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(D) We know that the binomial expansion is given by:$(1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \ldots + C_n x^n$Putting $x=1$,we get:$2^n = C_0 + C_

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Both $1$ and $2$ are true

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(D) We know that the binomial expansion is given by:$(1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \ldots + C_n x^n$Putting $x=1$,we get:$2^n = C_0 + C_1 + C_2 + C_3 + \ldots + C_n$ $(i)$Putting $x=-1$,we get:$0 = C_0 - C_1 + C_2 - C_3 + \ldots + (-1)^n C_n$ (ii)If $n$ is even,then $(-1)^n = 1$,so equation (ii) becomes:$0 = C_0 - C_1 + C_2 - C_3 + \ldots + C_n$ (iii)Adding $(i)$ and (iii):$2^n + 0 = 2(C_0 + C_2 + C_4 + \ldots + C_n)$$\Rightarrow C_0 + C_2 + C_4 + \ldots + C_n = 2^{n-1}$Subtracting (iii) from $(i)$:$2^n - 0 = 2(C_1 + C_3 + C_5 + \ldots + C_{n-1})$$\Rightarrow C_1 + C_3 + C_5 + \ldots + C_{n-1} = 2^{n-1}$Thus,both statements are true.

Choose the correct option regarding the following statements:
$1$. $C_0+C_2+C_4+\ldots+C_n=2^{n-1}$,if $n$ is even
$2$. $C_1+C_3+C_5+\ldots+C_{n-1}=2^{n-1}$,if $n$ is even

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Choose the correct option regarding the following statements:$1$. $C_0+C_2+C_4+\ldots+C_n=2^{n-1}$,if $n$ is even$2$. $C_1+C_3+C_5+\ldots+C_{n-1}=2^{n-1}$,if $n$ is even