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JEE Main202312 Apr 2023Morning ShiftMathematicsBinomial TheoremActual

The sum, of the coefficients of the first 50 terms in the binomial expansion of 1 - x 100 , is equal to

Options

  1. A101 C 50
  2. B99 C 49
  3. C- 101 C 50
  4. D- 99 C 49

Correct answer

D. - 99 C 49

Step-by-step solution

We know that 1 - x 100 = C 0 100 - C 1 100 · x + C 2 100 · x 2 - . . . . . . . - C 49 100 · x 49 + . . . . . . . + C 100 100 · x 100 Now let, the sum of first fifty coefficients be S . ⇒ S = C 0 100 - C 1 100 + C 2 100 - . . . . . . . - C 49 100 Let us substitute x = 1 in the expansion. ⇒ 1 - 1 100 = C 0 100 - C 1 100 · 1 + C 2 100 · 1 2 - . . . . . . . - C 49 100 · 1 49 + . . . . . . . + C 100 100 · 1 100 ⇒ 0 = C 0 100 - C 1 100 + C 2 100 - . . . . . . . -

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