A particle of mass $$\mathrm{m}$$ is projected with a velocity '$$\mathrm{u}$$' making an angle of $$30^{\circ}$$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $$\mathrm{h}$$ is :

The diffraction pattern of a light of wavelength $$400 \mathrm{~nm}$$ diffracting from a slit of width $$0.2 \mathrm{~mm}$$ is focused on the focal plane of a convex lens of focal length $$100 \mathrm{~cm}$$. The width of the $$1^{\text {st }}$$ secondary maxima will be :

A series L.R circuit connected with an ac source $$E=(25 \sin 1000 t) V$$ has a power factor of $$\frac{1}{\sqrt{2}}$$. If the source of emf is changed to $$\mathrm{E}=(20 \sin 2000 \mathrm{t}) \mathrm{V}$$, the new power factor of the circuit will be :

The electrostatic potential due to an electric dipole at a distance '$$r$$' varies as :