JEE Main 2023 (Online) 15th April Morning ShiftQuestion 1
Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A\times A$ defined by $R=\{((a,b),(c,d)):2a+3b=4c+5d\}$. Then the number of elements in $R$ is $\_\_\_\_\_\_$ .
Sets, Relations and Function
Answer$6$
Solution
$2a+3b=4c+5d$ with all in $\{1,..,4\}$. Solutions $(a,b,c,d)$: $(1,4,1,2),(2,3,2,1),(3,1,1,1),(3,4,2,2),(4,2,1,2),(4,3,3,1)$ (e.g. $2+12=14=4+10$). Number of elements $=6$.