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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2017 · Mathematics · Binomial Theorem

The number of terms in the expansion of (x+a)^ 100 +(x-a)^ 100...

The number of terms in the expansion of (x+a)100+(x−a)100(x+a)^{100}+(x-a)^{100} after simplification is

Options

  1. A202202
  2. B101101
  3. C5151
  4. D5050

Correct answer

C. 5151

Step-by-step solution

(x+a)100+(x−a)100(x+a)^{100}+(x-a)^{100} Simple logic is we get nc0,nc2,nc4….nc100{ }^n c_0,{ }^n c_2,{ }^n c_4 \ldots.{ }^n c_{100} in this expansion. The number of terms from nc0\mathrm{n}_{\mathrm{c}_0} to nc100\mathrm{n}_{\mathrm{c}_{100}} are 51 ∴\therefore There are 51 terms.
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