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JEE Main202330 Jan 2023Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x 301 in 1 + x 500 + x 1 + x 499 + x 2 1 + x 498 + … . . + x 500 is:

Options

  1. AC 302 501
  2. BC 301 500
  3. CC 300 500
  4. DC 200 501

Correct answer

D. C 200 501

Step-by-step solution

We have, 1 + x 500 + x 1 + x 499 + x 2 1 + x 498 + … . . + x 500 This is a geometric progression. = 1 + x 500 · 1 - x 1 + x 501 1 - x 1 + x = 1 + x 500 1 + x 501 - x 501 1 + x 501 · 1 + x = ( 1 + x ) 501 - x 501 Coefficient of x 301 in ( 1 + x ) 501 - x 501 is given by C 301 501 = C 200 501

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