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JEE Main202529 Jan 2025Evening ShiftMathematicsSets and RelationsActual

Let S= N 0 . Define a relation R from S to R by : R = (x, y): _ e y=x _ e ( 2 5 ), x ~S , y R Then, the sum of all the elements in the range of R is equal to :

Options

  1. A10 9
  2. B3 2
  3. C5 2
  4. D5 3

Correct answer

D. 5 3

Step-by-step solution

aligned & S= 0,1,2,3 & _y y= _e ( 2 5 ) & y= ( 2 5 )^x aligned Required Sum =1+ ( 2 5 )^1+ ( 2 5 )^2+ ( 2 5 )^3+ . .-= 1 1- 2 5 = 5 3

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