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

When a capacitor is connected in series to an $LR$ circuit,the alternating current flowing in the circuit

In a competition, $A, B$, and $C$ are participating. The probability that $A$ wins is twice that of $B$, and the probability that $B$ wins is twice that of $C$. What is the probability that $A$ loses?

$A$ molecule that can act as a genetic material must fulfill the traits given below,except.

Five point charges,each having magnitude $q$,are placed at the corners of a hexagon as shown in the figure. The net electric field at the centre $O$ is $\vec{E}$. To make the net electric field at $O$ equal to $6\vec{E}$,the charge to be placed on the remaining sixth corner should be: (in $q$)

When $100 \, V$ $DC$ is applied across a solenoid,a current of $1 \, A$ flows in it. When $100 \, V$ $AC$ is applied across the same coil,the current drops to $0.5 \, A$. If the frequency of the $AC$ source is $50 \, Hz$,the impedance and inductance of the solenoid are: