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722
GATE ECE 2003 | Question: 58
The circuit shown in the figure converts BCD to binary code Binary to excess $-3$ code Excess $-3$ to Gray code Gray to Binary code
The circuit shown in the figure convertsBCD to binary codeBinary to excess $-3$ codeExcess $-3$ to Gray codeGray to Binary code
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725
GATE ECE 2003 | Question: 61
Let $X$ and $Y$ be two statistically independent random variables uniformly distributed in the ranges $(-1,1)$ and $(-2,1)$ respectively. Let $Z=X+Y$. Then the probability that $(Z \leq-2)$ is zero $\frac{1}{6}$ $\frac{1}{3}$ $\frac{1}{12}$
Let $X$ and $Y$ be two statistically independent random variables uniformly distributed in the ranges $(-1,1)$ and $(-2,1)$ respectively. Let $Z=X+Y$. Then the probabilit...
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730
GATE ECE 2003 | Question: 66
Let $Y$ and $Z$ be the random variables obtained by sampling $X(t)$ at $t=2$ and $t=4$ respectively. Let $W$ $=Y-Z$. The variance of $W$ is $13.36$ $9.36$ $2.64$ $8.00$
Let $Y$ and $Z$ be the random variables obtained by sampling $X(t)$ at $t=2$ and $t=4$ respectively. Let $W$ $=Y-Z$. The variance of $W$ is$13.36$$9.36$$2.64$$8.00$
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732
GATE ECE 2003 | Question: 68
The signal flow graph of a system is shown in the figure. The transfer function $\frac{C(s)}{R(s)}$ of the system is $\frac{6}{s^{2}+29 s+6}$ $\frac{6 s}{s^{2}+29 s+6}$ $\frac{s(s+2)}{s^{2}+29 s+6}$ $\frac{s(s+27)}{s^{2}+29 s+6}$
The signal flow graph of a system is shown in the figure. The transfer function $\frac{C(s)}{R(s)}$ of the system is$\frac{6}{s^{2}+29 s+6}$$\frac{6 s}{s^{2}+29 s+6}$$\fr...
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733
GATE ECE 2003 | Question: 69
The root locus of the system $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)$ $=\frac{\mathrm{K}}{s(s+2)(s+3)}$ has the break-away point located at $(-0.5,0)$ $(-2.548,0)$ $(-4,0)$ $(-0.784,0)$
The root locus of the system $\mathrm{G}(\mathrm{s}) \mathrm{H}(s)$ $=\frac{\mathrm{K}}{s(s+2)(s+3)}$ has the break-away point located at$(-0.5,0)$$(-2.548,0)$$(-4,0)$$(-...
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734
GATE ECE 2003 | Question: 70
The approximate Bode magnitude plot of a minimum-phase system is shown in the figure. The transfer function of the system is $10^8 \frac{(s+0.1)^3}{(s+10)^2(s+100)}$ $10^{7} \frac{(s+0.1)^3}{(s+10)(s+100)}$ $10^8 \frac{(s+0.1)^2}{(s+10)^2(s+100)}$ $10^9 \frac{(s+0.1)^3}{(s+10)(s+100)^2}$
The approximate Bode magnitude plot of a minimum-phase system is shown in the figure. The transfer function of the system is$10^8 \frac{(s+0.1)^3}{(s+10)^2(s+100)}$$10^{7...
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735
GATE ECE 2003 | Question: 71
A second-order system has the transfer function $\frac{C(s)}{R(s)}=\frac{4}{s^{2}+4 s+4}$. With $r(t)$ as the unit-step function, the response $c(t)$ of the system is represented by Fig. $(a)$ Fig. $(b)$ Fig. $(c)$ Fig. $(d)$
A second-order system has the transfer function$\frac{C(s)}{R(s)}=\frac{4}{s^{2}+4 s+4}$.With $r(t)$ as the unit-step function, the response $c(t)$ of the system is repre...
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736
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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737
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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739
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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741
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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743
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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746
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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747
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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749
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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750
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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753
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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755
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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756
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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757
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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759
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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760
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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