If ${(1 - x + {x^2})^n} = {a_0} + {a_1}x + {a_2}{x^2} + .... + {a_{2n}}{x^{2n}}$, then ${a_0} + {a_2} + {a_4} + .... + {a_{2n}} = $

  • A

    $\frac{{{3^n} + 1}}{2}$

  • B

    $\frac{{{3^n} - 1}}{2}$

  • C

    $\frac{{1 - {3^n}}}{2}$

  • D

    ${3^n} + \frac{1}{2}$

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{21}\\
3
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{10}\\
3
\end{array}} \right)} \right) + \;.\;.\;.$$ + \left( {\left( {\begin{array}{*{20}{c}}
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In the expansion of ${(1 + x)^n}$ the sum of coefficients of odd powers of $x$ is