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881
GATE ECE 2003 | Question: 72
The gain margin and the phase margin of a feedback system with $\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\frac{\mathrm{s}}{(\mathrm{s}+100)^{3}}$ are $0 \mathrm{~dB}, 0^{\circ}$ $\infty, \infty$ $\infty, 0^{\circ}$ $88.5 \mathrm{~dB}, \infty$
The gain margin and the phase margin of a feedback system with $\mathrm{G}(\mathrm{s}) \mathrm{H}(\mathrm{s})=\frac{\mathrm{s}}{(\mathrm{s}+100)^{3}}$ are$0 \mathrm{~dB},...
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882
GATE ECE 2003 | Question: 73
The zero-input response of a system given by the state-space equation $\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]\left[\begin{array}{l}x_{1} \\ x_{2}\end{array}\right]$ ... $\left[\begin{array}{c}t \\ t e^{t}\end{array}\right]$
The zero-input response of a system given by the state-space equation$\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2}\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 1...
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884
GATE ECE 2003 | Question: 75
The data for Q. 75-76 are given below. Solve the problems and choose the correct answers. Let $m(t)=\cos \left[\left(4 \pi \times 10^{3}\right) t\right]$ be the message signal and $\left.c(t)=5 \cos \left[2 \pi \times 10^{b}\right) t\right]$ ... $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{8}$
The data for Q. 75-76 are given below. Solve the problems and choose the correct answers.Let $m(t)=\cos \left[\left(4 \pi \times 10^{3}\right) t\right]$ be the message si...
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886
GATE ECE 2003 | Question: 77
Choose the correct one from among the alternative $\text{A, B, C. D}$ after matching an item in Group $1$ with the most appropriate item in Group $2.$ ... $\text{P - 6 Q - 1 R - 3 S - 2}$ $\text{P - 5 Q - 6 R - 1 S - 3}$
Choose the correct one from among the alternative $\text{A, B, C. D}$ after matching an item in Group $1$ with the most appropriate item in Group $2.$$\begin{array}{ll}\q...
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888
GATE ECE 2003 | Question: 79
A sinusoidal signal with peak-to-peak amplitude of $1.536 \mathrm{~V}$ is quantized into $128$ levels using a mid-rise uniform quantizer. The quantization-noise power is $0.768 \mathrm{~V}$ $48 \times 10^{-6} \mathrm{~V}^{2}$ $12 \times 10^{-6} \mathrm{~V}^{2}$ $3.072 \mathrm{~V}$
A sinusoidal signal with peak-to-peak amplitude of $1.536 \mathrm{~V}$ is quantized into $128$ levels using a mid-rise uniform quantizer. The quantization-noise power is$...
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891
GATE ECE 2003 | Question: 82
If $\text{S}$ represents the carrier synchronization at the receiver and $\rho$ represents the bandwidth efficiency, then the correct statement for the coherent binary $\text{PSK}$ is $\rho=0.5, S$ is required $\rho=1.0, S$ is required $\rho=0.5, \mathrm{~S}$ is not required $\rho=1.0, S$ is not required
If $\text{S}$ represents the carrier synchronization at the receiver and $\rho$ represents the bandwidth efficiency, then the correct statement for the coherent binary $\...
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892
GATE ECE 2003 | Question: 83
A signal is sampled at $8 \; \mathrm{kHz}$ and is quantized using $8$-bit uniform quantizer. Assuming $\mathrm{SNR}_q$ for a sinusoidal signal, the correct statement for $P C M$ signal with a bit rate of $R$ ... $\mathrm{R}=32 \; \mathrm{kbps}, \quad \mathrm{SNR}_q=49.8 \mathrm{~dB}$
A signal is sampled at $8 \; \mathrm{kHz}$ and is quantized using $8$-bit uniform quantizer. Assuming $\mathrm{SNR}_q$ for a sinusoidal signal, the correct statement for ...
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894
GATE ECE 2003 | Question: 85
If the electric field intensity is given by \[\mathrm{E}=\left(x u_{x}+y u_{y}+z u_{z}\right) \text { volt } / \mathrm{m} \text {, }\] the potential difference between $X(2,0,0)$ and $Y(1,2,3)$ is $+1$ volt $-1$ volt $+5$ volt $+6$ volt
If the electric field intensity is given by\[\mathrm{E}=\left(x u_{x}+y u_{y}+z u_{z}\right) \text { volt } / \mathrm{m} \text {, }\]the potential difference between $X(2...
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895
GATE ECE 2003 | Question: 86
A uniform plane wave travelling in air is incident on the plane boundary between air and another dielectric medium with $\varepsilon_{r}=4$. The reflection coefficient for the normal incidence, is zero $0.5 \angle 180^{\circ}$ $0.333 \angle 0^{\circ}$ $0.333 \angle 180^{\circ}$
A uniform plane wave travelling in air is incident on the plane boundary between air and another dielectric medium with $\varepsilon_{r}=4$. The reflection coefficient fo...
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898
GATE ECE 2003 | Question: 89
A rectangular metal wave guide filled with a dielectric material of relative permittivity $\varepsilon_{r}=4$ has the inside dimensions $3.0 \mathrm{~cm} \times 1.2 \mathrm{~cm}$. The cut-off frequency for the dominant mode is $2.5 \; \mathrm{GHz}$ $5.0 \; \mathrm{GHz}$ $10.0 \; \mathrm{GHz}$ $12.5 \; \mathrm{GHz}$
A rectangular metal wave guide filled with a dielectric material of relative permittivity $\varepsilon_{r}=4$ has the inside dimensions $3.0 \mathrm{~cm} \times 1.2 \math...
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900
GATE ECE 2004 | Question: 1
Consider the network graph shown in the figure. Which one of the following is NOT a 'tree' of this graph?
Consider the network graph shown in the figure. Which one of the following is NOT a 'tree' of this graph?
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901
GATE ECE 2004 | Question: 2
The equivalent inductance measured between the terminals $1$ and $2$ for the circuit shown in the figure is $\mathrm{L}_{1}+\mathrm{L}_{2}+\mathrm{M}$ $\mathrm{L}_{1}+\mathrm{L}_{2}-\mathrm{M}$ $\mathrm{L}_{1}+\mathrm{L}_{2}+2 \mathrm{M}$ $\mathrm{L}_{1}+\mathrm{L}_{2}-2 \mathrm{M}$
The equivalent inductance measured between the terminals $1$ and $2$ for the circuit shown in the figure is$\mathrm{L}_{1}+\mathrm{L}_{2}+\mathrm{M}$$\mathrm{L}_{1}+\math...
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902
GATE ECE 2004 | Question: 3
The circuit shown in in the figure, with $R=\frac{1}{3} \Omega$, $\mathrm{L}=\frac{1}{4} \mathrm{H}, \mathrm{C}=3 \mathrm{~F}$ has input voltage $v(t)=\sin 2 t$. The resulting current $i(t)$ is $5 \sin (2t + 53.1^{\circ})$ $5 \sin (2t - 53.1^{\circ})$ $25 \sin (2t + 53.1^{\circ})$ $25 \sin (2t - 53.1^{\circ})$
The circuit shown in in the figure, with $R=\frac{1}{3} \Omega$, $\mathrm{L}=\frac{1}{4} \mathrm{H}, \mathrm{C}=3 \mathrm{~F}$ has input voltage $v(t)=\sin 2 t$. The resu...
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904
GATE ECE 2004 | Question: 5
For the $\text{R-L}$ circuit shown in the figure, the input voltage $v_{i}(t)=u(t)$. The current $i(t)$ is
For the $\text{R-L}$ circuit shown in the figure, the input voltage $v_{i}(t)=u(t)$. The current $i(t)$ is
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905
GATE ECE 2004 | Question: 6
The impurity commonly used for realizing the base region of a silicon $n-p-n$ transistor is Gallium Indium Boron Phosphorus
The impurity commonly used for realizing the base region of a silicon $n-p-n$ transistor isGalliumIndiumBoronPhosphorus
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908
GATE ECE 2004 | Question: 9
An ideal $\text{op-amp}$ is an ideal voltage controlled current source voltage controlled voltage source current controlled current source current controlled voltage source
An ideal $\text{op-amp}$ is an idealvoltage controlled current sourcevoltage controlled voltage sourcecurrent controlled current sourcecurrent controlled voltage source
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909
GATE ECE 2004 | Question: 10
Voltage series feedback (also called series-shunt feedback) results in increase in both input and output impedances decrease in both input and output impedances increase in input impedance and decrease in output impedance decrease in input impedance and increase in output impedance
Voltage series feedback (also called series-shunt feedback) results inincrease in both input and output impedancesdecrease in both input and output impedancesincrease in ...
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910
GATE ECE 2004 | Question: 11
The circuit in the given figure is a low-pass filter high-pass filter band-pass filter band-reject filter
The circuit in the given figure is alow-pass filterhigh-pass filterband-pass filterband-reject filter
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911
GATE ECE 2004 | Question: 12
Assuming $\mathrm{V}_{\text {CEsat }}=0.2 \mathrm{~V}$ and $\beta=50$, the minimum base current $\left(I_{v}\right)$ required to drive the transistor in the given figure to saturation is $56 \; \mu \mathrm{A}$ $140 \mathrm{~mA}$ $60 \mu \mathrm{A}$ $3 \; \mathrm{~mA}$
Assuming $\mathrm{V}_{\text {CEsat }}=0.2 \mathrm{~V}$ and $\beta=50$, the minimum base current $\left(I_{v}\right)$ required to drive the transistor in the given figure ...
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912
GATE ECE 2004 | Question: 13
A master-slave flip-flop has the characteristic that change in the input immediately reflected in the output change in the output occurs when the state of the master is affected change in the output occurs when the state of the slave is affected both the master and the slave states are affected at the same time
A master-slave flip-flop has the characteristic thatchange in the input immediately reflected in the outputchange in the output occurs when the state of the master is aff...
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913
GATE ECE 2004 | Question: 14
The range of signed decimal numbers that can be represented by $6$-bite $1$'s complement number is $-31$ to $+31$ $-63$ to $+64$ $-64$ to $+63$ $-32$ to $+31$
The range of signed decimal numbers that can be represented by $6$-bite $1$'s complement number is$-31$ to $+31$$-63$ to $+64$$-64$ to $+63$$-32$ to $+31$
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914
GATE ECE 2004 | Question: 15
A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in $100$ increments. The minimum number of bits required to encode, in straight binary, is $8$ $6$ $5$ $7$
A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in $100$ i...
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915
GATE ECE 2004 | Question: 16
Choose the correct one from among the alternatives $\text{A, B, C, D}$ after matching an item from Group $1$ with the most appropriate item in Group $2.$ ... $\mathrm{P}-2, \mathrm{Q}-1, \mathrm{R}-3$ $\text{P - 1, Q - 2, R - 2}$
Choose the correct one from among the alternatives $\text{A, B, C, D}$ after matching an item from Group $1$ with the most appropriate item in Group $2.$$$\begin{array}{|...
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916
GATE ECE 2004 | Question: 17
Figure given below shows the internal schematic of a $\text{TTL AND-OR}$ -Invert $\text{(AOI)}$ gate. For the inputs shown in the given figure, the output $\text{Y}$ is $0$ $1$ $\mathrm{AB}$ $\overline{\mathrm{AB}}$
Figure given below shows the internal schematic of a $\text{TTL AND-OR}$ -Invert $\text{(AOI)}$ gate. For the inputs shown in the given figure, the output $\text{Y}$ is $...
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917
GATE ECE 2004 | Question: 18
Given figure is the voltage transfer characteristic of an NMOS inverter with enhancement mode transistor as load an NMOS inverter with depletion mode transistor as load a CMOS inverter a BJT inverter
Given figure is the voltage transfer characteristic ofan NMOS inverter with enhancement mode transistor as loadan NMOS inverter with depletion mode transistor as loada CM...
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918
GATE ECE 2004 | Question: 19
The impulse response $h[n]$ of a linear time-invariant system is given by \[h[n]=u[n+3]+u[n-2]-2 u[n-7]\] where $u[n]$ is the unit step sequence. The above system is stable but not causal stable and causal causal but unstable unstable and not causal
The impulse response $h[n]$ of a linear time-invariant system is given by\[h[n]=u[n+3]+u[n-2]-2 u[n-7]\]where $u[n]$ is the unit step sequence. The above system isstable ...
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919
GATE ECE 2004 | Question: 20
The distribution function $\mathrm{F}_{1}(x)$ of a random variable $\mathrm{X}$ is shown in the figure. The probability that $X=1$ is zero $0.25$ $0.55$ $0.30$
The distribution function $\mathrm{F}_{1}(x)$ of a random variable $\mathrm{X}$ is shown in the figure. The probability that $X=1$ iszero$0.25$$0.55$$0.30$
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920
GATE ECE 2004 | Question: 21
The $z$-transform of a system is $H(z)=\frac{z}{z-0.2}.$ If the ROC is $|z|<0.2$, then the impulse response of the system is $(0.2)^{n} u[n]$ $(0.2)^{n} u[-n-1]$ $-(0.2)^{n} u[n]$ $-(0.2)^{n} u[-n-1]$
The $z$-transform of a system is $H(z)=\frac{z}{z-0.2}.$ If the ROC is $|z|<0.2$, then the impulse response of the system is$(0.2)^{n} u[n]$$(0.2)^{n} u[-n-1]$$-(0.2)^{n}...
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