If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . + C_{n} x^{n}$ , then the value of $(C_{0} - C_{1} + C_{2} - C_{3} + . . . . . + (- 1)^{n} C_{n})$ is

2^{n}

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2^{n} - 1

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0

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2^{n - 1}

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Solution

The correct option is B $0$
For $(X + A)^{n} = {C_{0}^{n} X}^{n} + . . . . C_{r}^{n} X^{n - r} A^{r} + . . . . C_{n}^{n} A^{n}$
Now substitute
$X = 1, A = - 1$
and
we see that $0 = C_{0}^{n} - C_{1}^{n} + C_{2}^{n} - C_{3}^{n} + C_{4}^{n} - C_{5}^{n} + . . . . . . . {(- 1)}^{n} C_{n}^{n}$
Hence here the answer is 0

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If (1+x)n=C0+C1x+C2x2+.....+Cnxn, then the value of (C0−C1+C2−C3+.....+(−1)nCn) is

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If $(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + . . . . . + C_{n} x^{n}$ , then the value of $(C_{0} - C_{1} + C_{2} - C_{3} + . . . . . + (- 1)^{n} C_{n})$ is