1
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 8th April Morning Slot

A signal of frequency 20 kHz and peak voltage of 5 Volt is used to modulate a carrier wave of frequency 1.2 MHz and peak voltage 25 Volts. Choose the correct statement.
A
Modulation index = 5, side frequency bands are at 1400 kHz and 1000 kHz
B
Modulation index = 5, side frequency bands are at 21.2 kHz and 18.8 kHz
C
Modulation index = 0.8, side frequency bands are at 1180 kHz and 1220 kHz
D
Modulation index = 0.2, side frequency bands are at 1220 kHz and 1180 kHz

Explanation

Modulation index (m) = $${{{V_m}} \over {{V_0}}} = {5 \over {25}} = 0.2$$

Given, carrier wave,

Fc = 1.2 $$ \times $$ 106 Hz = 1200 kHz

and frequency of modulate wave,

Fm = 20 kHz

$$\therefore\,\,\,$$ Side frequency bands are

F1 = 1200 + 20 = 1220 kHz

F2 = 1200 $$-$$ 80 = 1180 kHz
2
MCQ (Single Correct Answer)

JEE Main 2017 (Online) 9th April Morning Slot

A signal is to be transmitted through a wave of wavelength $$\lambda $$, using a linear antenna. The length l of the antenna and effective power radiated Peff will be given respectively as :

(K is a constant of proportionality)
A
$$\lambda $$, Peff = K $$\left( {{1 \over \lambda }} \right)$$2
B
$${{\lambda \over 8}}$$, Peff = K $$\left( {{1 \over \lambda }} \right)$$
C
$${{\lambda \over 16}}$$, Peff = K $$\left( {{1 \over \lambda }} \right)$$3
D
$${{\lambda \over 5}}$$, Peff = K $$\left( {{1 \over \lambda }} \right)$$$${\left( {{1 \over \lambda }} \right)^{{1 \over 2}}}$$
3
MCQ (Single Correct Answer)

JEE Main 2018 (Offline)

A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz ?
A
2 $$\times$$ 106
B
2 $$\times$$ 103
C
2 $$\times$$ 105
D
2 $$\times$$ 104

Explanation

Given,

Carrier frequency = 10 GHz = 10 $$ \times $$ 109 Hz

As only 10% of 10 GHz is utilised for transmission.

$$\therefore\,\,\,$$ Bondwidth available for transmission

= 10$$ \times $$ 109 $$ \times $$ $${{10} \over {100}}$$ = 109 Hz

Let, there are n channels each requires 5 kHz bandwidth.

$$\therefore\,\,\,$$ n $$ \times $$ 5 $$ \times $$ 103 = 109

$$ \Rightarrow $$$$\,\,\,$$ n = 2 $$ \times $$ 103
4
MCQ (Single Correct Answer)

JEE Main 2018 (Online) 15th April Morning Slot

The number of amplitude modulted broadcast stations that can be accomodated in a $$300$$ $$kHz$$ band width for the highest modulating frequency $$15$$ $$kHz$$ will be :
A
$$20$$
B
$$15$$
C
$$10$$
D
$$8$$

Explanation

Given, modulating frequency = 15 kHz

$$\therefore\,\,\,\,$$ Bandwidth of one channel = 2 $$ \times $$ 15 = 30 kHz

$$\therefore\,\,\,\,$$ No of stations = $${{300} \over {30}}$$ = 10

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