Find the modulation index of an $AM$ wave having $8\,V$ variation where maximum amplitude of the $AM$ wave is $9\,V$.

$A$ diode detector is used to detect an amplitude modulated wave with $60\%$ modulation,using a capacitor of $250 \ pF$ in parallel with a resistor of $100 \ k\Omega$. What is the maximum modulation frequency that can be detected by this circuit?

$A$ carrier is simultaneously modulated by two sine waves with modulation indices of $0.3$ and $0.4$; then the total modulation index is

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

List-$I$	List-$II$
$A$. $AM$ Broadcast	$I$. $88-108\,MHz$
$B$. $FM$ Broadcast	$II$. $540-1600\,kHz$
$C$. Television	$III$. $3.7-4.2\,GHz$
$D$. Satellite Communication	$IV$. $54-890\,MHz$

Choose the correct answer from the options given below:

We do not transmit low frequency signals to long distances because:
$(a)$ The size of the antenna should be comparable to signal wavelength,which is impractical for a signal of longer wavelength.
$(b)$ Effective power radiated by a long wavelength baseband signal would be high.
$(c)$ We want to avoid mixing up signals transmitted by different transmitters simultaneously.
$(d)$ Low frequency signals can be sent to long distances by superimposing them with a high frequency wave.
Therefore,the most suitable options are:

$A$ $500\, Hz$ modulating voltage fed into an $FM$ generator produces a frequency deviation of $2.25\, kHz$. If the amplitude of the voltage is kept constant but the frequency is raised to $6\, kHz$,then the new frequency deviation will be.......$kHz$.