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1.Relation and Function
hard
વિધેય $f:\{1,2,3,4\} \to \{1,2,3,4,5,6\}$ કેટલા મળે કે જેથી $f (1)+ f (2)= f (3)$ થાય.
A
$60$
B
$90$
C
$108$
D
$126$
(JEE MAIN-2022)
Solution
$A =\{1,2,3,4\}$
$B =\{1,2,3,4,5,6\}$
Here $f(3)$ can be 2, 3, 4, 5, 6
$f (3)=2,( f (1), f (2)) \rightarrow(1,1) \rightarrow 6 \text { cases }$
$f (3)=3,( f (1), f (2)) \rightarrow(1,2),(2,1)$
$\rightarrow 2 \times 6=12 \text { cases }$
$f (3)=4,( f (1), f (2)) \rightarrow(1,3),(3,1),(2,2)$
$\rightarrow 3 \times 6=18 \text { cases }$
$f (3)=5,( f (1), f (2)) \rightarrow(1,4),(4,1),(2,3),(3,2)$
$\rightarrow 4 \times 6=24 \text { cases }$
$f (3)=6,( f (1), f (2)) \rightarrow(1,5),(5,1),(2,4),(4,2),(3,3)$
$\rightarrow 5 \times 6=30 \text { cases }$
Total number of cases $=6+12+18+24+30=90$
Standard 12
Mathematics
