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JEE Mains | PYQ

The height of a transmitting antenna at the top of a tower is \( 25 \, \text{m} \) and that of receiving antenna is , \( 49 \, \text{m} \). The maximum distance between them, for satisfactory communication in LOS (Line-OF-Sight) is \( K \sqrt{5} \times 10^{2} \, \text{m} \). The value of \( K \) is _______.
(Assume radius of Earth is \( 64 \times 10^{+5} \, \text{m} \) ) [Calculate upto nearest integer value]

A sinusoidal wave \( y(t) = 40 \sin(10 \times 10^{6} \pi t) \) is amplitude modulated by another sinusoidal wave \( x(t) = 20 \sin(1000 \pi t) \). The amplitude of minimum frequency component of modulated signal is:

Find the modulation index of an AM wave having \( 8 \, \text{V} \) variation where maximum amplitude of the AM wave is \( 9 \, \text{V} \).

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 ___ \( \text{MHz} \).

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 __________ \( \text{m} \).

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:

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:

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:

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

Which is the correct ascending order of wavelengths?

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:

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:

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?

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

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?