The area bounded by the curves $$y=(x-1)^2, y=(x+1)^2$$ and $$y=\frac{1}{4}$$ is

A sphere and a cube, both of copper have equal volumes and are black. They are allowed to cool at same temperature and in same atmosphere. The ratio of their rate of loss of heat will be

An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by $$45^{\circ}$$, then $$\left(\tan 45^{\circ}=1\right)$$

A horizontal wire of mass '$$m$$', length '$$l$$' and resistance '$$R$$' is sliding on the vertical rails on which uniform magnetic field '$$B$$' is directed perpendicular. The terminal speed of the wire as it falls under the force of gravity is ( $$\mathrm{g}=$$ acceleration due to gravity)