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

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