The equivalent resistance between A and B is :

An astronaut takes a ball of mass $$m$$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $$318.5 \mathrm{~km}$$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $$x \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{m}}{21 \mathrm{R}_{\mathrm{e}}}$$. The value of $$x$$ is (take $$\mathrm{R}_{\mathrm{e}}=6370 \mathrm{~km})$$ :

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :