Match List $I$ with List $II$ and select the correct answer using the code given below the lists: $\,\,\,\,\,\,\,\,\,\,\,\,$ List-$I$ (P.) $\,\,\,\,$ Let $$y\left( x \right) = \cos \left( {3{{\cos }^{ - 1}}x} \right),x \in \left[ { - 1,1} \right],x e \pm {{\sqrt 3 } \over 2}.$$ Then $${1 \over {y\left( x \right)}}\left\{ {\left( {{x^2} - 1} \right){{{d^2}y\left( x \right)} \over {d{x^2}}} + x{{dy\left( x \right)} \over {dx}}} \right\}$$ equals (Q.) $\,\,\,\,$ Let $${A_1},{A_2},....,{A_n}\left( {n \gt 2} \right)$$ be the vertices of a regular polygon of $n$ sides with its centre at the origin. Let ${\overrightarrow {{a_k}} }$ be the position vector of the point ${A_k},k = 1,2,......,n.f\left| {\sum olimits_{k = 1}^{n - 1} {\left( {\overrightarrow {{a_k}} \times \overrightarrow {{a_{k + 1}}} } \right)} } \right| = \left| {\sum\limits_{k = 1}^{n - 1} {\left( {\overrightarrow {{a_k}} .\,\overrightarrow {{a_{k + 1}}} } \right)} } \right|,$ then the minimum value of $n$ is (R.) $\,\,\,\,$ If the normal from the point $P(h, 1)$ on the ellipse ${{{x^2}} \over 6} + {{{y^2}} \over 3} = 1$ is perpendicular to the line $x+y=8,$ then the value of $h$ is (S.) $\,\,\,\,$ Number of positive solutions satisfying the equation $${\tan ^{ - 1}}\left( {{1 \over {2x + 1}}} \right) + {\tan ^{ - 1}}\left( {{1 \over {4x + 1}}} \right) = {\tan ^{ - 1}}\left( {{2 \over {{x^2}}}} \right)$$ is $\,\,\,\,\,\,\,\,\,\,\,\,$ List-$II$ (1.) $\,\,\,\,1$ (2.) $\,\,\,\,2$ (3.) $\,\,\,\,8$ (4.) $\,\,\,\,9$