A carrier signal C(t) = 25 sin(2.512 $$\times$$ 10¹⁰t) is amplitude modulated by a message signal m(t) = 5 sin(1.57 $$\times$$ 10⁸t) and transmitted through an antenna. What will be the bandwidth of the modulated signal?

Match List - I with List - II

	List - I		List - II
(a)	Phase difference between current and voltage in a purely resistive AC circuit	(i)	$${\pi \over 2}$$; current leads voltage
(b)	Phase difference between current and voltage in a pure inductive AC circuit	(ii)	zero
(c)	Phase difference between current and voltage in a pure capacitive AC circuit	(iii)	$${\pi \over 2}$$; current lags voltage
(d)	Phase difference between current and voltage in an LCR series circuit	(iv)	$${\tan ^{ - 1}}\left( {{{{X_C} - {X_L}} \over R}} \right)$$

Choose the most appropriate answer from the options given below :

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?