Two cars $S_1$ and $S_2$ are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution $3 \min$ and $24 \min$, respectively. At the time $t=0,$ the cars are the farthest apart. Then, the two cars will be, 

Two parallel discs are connected by a rigid rod of length $L=0.5 \mathrm{m}$ centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms is incident on one of the discs axially at different velocities $v$, while the system is rotated at angular speed of, $600 \mathrm{rev} {\mathrm{s}}^{-1}$, so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in meter/second) of the atoms that will emerge at the other end.

If $\overrightarrow{A}=3\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $\overrightarrow{B}=2\hat{\mathrm{i}}-2\hat{\mathrm{j}}+4\hat{\mathrm{k}}$, then the value of $\left|\overrightarrow{A}\times \overrightarrow{B}\right|$ will be