JEE Main 2026 (Online) 5th April Evening ShiftQuestion 1
Let $A=\{1,4,7\}$ and $B=\{2,3,8\}$. Then the number of elements, in the relation $R=\{((a_1,b_1),(a_2,b_2))\in((A\times B)\times(A\times B)):a_1+b_2$ divides $a_2+b_1\}$ is $\_\_\_\_\_\_$ .
Sets, Relations and Function
Answer$18$
Solution
Condition: $(a_1+b_2)\mid(a_2+b_1)$ over $a_1,a_2\in\{1,4,7\}$, $b_1,b_2\in\{2,3,8\}$ (81 ordered quadruples). Enumerating all cases gives $18$ satisfying quadruples. $|R|=18$.