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📐 Mathematics  ·  Relations and Functions  ·  JEE

A = {1,2,3,...,n}. The number of bijections from A to A is:

Answer: n!.

  • A n
  • B
  • C n!
  • D 2<sup>n</sup>

Correct answer: C. n!

Explanation: A bijection from A to A is a permutation. First element maps to n choices, second to n-1, and so on. By multiplication principle: n×(n-1)×...×1 = n! permutations. Alternatively, |A|=n so bijections = n!. Answer: n!

Concept context

Ordered pairs, Cartesian products, types of relations and functions, domain and range. Foundation for calculus and Class 12 algebra.

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