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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2015 · Mathematics · Binomial Theorem

Consider the expansion of (1+x)^ 2 n+1 The sum of the coefficients...

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

Options

  1. A22n−12^{2 \mathrm{n}-1}
  2. B4n−14^{\mathrm{n}-1}
  3. C2×4n2 \times 4^{\mathrm{n}}
  4. DNone of the above

Correct answer

C. 2×4n2 \times 4^{\mathrm{n}}

Step-by-step solution

Sum of allcoefficientall coefficient=(2n+1)C0+(2n+1)C1+……..+(2n+1)C2n+1=(1+1)2n+1=2(2n+1)=2.22n=2.4n\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}$$
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