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"A technician has only two resistance coils.By using them either in series or in parallel he is able to obtain the resistance of 3,4,12 and 16 ohms.The

resistance of two coils is"


The minimum resistance i.e., 3 ohms can be obtained only by connecting the two coils in parallel.
So, xy/x+y =3
or, xy=3x+3y

and the maximum resistance can be obtained by series
Hence x=4 and y=12
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With two resistances R1 and R2 we have the 4 following combinations possible:

R1  or  R2 if they are used individually. 
   let R2  be the larger of the two.

R1 R2 / (R1 + R2)  if used in parallel.      
     -- This is the smallest value.  It is  < R1 and < R2.

R1 + R2  if used in series.    This is the largest value.  SO it is  > R1 and > R2.

Hence, from the given values,
      R1 + R2 = 16 Ω
       R1 R2 / (R1 + R2) =  3 Ω

So, R1 and R2 are 4 Ω and 12 Ω respectively.

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