[Q.] If $\cos x + \cos y + \cos z = 0 = \sin x + \sin y + \sin z$ then possible value of $\cos \frac { x - y } { 2 }$ is
[R.] If $\cos \left( \frac { \pi } { 4 } - x \right) \cos 2 x + \sin x \sin 2 x \sec x = \cos x \sin 2 x \sec x + \cos \left( \frac { \pi } { 4 } + x \right) \cos 2 x$ then possible value of $\sec x$ is
[S.] If $\cot \left( \sin ^ { - 1 } \sqrt { 1 - x ^ { 2 } } \right) = \sin \left( \tan ^ { - 1 } ( x \sqrt { 6 } ) \right) , x \neq 0$, then possible value of $x$ is
List II
$\frac { 1 } { 2 } \sqrt { \frac { 5 } { 3 } }$
$\sqrt { 2 }$
$\frac { 1 } { 2 }$
$1$
Codes:
P
Q
R
S
(A)
4
3
1
2
(B)
4
3
2
1
(C)
3
4
2
1
(D)
3
4
1
2
Match List I with List II and select the correct answer using the code given below the lists:
\textbf{List I}
\begin{itemize}
\item[P.] $\left( \frac { 1 } { y ^ { 2 } } \left( \frac { \cos \left( \tan ^ { - 1 } y \right) + y \sin \left( \tan ^ { - 1 } y \right) } { \cot \left( \sin ^ { - 1 } y \right) + \tan \left( \sin ^ { - 1 } y \right) } \right) ^ { 2 } + y ^ { 4 } \right) ^ { 1 / 2 }$ takes value
\item[Q.] If $\cos x + \cos y + \cos z = 0 = \sin x + \sin y + \sin z$ then possible value of $\cos \frac { x - y } { 2 }$ is
\item[R.] If $\cos \left( \frac { \pi } { 4 } - x \right) \cos 2 x + \sin x \sin 2 x \sec x = \cos x \sin 2 x \sec x + \cos \left( \frac { \pi } { 4 } + x \right) \cos 2 x$ then possible value of $\sec x$ is
\item[S.] If $\cot \left( \sin ^ { - 1 } \sqrt { 1 - x ^ { 2 } } \right) = \sin \left( \tan ^ { - 1 } ( x \sqrt { 6 } ) \right) , x \neq 0$, then possible value of $x$ is
\end{itemize}
\textbf{List II}
\begin{enumerate}
\item $\frac { 1 } { 2 } \sqrt { \frac { 5 } { 3 } }$
\item $\sqrt { 2 }$
\item $\frac { 1 } { 2 }$
\item $1$
\end{enumerate}
\textbf{Codes:}
\begin{tabular}{ l l l l l }
& P & Q & R & S \\
(A) & 4 & 3 & 1 & 2 \\
(B) & 4 & 3 & 2 & 1 \\
(C) & 3 & 4 & 2 & 1 \\
(D) & 3 & 4 & 1 & 2 \\
\end{tabular}