Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the center of mass of the system is:

Which one of the following elements on doping with germanium,makes it a $p$-type semiconductor?

$A$ ring of radius $4a$ is rigidly fixed in a vertical position on a table. $A$ small disc of mass $m$ and radius $a$ is released as shown in the figure. When the disc rolls down,without slipping,to the lowest point of the ring,then its speed will be

The solution of the differential equation $\frac{dy}{dx} = \frac{xy+y}{xy+x}$ is

Magnetic lines of force due to a bar magnet do not intersect because

$KO_2$ exhibits paramagnetic behaviour. This is due to the paramagnetic nature of