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1.Relation and Function
hard
ધારોકે $A =\{1,2,3,4,5\}$ અને $B =\{1,2,3,4,5,6\}$. તો $f(1)+f(2)=f(4)-1$ નું સમાધાન કરતા વિધેયો $f: A \rightarrow B$ ની સંખ્યા $=.........$
A
$360$
B
$361$
C
$362$
D
$363$
(JEE MAIN-2023)
Solution
$f(1)+f(2)+1=f(4) \leq 6$
$f(1)+f(2) \leq 5$
Case $(i)$ $f(1)=1 \Rightarrow f(2)=1,2,3,4 \Rightarrow 4$ mappings
Case $(ii)$ $f(1)=2 \Rightarrow f(2)=1,2,3 \Rightarrow 3$ mappings
Case $(iii)$ $f(1)=3 \Rightarrow f(2)=1,2 \Rightarrow 2$ mappings
Case $(iv)$ $f(1)=4 \Rightarrow f(2)=1 \Rightarrow 1$ mapping
$f(5)$ and $f(6)$ both have $6$ mappings each
Number of functions $=(4+3+2+1) \times 6 \times 6=360$
Standard 12
Mathematics
