Which of the following correctly represents the variation of electric potential $$(\mathrm{V})$$ of a charged spherical conductor of radius $$(\mathrm{R})$$ with radial distance $$(\mathrm{r})$$ from the center?

The amplitude of $$15 \sin (1000 \pi \mathrm{t})$$ is modulated by $$10 \sin (4 \pi \mathrm{t})$$ signal. The amplitude modulated signal contains frequency (ies) of

A. $$500 \mathrm{~Hz}$$

B. $$2 \mathrm{~Hz}$$

C. $$250 \mathrm{~Hz}$$

D. $$498 \mathrm{~Hz}$$

E. $$502 \mathrm{~Hz}$$

Choose the correct answer from the options given below:

The drift velocity of electrons for a conductor connected in an electrical circuit is $$\mathrm{V}_{\mathrm{d}}$$. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

A rod with circular cross-section area $$2 \mathrm{~cm}^{2}$$ and length $$40 \mathrm{~cm}$$ is wound uniformly with 400 turns of an insulated wire. If a current of $$0.4 \mathrm{~A}$$ flows in the wire windings, the total magnetic flux produced inside windings is $$4 \pi \times 10^{-6} \mathrm{~Wb}$$. The relative permeability of the rod is

(Given : Permeability of vacuum $$\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$$)