Which one of the following is used in the preparation of styrene?

$A$ solid sphere is rolling on a frictionless surface with a translational velocity $v \ m/s$,as shown in the figure. If it is to climb the inclined surface to a height $h$,then $v$ should be:

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ (where $k > 0$). Then the terminal speed of the ball is:

If a point $P$ moves such that its distances from the point $A(1,1)$ and the line $x+y+2=0$ are equal,then the locus of $P$ is

$\cos A \cos 2 A \cos 4 A \ldots \cos 2^{n-1} A$ equals

If all the seven letters of the word $LEADING$ are permuted in all possible ways and the words thus formed are arranged as in the dictionary order,then the word in $2017^{\text{th}}$ place is