Q197 / 270 · NDA 2021 (Phase 1) · Mathematics

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

  • A
    $1$
  • Correct answer
    B
    $2$
  • C
    $n$
  • D
    $2 n$

Solution

$(1+x)^{2 n}={ }^{2 n} C_0+{ }^{2 n} C_1 2 x+\ldots \ldots .+{ }^{2 n} c_{2 n} x^{2 x}$ Sum of co-efficient of first and last term $={ }^{2 n} C_0+{ }^{2 n} C_{2 n}=1+1=2$

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

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