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Graduate Aptitude Test in Engineering

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1

MCQ (Single Correct Answer)

An amplitude modulated signal is plotted below :

Which one of the following best describes the above signal ?

Which one of the following best describes the above signal ?

A

(1 + 9sin (2$$\pi $$ $$ \times $$ 10^{4} t)) sin(2.5$$\pi $$ $$ \times $$ 10^{5}t) V

B

(9 + sin (4$$\pi $$ $$ \times $$ 10^{4} t)) sin(5$$\pi $$ $$ \times $$ 10^{5}t) V

C

(9 + sin (2$$\pi $$ $$ \times $$ 10^{4} t)) sin(2.5$$\pi $$ $$ \times $$ 10^{5}t) V

D

(9 + sin (2.5$$\pi $$ $$ \times $$ 10^{4} t)) sin(2$$\pi $$ $$ \times $$ 10^{4}t) V

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$$\pi $$ $$ \times $$ 10^{4}t) sin 2.5$$\pi $$ $$ \times $$ 10^{5} t

(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$$\pi $$ $$ \times $$ 10

2

MCQ (Single Correct Answer)

An amplitude modulated signal is given by V(t) = 10[1 + 0.3cos(2.2 $$ \times $$ 10^{4}
t)] sin(5.5 $$ \times $$ 10^{5}
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

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 $$ \times $$ 10^{4} t) $$-$$ sin(52.8 $$ \times $$ 10^{4} t)]

$$\omega $$_{1} = 57.2 $$ \times $$ 10^{4} = 2$$\pi $$f_{1}

f_{1} = $${{57.2 \times {{10}^4}} \over {2 \times \left( {{{22} \over 7}} \right)}} = 9.1 \times {10^4}$$

$$ \simeq $$ 91KHz

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

$$ \simeq $$ 84 KHz

Side band frequency are

f_{1} = f_{c} $$-$$ f_{w} = $${{52.8 \times {{10}^4}} \over {2\pi }}$$ $$ \simeq $$ 85.00 kHz

f_{2} = f_{c} + f_{w} = $${{57.2 \times {{10}^4}} \over {2\pi }}$$ $$ \simeq $$ 90.00 kHz

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

= 10+$${3 \over 2}$$[sin (57.2 $$ \times $$ 10

$$\omega $$

f

$$ \simeq $$ 91KHz

f

$$ \simeq $$ 84 KHz

Side band frequency are

f

f

3

MCQ (Single Correct Answer)

The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot ?

A

2900 kHz

B

2750 kHz

C

2250 kHz

D

2000 kz

f_{carrier} = $${{250} \over {0.1}}$$ = 2500 KHZ

$$ \therefore $$ Range of signal = 2250 Hz to 2750 Hz

Now check all options : for 2000 KHZ

f_{mod} = 200 Hz

$$ \therefore $$ Range = 1800 KHZ to 2200 KHZ

$$ \therefore $$ Range of signal = 2250 Hz to 2750 Hz

Now check all options : for 2000 KHZ

f

$$ \therefore $$ Range = 1800 KHZ to 2200 KHZ

4

MCQ (Single Correct Answer)

A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower is LOS (Line of Sight) mode ? (Given : radius of earth = 6.4 × 10^{6} m).

A

40 km

B

65 km

C

48 km

D

80 km

Maximum distance upto which signal can be broadcasted is

d_{max} = $$\sqrt {2R{h_T}} + \sqrt {2R{h_R}} $$

where h_{T} and h_{R} are heights of transmitter tower and height of reserver respectively. Putting all values -

d_{max} = $$\sqrt {2 \times 6.4 \times 106} \left[ {\sqrt {104} + \sqrt {40} } \right]$$

on solving, d_{max} = 65 km

d

where h

d

on solving, d

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