A carnot engine operates with source at $$227^{\circ} \mathrm{C}$$ and sink at $$27^{\circ} \mathrm{C}$$. If the source supplies $$50 \mathrm{~kJ}$$ of heat energy, the work done by the engine is

Doping of a semiconductor (with small impurity atoms) generally changes the resistivity as follows.

A stone is projected at angle $$\theta$$ with velocity $$u$$. If it executes nearly a circular motion at its maximum point for short time, then the radius of the circular path will be ( $$g=$$ acceleration due to gravity)

When radiations of wavelength $$\lambda$$ is incident on a metallic surface the stopping potential required is $$4.8 \mathrm{~V}$$. If same surface is illuminated with radiations of double the wavelength, then required stopping potential becomes $$1.6 \mathrm{~V}$$, then the value of threshold wavelength for the surface is