Q183 / 270 · NDA 2015 (Phase 2) · Mathematics

Consider the expansion of $(1+x)^{2 n+1}$ The sum of the coefficients of all the terms in the expansion is

  • A
    $2^{2 \mathrm{n}-1}$
  • B
    $4^{\mathrm{n}-1}$
  • Correct answer
    C
    $2 \times 4^{\mathrm{n}}$
  • D
    None of the above

Solution

Sum of all coefficient $\begin{aligned} & ={ }^{(2 \mathrm{n}+1)} \mathrm{C}_0+{ }^{(2 \mathrm{n}+1)} \mathrm{C}_1+\ldots \ldots . .+{ }^{(2 \mathrm{n}+1)} \mathrm{C}_{2 \mathrm{n}+1} \\ & =(1+1)^{2 \mathrm{n}+1} \\ & =2^{(2 \mathrm{n}+1)} \\ & =2.2^{2 \mathrm{n}} \\ & =2.4^{\mathrm{n}} \end{aligned}$

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

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