1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Morning Slot

An amplitude modulated signal is given by V(t) = 10[1 + 0.3cos(2.2 $$ \times $$ 104 t)] sin(5.5 $$ \times $$ 105 t). Here t is in seconds. The sideband frequencies (in kHz) are, [Given $$\pi $$ = 22/7]
A
892.5 and 857.5
B
89.25 and 85.75
C
1785 and 1715
D
178.5 and 171.5

Explanation

V(t) = 10 + $${3 \over 2}$$ [2cos A sinB]

= 10 + $${3 \over 2}$$ [sin(A+B) $$-$$ sin(A $$-$$ B)]

= 10+$${3 \over 2}$$[sin (57.2 $$ \times $$ 104 t) $$-$$ sin(52.8 $$ \times $$ 104 t)]

$$\omega $$1 = 57.2 $$ \times $$ 104 = 2$$\pi $$f1

f1 = $${{57.2 \times {{10}^4}} \over {2 \times \left( {{{22} \over 7}} \right)}} = 9.1 \times {10^4}$$

$$ \simeq $$ 91KHz

f2 = $${{52.8 \times {{10}^4}} \over {2 \times \left( {{{22} \over 7}} \right)}}$$

$$ \simeq $$ 84 KHz



Side band frequency are

f1 = fc $$-$$ fw = $${{52.8 \times {{10}^4}} \over {2\pi }}$$ $$ \simeq $$ 85.00 kHz

f2 = fc + fw = $${{57.2 \times {{10}^4}} \over {2\pi }}$$ $$ \simeq $$ 90.00 kHz
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

An amplitude modulated signal is plotted below :



Which one of the following best describes the above signal ?
A
(1 + 9sin (2$$\pi $$ $$ \times $$ 104 t)) sin(2.5$$\pi $$ $$ \times $$ 105t) V
B
(9 + sin (4$$\pi $$ $$ \times $$ 104 t)) sin(5$$\pi $$ $$ \times $$ 105t) V
C
(9 + sin (2$$\pi $$ $$ \times $$ 104 t)) sin(2.5$$\pi $$ $$ \times $$ 105t) V
D
(9 + sin (2.5$$\pi $$ $$ \times $$ 104 t)) sin(2$$\pi $$ $$ \times $$ 104t) V

Explanation

Analysis of graph says

(1)   Amplitude varies as 8 $$-$$ 10 V or 9 $$ \pm $$ 1

(2)  Two time period as

100 $$\mu $$s (signal wave) & 8 $$\mu $$s (carrier wave)

Hence signal is $$\left[ {9 \pm 1\sin \left( {{{2\pi t} \over {{T_1}}}} \right)} \right]\sin \left( {{{2\pi t} \over {{T_2}}}} \right)$$

= 9 $$ \pm $$ 1sin (2$$\pi $$ $$ \times $$ 104t) sin 2.5$$\pi $$ $$ \times $$ 105 t
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 12th January Morning Slot

A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index ?
A
0.5
B
0.6
C
0.4
D
0.3

Explanation

Em + Ec = 160

Em + 100 = 160

Em = 60

$$\mu = {{{E_m}} \over {{E_C}}} = {{60} \over {100}}$$

$$\mu $$ = 0.6
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 12th January Evening Slot

To double the covering range of a TV transmittion tower, its height should be multiplied by :
A
4
B
2
C
$$\sqrt 2 $$
D
$${1 \over {\sqrt 2 }}$$

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