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1.Relation and Function
hard
અહી $A=\{0,1,2,3,4,5,6,7\} $ આપેલ છે. જો એક-એક અને વ્યાપ્ત વિધેય $f: A \rightarrow A$ ની સંખ્યા મેળવો કે જેથી $f(1)+f(2)=3-f(3)$ થાય.
A
$500$
B
$620$
C
$720$
D
$885$
(JEE MAIN-2021)
Solution
$f(1)+f(2)=3-f(3)$
$\Rightarrow f(1)+f(2)+f(3)=3$
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.
$=\lfloor 3 \times\lfloor 5=720$
Standard 12
Mathematics