QJEEM24Ma3889: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3889 Solution: Let and . Then the total number of one-one maps , such that ,…

$f(1)+f(3)=14$

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

$\begin{aligned}& =2 \times 5 \times 4 \times 3 \\& =120 \\& \text { Total cases }=120+120=240\end{aligned}$