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JEE Main202120 Jul 2021Morning ShiftMathematicsBinomial TheoremActual

The coefficient of x 256 in the expansion of 1 - x 101 x 2 + x + 1 100 is:

Options

  1. AC 16 100
  2. BC 15 100
  3. CC 16 - 100
  4. DC 15 - 100

Correct answer

B. C 15 100

Step-by-step solution

We have, 1 - x 101 x 2 + x + 1 100 = 1 - x 100 x 2 + x + 1 100 1 - x = 1 - x x 2 + x + 1 100 · 1 - x = 1 - x 3 100 · 1 - x = 1 - x 3 100 ⏟ No   term   of   x 256 - x 1 - x 3 100 ⏟ we   find   cofficient   of   x 255 Now, 1 - x 3 100 = C 0 100 - C 1 100 x 3 + C 2 100 x 6 - . . . - C 85 100 - x 255 ⇒ x 1 - x 3 100 = C 0 100 x - C 1 100 x 4 + C 2 100 x 7 - . . . + C 85 100 x 256 Required coefficient = C 85 100 = C 15 100

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