In an amplitude modulated wave for an audio frequency of $500 \, \text{cycles/second}$, the appropriate carrier frequency will be ........ $\text{cycles/second}$.

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:

$A$ radar has a power of $1 \ kW$ and is operating at a frequency of $10 \ GHz$. It is located on a mountain top of height $500 \ m$. The maximum distance up to which it can detect an object located on the surface of the earth (Radius of earth $= 6.4 \times 10^6 \ m$) is ....... $km$.

The radio horizon of a transmitting antenna of height $39.2 \ m$ is (Radius of the earth $= 6400 \ km$) (in $km$)

$A$ bandwidth of $6 \, \text{MHz}$ is available for $A.M.$ transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed $6 \, \text{kHz}$,the number of stations that can be broadcasted within this band simultaneously without interfering with each other will be ..... .

The maximum distance up to which $TV$ transmission from a $TV$ tower of height $h$ can be received is proportional to