$A$ solution which is $10^{-3} \ M$ each in $Mn^{2+}$,$Fe^{2+}$,$Zn^{2+}$ and $Hg^{2+}$ is treated with $10^{-16} \ M$ sulphide ion. If the $K_{sp}$ of $MnS$,$FeS$,$ZnS$ and $HgS$ are $10^{-15}$,$10^{-23}$,$10^{-20}$ and $10^{-54}$ respectively,which one will precipitate first?

If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

Drift velocity ${v_d}$ varies with the intensity of the electric field $E$ as per the relation:

$A$ stationary charge produces . . . . . . .

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the centre of mass of the system will be

At $25 \, ^oC$,the equilibrium $SO_2Cl_2(g) \rightleftharpoons SO_2(g) + Cl_2(g)$ is established in a closed vessel. When $Cl_2$ is added to this equilibrium mixture,which of the following statements is true for the system?
$(1)$ The concentrations of $SO_2Cl_2$ and $SO_2$ change.
$(2)$ More $Cl_2$ is produced.
$(3)$ The concentration of $SO_2$ decreases and $SO_2Cl_2$ increases.