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Question 410009
JEE Mathematics · Hard

Sets, Relations and Functions: JEE Advanced MCQ

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JEE AdvancedHardQuestion 410009

Question

The number of onto functions from a set with 3 elements to a set with 2 elements is:
  1. A
    6
    Correct
  2. B
    8
  3. C
    4
  4. D
    2

Correct answer

6

Explanation

Total functions: 2³ = 8. Functions where all map to {a}: 1. All to {b}: 1. Onto = 8 − 2 = 6. Using inclusion-exclusion: 2³ − C(2,1)×1³ + C(2,2)×0³ = 8 − 2 + 0 = 6.

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