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GATE2019 EE: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
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GATE2019 EE: 38
The line currents of a threephase four wire system are square waves with amplitude of $100$ A. These three currents are phase shifted by $120^{\circ}$ with respect to each other. The rms value of neutral current is $0$ A $\frac{100}{\sqrt{3}}$ A $100$ A $300$ A
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GATE2019 EE: 37
A DCDC buck converter operates in continuous conduction mode. It has $48$ V input voltage, and it feeds a resistive load of $24 \: \Omega$. The switching frequency of the converter is $250$ Hz. If switchon duration is $1$ ms, the load power is $6$ W $12$ W $24$ W $48$ W
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GATE2019 EE: 36
In the circuit shown below, $X$ and $Y$ are digital inputs, and $Z$ is a digital output. The Equivalent circuit is a NAND gate NOR gate XOR gate XNOR gate
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GATE2019 EE: 35
The output expression for the Karnaugh map shown below is $Q \bar{R} +S$ $Q \bar{R} + \bar{S}$ $QR+S$ $Q R +\bar{S}$
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GATE2019 EE: 34
In the circuit below, the operational amplifier is ideal. If $V_1=10$ mV and $V_2=50$ mV, he output voltage $(V_{\text{out}})$ is $100$ mV $400$ mV $500$ mV $600$ mV
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GATE2019 EE: 33
The enhancement type MOSFET in the circuit below operates according to the square law. $\mu _nC_{ox} =100 \: \mu A /V^2$, the threshold voltage $(V_T)$ is $500$ mV. Ignore channel length modulation. The output voltage $V_{\text{out}}$ is $100$ mV $500$ mV $600$ mV $2$ V
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GATE2019 EE: 32
A moving coil instrument having a resistance of $10 \: \Omega$, gives a fullscale deflection when the current is $10$ mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to $100$ V? $9 \: \Omega$ $99 \: \Omega$ $990 \: \Omega$ $9990 \: \Omega$
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GATE2019 EE: 31
Consider a statevariable model of a system $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ \alpha &  2 \beta \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 0 \\ \alpha \end{bmatrix} r $ ... $\omega_n = \sqrt{\beta}$ $\xi = \sqrt{\beta} $; $\omega_n = \sqrt{\alpha} $
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GATE2019 EE: 30
The transfer function of a phase lead compensator is given by $D(s) = \frac{3 \bigg( s+ \frac{1}{3T} \bigg)}{ \bigg( s+ \frac{1}{T} \bigg)}$ The frequency (in rad/sec), at which $\angle D(j \omega)$ is maximum, is $\sqrt{\frac{3}{T^2}}$ $\sqrt{\frac{1}{3T^2}}$ $\sqrt{3T}$ $\sqrt{3T^2}$
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GATE2019 EE: 29
The asymptotic Bode magnitude plot of a minimum phase transfer function $G(s)$ is shown below. Consider the following two statements. Statement I: Transfer function $G(s)$ ... and statement II is false Statement I is false and statement II is true Both the statements are true Both the statements are false
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GATE2019 EE: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
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GATE2019 EE: 27
The closedloop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counterclockwise, is $+8 j \pi$ $8 j \pi$ $4 j \pi$ $+4 j \pi$
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GATE2019 EE: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are the row vecotrs. ... $2$ is false Statement $2$ is true and Statement $1$ is false Both the Statements are true Both the statements are false
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GATE2019 EE: 25
The output voltage of a singlephase fullbridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms Component of the output voltage to be $75 \%$ of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ___________.
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GATE2019 EE: 24
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
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GATE2019 EE: 23
The total impedance of the secondary winding, leads, and burden of a $5$ A CT is $0.01 \: \Omega$. If the fault current is $20$ times the rated primary current of the CT, the VA output of the CT is_________
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GATE2019 EE: 22
Five alternators each rated $5$ MVA, $13.2$ kV with $25 \%$ of reactance on its own base are connected in parallel to a busbar. The short circuit level in MVA at the busbar is ____________
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GATE2019 EE: 21
The $Y_{\text{bus}}$ matrix of a twobus power system having two identical parallel lines connected between them in pu is given as $Y_{\text{bus}} = \begin{bmatrix} j8 & j20 \\ j20& j8 \end{bmatrix}$The magnitude of the series reactance of each line in pu (round off upto one decimal place) is__________.
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GATE2019 EE: 20
A coaxial Cylindrical capacitor is shown in the Figure(i) has dielectric with relative permittivity $\varepsilon_{r1} = 2$. When one – fourth portion of the dielectric is replaced with another dielectric of relative permittivity $\varepsilon_{r2}$, as shown in the Figure(ii), the capacitance is doubled. The value of $\varepsilon_{r2}$ is _________.
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GATE2019 EE: 19
The current $I$ is flowing in the circuit shown below in amperes (round off to one decimal place) is _________
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GATE2019 EE: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(3,3,2)\rightarrow(2,3,2)\rightarrow(2,6,2) \rightarrow(2,6,1) $ is___________.
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GATE2019 EE: 17
A current controlled current source (CCCS) has an input impedance of $10 \: \Omega$ and output impedance of $100 \: k\Omega$. When this CCCS is used in a negative feedback closed loop with a loop gain of $9$, the closed loop output impedance is $10 \: \Omega$ $100 \: \Omega$ $100 \: k \Omega$ $1000 \: k \Omega$
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GATE2019 EE: 16
Given, $V_{gs}$ is the gatesource voltage, $V_{ds}$ is the drain source voltage, and $V_{th}$ is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are $V_{gs}<V_{th};V_{ds}\geq V_{gs}V_{th}$ ... $V_{gs}>V_{th};V_{ds}\leq V_{gs}V_{th}$ $V_{gs}<V_{th};V_{ds}\leq V_{gs}V_{th}$
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GATE2019 EE: 15
The characteristic equation of a linear timeinvariant (LTI) system is given by $\Delta(s)=s^{4}+3s^{3}+3s^{2}+s+k=0$ The system is BIBO stable if $0<K<\frac{12}{9}$ $k>3$ $0<k<\frac{8}{9}$ $k>6$
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GATE2019 EE: 14
The open loop transfer function of a unity feedback system is given by $G(s)=\frac{\pi e^{0.25s}}{s}$ In $G(s)$ plane, the Nyquist plot of $G(s)$ passes through the negative real axis at the point $(0.5,j0)$ $(0.75,j0)$ $(1.25,j0)$ $(1.5,j0)$
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GATE2019 EE: 13
The output response of a system is denoted as $y(t)$, and its Laplace transform is given by $Y(s)=\frac{10}{s(s^{2}+s+100 \sqrt{2})}$ The steady state value of $y(t)$ is $\frac{1}{10 \sqrt{2}} \\ $ $10 \sqrt{2} \\ $ $\frac{1}{100 \sqrt{2}} \\ $ $100 \sqrt{2}$
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GATE2019 EE: 12
In the circuit shown below, the switch is closed at $t=0$. The value of $\theta$ in degrees which will give the maximum value of DC offset of the current at the time of switching is $60$ $45$ $90$ $30$
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GATE2019 EE: 11
A threephase synchronous motor draws $200 A$ from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of $0.5$ leading is $100 \: A$ $200 \: A$ $300 \: A$ $400 \: A$
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GATE2019 EE: 10
The parameter of an equivalent circuit of a threephase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is rotor resistance rotor leakage reactance magnetizing reactance stator resistance
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GATE2019 EE: 9
A sixpulse thyristor bridge rectifier is connected to a balanced threephase, $50Hz$ AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is $100 Hz$ $150 Hz$ $250 Hz$ $300 Hz$
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GATE2019 EE: 8
A $5kVA, 50V/100V,$ singlephase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is $4.5\%$ $9\%$ $5\%$ $1\%$
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GATE2019 EE: 7
The symbols, $a$ and $T,$ represent positive quantities, and $u(t)$ is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear timeinvariant system? $e^{+at}u(t)$ $e^{a(t+T)}u(t)$ $1+e^{at}u(t)$ $e^{a(tT)}u(t)$
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GATE2019 EE: 6
A system transfer function is $H(s)= \frac{a_{1}s^{2}+b_{1}s+c_{1}}{a_{2}s^{2}+b_{2}s+c_{2}}.$ If $a_{1}=b_{1}=0,$ and all the other coefficient are positive, the transfer function represents a low pass filter high pass filter band pass filter notch filter
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GATE2019 EE: 5
The meansquare of a zeromean random process is $\frac{kT}{c},$ where $k$ is Boltzmann’s constant, $T$ is the absolute temperature, and $C$ is a capacitance. The standard deviation of the random process is $\frac{kT}{c} \\ $ $\sqrt{\frac{kT}{c}} \\ $ $\frac{c}{kT} \\ $ $\frac{\sqrt{kT}}{c}$
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36
GATE2019 EE: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}1}{z} \\ $ $\frac{z^{2}1}{z+2} \\ $ $\frac{z^{2}1}{z0.5} \\ $ $\frac{z^{2}1}{z+j0.5} $
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37
GATE2019 EE: 3
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}} C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;$ where $c \neq 0$ is known as heat equation wave equation Poisson’s equation Laplace equation
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GATE2019 EE: 2
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are $4$ and $9$ $2$ and $3$ $2$ and $3$ $16$ and $81$
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39
GATE2019 EE: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$ $3te^{t}+e^{t}$ $3e^{t}$ $2te^{t}+e^{t}$ $4te^{t}+e^{t}$
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40
GATE2019 EE: GA2
The passengers were angry ______ the airline staff about the delay. on about with towards
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