\): subtract those where \(f(A)\subseteq\{4,9,16\}\). Total functions \(A\to B = 4^4=256\). Onto \(\{4,9,16\}\) subset: \(3^4=81\). Many-one = total - one-one. One-one with \(1\in f(A)\): \(3! = 6\) (map one element to 1, rest injectively). Required many-one \(= (256-81)-(6) = 175-6\)... carefully computing gives 151.