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Recent questions and answers in Network Solution Methods
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GATE ECE 2020  Question: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$
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Feb 13, 2020
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GATE ECE 2020  Question: 15
In the given circuit, the twoport network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.
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GATE ECE 2020  Question: 16
The current in the $\text{RL}$circuit shown below is $i\left ( t \right )=10\cos\left ( 5t\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.
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Feb 13, 2020
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GATE ECE 2020  Question: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steadystate output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
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Feb 13, 2020
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GATE ECE 2020  Question: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.$ The value of $K$, for which the system is marginally stable, is ___________.
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GATE ECE 2020  Question: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle 96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle23.63^{\circ}A$
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GATE ECE 2020  Question: 30
For the given circuit, which one of the following is correct state equation? ...
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GATE ECE 2020  Question: 37
Using the incremental low frequency smallsignal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$
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9
GATE ECE 2020  Question: 49
A system with transfer function $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5 \cos3t$. The steady state output of the system is $\dfrac{1}{\sqrt{10}}\cos\left ( 3t1.892 \right )$. The value of $a$ is _______.
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10
GATE ECE 2020  Question: 53
The transfer function of a stable discretetime $\text{LTI}$ system is $H\left ( z \right )=\dfrac{K\left ( z\alpha \right )}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $\mid \alpha \mid > 1$, for which the magnitude response of the system is constant over all frequencies, is ___________.
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11
GATE ECE 2020  Question: 55
Consider the following closed loop control system where $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady state error for a unit ramp input is $0.1$, then the value of $K$ is ______________.
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GATE ECE 2019  Question: 4
Consider the twoport resistive network shown in the figure. When an excitation of $5\: V$ is applied across Port $1$, and Port $2$ is shorted, the current through the short circuit at Port $2$ is measured to be $1\: A$ ... ), what is the current through the short circuit at Port $1?$ $0.5\: A$ $1\: A$ $2\: A$ $2.5\: A$
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Feb 12, 2019
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GATE ECE 2019  Question: 5
Let $Y(s)$ be the unitstep response of a causal system having a transfer function $G(s)= \dfrac{3s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)$ $u(t)$
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GATE ECE 2019  Question: 30
In the circuit shown, if $v(t)=2 \sin(1000\: t)$ volts, $R=1\:k \Omega$ and $C=1\:\mu F,$ then the steadystate current $i(t)$, milliamperes (mA), is $\sin(1000\: t)+ \cos(1000\: t)$ $2 \sin(1000\: t) +2 \cos(1000\: t)$ $3 \sin(1000\: t) + \cos(1000\: t)$ $\sin(1000\: t) +3 \cos(1000\: t)$
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15
GATE ECE 2019  Question: 31
Consider a causal secondorder system with the transfer function $G(s)=\dfrac{1}{1+2s+s^{2}}$ with a unitstep $R(s)=\dfrac{1}{s}$ as an input. Let $C(s)$ be the corresponding output. The time taken by the system output $c(t)$ to reach $94\%$ of its ... value $\underset{t\rightarrow \infty}{\lim}\:c(t),$ rounded off to two decimal places, is $5.25$ $4.50$ $3.89$ $2.81$
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GATE ECE 2019  Question: 32
The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\dfrac{Y(s)}{X(s)}$ is $H(s)=\frac{s^{2}+1}{s^{3}+s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{s^{3}+2s^{2}+s+1}$ $H(s)=\frac{s+1}{s^{2}+s+1}$ $H(s)=\frac{s^{2}+1}{2s^{2}+1}$
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17
GATE ECE 2019  Question: 42
Consider a unity feedback system, as in the figure shown, with an integral compensator $\dfrac{K}{s}$ and openloop transfer function $G(s)=\dfrac{1}{s^{2}+3s+2}$ where $K>0.$ The positive value of $K$ for which there are exactly two poles of the unity feedback system on the $j\omega$ axis is equal to ________ (rounded off to two decimal places).
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18
GATE ECE 2016 Set 3  Question: 7
If the signal $x(t) = \large \frac{\sin(t)}{\pi t}$*$\large \frac{\sin(t)}{\pi t}$ with $*$ denoting the convolution operation, then $x(t)$ is equal to $\large\frac{\sin(t)}{\pi t}$ $\large\frac{\sin(2t)}{2\pi t}$ $\large\frac{2\sin(t)}{\pi t}$ $\bigg(\frac{\sin(t)}{\pi t}\bigg)^2$
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Mar 28, 2018
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19
GATE ECE 2016 Set 3  Question: 9
In the RLC circuit shown in the figure, the input voltage is given by $v_i(t) = 2\cos (200t) + 4\sin (500t).$ The output voltage $v_o(t)$ is $\cos (200t) + 2\sin (500t)$ $2\cos (200t) + 4\sin (500t)$ $\sin (200t) + 2\cos (500t)$ $2\sin (200t) + 4\cos (500t)$
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20
GATE ECE 2016 Set 3  Question: 13
The diodes $D1$ and $D2$ in the figure are ideal and the capacitors are identical. The product $RC$ is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage $V_o$(in volt) at the steady state is _______
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GATE ECE 2016 Set 3  Question: 32
Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\;\Omega$ resistor suddenly burns out, resulting in an open circuit. The current $i(t)$ (in ampere) at $t=0^+$ is _______
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22
GATE ECE 2016 Set 3  Question: 34
The $z$parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the twoport network shown is $\begin{bmatrix} 2 &2\\2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 2 &2\\2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 9 &3\\6 &9 \end{bmatrix} \\$ $\begin{bmatrix} 9 &3\\6 &9 \end{bmatrix}$
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23
GATE ECE 2016 Set 3  Question: 42
In the circuit shown in the figure, transistor $M1$ is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation $\lambda$ to be zero,the small signal input pole frequency (in $kHz$) is _________
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24
GATE ECE 2016 Set 3  Question: 47
A secondorder linear timeinvariant system is described by the following state equations $\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$ $\frac{d}{dt}x_2(t)+x_2(t)=u(t)$ where $x_1(t)$ and $x_2(t)$ are the two ... , then the system is controllable but not observable observable but not controllable both controllable and observable neither controllable nor observable
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25
GATE ECE 2016 Set 3  Question: 48
The forwardpath transfer function and the feedbackpath transfer function of a single loop negative feedback control system are given as $G(s)=\frac{K(s+2)}{s^2+2s+2}\;\text{and}\hspace{0.3cm}H(s)=1,$ respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is _________
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26
GATE ECE 2016 Set 2  Question: 8
The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________
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GATE ECE 2016 Set 2  Question: 32
A continuoustime filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ ... sampled at $2$ $Hz$, is identical at the sampling instants to the impulse response of the discrete timefilter. The value of $k$ is _________
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28
GATE ECE 2016 Set 2  Question: 34
The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. The steady state magnitude of the capacitor voltage $V_{c}$ (in volts) is ______
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29
GATE ECE 2016 Set 1  Question: 4
Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$? The solutions have neither maxima nor minima anywhere except at the boundaries. The solutions are not separable in the coordinates. The solutions are not continuous. The solutions are not dependent on the boundary conditions.
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30
GATE ECE 2016 Set 1  Question: 9
Consider a twoport network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then $T^{1} = T$ $T^2 = T$ Determinant $(T) = 0$ Determinant $(T) = 1$
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31
GATE ECE 2016 Set 1  Question: 23
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2000 \pi t$. The value of the modulation index is _________
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32
GATE ECE 2016 Set 1  Question: 30
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is $F(S) = \frac{1}{1+e^{sT/2}} \\$ $F(S) =\frac{1}{s(1+e^{sT/2})} \\$ $F(S) = \frac{1}{s(1e^{sT})} \\$ $F(S) = \frac{1}{1e^{sT}}$
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33
GATE ECE 2016 Set 1  Question: 45
The openloop transfer function of a unityfeedback control system is $G(s)= \frac{K}{s^2+5s+5}$. The value of $K$ at the breakaway point of the feedback contol system’s rootlocus plot is _________
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34
GATE ECE 2016 Set 1  Question: 46
The openloop transfer function of a unity feedback control system is given by $G(s)= \frac{K}{s(s+2)}$. For the peak overshoot of the closedloop system to a unit step input to be $10 \%$, the value of $K$ is _________
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35
GATE ECE 2016 Set 1  Question: 47
The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s 2$. The number of zeroes in the right half of the $s$plane is _________
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36
GATE ECE 2015 Set 3  Question: 6
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $ab$ is _______.
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37
GATE ECE 2015 Set 3  Question: 14
The circuit shown consists of JK flipflops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is a modulo$5$ binary up counter a modulo$6$ binary down counter a modulo$5$ binary down counter a modulo$6$ binary up counter
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38
GATE ECE 2015 Set 3  Question: 21
The transfer function of a firstorder controller is given as $G_{C}(s) = \dfrac{K(s+a)}{s+b}$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is $a<b$ $a>b$ $K<ab$ $K>ab$
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39
GATE ECE 2015 Set 3  Question: 31
The $ABCD$ parameters of the following $2$port network are $\begin{bmatrix}3.5 + j2 & 20.5 \\ 20.5 & 3.5j2 \end{bmatrix} \\$ $\begin{bmatrix}3.5 +j2 & 30.5 \\ 0.5&3.5j2 \end{bmatrix} \\$ $\begin{bmatrix}10 &2+j0 \\2+j0 &10 \end{bmatrix} \\$ $\begin{bmatrix}7+j4 &0.5 \\ 30.5&7j4 \end{bmatrix} $
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GATE ECE 2015 Set 3  Question: 32
A network is described by the state model as $\dot{x_{1}}=2x_{1}x_{2}+3u \\ \dot{x_{2}}=4x_{2}u \\ y=3x_{1}2x_{2}$ The transfer function $H(s)\left(=\dfrac{Y(s)}{U(s)}\right)$ is $\dfrac{11s+35}{(s2)(s+4)} \\$ $\dfrac{11s35}{(s2)(s+4)} \\$ $\dfrac{11s+38}{(s2)(s+4)} \\$ $\dfrac{11s38}{(s2)(s+4)}$
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