Mathematics
Functions
Easy

Question

Let A and B are two sets such that A intersection B equals left curly bracket 1 comma 2 right curly bracket comma A union B equals left curly bracket 1 comma 2 comma 3 comma 4 comma 5 right curly bracket text . If  end text n subscript 1 comma n subscript 2 text  are  end textmaximum and minimum number of functions from A to B respectively, then n1 - n2 =

  1. 25
  2. 81
  3. 56
  4. 106

The correct answer is: 56


    n left parenthesis A right parenthesis space space space space space space space space space space space n left parenthesis B right parenthesis space space space space space space space space space space space space space space space space space space space space space space n u m b e r space o f space f u n c t i o n s
2 space space space space space space space space space space space space space space space space space space space space space space 5 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 5 squared equals 25
3 space space space space space space space space space space space space space space space space space space space space space space space 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 4 cubed equals 64
4 space space space space space space space space space space space space space space space space space space space space space space space space 3 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 3 to the power of 4 equals 81
5 space space space space space space space space space space space space space space space space space space space space space space space space space 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 to the power of 5 equals 32
therefore n subscript 1 equals 81 comma n subscript 2 equals 25 not stretchy rightwards double arrow n subscript 1 minus n subscript 2 equals 56 space space space space space space space

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