JEE MAIN - Mathematics (2024 - 5th April Morning Shift - No. 2)
Let $$A=\{1,3,7,9,11\}$$ and $$B=\{2,4,5,7,8,10,12\}$$. Then the total number of one-one maps $$f: A \rightarrow B$$, such that $$f(1)+f(3)=14$$, is :
120
180
240
480
Explanation
$$f(1)+f(3)=14$$
Case I
$$\begin{aligned} & f(1)=2, f(3)=12 \\ & f(1)=12, f(3)=2 \end{aligned}$$
Total one-one function
$$\begin{aligned} & =2 \times 5 \times 4 \times 3 \\ & =120 \end{aligned}$$
Case II
$$\begin{aligned} & f(1)=4, f(3)=10 \\ & f(1)=10, f(3)=4 \end{aligned}$$
Total one-one function
$$\begin{aligned} & =2 \times 5 \times 4 \times 3 \\ & =120 \\ & \text { Total cases }=120+120=240 \end{aligned}$$
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