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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:

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:

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:

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

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:

Match List-I with List-II.

List-I (Layer of atmosphere)	List-II (Approximate height over earth’s surface)
(A) \( F_{1} \)-Layer	(I) \( 10 \, \text{km} \)
(B) D-layer	(II) \( 170\text{-}190 \, \text{km} \)
(C) Troposphere	(III) \( 100 \, \text{km} \)
(D) E-layer	(IV) \( 65\text{-}75 \, \text{km} \)

Choose the correct answer from the options given below:

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:

10.

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:

11.

The power radiated from a linear antenna of length \( l \) is proportional to: (Given, \( \lambda \) \(=\) Wavelength of wave)

12.

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.

13.

Match List I with List II:

Choose the correct answer from the options given below:

14.

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:

15.

Match List I and List II :

Choose the correct answer from the options given below :

16.

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:

17.

Match List I with List II.

Choose the correct answer from the options given below:

18.

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

19.

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

20.

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:

21.

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

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JEE Main 2023 30th Jan Evening Shift

Match List I and List II :

Choose the correct answer from the options given below :

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