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JEE Mains | PYQ

A message signal of frequency \( 3 \, \text{kHz} \) is used to modulate a carrier signal of frequency \( 1.5 \, \text{MHz} \). The bandwidth of the amplitude modulate wave is:

The TV transmission tower at a particular station has a height of \( 125 \ \text{m} \). For doubling the coverage of its range, the height of the tower should be increased by:

Math List I with List II

Choose the correct answer from the following options:

A modulating signal \( 2\sin\left(6.28\times10^6\right)t \) is added to the carrier signal \( 4\sin\left(12.56\times10^9\right)t \) for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will ___ \( \text{MHz} \).

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 ________.

A message signal of frequency \( 5 \, \text{kHz} \) is used to modulate a carrier signal of frequency \( 2 \, \text{MHz} \). The bandwidth for amplitude modulation 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 transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at \( 4 \; \text{km} \) distance from it is \( x \times 10^{-2} \; \text{m} \). The value of \( x \) is ________ .

In satellite communication, the uplink frequency band used is :

To radiate EM signal of wavelength \( \lambda \) with high efficiency, the antennas should have a minimum size equal to:

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 required height of a TV tower which can cover the popular of \( 6.03 \) lakh is \( h \). If the average population density is \( 100 \) per square \( \text{km} \) and the radius of earth is \( 6400 \, \text{km} \), then the value of \( h \) will be __________ \( \text{m} \).

Two identical bodies A and B of equal masses have initial velocities \( \vec{v}_1 = 4\hat{i} \, \text{m/s} \) and \( \vec{v}_2 = 4\hat{j} \, \text{m/s} \) respectively. The body A has acceleration \( \vec{a}_1 = 6\hat{i} + 6\hat{j} \, \text{m/s}^2 \) while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ______ path.

A FM Broad cast transmitter, unsing modulating signal of frequency \( 20 \, \text{kHz} \) has a deviation ratio of \( 10 \). The Bandwidth required for transmission is:

The height of transmitting antenna is \( 180 \, \text{m} \) and the height of the receiving antenna is \( 245 \, \text{m} \). The maximum distance between them for satisfactory communication in line of sight will be:
(Given \( R = 6400 \, \text{km} \))

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 \( 6400 \, \text{km} \))

An antenna is placed in a dielectric medium of dielectric constant \( 6.25 \). If the maximum size of that antenna is \( 5.0 \, \text{mm} \), it can radiate a signal of minimum frequency of _______ \( \text{GHz} \). (Given \( \mu_1 = 1 \) for dielectric medium)

At a particular station, the TV transmission tower has a height of \( 100 \, \text{m} \). To triple its coverage range, height of the tower should be increased to:

Given below are two statements:
Statement I: For transmitting a signal, size of antenna \( (l) \) should be comparable to wavelength of signal (at least \( l = \dfrac{\lambda}{4} \) in dimension)
Statement II: In amplitude modulation, amplitude of carrier wave remains constant (unchanged).
In the light of the above statements, choose the most appropriate answer from the options given below:

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 \( R_e = 6.5 \times 10^{6} \, \text{m} \).

In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be \( 6 \, \text{V} \) and \( 2 \, \text{V} \) respectively. The modulation index is:

The maximum and minimum voltage of an amplitude modulated signal are \( 60 \, \text{V} \) and \( 20 \, \text{V} \) respectively. The percentage modulation index will be:

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 \( \pi = 3.14 \))

Match List-I with List-II.

Choose the correct answer from the options given below:

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 ________.

For an amplitude modulated wave the minimum amplitude is \( 3 \, \text{V} \), while the modulation index is \( 60\% \). The maximum amplitude of the modulated wave 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:

A modulating signal is a square wave, as shown in the figure.

If the carrier wave is given as \( c(t) = 2\sin(8\pi t) \) volts, the modulation index is:

In the case of amplitude modulation to avoid distortion the modulation index \( (\mu) \) should be:

A TV transmitting antenna is \( 98 \, \text{m} \) high and the receiving antenna is at the ground level. If the radius of the earth is \( 6400 \, \text{km} \), the surface area covered by the transmitting antenna is approximately.

Which is the correct ascending order of wavelengths?

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?

Match List I with List II:

Choose the correct answer from the options given below:

Amplitude modulated wave is represented by \( V_{AM} = 10 \left[ 1 + 0.4 \cos \left( 2\pi \times 10^{4} \, t \right) \right] \cos \left( 2\pi \times 10^{7} \, t \right) \). The total bandwidth of the amplitude modulated wave is:

Choose the correct statement for amplitude modulation:

The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of \( 14 \, \text{mV} \) and \( 6 \, \text{mV} \) respectively is:

Match List I and List II :

Choose the correct answer from the options given below :

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 carrier wave of amplitude \( 15 \, \text{V} \) is modulated by a sinusoidal base band signal of amplitude \( 3 \, \text{V} \). The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is:

A square wave of the modulating signal is shown in the figure. The carrier wave is given by \( C(t) = 5 \sin(8\pi t)\, \text{Volt} \). The modulation index is:
 

Match List I with List II.

Choose the correct answer from the options given below:

The amplitude of \( 15\sin(1000\pi t) \) is modulated by \( 10\sin(4\pi t) \) single. The amplitude modulated signal contains frequency (ies) of.
(A) \( 500\,\text{Hz} \)    (B) \( 2\,\text{Hz} \)    (C) \( 250\,\text{Hz} \)    (D) \( 498\,\text{Hz} \)    (E) \( 502\,\text{Hz} \)
Choose the correct answer from the options given below:
(1) A and B only    (2) B only    (3) A only    (4) A, D and E only

Match List-I with List-II

Choose the correct answer from the options given below:

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 ________.

Only \( 2\% \) of the optical source frequency is the available channel bandwidth for an optical communicating system operating at \( 1000 \, \text{nm} \). If an audio signal requires a bandwidth of \( 8 \, \text{kHz} \), how many channels can be accommodated for transmission?

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 \( 44 \, \text{km} \)?

The output from a NAND gate having inputs A and B given below will be:

A signal of \( 100 \, \text{THz} \) frequency can be transmitted with maximum efficiency by :

In an amplitude modulation, a modulating signal having amplitude of \( X \) \( \text{V} \) is superimposed with a carrier signal of amplitude \( Y \) \( \text{V} \) in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude \( 2Y \) \( \text{V} \). The ratio of modulation index in the two cases respectively will be:

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by \( 21\% \) ?

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:

A baseband signal of \( 3.5 \, \mathrm{MHz} \) frequency is modulated with a carrier signal of \( 3.5 \, \mathrm{GHz} \) frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?

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 ________.