Q175 / 270 · NDA 2013 (Phase 2) · Mathematics

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

  • A
    11
  • B
    20
  • Correct answer
    C
    21
  • D
    30

Solution

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

Hence, the correct answer is option: 'C'.

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