1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A= 0,1,2,3,4,5,6,7 . Then the number of bijective functions f: A arrow A such that f(1)+f(2)=3-f(3) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $A=\{0,1,2,3,4,5,6,7\}$. Then the number of bijective functions $f: A \rightarrow A$ such that $f(1)+f(2)=3-f(3)$ is equal to

JEE MainJEE Main 2021Relations and Functions - Part 2

Solution:

$f(1)+f(2)=3-f(3)$
$\Rightarrow f(1)+f(2)=3+f(3)=3$
The only possibility is: $0+1+2=3$
$\Rightarrow$ Elements $1,2,3$ in the domain can be mapped with $0,1,2$ only.
So number of bijective functions.
$=3 ! \times 5 !=720$