$A$ message signal of frequency $14 kHz$ is used to modulate a carrier of frequency $900 kHz$. The frequencies of the sidebands are:

In amplitude modulation,the sinusoidal carrier frequency is denoted by $\omega_c$ and the signal frequency is denoted by $\omega_m$. The bandwidth of the signal is such that $\omega_m << \omega_c$. Which of the following frequencies is not contained in the modulated wave?

$A$ transmitting antenna covers a range of $12.8 \ km$. Find the height of the antenna in $m$. (Radius of the Earth $= 6400 \ km$)

Ultra high frequency $(UHF)$ band stands for

Match List-$I$ with List-$II$:

List-$I$ (Layer of atmosphere)	List-$II$ (Approximate height over earth's surface)
$(A)$ $F_1$-Layer	$(I)$ $10\,km$
$(B)$ $D$-Layer	$(II)$ $170-190\,km$
$(C)$ Troposphere	$(III)$ $100\,km$
$(D)$ $E$-Layer	$(IV)$ $65-75\,km$

Choose the correct answer from the options given below:

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ V}$. For the given $AM$ wave,the carrier frequency is ....... and the modulating frequency is .......