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JEE Main202622 January 2026Morning ShiftMathematicsSets and RelationsActual

Let the relation R on the set M = 1,2,3, , 16 be given by R = (x, y): 4 y=5 x-3, x, y M . Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

Options

  1. A4
  2. B1
  3. C2
  4. D3

Correct answer

C. 2

Step-by-step solution

Given R = (x, y) : 4y = 5x - 3, x, y M where M = 1, 2, , 16 . From 4y = 5x - 3 , we get y = 5x-3 4 . For y to be a positive integer, 5x - 3 0 4 , i.e., x 3 4 . So x = 3, 7, 11, 15 . x=3 y=3 , x=7 y=8 , x=11 y=13 , x=15 y=18 M . R = (3,3), (7,8), (11,13) . For symmetry, (7,8) R requires (8,7) R and (11,13) R requires (13,11) R . (3,3) is already symmetric. Minimum elements to be added = 2 .

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