Match the items of column-I with of column-II. \begin{tabular}{|c|c|c|c|} \hline \multicolumn{2}....

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Match the items of column-I with of column-II.
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{2}{|r|}{ Column I } & \multicolumn{2}{|c|}{ Column II } \\
\hline (A) & \begin{tabular}{l}
Value of \( \left(\cos 24^{\circ} \cos 36^{\circ}\right. \) \\
\( \left.\cos 84^{\circ}\right) \) is \( \frac{\sqrt{a}-b}{b} \) \\
(a and b are coprime \\
numbers), then the value of \\
of \( (a+b) \) is
\end{tabular} & (p) & 12 \\
\hline (B) & \begin{tabular}{l}
Let \\
\( \alpha+\beta=\frac{\pi}{5}, \alpha, \beta \in\left(0, \frac{\pi}{2}\right) \), if \\
then the maximum value of \\
\( \sin \alpha+\sin \beta \) is \( \frac{\sqrt{a}-1}{b} \), (a \\
and \( b \) are coprime numbers), \\
then the value of \( (2 a+b) \) is
\end{tabular} & (q) & 21 \\
\hline (C) & \begin{tabular}{l}
Value of \\
\( \left(\cot \frac{\pi}{12}+\cot \frac{\pi}{8}-\tan \frac{\pi}{8}\right) \) is \\
\( (a+\sqrt{b}) \) (a and \( b \) are \\
coprime numbers), then the \\
value of \( (2 a+3 b) \) is
\end{tabular} & (r) & 7 \\
\hline (D) & \begin{tabular}{l}
If the solution of \( \cos ^{2} 5^{\circ}+ \) \\
\( \cos ^{2} 10^{\circ}+\cos ^{2} 15^{\circ}+\ldots . .+ \) \\
\( \cos ^{2} 85^{\circ}=\frac{a}{b} \) (where \( a \) and \\
\( b \) are prime numbers), then \\
the value of \( (a-5 b) \) is
\end{tabular} & (s) & 17 \\
\hline
\end{tabular}
(1) (A) \( -\mathrm{p} \); (B) \( -\mathrm{q} \); (C) \( -\mathrm{r} \); (D) \( -\mathrm{s} \)
(2) (A) \( -\mathrm{q} \); (B) \( -\mathrm{r} \); (C) \( -\mathrm{p} \); (D) \( -\mathrm{s} \)
(3) (A) \( -\mathrm{q} \); (B) \( -\mathrm{p} \); (C) \( -\mathrm{r} \); (D) \( -\mathrm{s} \)
(4) (A) \( -\mathrm{q} \); (B) \( -\mathrm{p} \); (C) \( -\mathrm{s} \); (D) \( -\mathrm{r} \)


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