JEE Main 2026 · 5 Apr · Shift 2 · Mathematics Q21

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MathematicsInteger+4 / -1Question 21 of 75

Let $A=\{1,4,7\}$ and $B=\{2,3,8\}$ . Then the number of elements, in the relation $R=\left\{\left((a_1,b_1),(a_2,b_2)\right)\in(A\times B)\times(A\times B):a_1+b_2\text{ divides }a_2+b_1\right\}$ is ________.

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Answer and worked solution

Official answer: 18

Multisets. The sums $a+b$ for $a\in A$ , $b\in B$ are 3, 4, 9, 6, 7, 12, 9, 10, 15. The divisor $a_1+b_2$ and the dividend $a_2+b_1$ each range over this list once.

Count the dividends each divisor divides.

Divisor	3	4	9 (twice)	6	7	12	10	15
Dividends	3,6,9,9,12,15	4,12	9,9 each	6,12	7	12	10	15
Count	6	2	2+2	2	1	1	1	1

Total: 18.

Answer: 18

Topics:Relations

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JEE Main 2026 · 5 Apr · Shift 2, Mathematics question 21