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JEE Main202621 January 2026Evening ShiftMathematicsSets and RelationsActual

Let A = 2,3,5,7,9 . Let R be the relation on A defined by x R y if and only if 2 x 3 y . Let l be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then l+ m is equal to :

Options

  1. A21
  2. B27
  3. C23
  4. D25

Correct answer

D. 25

Step-by-step solution

Given A = 2, 3, 5, 7, 9 and xRy iff 2x 3y , i.e., y 2x 3 . For x=2 : y 2,3,5,7,9 → 5 pairs For x=3 : y 2,3,5,7,9 → 5 pairs For x=5 : y 5,7,9 → 3 pairs For x=7 : y 5,7,9 → 3 pairs For x=9 : y 7,9 → 2 pairs So l = 18 . For symmetry, pairs in R whose reversal is missing: (2,5),(2,7),(2,9),(3,5),(3,7),(3,9),(5,9) require adding (5,2),(7,2),(9,2),(5,3),(7,3),(9,3),(9,5) → m = 7 . l + m = 18 + 7 = 25 .

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