Match the items of Column I with those of Column II. \begin{tabular}{|l|l|l|l|} \hline \multicol....

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Match the items of Column I with those of Column
\( \mathrm{P} \)
II.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{|c|}{ Column-II } \\
\hline (A) & \( \lim _{x \rightarrow 0} \frac{2^{x}-1}{\sqrt{1+x}-1} \) is & (P) & \( 2 \log 2 \) \\
\hline (B) & \begin{tabular}{l}
\( f(x)=\frac{\sqrt{1+2 x}-\sqrt{3 x}}{\sqrt{3+x}-2 \sqrt{x}} \), then \\
\( \lim _{x \rightarrow 1} f(x) \) equals
\end{tabular} & (Q) & 1 \\
\hline (C) & \( \lim _{x \rightarrow 0}\left(\frac{2 \sin x-\sin 2 x}{x^{3}}\right) \) is & (R) & 2 \\
\hline (D) & \begin{tabular}{l}
\( x_{1}=1 \) and \( x_{n+1}=\sqrt{2+x_{n}} \). \\
Define \( y_{n}=\frac{x_{1}+x_{2}+\cdots+x_{n}}{n} \) \\
Then \( \lim _{n \rightarrow \infty} y_{n} \) is
\end{tabular} & (S) & \( \frac{2}{3 \sqrt{3}} \) \\
\hline
\end{tabular}
(1) A-R; B-Q; C-P; D-S
(2) A-P; B-S; C-Q; D-R
(3) A-S; B-P; C-Q; D-R
(4) A-P; B-R; C-S; D-Q


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