An LCR circuit contains resistance of 110$$\Omega$$ and a supply of 220 V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45$$^\circ$$. If on the other hand, only inductor is removed the current leads by 45$$^\circ$$ with the applied voltage. The rms current flowing in the circuit will be :

An electron with kinetic energy K₁ enters between parallel plates of a capacitor at an angle '$$\alpha$$' with the plates. It leaves the plates at angle '$$\beta$$' with kinetic energy K₂. Then the ratio of kinetic energies K₁ : K₂ will be :

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v₀. It encounters an inclined plane at angle $$\theta$$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

An electron of mass m_e and a proton of mass m_p = 1836 m_e are moving with the same speed. The ratio of their de Broglie wavelength $${{{}^\lambda electron} \over {{}^\lambda proton}}$$ will be :