$C_{0} - C_{1} + C_{2} - C_{3} + . . . . . . . . . . + (- 1)^{n}$ $C_{n}$ is equal to

2^{n}

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2^{n} - 1

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2^{n - 1}

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Solution

The correct option is A 0
$\begin{matrix} C_{0} - C_{1} + C_{2} - C_{3} + \dots + (- 1)^{n} C_{n} ∵ C_{0} =^{n} C_{0};^{n} C_{1} = C_{1} \Rightarrow \begin{matrix} (1 - x)^{n} = {^{n} C_{0} |}_{0}^{n} -^{n} C_{1} x +^{n} C_{2} x^{2} + \dots + (- 1)^{n}^{n} C_{n} x^{n} x & = 1 0 & =^{n} C_{0} -^{n} C_{1} +^{n} C_{2} + \dots + (- 1)^{n} C_{n} \end{matrix} Hence, (C) is the correct option. \end{matrix}$

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