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161
GATE Electrical 2022 | Question: 43
As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that the potential $\text{V(r)}$ at $r = c$ is $V_{1}$ and $\text{V(r)}$ at $r = d$ is $V_{2}$. Assume ...
As shown in the figure below, two concentric conducting spherical shells, centered at $r = 0$ and having radii $r = c$ and $r = d$ are maintained at potentials such that ...
Arjun
15.9k
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Arjun
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Feb 15, 2022
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162
GATE Electrical 2022 | Question: 44
Let the probability density function of a random variable $x$ be given as $f\left ( x \right ) = ae^{-2\left | x \right |}$ The value of $’a’$ is _________________.
Let the probability density function of a random variable $x$ be given as $$f\left ( x \right ) = ae^{-2\left | x \right |}$$ The value of $’a’$ is _________________....
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Arjun
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163
GATE Electrical 2022 | Question: 45
In the circuit shown below, the magnitude of the voltage $V_{1}$ in volts, across the $8\:k\Omega$ resistor is ______. (round off to nearest integer)
In the circuit shown below, the magnitude of the voltage $V_{1}$ in volts, across the $8\:k\Omega$ resistor is ______. (round off to nearest integer)
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164
GATE Electrical 2022 | Question: 46
Two generating units rated for $250$ $\text{MW}$ and $400$ $\text{MW}$ have governor speed regulations of $6\%$ and $6.4\%$, respectively, from no load to full load. Both the generating units are operating in parallel to share a load ... the load shared in $\text{MW}$, by the $250$ $\text{MW}$ generating unit is __________________.(round off to nearest integer)
Two generating units rated for $250$ $\text{MW}$ and $400$ $\text{MW}$ have governor speed regulations of $6\%$ and $6.4\%$, respectively, from no load to full load. Both...
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165
GATE Electrical 2022 | Question: 47
A $20$ $\text{MVA}$, $11.2$ $\text{kV}$, $4$-pole, $50$ $\text{Hz}$ alternator has an inertia constant of $15$ $\text{MJ/MVA}$. If the input and output powers of the alternator are $15$ $\text{MW}$ and $10$ $\text{MW}$, respectively, the angular acceleration in mechanical degree/$s^{2}$ is _____________.(round off to nearest integer)
A $20$ $\text{MVA}$, $11.2$ $\text{kV}$, $4$-pole, $50$ $\text{Hz}$ alternator has an inertia constant of $15$ $\text{MJ/MVA}$. If the input and output powers of the alte...
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GATE Electrical 2022 | Question: 48
Consider an ideal full-bridge single-phase $\text{DC-AC}$ inverter with a $\text{DC}$ bus voltage magnitude of $1000$ $\text{V}$. The inverter output voltage $v\left ( t \right )$ shown below, is obtained when diagonal switches of the ... . The active power, in watts, delivered to the load is _____________. (round off to nearest integer)
Consider an ideal full-bridge single-phase $\text{DC-AC}$ inverter with a $\text{DC}$ bus voltage magnitude of $1000$ $\text{V}$. The inverter output voltage $v\left ( t ...
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167
GATE Electrical 2022 | Question: 49
For the ideal $\text{AC-DC}$ rectifier circuit shown in the figure below, the load current magnitude is $I_{dc} = 15 A$ and is ripple free. The thyristors are fired with a delay angle of $45^{\circ}$. The amplitude of the fundamental component of the source current, in amperes, is _______________. (round off to two decimal places)
For the ideal $\text{AC-DC}$ rectifier circuit shown in the figure below, the load current magnitude is $I_{dc} = 15 A$ and is ripple free. The thyristors are fired with ...
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168
GATE Electrical 2022 | Question: 50
A $3$-phase grid-connected voltage source converter with $\text{DC}$ link voltage of $1000$ $\text{V}$ is switched using sinusoidal Pulse Width Modulation $\text{(PWM)}$ technique. If the grid phase current is $10$\text{ A}$ and the $ ... $\text{VA}$, then the modulation index used in sinusoidal $\text{PWM}$ is _____________. (round off to two decimal places)
A $3$-phase grid-connected voltage source converter with $\text{DC}$ link voltage of $1000$ $\text{V}$ is switched using sinusoidal Pulse Width Modulation $\text{(PWM)}$ ...
Arjun
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169
GATE Electrical 2022 | Question: 51
The steady state current flowing through the inductor of a $\text{DC – DC}$ buck boost converter is given in the figure below. If the peak-to-peak ripple in the output voltage of the converter is $1 V$, then the value of the output capacitor, in $\mu F$, is ________________. (round off to nearest integer)
The steady state current flowing through the inductor of a $\text{DC – DC}$ buck boost converter is given in the figure below. If the peak-to-peak ripple in the output ...
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170
GATE Electrical 2022 | Question: 52
A $280 \;V$, separately excited $\text{DC}$ motor with armature resistance of $1\:\Omega$ and constant field excitation drives a load. The load torque is proportional to the speed. The motor draws a current of $30 A$ when ... additional resistance of value $10\:\Omega$ is connected in series with the armature, is _____________. (round off to nearest integer)
A $280 \;V$, separately excited $\text{DC}$ motor with armature resistance of $1\:\Omega$ and constant field excitation drives a load. The load torque is proportional to ...
Arjun
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Arjun
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Feb 15, 2022
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171
GATE Electrical 2022 | Question: 53
A $4$-pole induction motor with inertia of $0.1\; kg-m^{2}$ drives a constant load torque of $2\; Nm$. The speed of the motor is increased linearly from $1000$ $\text{rpm}$ to $1500$ $\text{rpm}$ in $4$ ... Neglect losses in the motor. The energy, in joules, consumed by the motor during the speed change is ____________________. (round off to nearest integer)
A $4$-pole induction motor with inertia of $0.1\; kg-m^{2}$ drives a constant load torque of $2\; Nm$. The speed of the motor is increased linearly from $1000$ $\text{rpm...
Arjun
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Arjun
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172
GATE Electrical 2022 | Question: 54
A star-connected $3$-phase, $400\; V$, $50$ $\text{ kVA}$, $50\; Hz$ synchronous motor has a synchronous reactance of $1$ $\text{ohm}$ per phase with negligible armature resistance. The shaft load on the motor is $10$ $\text{kW}$ ... $2\:kW$. The magnitude of the per phase excitation emf of the motor, in volts, is ______________. (round off to nearest integer).
A star-connected $3$-phase, $400\; V$, $50$ $\text{ kVA}$, $50\; Hz$ synchronous motor has a synchronous reactance of $1$ $\text{ohm}$ per phase with negligible armature ...
Arjun
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173
GATE Electrical 2022 | Question: 55
A $3$-phase, $415\; V$, $4$-pole, $50\:Hz$ induction motor draws $5$ times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to $2$ times of ... of the autotransformer is neglected, then the transformation ratio of the autotransformer is given by ________________. (round off to two decimal places).
A $3$-phase, $415\; V$, $4$-pole, $50\:Hz$ induction motor draws $5$ times the rated current at rated voltage at starting. It is required to bring down the starting curre...
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175
Gate 2000 signals and systems
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176
GATE Electrical 2021 | Question: 2
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ ... $p\left ( z \right )=0$ come in conjugate pairs All the roots cannot be real
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ is a complex number.Which one of the following is true?$\text{conjugate}\:\lef...
Arjun
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Arjun
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Feb 19, 2021
Complex Variables
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GATE Electrical 2021 | Question: 3
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right )> 0$ for all $x \in \left ( 0,1 \right )$. ... has no local minimum in $(0,1)$ one local maximum in $(0,1)$ exactly one local minimum in $(0,1)$ two distinct local minima in $(0,1)$
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right ) 0$ fo...
Arjun
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Calculus
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178
GATE Electrical 2021 | Question: 4
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is $\text{10 V}$ in series with $12\:\Omega$ $\text{65 V}$ in series with $15\:\Omega$ $\text{50 V}$ in series with $2\:\Omega$ $\text{35 V}$ in series with $2\:\Omega$
For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘$\text{ab}$’ is$\text{10 V}$ in series with $12\:\Omega$$\text...
Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 5
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$? $\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively)}$ $10x\hat{X}+20y\hat{Y}-30z\hat{Z}$ $10y\hat{X}+20x\hat{Y}-10z\hat{Z}$ $10z\hat{X}+20y\hat{Y}-30x\hat{Z}$ $10x\hat{X}-30z\hat{Y}+20y\hat{Z}$
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$?$\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axi...
Arjun
15.9k
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Arjun
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Feb 19, 2021
Calculus
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calculus
field-vectors
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GATE Electrical 2021 | Question: 6
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system is linear and time-variant linear and time-invariant non-linear and time-variant non-linear and time-invariant
If the input $x(t)$ and output $y(t)$ of a system are related as $y\left ( t \right )=\text{max}\left ( 0,x\left ( t \right ) \right ),$ then the system islinear and time...
Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 7
Two discrete-time linear time-invariant systems with impulse responses $h_{1}\left [ n \right ]=\delta \left [ n-1 \right ]+\delta \left [ n+1 \right ]$ and $h_{2}\left [ n \right ]=\delta \left [ n\right ]+\delta \left [ n-1 \right ]$ are connected in ... $\delta \left [ n\right ]\delta \left [ n-1\right ]+\delta \left [ n-2\right ]\delta \left [ n+1 \right ]$
Two discrete-time linear time-invariant systems with impulse responses $h_{1}\left [ n \right ]=\delta \left [ n-1 \right ]+\delta \left [ n+1 \right ]$ and $h_{2}\left [...
Arjun
15.9k
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Arjun
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Feb 19, 2021
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182
GATE Electrical 2021 | Question: 8
Consider the table given: ... $\text{P-T-Y, Q-V-Z, R-S-X}$ $\text{P-U-X, Q-V-Y, R-T-Z}$
Consider the table given:$\begin{array}{|cl|cI|cI|}\hline&\textbf{Constructional feature} & \textbf{Machine type} & \textbf{Mitigation} \\ \hline &\text{P. Damper bars} ...
Arjun
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Arjun
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183
GATE Electrical 2021 | Question: 9
Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus, $PV$ buses and $PQ$ buses for load flow study. The number of $PQ$ buses is $N_{L}$. The balanced Newton-Raphson method is used to carry out load flow study ... $\left ( N-1 \right )\times \left ( N-1+N_{L} \right )$
Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus, $PV$ buses and $PQ$ buses for load flow study. The n...
Arjun
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Arjun
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Feb 19, 2021
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184
GATE Electrical 2021 | Question: 10
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are $\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$ $\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}$ They need to deliver a combined load of $260$ $\text{MW}$. Ignoring the network losses, for ... $P_{1}=P_{2}=130$ $P_{1}=160, P_{2}=100$ $P_{1}=140, P_{2}=120$ $P_{1}=120, P_{2}=140$
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are$\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$$\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}...
Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 11
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is $\frac{G}{1+GH}$ $\frac{GH}{1+GH}$ $\frac{1}{1+GH}$ $\frac{1}{1+G}$
For the closed-loop system shown, the transfer function $\dfrac{E\left ( s \right )}{R\left ( s \right )}$ is$\frac{G}{1+GH}$$\frac{GH}{1+GH}$$\frac{1}{1+GH}$$\frac{1}{1+...
Arjun
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GATE Electrical 2021 | Question: 12
Inductance is measured by Schering bridge Maxwell bridge Kelvin bridge Wien bridge
Inductance is measured bySchering bridgeMaxwell bridgeKelvin bridgeWien bridge
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GATE Electrical 2021 | Question: 13
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Then $u+v=$ _______________.
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Th...
Arjun
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Arjun
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Feb 19, 2021
Calculus
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curves
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GATE Electrical 2021 | Question: 14
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.
In the given circuit, the value of capacitor $C$ that makes current $I=0$ is ________________ $\mu F$.
Arjun
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GATE Electrical 2021 | Question: 15
Two single-core power cables have total conductor resistances of $0.7\;\Omega$ and $0.5\;\Omega$, respectively, and their insulation resistances (between core and sheath) are $600\;M\Omega$ and $900\;M\Omega$, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is ___________$\times 10^{6}$.
Two single-core power cables have total conductor resistances of $0.7\;\Omega$ and $0.5\;\Omega$, respectively, and their insulation resistances (between core and sheath)...
Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 16
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be _________. (Round off to $2$ decimal places).
Arjun
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GATE Electrical 2021 | Question: 17
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\left ( 5,5,5\right )$ and subsequently to $\left ( 5,0,0\right )$, ... decimal places). Take $\dfrac{1}{4\pi \varepsilon _{0}}=9\times 10^{9}$ in $\text{SI}$ units. All coordinates are in meters.
A $1\;\mu C$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10\;\mu C$ is moved from $\left ( 0,10,0 \right )$ to $\lef...
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GATE Electrical 2021 | Question: 18
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. If the total friction and windage losses are $2.025\text{ kW}$, then the efficiency is _____________$\%$.
The power input to a $\text{500 V, 50 Hz, 6-pole, 3-phase}$ induction motor running at $975 \text{RPM}$ is $40 \text{ kW}$ . The total stator losses are $1 \text{ kW}$. I...
Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 19
An alternator with internal voltage of $1\angle \delta _{1}\text{p.u}$ and synchronous reactance of $\text{0.4 p.u}$ is connected by a transmission line of reactance $\text{0.1 p.u}$ ... $2$ decimal places.) (Machines are of non-salient type. Neglect resistances.)
An alternator with internal voltage of $1\angle \delta _{1}\text{p.u}$ and synchronous reactance of $\text{0.4 p.u}$ is connected by a transmission line of reactance $\te...
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GATE Electrical 2021 | Question: 20
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$\Omega$. (Round off to $2$ decimal places.)
The Bode magnitude plot for the transfer function $\frac{V_{o}\left ( s \right )}{V_{i}\left ( s \right )}$ of the circuit is as shown. The value of $R$ is _____________$...
Arjun
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GATE Electrical 2021 | Question: 21
A signal generator having a source resistance of $50\:\Omega$ is set to generate a $\text{1 kHz}$ sinewave. Open circuit terminal voltage is $\text{10 V}$ peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to $\text{8 V}$ peak-to-peak. The value of this capacitor is _____________$\mu F$. (Round off to $2$ decimal places.)
A signal generator having a source resistance of $50\:\Omega$ is set to generate a $\text{1 kHz}$ sinewave. Open circuit terminal voltage is $\text{10 V}$ peak-to-peak. C...
Arjun
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Arjun
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Feb 19, 2021
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GATE Electrical 2021 | Question: 22
A $16$-bit synchronous binary up-counter is clocked with a frequency $f_{\text{CLK}}$.The two most significant bits are $\text{OR-ed}$ together to form an output $Y$. Measurements show that $Y$ is periodic, and the duration for which $Y$ remains high ... $f_{\text{CLK}}$ is ____________$\text{MHz}.$ (Round off to $2$ decimal places.)
A $16$-bit synchronous binary up-counter is clocked with a frequency $f_{\text{CLK}}$.The two most significant bits are $\text{OR-ed}$ together to form an output $Y$. Mea...
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Feb 19, 2021
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GATE Electrical 2021 | Question: 23
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{2}$ is __________ $k \Omega$. (Round off to $2$ decimal places.)
In the $\text{BJT}$ circuit shown, beta of the $\text{PNP}$ transistor is $100$. Assume $V_{\text{BE}}=-0.7\;V$. The voltage across $R_{c}$ will be $\text{5 V}$ when $R_{...
Arjun
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GATE Electrical 2021 | Question: 24
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen across any diode is ____________$V$. (Round off to $2$ decimal places.)
In the circuit shown, the input $V_{i}$ is a sinusoidal $\text{AC}$ voltage having an $\text{RMS}$ value of $230\;V\pm 20\%$. The worst-case peak-inverse voltage seen ac...
Arjun
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GATE Electrical 2021 | Question: 26
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ has two real roots one real root three real roots no real roots
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ hastwo real rootsone real rootthree real rootsno real roots
Arjun
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Arjun
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Feb 19, 2021
Calculus
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calculus
polynomials
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200
GATE Electrical 2021 | Question: 27
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses required is $p/\left ( 1-p \right )$ $\left ( 1-p \right )/p$ $1/p$ $1/p^{2}$
Suppose the probability that a coin toss shows "head" is $p$, where $0<p<1$. The coin is tossed repeatedly until the first "head" appears. The expected number of tosses r...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
new
gateee-2021
probability-and-statistics
probability
+
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