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GATE2020EC: 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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GATE2020EC: 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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GATE2020EC: 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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GATE2020EC: 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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GATE2020EC: 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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GATE2020EC: 30
For the given circuit, which one of the following is correct state equation? ...
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GATE2020EC: 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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8
GATE2020EC: 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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9
GATE2019 EC: 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 $1\: A$ ... figure), 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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10
GATE2019 EC: 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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11
GATE2019 EC: 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 steadystate 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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GATE2019 EC: 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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13
GATE201639
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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14
GATE2016313
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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15
GATE2016332
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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16
GATE2016347
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 state variables ... $c(t)=x_1(t)$, then the system is controllable but not observable observable but not controllable both controllable and observable neither controllable nor observable
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17
GATE2016348
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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18
GATE201627
The switch has been in position $1$ for a long time and abruptly changes to position $2$ at $t = 0$. If time $t$ is in seconds, the capacitor voltage $V_{C}$ (in volts) for $t > 0$ is given by $4\left ( 1 \text{ exp }\left ( t/0.5 \right ) \right )$ ... $4\left ( 1\text{ exp }\left ( t/0.6 \right ) \right )$ $10 6 \text{ exp }\left ( t/0.6 \right )$
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19
GATE201628
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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20
GATE2016232
A continuoustime filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discretetime filter with transfer function $G\left ( z\right )= \frac{2z^{2}0.5032 \: z}{z^{2}0.5032 \: z+k}$ so ... filter, 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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21
GATE2016234
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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22
GATE2016235
A voltage $V_{G}$ is applied across a $MOS$ capacitor with metal gate and $p$type silicon substrate at $T=300$ $K$. The inversion carrier density (in number of carriers per unit area) for $V_{G}= 0.8$ $V$ is $2\times 10^{11} cm^{2}.$ For $V_{G}= 1.3$ $V$, the inversion carrier ... $6.0\times 10^{11}cm^{2}$ $7.2\times 10^{11}cm^{2}$ $8.4\times 10^{11}cm^{2}$
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GATE2016253
A lossless microstrip transmission line consists of a trace of width $w$. It is drawn over a pratically infinite ground plane and is separated by a dielectric slab of thickness $t$ and relative permittivity $\varepsilon _{r}> 1.$ The inductance per unit length and the characteristic ... $Z_{0}< \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}t}}$
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24
GATE201614
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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25
GATE201619
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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26
GATE2016130
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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27
GATE2016131
A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form $\sum_{k=1}^{3} a_k\cos(k\omega_0t) ,\text{where } \thinspace a_k\neq 0, \omega_0\neq0$ The ... $\sum_{k=1}^{3} a_k\cos(k\omega_0t+\phi_k) \\$ $\sum_{k=1}^{2} a_k\cos(k\omega_0t+\phi_k)$
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GATE2016133
An AC voltage source $V = 10 \sin(t)$ volts is applied to the following network. Assume that $R_1 = 3 k\Omega$, $R_2 = 6 k\Omega$ and $R_3 = 9k\Omega$, and that the diode is ideal. RMS current $I_{rms}$(in mA) through the diode is _______
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29
GATE2016134
In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor $R$ is _______
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30
GATE2016145
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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31
GATE2016146
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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32
GATE2016147
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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33
GATE201536
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $ab$ is _______.
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34
GATE2015314
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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35
GATE2015321
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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36
GATE2015331
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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37
GATE2015332
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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38
GATE2015343
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is $4\left(\dfrac{1}{3}\right)^{n}\:u[n]5\left(\dfrac{2}{3}\right)^{n}\:u[n]$ ... $5\left(\dfrac{2}{3}\right)^{n}\:u[n]5\left(\dfrac{1}{3}\right)^{n}\:u[n]$
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39
GATE2015346
The position control of a DC servomotor is given in the figure. The values of the parameters are $K_{T}=1 \: Nm/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kgm^{2},B=1Nm/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steadystate position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.
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40
GATE2015347
For the system shown in the figure, $s=2.75$ lies on the root locus if $K$ is _______.
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