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

A thin uniform $$\operatorname{rod} A B$$ of mass $$m$$ and length $$l$$ is hinged at one end $$A$$ to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its end $$B$$ strikes the ground is ( $$g=$$ acceleration due to gravity)