For some positive integer \( n \) \[ \left(1+x+x^{2}\right)^{n}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots....
0For some positive integer \( n \)
\[
\left(1+x+x^{2}\right)^{n}=a_{0}+a_{1} x+a_{2} x^{2}+\ldots . .+a_{2 n} x^{2 n}
\]
then match the following column.
\( \mathrm{P} \)
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline (A) & \( \sum_{\mathrm{r}=0}^{2 n} \mathrm{a}_{\mathrm{r}} \) is equal to & (P) & \begin{tabular}{l}
\( (n-r) a_{r}+ \) \\
\( (2 n-r+1) a_{r-1} \)
\end{tabular} \\
\hline (B) & \begin{tabular}{l}
\( a_{r} \) is equal to \( (0 \leq r \) \\
\( \leq 2 n) \)
\end{tabular} & (Q) & \( 3^{n} \) \\
\hline (C) & \begin{tabular}{l}
The value of \\
\( (r+1) a_{r+1} \)
\end{tabular} & (R) & \( \frac{3^{n}-a_{n}}{2} \) \\
\hline (D) & \begin{tabular}{l}
The value of \( a_{0}+ \) \\
\( a_{1}+a_{2}+\ldots .+a_{n-1} \) \\
is
\end{tabular} & (S) & \( a_{2 n-r} \) \\
\hline
\end{tabular}
(1) \( \mathrm{A} \rightarrow \mathrm{S} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{R} ; \mathrm{D} \rightarrow \mathrm{Q} \)
(2) \( \mathrm{A} \rightarrow \mathrm{Q} ; \mathrm{B} \rightarrow \mathrm{S} ; \mathrm{C} \rightarrow \mathrm{P} ; \mathrm{D} \rightarrow \mathrm{R} \)
(3) \( \mathrm{A} \rightarrow \mathrm{R} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{Q} ; \mathrm{D} \rightarrow \mathrm{S} \)
(4) \( \mathrm{A} \rightarrow \mathrm{P} ; \mathrm{B} \rightarrow \mathrm{Q} ; \mathrm{C} \rightarrow \mathrm{R} ; \mathrm{D} \rightarrow \mathrm{S} \)
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