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1362
GATE ECE 2007 | Question: 27
If the semi-circular contour $D$ of radius $2$ is as shown in the figure, then the value of the integral $\displaystyle{}\oint_{D} \dfrac{1}{\left(s^{2}-1\right)} d s$ is $j \pi$ $-j \pi$ $-\pi$ $\pi$
If the semi-circular contour $D$ of radius $2$ is as shown in the figure, then the value of the integral $\displaystyle{}\oint_{D} \dfrac{1}{\left(s^{2}-1\right)} d s$ is...
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1363
GATE ECE 2007 | Question: 28
Two series resonant filters are as shown in the figure. Let the $\text{3-dB}$ bandwidth of Filter $1$ be $B_{1}$ and that of Filter $2$ be $B_{2}$. The value of $\dfrac{B_{1}}{B_{2}}$ is $4$ $1$ $\frac{1}{2}$ $\frac{1}{4}$
Two series resonant filters are as shown in the figure. Let the $\text{3-dB}$ bandwidth of Filter $1$ be $B_{1}$ and that of Filter $2$ be $B_{2}$. The value of $\dfrac{B...
1 votes
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1364
GATE ECE 2007 | Question: 29
For the circuit shown in the figure, the Thevenin voltage and resistance looking into $\mathrm{X}-\mathrm{Y}$ are $4 / 3 \mathrm{~V}, 2 \; \Omega$ $4 \mathrm{~V}, 2 / 3 \; \Omega$ $4 / 3 \mathrm{~V}, 2 / 3 \; \Omega$ $4 \mathrm{~V}, 2 \; \Omega$
For the circuit shown in the figure, the Thevenin voltage and resistance looking into $\mathrm{X}-\mathrm{Y}$ are$4 / 3 \mathrm{~V}, 2 \; \Omega$$4 \mathrm{~V}, 2 / 3 \; ...
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1365
GATE ECE 2007 | Question: 30
In the circuit shown, $V_{C}$ is $0$ volts at $t=0 \; \mathrm{sec}$. For $t>0$, the capacitor current $i_{c}(t)$, where $t$ is in seconds, is given by $0.50 \exp (-25 t) \; \mathrm{mA}$ $0.25 \exp (-25 t) \; \mathrm{mA}$ $0.50 \exp (-12.5 t) \; \mathrm{mA}$ $0.25 \exp (-6.25 t) \; \mathrm{mA}$
In the circuit shown, $V_{C}$ is $0$ volts at $t=0 \; \mathrm{sec}$. For $t>0$, the capacitor current $i_{c}(t)$, where $t$ is in seconds, is given by$0.50 \exp (-25 t) \...
1 votes
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1366
GATE ECE 2007 | Question: 31
In the $\text{AC}$ network shown in the figure, the phasor voltage $\text{V}_{\text{AB}}$ (in Volts) is $0$ $5 \angle 30^{\circ}$ $12.5 \angle 30^{\circ}$ $17 \angle 30^{\circ}$
In the $\text{AC}$ network shown in the figure, the phasor voltage $\text{V}_{\text{AB}}$ (in Volts) is$0$$5 \angle 30^{\circ}$$12.5 \angle 30^{\circ}$$17 \angle 30^{\cir...
1 votes
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1368
GATE ECE 2007 | Question: 33
Group I lists four types of $p-n$ ... $\mathrm{P}-2, \mathrm{Q}-1, \mathrm{R}-2, \mathrm{S}-2$
Group I lists four types of $p-n$ junction diodes. Match each device in Group I with one of the options in Group II to indicate the bias condition of that device in its n...
1 votes
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1369
GATE ECE 2007 | Question: 34
The $\text{DC}$ current gain ($\beta$ ) of a $\text{BJT}$ is $50.$ Assuming that the emitter injection efficiency is $0.995$, the base transport factor is $0.980$ $0.985$ $0.990$ $0.995$
The $\text{DC}$ current gain ($\beta$ ) of a $\text{BJT}$ is $50.$ Assuming that the emitter injection efficiency is $0.995$, the base transport factor is$0.980$$0.985$$0...
1 votes
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1370
GATE ECE 2007 | Question: 35
Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II. ... $\text{P-3, Q-4, R-1, S-2}$ $\text{P-3, Q-2, R-1, S-4}$
Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II.$$\begin{array}{ll} \textbf{Group I} & \qqua...
1 votes
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1371
GATE ECE 2007 | Question: 36
For the $\text{Op-Amp}$ circuit shown in the figure, $V_{o}$ is $-2 \mathrm{~V}$ $-1 \mathrm{~V}$ $-0.5 \mathrm{~V}$ $0.5 \mathrm{~V}$
For the $\text{Op-Amp}$ circuit shown in the figure, $V_{o}$ is$-2 \mathrm{~V}$$-1 \mathrm{~V}$$-0.5 \mathrm{~V}$$0.5 \mathrm{~V}$
1 votes
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1372
GATE ECE 2007 | Question: 37
For the $\text{BJT}$ circuit shown, assume that the $\beta$ of the transistor is very large and $V_{B E}=0.7 \mathrm{~V}$. The mode of operation of the $\text{BJT}$ is cut-off saturation normal active reverse active
For the $\text{BJT}$ circuit shown, assume that the $\beta$ of the transistor is very large and $V_{B E}=0.7 \mathrm{~V}$. The mode of operation of the $\text{BJT}$ iscut...
1 votes
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1376
GATE ECE 2007 | Question: 41
The Boolean expression $Y=\overline{A} \;\overline{B}\; \overline{C} D+\overline{A} B C \overline{D}+A \overline{B}\; \overline{C} D+A B \overline{C}\; \overline{D}$ ... $Y=\overline{A} B C \overline{D}+\overline{B}\; \overline{C} D+A B \overline{C} \;\overline{D}$
The Boolean expression $Y=\overline{A} \;\overline{B}\; \overline{C} D+\overline{A} B C \overline{D}+A \overline{B}\; \overline{C} D+A B \overline{C}\; \overline{D}$ can ...
1 votes
1 answer
1379
GATE ECE 2007 | Question: 44
The following binary values were applied to the $\mathrm{X}$ and $\mathrm{Y}$ inputs of the NAND latch shown in the figure in the sequence indicated below: \[ \mathrm{X}=0, \mathrm{Y}=1 ; \quad \mathrm{X}=0, \mathrm{Y}=0 ; \quad \mathrm{X}=1, \mathrm{Y}=1 \ ...
The following binary values were applied to the $\mathrm{X}$ and $\mathrm{Y}$ inputs of the NAND latch shown in the figure in the sequence indicated below:\[ \mathrm{X}=0...
1 votes
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1380
GATE ECE 2007 | Question: 45
For the circuit shown, the counter state $\left(\mathrm{Q}_{1} \mathrm{Q}_{0}\right)$ follows the sequence $00,01,10,11,00 \ldots$ $00,01,10,00,01 \ldots$ $00,01,11,00,01 \ldots$ $00,10,11,00,10 \ldots$
For the circuit shown, the counter state $\left(\mathrm{Q}_{1} \mathrm{Q}_{0}\right)$ follows the sequence$00,01,10,11,00 \ldots$$00,01,10,00,01 \ldots$$00,01,11,00,01 \l...
1 votes
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1382
GATE ECE 2007 | Question: 47
The $\text{3-dB}$ bandwidth of the low-pass signal $e^{-t} u(t)$, where $u(t)$ is the unit step function, is given by $\frac{1}{2 \pi} \mathrm{Hz}$ $\frac{1}{2 \pi} \sqrt{\sqrt{2}-1} \mathrm{~Hz}$ $\infty$ $1 \mathrm{~Hz}$
The $\text{3-dB}$ bandwidth of the low-pass signal $e^{-t} u(t)$, where $u(t)$ is the unit step function, is given by$\frac{1}{2 \pi} \mathrm{Hz}$$\frac{1}{2 \pi} \sqrt{\...
1 votes
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1383
GATE ECE 2007 | Question: 48
A Hilbert transformer is a non-linear system non-causal system time-varying system low-pass system
A Hilbert transformer is anon-linear systemnon-causal systemtime-varying systemlow-pass system
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1384
GATE ECE 2007 | Question: 49
The frequency response of a linear, time-invariant system is given by $H(f)=\dfrac{5}{1+j 10 \pi f}$. The step response of the system is $5\left(1-e^{-5 t}\right) u(t)$ $5\left(1-e^{-\frac{t}{5}}\right) u(t)$ $\frac{1}{5}\left(1-e^{-5 t}\right) u(t)$ $\frac{1}{5}\left(1-e^{-\frac{t}{5}}\right) u(t)$
The frequency response of a linear, time-invariant system is given by $H(f)=\dfrac{5}{1+j 10 \pi f}$. The step response of the system is$5\left(1-e^{-5 t}\right) u(t)$$5\...
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1386
GATE ECE 2007 | Question: 51
The $z$-transform $X[z]$ of a sequence $x[n]$ is given by $X[z]=\dfrac{0.5}{1-2 z^{-1}}$. It is given that the region of convergence of $X[z]$ includes the unit circle. The value of $x[0]$ is $-0.5$ $0$ $0.25$ $0.5$
The $z$-transform $X[z]$ of a sequence $x[n]$ is given by $X[z]=\dfrac{0.5}{1-2 z^{-1}}$. It is given that the region of convergence of $X[z]$ includes the unit circle. T...
1 votes
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1387
GATE ECE 2007 | Question: 52
A control system with a $\text{PD}$ controller is shown in the figure. If the velocity error constant $K_{v}=1000$ and the damping ratio $\zeta=0.5$, then the values of $K_{P}$ and $K_{D}$ are $K_{P}=100, K_{D}=0.09$ $K_{P}=100, K_{D}=0.9$ $K_{P}=10, K_{D}=0.09$ $K_{P}=10, K_{D}=0.9$
A control system with a $\text{PD}$ controller is shown in the figure. If the velocity error constant $K_{v}=1000$ and the damping ratio $\zeta=0.5$, then the values of $...
1 votes
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1388
GATE ECE 2007 | Question: 53
The transfer function of a plant is $T(s)=\dfrac{5}{(s+5)\left(s^{2}+s+1\right)}$. The second-order approximation of $T(s)$ using dominant pole concept is $\frac{1}{(s+5)(s+1)}$ $\frac{5}{(s+5)(s+1)}$ $\frac{5}{s^{2}+s+1}$ $\frac{1}{s^{2}+s+1}$
The transfer function of a plant is $T(s)=\dfrac{5}{(s+5)\left(s^{2}+s+1\right)}$. The second-order approximation of $T(s)$ using dominant pole concept is$\frac{1}{(s+5)(...
1 votes
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1389
GATE ECE 2007 | Question: 54
The open-loop transfer function of a plant is given as $G(s)=\dfrac{1}{s^{2}-1}$. If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is $\frac{10(s-1)}{s+2}$ $\frac{10(s+4)}{s+2}$ $\frac{10(s+2)}{s+10}$ $\frac{2(s+2)}{s+10}$
The open-loop transfer function of a plant is given as $G(s)=\dfrac{1}{s^{2}-1}$. If the plant is operated in a unity feedback configuration, then the lead compensator th...
1 votes
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1390
GATE ECE 2007 | Question: 55
A unity feedback control system has an open-loop transfer function $G(s)=\dfrac{K}{s\left(s^{2}+7 s+12\right)}$. The gain $K$ for which $s=-1+j 1$ will lie on the root locus of this system is $4$ $5.5$ $6.5$ $10$
A unity feedback control system has an open-loop transfer function $G(s)=\dfrac{K}{s\left(s^{2}+7 s+12\right)}$. The gain $K$ for which $s=-1+j 1$ will lie on the root lo...
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1391
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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1393
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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1394
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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1395
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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1396
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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