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761
GATE ECE 1998 | Question 2.16
The $\text{ACF}$ of a rectangular pulse of duration $\mathrm{T}$ is a rectangular pulse of duration $\mathrm{T}$ a rectangular pulse of duration $\mathrm{2T}$ a triangular pulse of duration $\text{T}$ a triangular pulse of duration $2 \mathrm{T}$
The $\text{ACF}$ of a rectangular pulse of duration $\mathrm{T}$ isa rectangular pulse of duration $\mathrm{T}$a rectangular pulse of duration $\mathrm{2T}$a triangular p...
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762
GATE ECE 1998 | Question 2.17
The image channel selectivity of superheterodyne receiver depends upon $\text{IF}$ amplifiers only $\text{RF}$ and $\text{IF}$ amplifiers only Preselector, $\text{RF}$ and $\text{IF}$ amplifiers Preselector, and $\text{RF}$ amplifiers only
The image channel selectivity of superheterodyne receiver depends upon$\text{IF}$ amplifiers only$\text{RF}$ and $\text{IF}$ amplifiers onlyPreselector, $\text{RF}$ and $...
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763
GATE ECE 1998 | Question 2.18
In a $\text{PCM}$ system with uniform quantisation, increasing the number of bits from $8$ to $9$ will reduce the quantisation noise power by a factor of $9$ $8$ $4$ $2$
In a $\text{PCM}$ system with uniform quantisation, increasing the number of bits from $8$ to $9$ will reduce the quantisation noise power by a factor of$9$$8$$4$$2$
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764
GATE ECE 1998 | Question 2.19
The Fourier transform of a function $x(t)$ is $\mathrm{X}(f)$. The Fourier transform of $\frac{d \mathrm{X}(f)}{d f}$ will be $\frac{dX(f)}{d f}$ $j 2 \pi f X(f)$ $jf X(f)$ $\frac{X(f)}{if}$
The Fourier transform of a function $x(t)$ is $\mathrm{X}(f)$. The Fourier transform of $\frac{d \mathrm{X}(f)}{d f}$ will be$\frac{dX(f)}{d f}$$j 2 \pi f X(f)$$jf X(f)$$...
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765
GATE ECE 1998 | Question 2.20
Flat top sampling of low pass signals gives rise to aperture effect implies oversampling leads to aliasing introduces delay distortion
Flat top sampling of low pass signalsgives rise to aperture effectimplies oversamplingleads to aliasingintroduces delay distortion
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766
GATE ECE 1998 | Question 2.21
A $\text{DSB-SC}$ signal is generated using the carrier $\cos \left(\omega_{c}, t+\theta\right)$ and modulating signal $x(t)$. The envelope of the $\text{DSB-SC}$ signal is $x(t)$ $|x(t)|$ only positive portion of $x(t)$ $x(t) \cos \theta$
A $\text{DSB-SC}$ signal is generated using the carrier $\cos \left(\omega_{c}, t+\theta\right)$ and modulating signal $x(t)$. The envelope of the $\text{DSB-SC}$ signal ...
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767
GATE ECE 1998 | Question 2.22
Quadrature multiplexing is the same as $\text{FDM}$ the same as $\text{TDM}$ a combination of $\text{FDM}$ and $\text{TDM}$ quite different from $\text{FDM}$ and $\text{TDM}$
Quadrature multiplexing isthe same as $\text{FDM}$the same as $\text{TDM}$a combination of $\text{FDM}$ and $\text{TDM}$quite different from $\text{FDM}$ and $\text{TDM}$...
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768
GATE ECE 1998 | Question 2.23
The Fourier transform of a voltage signal $x(t)$ is $X(f)$. The unit of $|X(f)|$ is volt volt-sec volt/sec volt $^{2}$
The Fourier transform of a voltage signal $x(t)$ is $X(f)$. The unit of $|X(f)|$ isvoltvolt-secvolt/secvolt $^{2}$
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769
GATE ECE 1998 | Question 2.24
Compression in $\text{PCM}$ refers to relative compression of higher signal amplitudes lower signal amplitudes lower signal frequencies higher signal frequencies
Compression in $\text{PCM}$ refers to relative compression ofhigher signal amplitudeslower signal amplitudeslower signal frequencieshigher signal frequencies
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770
GATE ECE 1998 | Question 2.25
For a given data rate, the bandwidth $\mathrm{B}_{p}$ of a $\text{BPSK}$ signal and the bandwidth $\text{B}_{0}$ of the $\mathrm{OOK}$ signal are related as $\mathrm{B}_{p}=\frac{\mathrm{B}_{0}}{4}$ $\text{B}_{p}=\frac{\text{B}_{0}}{2}$ $\mathrm{B}_{p}=\mathrm{B}_{0}$ $\text{B}_{p}=\text{2B}_{0}$
For a given data rate, the bandwidth $\mathrm{B}_{p}$ of a $\text{BPSK}$ signal and the bandwidth $\text{B}_{0}$ of the $\mathrm{OOK}$ signal are related as$\mathrm{B}_{p...
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771
GATE ECE 1998 | Question 2.26
The spectral density of a real valued random process has an even symmetry an odd symmetry a conjugate symmetry no symmetry
The spectral density of a real valued random process hasan even symmetryan odd symmetrya conjugate symmetryno symmetry
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772
GATE ECE 1998 | Question 2.27
The probability density function of the envelope of narrow band Gaussian noise is Poisson Gaussian Rayleigh Rician
The probability density function of the envelope of narrow band Gaussian noise isPoissonGaussianRayleighRician
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773
GATE ECE 1998 | Question 2.28
The intrinsic impedance of copper at high frequencies is purely resistive purely inductive complex with a capacitive component complex with an inductive component
The intrinsic impedance of copper at high frequencies ispurely resistivepurely inductivecomplex with a capacitive componentcomplex with an inductive component
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774
GATE ECE 1998 | Question 2.29
The Maxwell equation $\mathrm{V} \times \mathrm{H}=\mathrm{J}+\frac{\partial \overline{D}}{\partial t}$ is based on Ampere's law Gauss' law Faraday's law Coulomb's law
The Maxwell equation $\mathrm{V} \times \mathrm{H}=\mathrm{J}+\frac{\partial \overline{D}}{\partial t}$ is based onAmpere's lawGauss' lawFaraday's lawCoulomb's law
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775
GATE ECE 1998 | Question 2.30
All transmission line sections shown in the figure is have a characteristic impedance $\text{R}_{0}+\text{j}_{0}$. The input impedance $\text{Z}_{\text {in}}$ equals $\frac{2}{3} \text{R}_{0}$ $\mathrm{R}_{0}$ $\frac{3}{2} \text{R}_{0}$ $2 \mathrm{R}_{\mathrm{0}}$
All transmission line sections shown in the figure is have a characteristic impedance $\text{R}_{0}+\text{j}_{0}$. The input impedance $\text{Z}_{\text {in}}$ equals$\fra...
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776
GATE ECE 1998 | Question 2.31
The time averages Poynting vector, in $W / m^{2}$, for a wave with $\vec{E}=24 \; e^{} \; a_{} \mathrm{~V} / \mathrm{m}$ in free space is $ – \frac{2.4}{\pi} \vec{a}_{z}$ $\frac{2.4}{\pi} \vec{a}_{z}$ $\frac{4.8}{\pi} \vec{a}_{z}$ $-\frac{4.8}{\pi} \vec{a}_{z}$
The time averages Poynting vector, in $W / m^{2}$, for a wave with $\vec{E}=24 \; e^{} \; a_{} \mathrm{~V} / \mathrm{m}$ in free space is$ – \frac{2.4}{\pi} \vec{a}_{z}...
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777
GATE ECE 1998 | Question 2.32
The wavelength of a wave with propagation constant $(0.1 \pi+j 0.2 \pi) \mathrm{m}^{-1}$ is $\frac{2}{\sqrt{0.05}} \mathrm{~m}$ $10 \mathrm{~m}$ $20 \mathrm{~m}$ $30 \mathrm{~m}$
The wavelength of a wave with propagation constant $(0.1 \pi+j 0.2 \pi) \mathrm{m}^{-1}$ is$\frac{2}{\sqrt{0.05}} \mathrm{~m}$$10 \mathrm{~m}$$20 \mathrm{~m}$$30 \mathrm{...
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778
GATE ECE 1998 | Question 2.33
The depth of penetration of wave in a lossy dielectric increases with increasing conductivity permeability wavelength permittivity
The depth of penetration of wave in a lossy dielectric increases with increasingconductivitypermeabilitywavelengthpermittivity
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779
GATE ECE 1998 | Question 2.34
The polarisation of wave with electric field vector $\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \; e^{j(\hat{\rho}(\omega t+\beta z)}\left(\vec{a}_{x}+\vec{a}_{y}\right)$ is linear elliptical left hand circular right hand circular
The polarisation of wave with electric field vector$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \; e^{j(\hat{\rho}(\omega t+\beta z)}\left(\vec{a}_{x}+\vec{a}_{y}\right)$ ...
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780
GATE ECE 1998 | Question 2.35
The vector $\mathrm{H}$ in the far field of an antenna satisfies $\nabla \cdot \overrightarrow{\mathrm{H}}=0$ and $\nabla \times \overrightarrow{\mathrm{H}}=0$ $\nabla \cdot \overrightarrow{\mathrm{H}} \neq 0$ ... $\nabla \cdot \overrightarrow{\mathrm{H}} \neq 0$ and $\nabla \times \overrightarrow{\mathrm{H}}=0$
The vector $\mathrm{H}$ in the far field of an antenna satisfies$\nabla \cdot \overrightarrow{\mathrm{H}}=0$ and $\nabla \times \overrightarrow{\mathrm{H}}=0$$\nabla \cdo...
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781
GATE ECE 1998 | Question 2.36
The radiation resistance of a circular loop of one turn is $0.01 \; \Omega$. The radiation resistance of five turns of such a loop will be $0.002 \; \Omega$ $0.01 \; \Omega$ $0.05 \; \Omega$ $0.25 \; \Omega$
The radiation resistance of a circular loop of one turn is $0.01 \; \Omega$. The radiation resistance of five turns of such a loop will be$0.002 \; \Omega$$0.01 \; \Omega...
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782
GATE ECE 1998 | Question 2.37
An antenna in free space receives $2 \; \mu \mathrm{W}$ of power when the incident electric field is $20 \mathrm{~m} \; \mathrm{V} / \mathrm{m} \; \mathrm{rms}$. The effective aperture of the antenna is $0.005 \mathrm{~m}^{2}$ $0.05 \mathrm{~m}^{2}$ $1.885 \mathrm{~m}^{2}$ $3.77 \mathrm{~m}^{2}$
An antenna in free space receives $2 \; \mu \mathrm{W}$ of power when the incident electric field is $20 \mathrm{~m} \; \mathrm{V} / \mathrm{m} \; \mathrm{rms}$. The effe...
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783
GATE ECE 1998 | Question 2.38
The maximum usable frequency of an ionospheric layer at $60^{\circ}$ incidence and with $8 \; \mathrm{mHz}$ critical frequency is $16 \; \mathrm{MHz}$ $\frac{16}{\sqrt{3}} \; \mathrm{MHz}$ $8 \; \mathrm{MHz}$ about $6.93 \; \mathrm{MHz}$
The maximum usable frequency of an ionospheric layer at $60^{\circ}$ incidence and with $8 \; \mathrm{mHz}$ critical frequency is$16 \; \mathrm{MHz}$$\frac{16}{\sqrt{3}} ...
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784
GATE ECE 1998 | Question 2.39
A loop is rotating about the $y$-axis in a magnetic field $\overrightarrow{\mathrm{E}}=\mathrm{B}_{0} \cos (\omega t+\phi) \vec{a}_{x} \mathrm{~T}$. The voltage in the loop is zero due to rotation only due to transformer action only due to both rotation and transformer action
A loop is rotating about the $y$-axis in a magnetic field $\overrightarrow{\mathrm{E}}=\mathrm{B}_{0} \cos (\omega t+\phi) \vec{a}_{x} \mathrm{~T}$. The voltage in the lo...
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785
GATE ECE 1998 | Question 2.40
The far field of an antenna varies with distance $\mathrm{r}$ as $\frac{1}{r}$ $\frac{1}{r^{2}}$ $\frac{1}{r^{3}}$ $\frac{1}{\sqrt{r}}$
The far field of an antenna varies with distance $\mathrm{r}$ as$\frac{1}{r}$$\frac{1}{r^{2}}$$\frac{1}{r^{3}}$$\frac{1}{\sqrt{r}}$
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786
GATE ECE 1998 | Question 3
Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in the figure is. What happens when $\text{L}=\mathrm{CR}^{2}$ ?
Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in the figure is. What happens when $\text{L}=\mathrm{CR}^{2}$ ?
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788
GATE ECE 1998 | Question: 5
Draw the transfer characteristic of the circuit of the figure assuming both $D_{1}$ and $D_{2}$ to be ideal. How would the characteristic change if $D_{2}$ is ideal, but $D_{1}$ is non-ideal in that it has forward resistance of $10 \; \Omega$ a reverse resistance of infinity?
Draw the transfer characteristic of the circuit of the figure assuming both $D_{1}$ and $D_{2}$ to be ideal.How would the characteristic change if $D_{2}$ is ideal, but $...
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789
GATE ECE 1998 | Question 6
Given an irrotational vector field $\overrightarrow{\mathrm{F}}=(k 1 x y+k 2) \vec{a}_{x}+\left(3 x 2-k 3 Z) \vec{a}_{y}+(3 x z 2-y) \vec{a}_{z}\right.$ Find $V . \vec{F}$ at $(1,1,-2)$.
Given an irrotational vector field$\overrightarrow{\mathrm{F}}=(k 1 x y+k 2) \vec{a}_{x}+\left(3 x 2-k 3 Z) \vec{a}_{y}+(3 x z 2-y) \vec{a}_{z}\right.$Find $V . \vec{F}$ ...
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790
GATE ECE 1998 | Question 7
The loop transfer function of a single loop control system is given by \[ \mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\frac{100}{s(1+0.01 s)} e^{-s \mathrm{T}} \] Using the Nyquist criterion, find the condition for the closed loop system to be stable.
The loop transfer function of a single loop control system is given by\[\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\frac{100}{s(1+0.01 s)} e^{-s \mathrm{T}}\]Using the...
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791
GATE ECE 1998 | Question 8
The characteristic equation of a feedback control system is \[s^{4}+20 s^{3}+15 s^{2}+2 s+K=0\] Determine the range of $K$ for the system to be stable. Can the system be marginally stable? If so, find the required value of $K$ and the frequency of sustained oscillation.
The characteristic equation of a feedback control system is\[s^{4}+20 s^{3}+15 s^{2}+2 s+K=0\]Determine the range of $K$ for the system to be stable.Can the system be mar...
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792
GATE ECE 1998 | Question 9
Draw a signal flow graph for the following set of algebraic equations \[\begin{array}{l} y_{2}=a \; y_{1}-g \; y_{3} \\ y_{3}=e \; y_{2}+c \; y_{4} \\ y_{4}=b \; y_{2}-d \; y_{4}\end{array}\] Hence, find the gains $\frac{y_{2}}{y_{1}}$ and $\frac{y_{3}}{y_{1}}$
Draw a signal flow graph for the following set of algebraic equations\[\begin{array}{l}y_{2}=a \; y_{1}-g \; y_{3} \\y_{3}=e \; y_{2}+c \; y_{4} \\y_{4}=b \; y_{2}-d \; y...
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793
GATE ECE 1998 | Question 10
Consider the system shown in the figure is. Determine the value of a such that the damping ratio is $0.5$. Also obtain the values of the rise time $t_{r}$ and maximum overshoot $M_{p}$ in its step response.
Consider the system shown in the figure is. Determine the value of a such that the damping ratio is $0.5$. Also obtain the values of the rise time $t_{r}$ and maximum ove...
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794
GATE ECE 1998 | Question 11
Determine the input impedance of the given and investigatie if it can be inductive.
Determine the input impedance of the given and investigatie if it can be inductive.
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795
GATE ECE 1998 | Question 12
Find the value of $R^{\prime}$ in the circuit of the figure is for generating sinusoidal oscillations. Find the frequency of oscillations.
Find the value of $R^{\prime}$ in the circuit of the figure is for generating sinusoidal oscillations. Find the frequency of oscillations.
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796
GATE ECE 1998 | Question 13
In the circuit of the figure is determine the resistance $R_{0}$ seen by the output terminals. Ignore the effects of $R_{1}$ and $R_{2}$.
In the circuit of the figure is determine the resistance $R_{0}$ seen by the output terminals. Ignore the effects of $R_{1}$ and $R_{2}$.
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797
GATE ECE 1998 | Question 14
The $\text{JFET}$ in the circuit of the figure is characterised by the parameters $\mathrm{I}_{\mathrm{DSS}}=4 \; \mathrm{MA}$ and $\mathrm{V}_{p}=-4 \mathrm{V}$. Find $\mathrm{V}_{0}$ if $\mathrm{V}_{1}=0$, and $\mathrm{V}_{i}$ if $\mathrm{V}_{0}=0$
The $\text{JFET}$ in the circuit of the figure is characterised by the parameters $\mathrm{I}_{\mathrm{DSS}}=4 \; \mathrm{MA}$ and $\mathrm{V}_{p}=-4 \mathrm{V}$.Find$\ma...
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799
GATE ECE 1998 | Question 16
For the $\text{TTL}$ circuit shown in the figure is find the current through the collector of transistor $Q_{4}$ when $V_{0}=0.2 \mathrm{~V}$. Assume $V_{C E(\text {sat)}}=0.2 \mathrm{~V}, \beta=100$ and $V_{BE(\text {sat})}=0.7 \mathrm{~V}$. The $\alpha$ of $Q_{1}$ in its inverse active mode is $0.01$.
For the $\text{TTL}$ circuit shown in the figure is find the current through the collector of transistor $Q_{4}$ when $V_{0}=0.2 \mathrm{~V}$. Assume $V_{C E(\text {sat)}...
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800
GATE ECE 1998 | Question 17
Write a short assembly language program, without using any arithmetic instruction, to store hexadecimal $5D$ in the flag register of $8085$ microprocessor. Data in other registers of the processor must not alter upon executing this program.
Write a short assembly language program, without using any arithmetic instruction, to store hexadecimal $5D$ in the flag register of $8085$ microprocessor. Data in other ...
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