A heat engine has an efficiency of $${1 \over 6}$$. When the temperature of sink is reduced by 62$$^\circ$$C, its efficiency get doubled. The temperature of the source is :

In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells, $${{{\varepsilon _1}} \over {{\varepsilon _2}}}$$ is :

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

A 10 $$\Omega$$ resistance is connected across 220V $$-$$ 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :