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JEE Main20253 Apr 2025Morning ShiftMathematicsSets and RelationsActual

Let A= -3,-2,-1,0,1,2,3 , . Let R be a relation on A defined by x R y if and only if 0 x^2+2 y 4 . 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 reflexive relation. then l+m is equal to

Options

  1. A19
  2. B20
  3. C17
  4. D18

Correct answer

D. 18

Step-by-step solution

aligned & A = -3,-2,-1,0,1,2,3 & -2 y x ^2 4-2 y aligned array lll y=-3 & 6 x^2 10 & x -3,3 y=-2 & 4 x^2 8 & x -2,2 y=-1 & 2 x^2 6 & x -2,2 y=0 & 0 x^2 4 & x -2,-1,0,1,2 y=1 & -2 x^2 2 & x -1,0,1 y=2 & -4 x^2 0 & x 0 y=3 & -6 x^2 -2 & No x -Exist array aligned & R = (-3,-3)(-3,3),(-2,-2)(-2,2)(-1,-2)(-1,2) & (0,-2)(0,-1)(0,0)(0,1)(0,2)(1,-1)(1,0)(1,1) & (2,0) & =15 aligned To make it reflexive we will add aligned & (-1,-1),(2,2),(3,3) m =3 & + m =15+3=18 aligned

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