A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

The ratio of the density of oxygen nucleus ($$_8^{16}O$$) and helium nucleus ($$_2^{4}\mathrm{He}$$) is

A car travels a distance of '$$x$$' with speed $$v_1$$ and then same distance '$$x$$' with speed $$v_2$$ in the same direction. The average speed of the car is :

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $$\lambda_0$$. IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :