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JEE Main201911 Jan 2019Evening ShiftMathematicsFunctionsActual

The number of functions f from 1,2,3, , 20 onto 1,2,3, , 20 such that f(k) is a multiple of 3, whenever k is a multiple of 4 is:

Options

  1. A6⁵ (15) !
  2. B5 ! 6 !
  3. C(15) ! 6 !
  4. D5⁶ 15

Correct answer

C. (15) ! 6 !

Step-by-step solution

Domain and codomain = 1,2,3, , 20 . There are five multiple of 4 as 4,8,12,16 and 20 . and there are 6 multiple of 3 as 3,6,9,12,15,18 . Since, when ever k is multiple of 4 then f(k) is multiple of 3 then total number of arrangement = ⁶ c₅ 5 !=6 ! Remaining 15 elements can be arranged in 15 ! ways. Since, for every input, there is an output function f(k) in onto Total number of arrangement =15 ! .6 !

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