Match the following columns: \begin{tabular}{|c|c|c|c|} \hline \multicolumn{2}{|r|}{ Column-I } ....
0Match the following columns:
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{2}{|r|}{ Column-I } & \multicolumn{2}{|c|}{ Column-II } \\
\hline (A) & \begin{tabular}{l}
The expression, \( x^{\ln y-\ln z} \cdot y^{\ln } \) \\
\( z-\ln x \) \\
\( z^{\ln x-\ln y} \) when \\
simplified reduces to
\end{tabular} & (P) & \( \frac{1}{8} \) \\
\hline (B) & \begin{tabular}{l}
Let \( p=\log _{5} \log _{5}(3) \). If \\
\( 3^{C+5^{-P}}=45 \), the value of \\
\( C \) equals
\end{tabular} & (Q) & \( \frac{1}{4} \) \\
\hline (C) & \begin{tabular}{l}
The real value of \( x \) for \\
which the statement \( \log _{6} 9- \) \\
\( \log _{9} 27+\log _{8} x=\log _{64} x- \) \\
\( \log _{6} 4 \) holds true, is
\end{tabular} & (R) & \( \frac{1}{2} \) \\
\hline (D) & \begin{tabular}{l}
\( \frac{1}{2} \log _{\sqrt{5}} \sin \left(\frac{\pi}{5}\right) \cdot \log \sqrt{\sin \frac{\pi}{5}} 5 \) \\
simplifies to
\end{tabular} & (S) & 1 \\
\hline & & \( (\mathrm{T}) \) & 2 \\
\hline
\end{tabular}
(1) \( \mathrm{A} \rightarrow \mathrm{R} ; \mathrm{B} \rightarrow \mathrm{T} ; \mathrm{C} \rightarrow \mathrm{P} ; \mathrm{D} \rightarrow \mathrm{Q} \)
(2) \( \mathrm{A} \rightarrow \mathrm{T} ; \mathrm{B} \rightarrow \mathrm{R} ; \mathrm{C} \rightarrow \mathrm{Q} ; \mathrm{D} \rightarrow \mathrm{P} \)
(3) \( \mathrm{A} \rightarrow \mathrm{R} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{T} ; \mathrm{D} \rightarrow \mathrm{Q} \)
(4) \( \mathrm{A} \rightarrow \mathrm{S} ; \mathrm{B} \rightarrow \mathrm{T} ; \mathrm{C} \rightarrow \mathrm{P} ; \mathrm{D} \rightarrow \mathrm{T} \)
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