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1601
GATE ECE 2011 | Question: 12
The value of the integral $\oint_c \frac{-3 z+4}{\left(z^2+4 z+5\right)} d z$ where $c$ is the circle $|z|=1$ is given by $0$ $1 / 10$ $4 / 5$ $1$
The value of the integral $\oint_c \frac{-3 z+4}{\left(z^2+4 z+5\right)} d z$ where $c$ is the circle $|z|=1$ is given by$0$$1 / 10$$4 / 5$$1$
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1602
GATE ECE 2011 | Question: 40
The output of a $3$-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all states of the counter to be unset initially. The waveform which represents the D/A converter output $\mathrm{V}_{\mathrm{o}}$ is
The output of a $3$-stage Johnson (twisted-ring) counter is fed to a digital-to-analog (D/A) converter as shown in the figure below. Assume all states of the counter to b...
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1603
GATE ECE 2011 | Question: 17
A system is defined by its impulse response $h(n)=2^n u(n-2)$. The system is stable and causal causal but not stable stable but not causal unstable and noncausal
A system is defined by its impulse response $h(n)=2^n u(n-2)$. The system isstable and causalcausal but not stablestable but not causalunstable and noncausal
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1604
GATE ECE 2011 | Question: 28
The block diagram of a system with one input $u$ and two outputs $y_1$ and $y_2$ is given below. A state space model of the above system in terms of the state vector $\underline{x}$ ...
The block diagram of a system with one input $u$ and two outputs $y_1$ and $y_2$ is given below.A state space model of the above system in terms of the state vector $\und...
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1605
GATE ECE 2011 | Question: 24
Consider a closed surface $S$ surrounding a volume V. If $\vec{r}$ is the position vector of a point inside $S$, with $\hat{n}$ the unit normal on $S$, the value of the integral $\unicode{x222F}_S \; 5 \vec{r} . \hat{n} d S$ is $3 \mathrm{V}$ $5 \mathrm{V}$ $10 \mathrm{V}$ $15 \mathrm{V}$
Consider a closed surface $S$ surrounding a volume V. If $\vec{r}$ is the position vector of a point inside $S$, with $\hat{n}$ the unit normal on $S$, the value of the i...
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1607
GATE ECE 2011 | Question: 51
The input-output transfer function of a plant $H(s)=\frac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below. The gain margin of the system under closed loop unity negative feedback is $0 \mathrm{~dB}$ $20 \mathrm{~dB}$ $26 \mathrm{~dB}$ $46 \mathrm{~dB}$
The input-output transfer function of a plant $H(s)=\frac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below.Th...
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1609
GATE ECE 2011 | Question: 3
The differential equation $100 \dfrac{d^2 y}{d t^2}-20 \dfrac{d y}{d t}+y=x(t)$ describes a system with an input $x(t)$ and an output $y(t)$. The system, which is initially relaxed, is excited by a unit step input. The output $y(t)$ can be represented by the waveform
The differential equation $100 \dfrac{d^2 y}{d t^2}-20 \dfrac{d y}{d t}+y=x(t)$ describes a system with an input $x(t)$ and an output $y(t)$. The system, which is initial...
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1610
GATE ECE 1991 | Question 2
(a) Find the Laplace transform of the waveform $x(t)$ shown in figure. (b) The network shown in figure is initially under steady state condition with the switch in position $1$. The switch is moved from position $1$ to position $2$ at $t \neq$ 0 . Calculate the current $i(t)$ through $R_1$ after switching.
(a) Find the Laplace transform of the waveform $x(t)$ shown in figure.(b) The network shown in figure is initially under steady state condition with the switch in positio...
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1611
GATE ECE 1991 | Question 1.12
A linear second order single input continuous time system is described by the following set of differential equations ... and $u(t)$ is the control variable. The system is: controllable and stable controllable but unstable uncontrollable and unstable uncontrollable and stable
A linear second order single input continuous time system is described by the following set of differential equations$$ \begin{aligned} &x_1(t)=-2 x_1(t)+4 x_2(t) \\ &x_2...
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1612
GATE ECE 1991 | Question 1.21
In figure, both transistors are identical and have a high value of beta. Take the $dc$ base-emitter voltage drop as $0.7$ volt and $\mathrm{KT} / \mathrm{q}=25 \; \mathrm{mV}$. The small signal low frequency voltage gain $\left(V_o / V_i\right)$ is equal to__________.
In figure, both transistors are identical and have a high value of beta. Take the $dc$ base-emitter voltage drop as $0.7$ volt and $\mathrm{KT} / \mathrm{q}=25 \; \mathrm...
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1615
GATE ECE 1991 | Question 10
(a) A signal $A \sin \omega_m \mathrm{t}$ is input to a square - law device $\left(e_0-e_{m 2}\right)$. The output of which is given to an $\mathrm{FM}$ ... is the carrier frequency. Determine the value of gain $\mathrm{K}$ so that the output is a suppressed carrier $\text{DSB}$ signal.
(a) A signal $A \sin \omega_m \mathrm{t}$ is input to a square - law device $\left(e_0-e_{m 2}\right)$. The output of which is given to an $\mathrm{FM}$ modulator as the ...
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1616
GATE ECE 1991 | Question 4
The current $I$ in a forward biased $P^{+} N$ junction shown in figure (a) is entirely due to diffusion of holes from $x=0$ to $x=L$. The injected hole concentration distribution in the $m$ ... coefficient holes is $12 \mathrm{~cm}^2 / \mathrm{sec}$. (b) The velocity of holes in the $n$-region at $x=0$.
The current $I$ in a forward biased $P^{+} N$ junction shown in figure (a) is entirely due to diffusion of holes from $x=0$ to $x=L$. The injected hole concentration dist...
1 votes
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1617
GATE ECE 2011 | Question: 55
In the circuit shown below, assume that the voltage drop across a forward biased diode is $0.7 \mathrm{~V}$. The thermal voltage $\mathrm{V}_{\mathrm{t}}=\mathrm{kT} / \mathrm{q}=25 \mathrm{mV}$ ... $2 \cos (\omega \mathrm{t}) \; \mathrm{mV}$ $22 \cos (\omega \mathrm{t}) \; \mathrm{mV}$
In the circuit shown below, assume that the voltage drop across a forward biased diode is $0.7 \mathrm{~V}$. The thermal voltage $\mathrm{V}_{\mathrm{t}}=\mathrm{kT} / \m...
0 votes
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1618
GATE ECE 1991 | Question 11
(a) A Gaussian random variable with zero mean and variance $\sigma$ ... the auto correlation function $R_y(i)$ and power spectral density $S_y(\omega)$ of $Y(t)$ in terms of those of $X(t)$.
(a) A Gaussian random variable with zero mean and variance $\sigma$ is input to a limiter with input output characteristic given by$$ \begin{array}{ll} e_{\text {out }}=e...
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1619
GATE ECE 1991 | Question 9
The four variable function $\mathrm{f}$ is given in terms of min-terms as: $ f(A, B, C, D)=\sum m(2,3,8,10,11,12,14,15) . $ Using the $K$-map minimize the function in the sum of products form. Also, given the realization using only two-input $\text{NAND}$ gates.
The four variable function $\mathrm{f}$ is given in terms of min-terms as:$$ f(A, B, C, D)=\sum m(2,3,8,10,11,12,14,15) . $$Using the $K$-map minimize the function in the...
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1620
GATE ECE 1991 | Question 5
It is required to use a $\text{JFET}$ of figure as linear resistor. The parameters of the $\text{JFET}$ ... are negligible. Determine the minimum value of the linear resistor which can be realized using this $\text{JFET}$ without forward biasing the gate junctions.
It is required to use a $\text{JFET}$ of figure as linear resistor. The parameters of the $\text{JFET}$ are as follows: $$ \mathrm{W}=100 \mu \mathrm{m}, \mathrm{L}=\mu \...
1 votes
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1621
GATE ECE 2011 | Question: 50
The input-output transfer function of a plant $H(s)=\frac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below. The signal flow graph that DOES NOT model the plant $\operatorname{transfer~function~} H(s)$ is
The input-output transfer function of a plant $H(s)=\frac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below.Th...
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1622
GATE ECE 1991 | Question 12
A uniform plane electromagnetic wave traveling in free space enters into a lossless medium at normal incidence. In the medium its velocity reduces by $50 \%$ and in free space sets up a standing wave having a reflection coefficient of $0.125$. Calculate the permeability and the permittivity of the medium.
A uniform plane electromagnetic wave traveling in free space enters into a lossless medium at normal incidence. In the medium its velocity reduces by $50 \%$ and in free ...
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1623
GATE ECE 1991 | Question 6
In figure, the operational amplifier is ideal and its output can swing between $-15$ and $+15$ volts. The input $v_\rho$ which is zero for $t<0$, is switched to $5$ volts at the instant $\mathrm{t}=0$. Given that the output $v_0$ is ... $v_0$ and $v_i$. You must give the values of important parameters of this sketch.
In figure, the operational amplifier is ideal and its output can swing between $-15$ and $+15$ volts. The input $v_\rho$ which is zero for $t<0$, is switched to $5$ volts...
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1624
GATE ECE 1991 | Question 7
In figure, the operational amplifiers are ideal and their output can swing between $-15$ and $+15$ volts. Sketch on same diagram, the waveform of voltages $V_1$ and $V_2$ as a function of time. You must give the values of important parameters of this sketch.
In figure, the operational amplifiers are ideal and their output can swing between $-15$ and $+15$ volts. Sketch on same diagram, the waveform of voltages $V_1$ and $V_2$...
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1625
GATE ECE 1991 | Question 3
The open loop transfer function of a feedback control system incorporating a dead time element is given by $ G(s)=\frac{K e^{-T s}}{s(s+1)} $ Where $\mathrm{K}>0$, and $\mathrm{T}>0$ are variable scalar parameters. (a) For a ... $\omega_0$ is the smallest value of $\omega$ satisfying the equation $\omega=\cot \omega T$
The open loop transfer function of a feedback control system incorporating a dead time element is given by$$ G(s)=\frac{K e^{-T s}}{s(s+1)} $$Where $\mathrm{K}>0$, and $\...
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1626
GATE ECE 1991 | Question 8
The program given below is run on an 8085 based microcomputer system. Determine the contents of the registers: $\mathrm{PC}, \mathrm{SP}, \mathrm{B}, \mathrm{C}, \mathrm{H}, \mathrm{L}$ after a half instruction is executed.
The program given below is run on an 8085 based microcomputer system. Determine the contents of the registers: $\mathrm{PC}, \mathrm{SP}, \mathrm{B}, \mathrm{C}, \mathrm{...
1 votes
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1627
GATE ECE 2011 | Question: 54
In the circuit shown below, assume that the voltage drop across a forward biased diode is $0.7 \mathrm{~V}$. The thermal voltage $\mathrm{V}_{\mathrm{t}}=\mathrm{kT} / \mathrm{q}=25 \mathrm{mV}$ ... $1 \mathrm{~mA}$ $1.28 \mathrm{~mA}$ $1.5 \mathrm{~mA}$ $2 \mathrm{~mA}$
In the circuit shown below, assume that the voltage drop across a forward biased diode is $0.7 \mathrm{~V}$. The thermal voltage $\mathrm{V}_{\mathrm{t}}=\mathrm{kT} / \m...
1 votes
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1629
GATE ECE 2011 | Question: 47
A numerical solution of the equation $f(x)=x+\sqrt{x}-3=0$ can be obtained using Newton-Raphson method. If the starting value is $x=2$ for the iteration, the value of $x$ that is to be used in the next step is $0.306$ $0.739$ $1.694$ $2.306$
A numerical solution of the equation $f(x)=x+\sqrt{x}-3=0$ can be obtained using Newton-Raphson method. If the starting value is $x=2$ for the iteration, the value of $x$...
1 votes
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1631
GATE ECE 2011 | Question: 46
In the circuit shown below, the current $\text{I}$ is equal to $1.4 \angle 0^{\circ} \; \mathrm{A}$ $2.0 \angle 0^{\circ} \; \mathrm{A}$ $2.8 \angle 0^{\circ} \; \mathrm{A}$ $3.2 \angle 0^{\circ} \; \mathrm{A}$
In the circuit shown below, the current $\text{I}$ is equal to$1.4 \angle 0^{\circ} \; \mathrm{A}$$2.0 \angle 0^{\circ} \; \mathrm{A}$$2.8 \angle 0^{\circ} \; \mathrm{A}$...
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1632
GATE ECE 2011 | Question: 43
An input $\mathrm{x(t)}=\exp (-2 \mathrm{t)u(t})+\delta(\mathrm{t}-6)$ is applied to an LTI system with impulse response $\mathrm{h(t)=u(t})$. The output is $[1-\exp (-2 \mathrm{t)] u(t)+u(t}+6)$ $[1-\exp (-2 \mathrm{t)] u(t)+u(t}-6)$ $0.5[1-\exp (-2 \mathrm{t)] u(t)+u(t}+6)$ $0.5[1-\exp (-2 \mathrm{t)] u(t)+u(t}-6)$
An input $\mathrm{x(t)}=\exp (-2 \mathrm{t)u(t})+\delta(\mathrm{t}-6)$ is applied to an LTI system with impulse response $\mathrm{h(t)=u(t})$. The output is$[1-\exp (-2 \...
1 votes
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1635
GATE ECE 2011 | Question: 48
The channel resistance of an $\text{N}$-channel $\text{JFET}$ shown in the figure below is $600 \; \Omega$ when the full channel thickness $\left(\mathrm{t}_{\mathrm{ch}}\right)$ of $10 \; \mu \mathrm{m}$ ... $480 \; \Omega$ $600 \; \Omega$ $750 \; \Omega$ $1000 \; \Omega$
The channel resistance of an $\text{N}$-channel $\text{JFET}$ shown in the figure below is $600 \; \Omega$ when the full channel thickness $\left(\mathrm{t}_{\mathrm{ch}}...
1 votes
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1637
GATE ECE 2011 | Question: 45
If $F(s)=L[f(t)]=\dfrac{2(s+1)}{s^2+4 s+7}$ then the initial and final values of $f(t)$ are respectively $0,2$ $2,0$ $0, 2 / 7$ $2 / 7,0$
If $F(s)=L[f(t)]=\dfrac{2(s+1)}{s^2+4 s+7}$ then the initial and final values of $f(t)$ are respectively$0,2$$2,0$$0, 2 / 7$$2 / 7,0$
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1638
GATE ECE 2022 | Question: 1
Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}$ denote the unit vectors along the $x - $axis and the $y - $ ... $0$ $1$ $8 + 2 \pi$ $ - 1$
Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}...
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