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JEE Main202623 January 2026Evening ShiftMathematicsFunctionsActual

Consider two sets A = x Z :|(|x-3|-3)| 1 and B = x R - 1,2 : (x-2)(x-4) x-1 _ e (|x-2|)=0 . Then the number of onto functions f: A B is equal to

Options

  1. A32
  2. B79
  3. C62
  4. D81

Correct answer

C. 62

Step-by-step solution

For set A : |(|x-3|-3)| 1 2 |x-3| 4 . If x 3 : 5 x 7 x 5,6,7 . If x So A = -1,0,1,5,6,7 , |A|=6 . For set B : (x-2)(x-4) x-1 _e(|x-2|) = 0 with x R - 1,2 . Either (x-2)(x-4) x-1 =0 x=4 (since x 1,2 ), or _e|x-2|=0 |x-2|=1 x=3 (since x 1 ). So B = 3,4 , |B|=2 . Number of onto functions from A to B= 2^6 - 2 = 62 .

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