In meter bridge experiment, null point was obtained at a distance '$$l$$' from left end. The values of resistances in the left and right gap are doubled and then interchanged. The new position of the null point is

The magnetic field at the centre of a circular coil of radius '$$R$$', carrying current $$2 A$$ is '$$B_1$$'. The magnetic field at the centre of another coil of radius '$$3 R$$' carrying current $$4 A$$ is '$$B_2$$'. The ratio $$B_1:B_2$$ is

If a capacitor of capacity $$900 ~\mu \mathrm{F}$$ is charged to $$100 \mathrm{~V}$$ and its total energy is transferred to a capacitor of capacity $$100 ~\mu \mathrm{F}$$, then its potential will be

The equation of wave is $$Y=6 \sin$$ $$\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)$$ where '$$x$$' is in $$m$$ and '$$t$$' in $$\mathrm{s}$$. The velocity of the wave is