Match the statement in Column-I with statements in Column-II. (Find number of solutions) \begin{...

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Match the statement in Column-I with statements in Column-II. (Find number of solutions)
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline A. & \( x^{2} \cot x=1, x \in[0,2 \pi] \) & p. & 5 \\
\hline B. & \( 2^{\cos x}=|\cos x|, x \in[0,2 \pi] \) & q. & 2 \\
\hline C. & \( \begin{array}{l}\text { If } f(x) \text { is a polynomial of degrees } 5 \\
\text { with real coefficients such that } f(|x|) \\
=0 \text { has } 8 \text { real and distinct roots, } \\
\text { then the number of roots of } f(x)=0\end{array} \) & r. & 1 \\
\hline D. & \( \pi|\mathrm{x}|(\pi-|x|)=1 \) & s. & 4 \\
\hline
\end{tabular}
(a) (A) \( \rightarrow \mathrm{s} \); (B) \( \rightarrow \mathrm{r} \); (C) \( \rightarrow \mathrm{p} \); (D) \( \rightarrow \mathrm{q} \)
(b) (A) \( \rightarrow \mathrm{p} \); (B) \( \rightarrow \) q ; (C) \( \rightarrow \mathrm{r} \); (D) \( \rightarrow \mathrm{s} \)
(c) (A) \( \rightarrow \mathrm{r} \); (B) \( \rightarrow \) q; (C) \( \rightarrow \mathrm{p} \); (D) \( \rightarrow \mathrm{s} \)
(d) (A) \( \rightarrow \mathrm{p} \); (B) \( \rightarrow \) q; (C) \( \rightarrow \mathrm{s} \); (D) \( \rightarrow \mathrm{r} \)
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