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General Aptitude

1

A modulated signal C_{m}(t) has the form C_{m}(t) = 30 sin 300 $$\pi $$t + 10 (cos 200 $$\pi $$t −cos 400 $$\pi $$t). The carrier frequency c, the modulating frequency (message frequency) f_{$$\omega $$}, and the modulation index $$\mu $$ are respectively given by :

A

f_{c} = 200 Hz; f_{$$\omega $$} = 50 Hz; $$\mu $$ = $${1 \over 2}$$

B

f_{c} = 150 Hz; f_{$$\omega $$} = 50 Hz; $$\mu $$ = $${2 \over 3}$$

C

f_{c} = 150 Hz; f_{$$\omega $$} = 30 Hz; $$\mu $$ = $${1 \over 3}$$

D

f_{c} = 200 Hz; f_{$$\omega $$} = 30 Hz; $$\mu $$ = $${1 \over 2}$$

Given,

C_{m}(t) = 30 sin 300$$\pi $$t + 10 (cos 200 $$\pi $$t $$-$$ cos 400 $$\pi $$t)

Standard equation of amplitude modulated wave,

C_{m}(t) = A_{c} sin ($$\omega $$_{c}t) $$-$$ $${{\mu {A_c}} \over 2}$$ cos $$\left( {{\omega _c} + {\omega _m}} \right)$$ t + $${{\mu {A_c}} \over 2}$$ cos $$\left( {{\omega _c} - {\omega _m}} \right)$$ t

By comparing we get,

A_{c} = 30 V

$$\omega $$_{c} = 300 $$\pi $$

$$ \Rightarrow $$ 2$$\pi $$f_{c} = 300 $$\pi $$

$$ \Rightarrow $$ f_{c} = 150 Hz

$$\omega $$_{c} $$-$$ $$\omega $$_{s} = 200 $$\pi $$

$$ \Rightarrow $$ 2$$\pi $$ (f_{c} $$-$$ f_{$$\omega $$}) = 200 $$\pi $$

$$ \Rightarrow $$ f_{c} $$-$$ f_{$$\omega $$} = 100 Hz

$$ \therefore $$ f_{$$\omega $$} = 150 $$-$$ 100 = 50 Hz

and $${{\mu {A_c}} \over 2}$$ = 10

$$ \Rightarrow $$ $$\mu $$ $$ \times $$ $${{30} \over 2}$$ = 10

$$ \Rightarrow $$ $$\mu $$ = $${{10} \over {15}}$$ = $${2 \over 3}$$

C

Standard equation of amplitude modulated wave,

C

By comparing we get,

A

$$\omega $$

$$ \Rightarrow $$ 2$$\pi $$f

$$ \Rightarrow $$ f

$$\omega $$

$$ \Rightarrow $$ 2$$\pi $$ (f

$$ \Rightarrow $$ f

$$ \therefore $$ f

and $${{\mu {A_c}} \over 2}$$ = 10

$$ \Rightarrow $$ $$\mu $$ $$ \times $$ $${{30} \over 2}$$ = 10

$$ \Rightarrow $$ $$\mu $$ = $${{10} \over {15}}$$ = $${2 \over 3}$$

2

In amplitude modulation, sinusoidal carrier frequency used is denoted by $${\omega _c}$$ and the signal frequency is
denoted by $${\omega _m}$$. The bandwidth ($$\Delta {\omega _m}$$) of the signal is such that $$\Delta {\omega _m}$$ < < $$\omega _c$$. Which of the following frequencies is not contained in the modulated wave?

A

$${\omega _m}$$

B

$${\omega _c}$$

C

$${\omega _m}$$ + $${\omega _c}$$

D

$${\omega _c}$$ - $${\omega _m}$$

Modulated carrier wave contains frequency $${\omega _c}$$ and
$${\omega _c}$$ ± $${\omega _m}$$.

3

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

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

Given, carrier wave,

F_{c} = 1.2 $$ \times $$ 10^{6} Hz = 1200 kHz

and frequency of modulate wave,

F_{m} = 20 kHz

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

F_{1} = 1200 + 20 = 1220 kHz

F_{2} = 1200 $$-$$ 80 = 1180 kHz

Given, carrier wave,

F

and frequency of modulate wave,

F

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

F

F

4

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 P_{eff} will be given respectively as :

(K is a constant of proportionality)

(K is a constant of proportionality)

A

$$\lambda $$, P_{eff} = K $$\left( {{1 \over \lambda }} \right)$$^{2}

B

$${{\lambda \over 8}}$$, P_{eff} = K $$\left( {{1 \over \lambda }} \right)$$

C

$${{\lambda \over 16}}$$, P_{eff} = K $$\left( {{1 \over \lambda }} \right)$$^{3}

D

$${{\lambda \over 5}}$$, P_{eff} = K $$\left( {{1 \over \lambda }} \right)$$$${\left( {{1 \over \lambda }} \right)^{{1 \over 2}}}$$

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