The amplitude of $15 \sin (1000 \pi t)$ is modulated by $10 \sin (4 \pi t)$ signal. The amplitude modulated signal contains frequencies of
$1. 500\,Hz$
$2. 2\,Hz$
$3. 250\,Hz$
$4. 498\,Hz$
$5. 502\,Hz$
Choose the correct answer from the options given below:

The intensity of a light pulse travelling along a communication channel decreases exponentially with distance $x$ according to the relation $I = I_0 e^{-\alpha x}$,where $I_0$ is the intensity at $x = 0$ and $\alpha$ is the attenuation constant. The attenuation in $dB/km$ for an optical fibre in which the intensity falls by $50$ percent over a distance of $50 \ km$ is

For transmission of e.m. wave of audible frequency,these waves are superimposed with waves of

$A$ message signal of frequency $10 kHz$ and peak voltage of $15 V$ is used to modulate a carrier frequency of $1 MHz$ and peak voltage of $30 V$. Determine the modulation index.

The height of a transmission antenna is $100 \, m$. The population density is $1000 \, \text{people}/km^2$. How many people can watch the program?

The wavelength of the carrier waves in a modern optical fiber communication network is close to ........ $nm$.