Two conducting circular loops of radii '$$R_1$$' and '$$R_2$$' are placed in the same plane with their centres coinciding. If $$R_1>R_2$$, the mutual inductance $$M$$ between them will be directly proportional to

The average force applied on the walls of a closed container depends on $$T^x$$ where $$T$$ is the temperature of an ideal gas. The value of '$$x$$' is

A black body radiates maximum energy at wavelength '$$\lambda$$' and its emissive power is $$\mathrm{E}$$. Now due to change in temperature of that body, it radiates maximum energy at wavelength $$\frac{2 \lambda}{3}$$. At that temperature emissive power is

A Carnot engine with efficiency $$50 \%$$ takes heat from a source at $$600 \mathrm{~K}$$. To increase the efficiency to $$70 \%$$, keeping the temperature of the sink same, the new temperature of the source will be