An inductor of $$0.5 \mathrm{~mH}$$, a capacitor of $$20 ~\mu \mathrm{F}$$ and a resistance of $$20 \Omega$$ are connected in series with a $$220 \mathrm{~V}$$ a.c. source. If the current is in phase with the e.m.f. the maximum current in the circuit is $$\sqrt{x} A$$. The value of '$$x$$' is

The wavelength of radiation emitted is '$$\lambda_0$$' when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $$\frac{20}{x} \lambda_0$$. The value of $$x$$ is

Two particles having mass '$$M$$' and '$$m$$' are moving in a circular path with radius '$$R$$' and '$$r$$' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second particle will be

The excess pressure inside a first spherical drop of water is three times that of second spherical drop of water. Then the ratio of mass of first spherical drop to that of second spherical drop is