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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: 48
A $220$ V(line), threephase, Yconnected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10$ A at $0.8$ pf leading. The rms value of linetoline internal voltage in volts (round off to two decimal places) is _________
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GATE2019 EE: 43
The voltage across and the current through a load are expressed as follows $v(t)=170 \sin \bigg( 377t \frac{\pi}{6} \bigg) V$ $i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \bigg) A$ The average power in watts (round off to one decimal place) consumed by the load 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: 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: 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: 55
A singlephase fullycontrolled thyristor converter is used to obtain an average voltage of $180$ V with $10$ A constant current to feed a DC load. It is fed from singlephase AC supply of $230$ V, $50$ Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________
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GATE2019 EE: 40
The probability of a resistor being deflective is $0.02$. There are $50$ such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is _______________
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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: 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: 53
In a DCDC boost converter, the duty ratio is controlled to regulate the output voltage at $48$ V. The input DC voltage is $24$ V. The output power is $120$ W. The switching frequency is $50$ kHz. Assume ideal components and a very ... converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in $\mu H$) is ________
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GATE2019 EE: 42
The current $I$ flowing in the circuit shown in amperes is ____________
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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: 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: 47
A deltaconnected, $3.7$ kW, $400$ V(line), threephase, $4$pole, $50$Hz squirrelcage induction moor has the following equivalent circuit parameters per phase referred to the stator: $R_1=5.39 \: \Omega$, $R_2=5.72 \: \Omega$ ... in amperes (round off to two decimal places) when it is connected to a $100$ V(line), $10$ Hz, threephase AC source 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: 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: 52
In a $132$ kV system, the series inductance up to the point of circuit breaker location is $50$ mH. The shunt capacitance at the circuit breaker terminal is $0.05 \: \mu F$. The critical value of resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is ______
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GATE2019 EE: 44
The magnetic circuit shown below has uniform crosssectional area and air gap of $0.2$ cm. The mean path length of the core is $40$ cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the ... to be $1000$ (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _______
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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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