Question
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
JEE Main
Mathematics
Functions
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 32
- B. 79
- C. 62
- D. 81
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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