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AP EAMCET202125 Aug 2021Morning ShiftMathematicsFunctionsActual

Let A= 1,2,3,4,5,6 number of functions f from A to A such that f(m)+f(n)=7 , whenever m+n=7 is

Options

  1. A525
  2. B216
  3. C200
  4. D729

Correct answer

B. 216

Step-by-step solution

We have, A= 1,2,3,4,5,6 f(m)+f(n)=7 of m+n=7 Order of (m, n) is (1,6),(2,5),(3,4),(4,3),(5,2) , (6,1) aligned & f(1)+f(6)=7, f(2)+f(5)=7, f(3)+f(4)=7 & f(1)+f(6)=7 has 36 2=72 functions aligned Similar for f(2)+f(5)=7 and f(3)+f(4)=72 Total number of functions =72+72+72=216

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