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JEE Main2014MathematicsBinomial TheoremActual

The number of terms in the expansion of 1 + x 101 1 - x + x 2 100 in powers of x is

Options

  1. A301
  2. B302
  3. C101
  4. D202

Correct answer

D. 202

Step-by-step solution

1 + x 1 0 1 1 + x 2 - x 1 0 0 = 1 + x 1 + x 1 0 0 1 - x + x 2 1 0 0 = 1 + x 1 + x 3 1 0 0 ∵ a 3 + b 3 = a + b a 2 - a b + b 2 1 + x 3 1 0 0 has 101 terms 1 + x 1 + x 3 1 0 0 = 1 1 + x 3 1 0 0 + x 1 + x 3 1 0 0 ⇒ No. of terms = 101 + 101 = 202

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