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1401
GATE ECE 2007 | Question: 56
The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function $G(s)$ corresponding to this Bode plot is $\frac{1}{(s+1)(s+20)}$ $\frac{1}{s(s+1)(s+20)}$ $\frac{100}{s(s+1)(s+20)}$ $\frac{100}{s(s+1)(1+0.05 s)}$
The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function $G(s)$ corresponding to this Bode plot is$\frac{1}{(s+1)(s+20)}$$\frac{1}...
1 votes
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1403
GATE ECE 2007 | Question: 58
In delta modulation, the slope overload distortion can be reduced by decreasing the step size decreasing the granular noise decreasing the sampling rate increasing the step size
In delta modulation, the slope overload distortion can be reduced bydecreasing the step sizedecreasing the granular noisedecreasing the sampling rateincreasing the step s...
1 votes
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1404
GATE ECE 2007 | Question: 59
The raised cosine pulse $p(t)$ is used for zero ISI in digital communications. The expression for $p(t)$ with unity roll-off factor is given by $p(t)=\dfrac{\sin 4 \pi W t}{4 \pi W t\left(1-16 W^{2} t^{2}\right)}$. The value of $p(t)$ at $t=\dfrac{1}{4 W}$ is $-0.5$ $0$ $0.5$ $\infty$
The raised cosine pulse $p(t)$ is used for zero ISI in digital communications. The expression for $p(t)$ with unity roll-off factor is given by $p(t)=\dfrac{\sin 4 \pi W ...
1 votes
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1405
GATE ECE 2007 | Question: 60
In the following scheme, if the spectrum $M(f)$ of $m(t)$ is as shown, then the spectrum $Y(f)$ of $y(t)$ will be
In the following scheme, if the spectrum $M(f)$ of $m(t)$ is as shown, then the spectrum $Y(f)$ of $y(t)$ will be
1 votes
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1406
GATE ECE 2007 | Question: 61
During transmission over a certain binary communication channel, bit errors occur independently with probability $p$. The probability of AT MOST one bit in error in a block of $n$ bits is given by $p^{n}$ $1-p^{n}$ $n p(1-p)^{n-1}+(1-p)^{n}$ $1-(1-p)^{n}$
During transmission over a certain binary communication channel, bit errors occur independently with probability $p$. The probability of AT MOST one bit in error in a blo...
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1412
GATE ECE 2007 | Question: 67
A load of $50\; \Omega$ is connected in shunt in a $2$-wire transmission line of $Z_{0}=50 \;\Omega$ as shown in the figure. The $2$-port scattering parameter matrix $\text{(S-matrix)}$ ...
A load of $50\; \Omega$ is connected in shunt in a $2$-wire transmission line of $Z_{0}=50 \;\Omega$ as shown in the figure. The $2$-port scattering parameter matrix $\te...
1 votes
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1414
GATE ECE 2007 | Question: 69
A $\dfrac{\lambda}{2}$ dipole is kept horizontally at a height of $\dfrac{\lambda_{0}}{2}$ above a perfectly conducting infinite ground plane. The radiation pattern in the plane of the dipole ( $\vec{E}$ plane) looks approximately as
A $\dfrac{\lambda}{2}$ dipole is kept horizontally at a height of $\dfrac{\lambda_{0}}{2}$ above a perfectly conducting infinite ground plane. The radiation pattern in th...
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1415
GATE ECE 2007 | Question: 70
A right circularly polarized (RCP) plane wave is incident at an angle of $60^{\circ}$ to the normal, on an air-dielectric interface. If the reflected wave is linearly polarized, the relative dielectric constant $\varepsilon_{r 2}$ is $\sqrt{2}$ $\sqrt{3}$ $2$ $3$
A right circularly polarized (RCP) plane wave is incident at an angle of $60^{\circ}$ to the normal, on an air-dielectric interface. If the reflected wave is linearly pol...
1 votes
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1416
GATE ECE 2007 | Question: 71
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of $1 \times 10^{-4} \mathrm{~cm}^{2}$ ... is $50 \; \mathrm{~nm}$ $143 \; \mathrm{~nm}$ $350 \; \mathrm{~nm}$ $1 \; \mu \mathrm{m}$
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of ...
1 votes
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1417
GATE ECE 2007 | Question: 72
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of $1 \times 10^{-4} \mathrm{~cm}^{2}$ ... $0.857 \; \mu \mathrm{m}$ $1 \; \mu \mathrm{m}$ $1.143 \; \mu \mathrm{m}$
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of ...
1 votes
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1418
GATE ECE 2007 | Question: 73
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of $1 \times 10^{-4} \mathrm{~cm}^{2}$ ... is false $\mathrm{S} 1$ is false and $\mathrm{S} 2$ is true Both $\text{S1}$ and $\text{S2}$ are false
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a $\mathrm{Metal} / \mathrm{SiO}_{2} / \text{silicon (MOS)}$ capacitor having an area of ...
1 votes
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1420
GATE ECE 2007 | Question: 75
Two $4$-ary signal constellations are shown. It is given that $\phi_{1}$ and $\phi_{2}$ ... both the constellations The value of $N_{0}$ will determine which of the two constellations has a lower probability of symbol error
Two $4$-ary signal constellations are shown. It is given that $\phi_{1}$ and $\phi_{2}$ constitute an orthonormal basis for the two constellations. Assume that the four s...
1 votes
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1421
GATE ECE 2007 | Question: 76
Consider the Op-Amp circuit shown in the figure. The transfer function $V_{o}(s) / V_{i}(s)$ is $\frac{1-s R C}{1+s R C}$ $\frac{1+s R C}{1-s R C}$ $\frac{1}{1-s R C}$ $\frac{1}{1+s R C}$
Consider the Op-Amp circuit shown in the figure.The transfer function $V_{o}(s) / V_{i}(s)$ is$\frac{1-s R C}{1+s R C}$$\frac{1+s R C}{1-s R C}$$\frac{1}{1-s R C}$$\frac{...
1 votes
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1422
GATE ECE 2007 | Question: 77
Consider the Op-Amp circuit shown in the figure. If $V_{i}=V_{1} \sin (\omega t)$ and $V_{o}=V_{2} \sin (\omega t+\phi)$, then the minimum and maximum values of $\phi$ (in radians) are respectively $-\pi / 2$ and $\pi / 2$ $0$ and $\pi / 2$ $-\pi$ and $0$ $-\pi / 2$ and $0$
Consider the Op-Amp circuit shown in the figure.If $V_{i}=V_{1} \sin (\omega t)$ and $V_{o}=V_{2} \sin (\omega t+\phi)$, then the minimum and maximum values of $\phi$ (in...
1 votes
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1423
GATE ECE 2007 | Question: 78
An $8085$ assembly language program is given below. Line 1: MVI A,B5H 2: MVI B0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLT The contents of the accumulator just after execution of the $\textsf{ADD}$ instruction in line $4$ will be $\text{C3H}$ $\text{EAH}$ $\mathrm{DCH}$ $69 \mathrm{H}$
An $8085$ assembly language program is given below.Line 1: MVI A,B5H 2: MVI B0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLTThe contents of the accumula...
1 votes
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1425
GATE ECE 2007 | Question: 80
Consider a linear system whose state space representation is $\dot{\mathbf{x}}(t)=\mathbf{A} \mathbf{x}(t)$. If the initial state vector of the system is $\mathbf{x}(0)=\left[\begin{array}{r}1 \\ -2\end{array}\right]$ ... $\left(1,\left[\begin{array}{r}1 \\ -2\end{array}\right]\right)$
Consider a linear system whose state space representation is $\dot{\mathbf{x}}(t)=\mathbf{A} \mathbf{x}(t)$. If the initial state vector of the system is $\mathbf{x}(0)=\...
1 votes
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1426
GATE ECE 2007 | Question: 81
Consider a linear system whose state space representation is $\dot{\mathbf{x}}(t)=\mathbf{A} \mathbf{x}(t)$. If the initial state vector of the system is $\mathbf{x}(0)=\left[\begin{array}{r}1 \\ -2\end{array}\right]$ ... $\left[\begin{array}{rr}0 & 1 \\ -2 & -3\end{array}\right]$
Consider a linear system whose state space representation is $\dot{\mathbf{x}}(t)=\mathbf{A} \mathbf{x}(t)$. If the initial state vector of the system is $\mathbf{x}(0)=\...
1 votes
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1429
GATE ECE 2007 | Question: 84
In the Digital-to-Analog converter circuit shown in the figure below, $V_{R}=10 \mathrm{~V}$ and $\mathrm{R}=10 \; \mathrm{k} \Omega$. The current $i$ is $31.25 \; \mu \mathrm{A}$ $62.5 \; \mu \mathrm{A}$ $125 \; \mu \mathrm{A}$ $250 \; \mu \mathrm{A}$
In the Digital-to-Analog converter circuit shown in the figure below, $V_{R}=10 \mathrm{~V}$ and $\mathrm{R}=10 \; \mathrm{k} \Omega$.The current $i$ is$31.25 \; \mu \mat...
1 votes
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1430
GATE ECE 2007 | Question: 85
In the Digital-to-Analog converter circuit shown in the figure below, $V_{R}=10 \mathrm{~V}$ and $\mathrm{R}=10 \; \mathrm{k} \Omega$. The voltage $V_{o}$ is $-0.781 \mathrm{~V}$ $-1.562 \mathrm{~V}$ $-3.125 \mathrm{~V}$ $-6.250 \mathrm{~V}$
In the Digital-to-Analog converter circuit shown in the figure below, $V_{R}=10 \mathrm{~V}$ and $\mathrm{R}=10 \; \mathrm{k} \Omega$.The voltage $V_{o}$ is$-0.781 \mathr...
0 votes
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1431
GATE ECE 1993 | Question 6.6
The built-in potential (Diffusion Potential) in a $p-n$ junction is equal to the difference in the Fermi level of the two sides, expressed in volts increases with the increase in the doping levels of the two sides increases with the increase in temperature is equal to the average of the Fermi levels of the two sides
The built-in potential (Diffusion Potential) in a $p-n$ junctionis equal to the difference in the Fermi level of the two sides, expressed in voltsincreases with the incre...
1 votes
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1433
GATE ECE 2008 | Question: 2
The system of linear equations \[ \begin{array}{l} 4 x+2 y=7 \\ 2 x+y=6 \end{array} \] has a unique solution no solution an infinite number of solutions exactly two distinct solutions
The system of linear equations\[ \begin{array}{l}4 x+2 y=7 \\2 x+y=6\end{array} \]hasa unique solutionno solutionan infinite number of solutionsexactly two distinct solut...
1 votes
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1434
GATE ECE 2008 | Question: 3
The equation $\sin (z)=10$ has no real or complex solution exactly two distinct complex solutions a unique solution an infinite number of complex solutions
The equation $\sin (z)=10$ hasno real or complex solutionexactly two distinct complex solutionsa unique solutionan infinite number of complex solutions
1 votes
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1435
GATE ECE 2008 | Question: 4
For real values of $x$, the minimum value of the function $f(x)=\exp (x)+\exp (-x)$ is $2$ $1$ $0.5$ $0$
For real values of $x$, the minimum value of the function $f(x)=\exp (x)+\exp (-x)$ is$2$$1$$0.5$$0$
1 votes
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1436
GATE ECE 2008 | Question: 5
Which of the following functions would have only odd powers of $x$ in its Taylor series expansion about the point $x=0?$ $\sin \left(x^{3}\right)$ $\sin \left(x^{2}\right)$ $\cos \left(x^{3}\right)$ $\cos \left(x^{2}\right)$
Which of the following functions would have only odd powers of $x$ in its Taylor series expansion about the point $x=0?$ $\sin \left(x^{3}\right)$$\sin \left(x^{2}\right)...
1 votes
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1437
GATE ECE 2008 | Question: 6
Which of the following is a solution to the differential equation $\dfrac{d x(t)}{d t}+3 x(t)=0?$ $x(t)=3 e^{-t}$ $x(t)=2 e^{-3 t}$ $x(t)=-\frac{3}{2} t^{2}$ $x(t)=3 t^{2}$
Which of the following is a solution to the differential equation $\dfrac{d x(t)}{d t}+3 x(t)=0?$ $x(t)=3 e^{-t}$$x(t)=2 e^{-3 t}$$x(t)=-\frac{3}{2} t^{2}$$x(t)=3 t^{2}$
1 votes
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1438
GATE ECE 2008 | Question: 7
In the following graph, the number of trees $\text{(P)}$ and the number of cut-sets $\text{(Q)}$ are $\mathrm{P}=2, \mathrm{Q}=2$ $\mathrm{P}=2, \mathrm{Q}=6$ $\mathrm{P}=4, \mathrm{Q}=6$ $\mathrm{P}=4, \mathrm{Q}=10$
In the following graph, the number of trees $\text{(P)}$ and the number of cut-sets $\text{(Q)}$ are$\mathrm{P}=2, \mathrm{Q}=2$$\mathrm{P}=2, \mathrm{Q}=6$$\mathrm{P}=4,...
1 votes
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1439
GATE ECE 2008 | Question: 8
In the following circuit, the switch $\mathrm{S}$ is closed at $t=0$. The rate of change of current $\dfrac{d i}{d t}(0+)$ is given by $0$ $\frac{R_{S} I_{S}}{L}$ $\frac{\left(R+R_{s}\right) I_{s}}{L}$ $\infty$
In the following circuit, the switch $\mathrm{S}$ is closed at $t=0$. The rate of change of current $\dfrac{d i}{d t}(0+)$ is given by$0$$\frac{R_{S} I_{S}}{L}$$\frac{\le...
1 votes
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1440
GATE ECE 2008 | Question: 9
The input and output of a continuous time system are respectively denoted by $x(t)$ and $y(t)$. Which of the following descriptions corresponds to a causal system? $y(t)=x(t-2)+x(t+4)$ $y(t)=(t-4) x(t+1)$ $y(t)=(t+4) x(t-1)$ $y(t)=(t+5) x(t+5)$
The input and output of a continuous time system are respectively denoted by $x(t)$ and $y(t)$. Which of the following descriptions corresponds to a causal system?$y(t)=x...
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