46. If $| z | = 1$ and $z \neq \pm 1$, then all the values of $\frac { z } { 1 - z ^ { 2 } }$ lie on (A) a line not passing through the origin (B) $| z | = \sqrt { 2 }$ (C) the $x$-axis (D) the $y$-axis
Let $E ^ { c }$ denote the complement of an event $E$. Let $E , F , G$ be pairwise independent events with $P ( G ) > 0$ and $P ( E \cap F \cap G ) = 0$. Then $P \left( E ^ { c } \cap F ^ { c } \mid G \right)$ equals (A) $P \left( E ^ { c } \right) + P \left( F ^ { c } \right)$ (B) $P \left( E ^ { c } \right) - P \left( F ^ { c } \right)$ (C) $P \left( E ^ { c } \right) - P ( F )$ (D) $P ( E ) - P \left( F ^ { c } \right)$
Answer ◯ (A) [Figure] (B) [Figure] (C) ◯ (D)
The tangent to the curve $\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }$ drawn at the point ( $\mathrm { c } , \mathrm { e } ^ { \mathrm { c } }$ ) intersects the line joining the points ( $\mathrm { c } - 1 , \mathrm { e } ^ { \mathrm { c } - 1 }$ ) and
46. If $| z | = 1$ and $z \neq \pm 1$, then all the values of $\frac { z } { 1 - z ^ { 2 } }$ lie on\\
(A) a line not passing through the origin\\
(B) $| z | = \sqrt { 2 }$\\
(C) the $x$-axis\\
(D) the $y$-axis
\section*{Answer}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e79946a0-735d-438d-ac42-5265ab72284d-20_99_97_580_335}
\captionsetup{labelformat=empty}
\caption{(A)}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e79946a0-735d-438d-ac42-5265ab72284d-20_93_93_580_494}
\captionsetup{labelformat=empty}
\caption{(B)}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e79946a0-735d-438d-ac42-5265ab72284d-20_97_98_580_644}
\captionsetup{labelformat=empty}
\caption{(C)}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e79946a0-735d-438d-ac42-5265ab72284d-20_93_98_584_794}
\captionsetup{labelformat=empty}
\caption{(D)}
\end{center}
\end{figure}
\begin{enumerate}
\setcounter{enumi}{46}
\item Let $E ^ { c }$ denote the complement of an event $E$. Let $E , F , G$ be pairwise independent events with $P ( G ) > 0$ and $P ( E \cap F \cap G ) = 0$. Then $P \left( E ^ { c } \cap F ^ { c } \mid G \right)$ equals\\
(A) $P \left( E ^ { c } \right) + P \left( F ^ { c } \right)$\\
(B) $P \left( E ^ { c } \right) - P \left( F ^ { c } \right)$\\
(C) $P \left( E ^ { c } \right) - P ( F )$\\
(D) $P ( E ) - P \left( F ^ { c } \right)$
\end{enumerate}
Answer ◯
(A)
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e79946a0-735d-438d-ac42-5265ab72284d-20_93_104_1190_485}
\captionsetup{labelformat=empty}
\caption{(B)}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e79946a0-735d-438d-ac42-5265ab72284d-20_95_96_1188_646}
\captionsetup{labelformat=empty}
\caption{(C)}
\end{center}
\end{figure}
◯
(D)\\