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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2021 · Mathematics · Binomial Theorem

What is the sum of the coefficients of first and last terms in the...

What is the sum of the coefficients of first and last terms in the expansion of (1+x)2n(1+x)^{2 n}, where nn is a natural number?

Options

  1. A11
  2. B22
  3. Cnn
  4. D2n2 n

Correct answer

B. 22

Step-by-step solution

(1+x)2n=2nC0+2nC12x+…….+2nc2nx2x(1+x)^{2 n}={ }^{2 n} C_0+{ }^{2 n} C_1 2 x+\ldots \ldots.+{ }^{2 n} c_{2 n} x^{2 x} Sum of co-efficient of first and last term =2nC0+(2n2n)=1+1=2={ }^{2 n} C_0+\binom{2 n}{2 n}=1+1=2
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