For an amplitude modulated wave,the modulation index is found to be $0.5$. If the maximum amplitude is found to be $10.0 \ V$,then the minimum amplitude is: (in $V$)

$A$ message signal of frequency $15 kHz$ is used to modulate a carrier of frequency $v_c$. If the side bands produced are $1515 kHz$ and $1485 kHz$,then $v_c$ is (in $MHz$)

$A$ $T$.$V$. tower has a height of $100 \, m$. The average population density around the tower is $1000 \, km^{-2}$ and the radius of the earth is $6.37 \times 10^6 \, m$. The population covered is

Which waves can be transmitted more efficiently by an antenna?

Given below are two statements:
Statement-$I$: $A$ speech signal of $2 \, kHz$ is used to modulate a carrier signal of $1 \, MHz$. The bandwidth requirement for the signal is $4 \, kHz$.
Statement-$II$: The sideband frequencies are $1002 \, kHz$ and $998 \, kHz$.
In the light of the above statements,choose the correct answer from the options given below:

Carrier waves are used for communicating signals over long distances because: