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 :

A particle is placed at the point $$A$$ of a frictionless track $$A B C$$ as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is :

(Take $$g=10 \mathrm{~m} / \mathrm{s}^2$$).

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $$\mathrm{C}_{\mathrm{A}}$$ and $$\mathrm{C}_{\mathrm{B}}$$. The molar heat capacity at constant pressure and constant volume are represented by $$\mathrm{C_P}$$ and $$\mathrm{C_V}$$, respectively. Choose the correct statement.