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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2013 · Mathematics · Binomial Theorem

How many terms are there in the expansion of (1+2 x+x^2)^ 10 ?

How many terms are there in the expansion of \left(1+2 x+x^2\right)^{10} ?

Options

  1. A11
  2. B20
  3. C21
  4. D30

Correct answer

C. 21

Step-by-step solution

(1+2x+x2)10={(1+x)2}10=(1+x)20\left(1+2 x+x^2\right)^{10}=\left\{(1+x)^2\right\}^{10}=(1+x)^{20} We know that number of terms in the expansion of (1+x)n(1+x)^n are n+1n+1 so, required number of terms =20+1=21=20+1=21.
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