Consider four functions,
\[
\begin{array}{l}
f(x)=\sqrt{5-x^{2}}, g(x)=\operatorname{sgn}\left(x^{3}-3 x-1\right) \\
h(x)=\left[\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)\right] \text { and } k(x)=\left(e^{|x|-1}-1\right)\left|x^{4}-x^{2}\right| .
\end{array}
\]
A function is selected at random, three events \( A, B \) and \( C \) are defined as
\( A \) : Selected function is continuous.
\( B: \) Selected function is derivable.
\( C \) : Selected function has 3 or more integers in its range.
Let \( P(E) \) denotes the probability of occurence of event \( E \).
Note: \( [y] \) and \( \operatorname{sgn}(y) \) denotes greatest integer function and signum function of \( y \) respectively.
\begin{tabular}{|l|l|c|c|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline A. & \( \begin{array}{l}\text { The value of } P\left(\frac{\bar{B}}{A}\right)+P\left(\frac{A}{B}\right) \text { is } \\
\text { equal to }\end{array} \) & p. & \( \frac{3}{4} \) \\
\hline B. & \( \begin{array}{l}\text { The value of } P\left(\frac{B}{C}\right)+P\left(\frac{\bar{A}}{C}\right) \text { is } \\
\text { equal to }\end{array} \) & q. & 1 \\
\hline C. & \( \begin{array}{l}\text { The value of } P(\bar{B} \cap C)+P\left(\frac{A}{C}\right) \\
\text { is equal to }\end{array} \) & r. & \( \frac{5}{4} \) \\
\hline D. & \( \begin{array}{l}\text { Thevalueof } P\left(\frac{C}{\bar{B}}\right)-P\left(\frac{(A \cap \bar{B})}{C}\right) \\
\text { is equal to }\end{array} \) & s. & \( \frac{3}{2} \) \\
\hline
\end{tabular}
(a) \( \mathrm{A}-\mathrm{q}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{r}, \mathrm{D}-\mathrm{r} \)
(b) \( \mathrm{A}-\mathrm{s}, \mathrm{B}-\mathrm{p}, \mathrm{C}-\mathrm{r}, \mathrm{D}-\mathrm{p} \)
(c) \( \mathrm{A}-\mathrm{p}, \mathrm{B}-\mathrm{r}, \mathrm{C}-\mathrm{q}, \mathrm{D}-\mathrm{s} \)
(d) \( \mathrm{A}-\mathrm{r}, \mathrm{B}-\mathrm{s}, \mathrm{C}-\mathrm{p}, \mathrm{D}-\mathrm{q} \)
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