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JEE Main202225 Jun 2022Evening ShiftMathematicsBinomial TheoremActual

The coefficient of x 101 in the expression 5 + x 500 + x 5 + x 499 + x 2 5 + x 498 + … … + x 500 , x > 0 is

Options

  1. A  501 C 101 × 5 399
  2. B  501 C 101 × 5 400
  3. C  501 C 100 × 5 400
  4. D500 C 101 × 5 399

Correct answer

A.   501 C 101 × 5 399

Step-by-step solution

Given, 5 + x 500 + x 5 + x 499 + x 2 5 + x 498 + … … + x 500 Using sum of the G.P in the given expression we get, ⇒ 5 + x 500 x 5 + x 501 - 1 x 5 + x - 1 = x 501 - 5 + x 501 - 5 = 1 5 5 + x 501 - x 501 5 Now coefficient of x 101 in 1 5 5 + x 501 will be 1 5 C 101 501 5 501 - 101 = 5 399 C 101 501

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