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1.Relation and Function
medium
જો $A=\{a, b, c\}$ અને $B=\{1,2,3,4\}$ હોય તો ગણ $C =\{ f : A \rightarrow B \mid 2 \in f ( A )$ અને $f$ એ એક એક વિધેય નથી.$\}$ માં કેટલા ઘટકો આવેલા છે
A
$18$
B
$19$
C
$17$
D
$20$
(JEE MAIN-2020)
Solution
$C =\{ f : A \rightarrow B \mid 2 \in f ( A )$ and $f$ is not one-one $\}$
Case-I : $\quad$ If $f(x)=2 \forall x \in A$ then number of function $=1$
Case-II : $\quad$ If $f(x)=2$ for exactly two elements then total number of many-one function $={ }^{3} C _{2}{ }^{3} C _{1}=9$
Case-III : If $f(x)=2$ for exactly one element then total number of many-one functions $={ }^{3} C _{1}{ }^{3} C _{1}=9$
Total $=19$
Standard 12
Mathematics
