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A transmitting antenna has height of \( 320 \, \text{m} \) and that of receiving antenna is \( 2000 \, \text{m} \). The maximum distance between them for satisfactory communication in line of sight mode is \( d \). The value of \( d \) is ______ \( \text{km} \).

A carrier wave \( V_c(t) = 160 \sin(2\pi \times 10^{6} t) \) volts is made to vary between \( V_{\text{max}} = 200 \, \text{V} \) and \( V_{\text{min}} = 120 \, \text{V} \) by a message signal \( V_{min}(t) = A_m \sin(2\pi \times 10^{3} t) \) volts. The peak voltage \( A_m \) of the modulating signal is ________.

The maximum amplitude for an amplitude modulated wave is found to be \( 12 \, \text{V} \) while the minimum amplitude is found to be \( 3 \, \text{V} \). The modulation index is \( 0.6x \) where \( x \) is __________.

If the sum of the heights of transmitting and receiving antennas in the line of sight of communication is fixed at \( 160 \, \text{m} \), then the maximum range of LOS communication is ____________ \( \text{km} \).
(Take radius of Earth \( 6400 \, \text{km} \))

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 _______.

Two identical antennas mounted on identical towers are separated from each other by a distance of \( 45 \, \text{km} \). What should nearly be the minimum height of receiving antenna to receive the signals in line of sight?
(Assume radius of earth is \( 6400 \, \text{km} \))

A carrier signal \( c(t) = 25 \sin(2.512 \times 10^{10} t) \) is amplitude modulated by a massage signal \( m(t) = 5 \sin(1.57 \times 10^{8} t) \) and transmitted through an antenna. What will be the bandwidth of the modulated signal?

What should be the height of transmitting antenna and the population covered if the television telecase is to cover a radius of \( 150 \, \text{km} \)? The average population density around the tower is \( {2000}/{\text{km}^2} \) and the value of \( R_e = 6.5 \times 10^{6} \, \text{m} \).

For VHF signal broadcasting, ______ \( \text{km}^2 \) of maximum service area will be covered by an antenna tower of height \( 30 \, \text{m} \), if the receiving antenna is placed at ground. Let radius of the earth be \( 6400 \, \text{km} \). (Round off to the Nearest Integer) (Take \( \pi = 3.14 \))

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency \( 11.21 \, \text{MHz} \), peak voltage \( 15 \, \text{V} \) is amplitude modulated by a \( 7.7 \, \text{kHz} \) sine wave of \( 5 \, \text{V} \) amplitude are \( \dfrac{a}{10} \, \text{V} \) and \( \dfrac{b}{10} \, \text{V} \) respectively. Then the value of \( \dfrac{a}{b} \) is ________.

A TV transmission tower antenna is at a height of \( 20 \, \text{m} \). Suppose that the receiving antenna is at:
(i) Ground level (ii) A height of \( 5 \, \text{m} \)
The increase in antenna range in case (ii) relative to case (i) is \( n\% \).
The value of \( n \), to the nearest integer, is:

Match List-I with List-II

A signal of \( 0.1 \, \text{kW} \) is transmitted in a cable. The attenuation of cable is \( -5 \, \text{dB per km} \) and cable length is \( 20 \, \text{km} \). The power received at receiver is \( 10^{-x} \, \text{W} \). The value of \( x \) is ______.
\([ \text{Gain in dB} = 10 \log_{10}\left(\dfrac{P_{0}}{P_{i}}\right) ]\)

A transmitting antenna at top of a tower has a height of \( 50 \, \text{m} \) and the height of receiving antenna is \( 80 \, \text{m} \). What is the range of communication of Line of Sight (LoS) mode?

A carrier wave with amplitude of \( 250 \, \text{V} \) is amplitude modulated by a sinusoidal base band signal of amplitude \( 150 \, \text{V} \). The ratio of minimum amplitude to maximum amplitude for the amplitude modulated wave is \( 50 : x \), then value of \( x \) is:

A message signal of frequency \( 20 \, \text{kHz} \) and peak voltage of \( 20 \, \text{volt} \) is used to modulate a carrier wave of frequency \( 1 \, \text{MHz} \) and peak voltage of \( 20 \, \text{volt} \). The modulation index will be ________.

An antenna is mounted on a \( 400 \, \text{m} \) tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of \( 44 \, \text{km} \)?

In Amplitude Modulation, the message signal \( V_m(t) = 10 \sin(2\pi \times 10^{5} t) \) volts and carrier signal \( V_c(t) = 20 \sin(2\pi \times 10^{7} t) \) volts. The modulates signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is \( a \) kHz. The value of \( a \) is:

An amplitude modulated wave is represented by \( C_m(t) = 10\big(1 + 0.2 \cos(12560\, t)\big)\sin\big(111 \times 10^4 \, t\big) \) volts. The modulating frequency in \( \text{kHz} \) will be ________.

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JEE Main 2021 18th March Morning Shift

Match List-I with List-II