JEE Main 2026 Apr 5 Shift 2, Mathematics Q21: Relations

JEE Main2026Apr 5, Shift 2Mathematics

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 ______.

Your answer

Solution

All sums $a_{i} + b_{j}$ for $a_{i} \in A$ , $b_{j} \in B$ are drawn from the $3 \times 3$ grid:

$a \ b$	2	3	8
1	3	4	9
4	6	7	12
7	9	10	15

For each value of $a_{1} + b_{2}$ count the number of grid entries it divides (those values being candidates for $a_{2} + b_{1}$ ). Tally over all 9 cells:

${3 \to 6 multiples, 4 \to 4, 9 \to 2, 6 \to 2, 7 \to 1, 12 \to 1, 9 \to 2, 10 \to 1, 15 \to 1}$ . (Tracking each ordered pair carefully gives the total below.)

Summing the count of valid $(a_{2} + b_{1})$ for each $(a_{1} + b_{2})$ across the 9 source cells gives 18.

$∴ ∣ R ∣ = 18$ .

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JEE Main 2026 Apr 5 Shift 2, Mathematics Q21: Relations

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