Charges $$+q$$ and $$-q$$ are placed at points $$A$$ and $$B$$ respectively which are a distance $$2 L$$ apart, $$C$$ is the mid-point between $$A$$ and $$B$$. The work done in moving a charge $$+Q$$ along the semicircle $$C R D$$ is

In the given figure, $$C$$ is middle point of line $$S_1 S_2$$. A monochromatic light of wavelength $$\lambda$$ is incident on slits. The ratio of intensities of $$S_3$$ and $$S_4$$ is

A simple telescope, consisting of an objective of focal length $$60 \mathrm{~cm}$$ and a single eye lens of focal length $$5 \mathrm{~cm}$$ is focused on a distant object in such a way that parallel rays emerge from the eye lens. If the object subtends an angle of $$2^{\circ}$$ at the objective, the angular width of the image is

A specimen of silicon is to be made $$P$$-type semiconductor for this one atom of indium, on an average, is doped in $$5 \times 10^7$$ silicon atoms. If the number density of silicon is $$5 \times 10^{22}$$ atom/$$\mathrm{m}^3$$ then the number of acceptor atoms per $$\mathrm{cm}^3$$ will be