Two identical charged spherical drops, each of capacitance $C$, merge to form a single drop. The resultant capacitance is:

If $arg(z) < 0$,then $arg(-z) - arg(z)$ is equal to

Consider the depicted hydrogen $( H )$ in the hydrocarbons given below. The most acidic hydrogen $( H )$ is

The order of the differential equation whose solution is $y = a \cos x + b \sin x + c e^{-x}$ is:

Two unknown resistances are connected in two gaps of a meter-bridge. The null point is obtained at $40 \ cm$ from left end. A $30 \Omega$ resistance is connected in series with the smaller of the two resistances, the null point shifts by $20 \ cm$ to the right end. The value of smaller resistance in $\Omega$ is

$A$ particle of mass $200\,g$ executes a simple harmonic motion. The restoring force is provided by a spring of spring constant $80\,N/m$. The time period is .... $sec$.