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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1
Given A={x:x∈N,1≤x≤9}A=\{x: x \in N, 1 \leq x \leq 9\}. The total number of bijective functions f:A→Af: A \rightarrow A such that f(x)=xf(x)=x, if xx is an odd integer and f(x)=xf(x)=x, if xx is an even integer, is
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Correct option: C
9
The correct answer is 9 because there are 2 even numbers that are not fixed, leading to a derangement problem with 2 elements, and the number of ways to arrange them is 1, multiplied by the number of ways to arrange the other 2 even numbers, which is also 1. This gives 3C2 * 2! = 3 * 2 = 6. Then we need to consider the case where both even numbers are swapped, which is 1. So 6 + 3 = 9

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