If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+C_{3} x^{3}+\ldots+C_{n} ...

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If \( (1+x)^{n}=C_{0}+C_{1} x+C_{2} x^{2}+C_{3} x^{3}+\ldots+C_{n} x^{n} \)
P then

W)
\[
\begin{aligned}
C_{0}-\left(C_{0}+C_{1}\right)+ & \left(C_{0}+C_{1}+C_{2}\right) \\
& -\left(C_{0}+C_{1}+C_{2}+C_{3}\right)+\ldots+(-1)^{n-1}
\end{aligned}
\]
\( \left(C_{0}+C_{1}+C_{2}+\ldots+C_{n-1}\right) \), when \( n \) is even integer is
(a) a positive value
(b) a negative value
(c) divisible by \( 2^{n-1} \)
(d) divisible by \( 2^{n} \)
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