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164
GATE Electrical 2023 | Question: 35
The expected number of trials for first occurrence of a "head" in a biased coin is known to be $4.$ The probability of first occurrence of a "head" in the second trial is ____________(Round off to $3$ decimal places).
The expected number of trials for first occurrence of a "head" in a biased coin is known to be $4.$ The probability of first occurrence of a "head" in the second trial is...
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165
GATE Electrical 2023 | Question: 36
Consider the state-space description of an $\text{LTI}$ ... for which the steady-state output of the system will be zero, is ________(Round off to the nearest integer).
Consider the state-space description of an $\text{LTI}$ system with matrices$\qquad A=\left[\begin{array}{cc}0 & 1 \\-1 & -2\end{array}\right], B=\left[\begin{array}{l}0 ...
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166
GATE Electrical 2023 | Question: 37
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ The corresponding excitation voltage in per unit is _________ (Round off to $2$ decimal places).
A three-phase synchronous motor with synchronous impedance of $0.1+\mathrm{j} 0.3 \text { per unit } $ per phase has a static stability limit of $2.5 \text { per unit.}$ ...
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168
GATE Electrical 2023 | Question: 39
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer). $x[n]=1+3 \sin \left(\frac{15 \pi}{8} n+\frac{3 \pi}{4}\right)-5 \sin \left(\frac{\pi}{3} n-\frac{\pi}{4}\right)$
The period of the discrete-time signal $ x[n]$ described by the equation below is $N=$________ (Round off to the nearest integer).$$x[n]=1+3 \sin \left(\frac{15 \pi}{8} n...
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169
GATE Electrical 2023 | Question: 40
The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N}=5$ ... $a_{3}$ is_____________ (Round off to $3$ decimal places).
The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N...
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170
GATE Electrical 2023 | Question: 41
For the circuit shown, if $ i=\sin 1000 t,$ the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals $a-b$ at time $t=5 \mathrm{~ms}$ is__________(Round off to $2$ decimal places).
For the circuit shown, if $ i=\sin 1000 t,$ the instantaneous value of the Thevenin's equivalent voltage (in Volts) across the terminals $a-b$ at time $t=5 \mathrm{~ms}$...
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171
GATE Electrical 2023 | Question: 42
The admittance parameters of the passive resistive two-port network shown in the figure are $y_{11}=5 S, y_{22}=1 S, y_{12}=y_{21}=-2.5 S$ The power delivered to the load resistor $ R_{L}$ in Watt is _______(Round off to $2$ decimal places).
The admittance parameters of the passive resistive two-port network shown in the figure are$$y_{11}=5 S, y_{22}=1 S, y_{12}=y_{21}=-2.5 S$$The power delivered to the load...
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175
GATE Electrical 2023 | Question: 47
In a given $8$-bit general purpose micro-controller there are following flags. $\text{C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity}$ ($0$ for even, $1$ for odd) $\text{R0}$ and $\text{R1}$ are the two general purpose registers of the micro-controller. After execution ...
In a given $8$-bit general purpose micro-controller there are following flags. $\text{C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity}$ ($0$ for even, $1$ for odd) ...
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180
GATE Electrical 2023 | Question: 52
The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integral of the vector field $ F=-y \hat{\imath}+x \hat{\jmath}$ around the closed curve is __________(Round off to $2$ decimal places).
The closed curve shown in the figure is described by $r=1+\cos \theta,$ where $r=\sqrt{x^{2}+y^{2}} ; x=r \cos \theta, y=r \sin \theta$ The magnitude of the line integra...
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183
GATE Electrical 2023 | Question: 55
A quadratic function of two variables is given as $ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$ The magnitude of the maximum rate of change of the function at the point $(1,1)$ is__________(Round off to the nearest integer). }
A quadratic function of two variables is given as $$ f\left(x_{1}, x_{2}\right)=x_{1}^{2}+2 x_{2}^{2}+3 x_{1}+3 x_{2}+x_{1} x_{2}+1$$The magnitude of the maximum rate of...
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185
GATE Electrical 2022 | Question: 1
The transfer function of a real system, $H(s)$, is given as: $H\left ( s \right ) = \dfrac{As + B}{S^{2} + Cs + D}$ where $\text{A, B, C}$ and $D$ are positive constants. This system cannot operate as low pass filter. high pass filter. band pass filter. an integrator.
The transfer function of a real system, $H(s)$, is given as:$H\left ( s \right ) = \dfrac{As + B}{S^{2} + Cs + D}$where $\text{A, B, C}$ and $D$ are positive constants. T...
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186
GATE Electrical 2022 | Question: 2
For an ideal $\text{MOSFET}$ biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is $0$ $1$ $100$ infinite
For an ideal $\text{MOSFET}$ biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is$0$$1$$100$infinite
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187
GATE Electrical 2022 | Question: 3
The most commonly used relay, for the protection of an alternator against loss of excitation, is offset Mho relay. over current relay. differential relay. Buchholz relay.
The most commonly used relay, for the protection of an alternator against loss of excitation, isoffset Mho relay.over current relay.differential relay.Buchholz relay.
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188
GATE Electrical 2022 | Question: 5
The valid positive, negative and zero sequence impedances (in p.u), respectively, for a $220$ $\text{kV}$, fully transposed three-phase transmission line, from the given choices are $1.1, \: 0.15$ and $0.08$ $0.15, \: 0.15$ and $0.35$ $0.2, \: 0.2$ and $0.2$ $0.1, \: 0.3$ and $0.1$
The valid positive, negative and zero sequence impedances (in p.u), respectively, for a $220$ $\text{kV}$, fully transposed three-phase transmission line, from the given ...
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189
GATE Electrical 2022 | Question: 6
The steady state output ($V_{\text{out}}$), of the circuit shown below, will saturate to $+V_{DD}$ saturate to $-V_{EE}$ become equal to $0.1\:V$ become equal to $-0.1\:V$
The steady state output ($V_{\text{out}}$), of the circuit shown below, willsaturate to $+V_{DD}$saturate to $-V_{EE}$become equal to $0.1\:V$become equal to $-0.1\:V$
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192
GATE Electrical 2022 | Question: 9
The open loop transfer function of a unity gain negative feedback system is given by $G\left ( s \right ) = \dfrac{k}{s^{2}+4s-5}$. The range of $k$ for which the system is stable, is $k> 3$ $k< 3$ $k> 5$ $k< 5$
The open loop transfer function of a unity gain negative feedback system is given by $G\left ( s \right ) = \dfrac{k}{s^{2}+4s-5}$. The range of $k$ for which the system ...
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193
GATE Electrical 2022 | Question: 10
Consider a $3\times 3$ matrix $A$ whose $(i,j)$-th element, $a_{i,j} = \left ( i- j \right )^{3}$. Then the matrix $A$ will be symmetric skew-symmetric unitary null
Consider a $3\times 3$ matrix $A$ whose $(i,j)$-th element, $a_{i,j} = \left ( i- j \right )^{3}$. Then the matrix $A$ will besymmetricskew-symmetricunitarynull
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195
GATE Electrical 2022 | Question: 12
A charger supplies $100\:W$ at $20\:V$ for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of $200$ $\text{kHz}$. Which power device is best suited for this purpose? $\text{IGBT}$ Thyristor $\text{MOSFET}$ $\text{BJT}$
A charger supplies $100\:W$ at $20\:V$ for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency...
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197
GATE Electrical 2022 | Question: 14
The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is split phase (resistance start). shaded pole. capacitor start. capacitor start, capacitor run.
The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, issplit phase (resistance start).shaded pole.ca...
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198
GATE Electrical 2022 | Question: 15
For the circuit shown below with ideal diodes, the output will be $V_{\text{out}} = V _{\text{in}}$ for $V_{\text{in}}> 0$ $V_{\text{out}} = V_{\text{in}}$ for $V_{\text{in}}< 0$ $V_{\text{out}} = -V_{\text{in}}$ for $V_{\text{in}}> 0$ $V_{\text{out}} = -V_{\text{in}}$ for $V_{\text{in}}< 0$
For the circuit shown below with ideal diodes, the output will be$V_{\text{out}} = V _{\text{in}}$ for $V_{\text{in}} 0$$V_{\text{out}} = V_{\text{in}}$ for $V_{\text{in...
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199
GATE Electrical 2022 | Question: 17
An inductor having a $Q$ – factor of $60$ is connected in series with a capacitor having a $Q$ – factor of $240$. The overall $Q$ -factor of the circuit is _______________. (round off to nearest integer)
An inductor having a $Q$ – factor of $60$ is connected in series with a capacitor having a $Q$ – factor of $240$. The overall $Q$ -factor of the circuit is __________...
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200
GATE Electrical 2022 | Question: 18
The network shown below has a resonant frequency of $150$ $\text{kHz}$ and a bandwidth of $600$ $\text{Hz}$. The $Q$ –factor of the network is ______________. (round off to nearest integer)
The network shown below has a resonant frequency of $150$ $\text{kHz}$ and a bandwidth of $600$ $\text{Hz}$. The $Q$ –factor of the network is ______________. (round of...
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