Q169 / 270 · NDA 2013 (Phase 2) · Mathematics

Let $n$ be a positive integer and $(1+x)^n=a_0+a_1 x+$ $a_2 x^2+\ldots+a_n x^n$ What is $a_0+a_1+a_2+\ldots+a_n$ equal to?

  • A
    1
  • Correct answer
    B
    $2^n$
  • C
    $2^{n-1}$
  • D
    $2^{n+1}$

Solution

Plug in $x=1$, we get $(1+1)^n=a_0+a_1+a_2+\ldots \ldots+a_n=(2)^n$

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

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