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241
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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GATE Electrical 2020 | Question: 46
A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is suppling $100 \: A$ current to a $0.9$ lagging power factor load. An ideal reactor is now connected in parallel with the load, as a ... power remains unchanged. The armature current is now ___________________ $\text{A}$ (rounded off to $2$ decimal places).
A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is suppling $100 \: A$ current to a $0.9$ lagging power factor loa...
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GATE Electrical 2023 | Question: 18
The bus admittance $\left(Y_{\text {bus }}\right)$ matrix of a $3$-bus power system is given below. Considering that there is no shunt inductor connected to any of the buses, which of the following can $\text{NOT}$ be true? Line charging ... capacitor of finite value is present in line$ 2-3$ only and shunt capacitor of finite value is present in bus $3$ only
The bus admittance $\left(Y_{\text {bus }}\right)$ matrix of a $3$-bus power system is given below.Considering that there is no shunt inductor connected to any of the bus...
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GATE Electrical 2023 | Question: 25
Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round off to $2$ decimal places)
Three points in the $x-y$ plane are $(-1,0.8),(0,2.2)$ and $(1,2.8).$ The value of the slope of the best fit straight line in the least square sense is___________(Round o...
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GATE Electrical 2020 | Question: 39
Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation: $y\left [ n \right ]-ay\left [ n-1 \right ]=b_{0}x\left [ n \right ]-b_{1}x\left [ n-1 \right ]$ $y[n]$ is unaffected by the ... $y\left [ n \right];n > 0$ is solely determined by the function $x[n]$.
Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:$$y\left [ n \right ]-ay\left [ n-1 \right ]=b_...
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GATE Electrical 2019 | Question: 11
A three-phase 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$
A three-phase 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 f...
Arjun
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GATE Electrical 2022 | Question: 22
A single-phase full-bridge diode rectifier feeds a resistive load of $50\; \Omega$ from a $200\:V$, $50\:Hz$ single phase $\text{AC}$ supply. If the diodes are ideal, then the active power, in watts, drawn by the load is __________________. (round off to nearest integer)
A single-phase full-bridge diode rectifier feeds a resistive load of $50\; \Omega$ from a $200\:V$, $50\:Hz$ single phase $\text{AC}$ supply. If the diodes are ideal, the...
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GATE Electrical 2019 | Question: 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
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 transfe...
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GATE Electrical 2012 | Question: 39
Consider the differential equation $\dfrac{d^2y(t)}{dt^2} + 2 \dfrac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \bigg \vert_{t=0^-}= -2$ and $\dfrac{dy}{dt} \bigg \vert _{t=0^-} =0$. The numerical value of $\dfrac{dy}{dt} \bigg \vert _{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation $\dfrac{d^2y(t)}{dt^2} + 2 \dfrac{dy(t)}{dt} + y(t)=\delta (t)$ with $y(t) \bigg \vert_{t=0^-}= -2$ and $\dfrac{dy}{dt} \bigg \vert _{t...
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GATE Electrical 2020 | Question: 34
Consider a permanent magnet dc $\text{(PMDC)}$ motor which is initially at rest. At $t=0$, a dc voltage of $5 V$ is applied to the motor. Its speed monotonically increase from $0 \text{ rad/s}$ to $6.32 \text{ rad/s}$ in $0.5 \: s$ ... $\dfrac{10}{0.5s+1} \\$ $\dfrac{2}{0.5s+1} \\$ $\dfrac{2}{s+0.5} \\$ $\dfrac{10}{s+0.5}$
Consider a permanent magnet dc $\text{(PMDC)}$ motor which is initially at rest. At $t=0$, a dc voltage of $5 V$ is applied to the motor. Its speed monotonically increase...
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GATE Electrical 2012 | Question: 8
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be $\dfrac{1}{3} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid < \dfrac{1}{2} \\$ $\dfrac{1}{2} < \mid z \mid < 3 \\$ $\dfrac{1}{3} < \mid z \mid $
If $x[n]=(1/3)^{\mid n \mid} – (1/2)^n \: u[n]$, then the region of convergence (ROC) of its $Z$-transform in the $Z$-plane will be$\dfrac{1}{3} < \mid z \mid < 3 \\$$\...
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GATE Electrical 2017 Set 2 | Question: 2
Consider a solid sphere of radius $5$ cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed Uniformly over the entire volume of the sphere. Uniformly over the ... the sphere. Concentrated around the centre of the sphere. Along a straight line passing through the centre of the sphere.
Consider a solid sphere of radius $5$ cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributedUnifo...
Arjun
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GATE Electrical 2023 | Question: 29
A $3$-phase, star-connected, balanced load is supplied from a $3$-phase, $400 \mathrm{~V (rms),}$ balanced voltage source with phase sequence $\text{R-Y-B},$ as shown in the figure. If the wattmeter reading is $-400 \mathrm{~W}$ and the line ... $0.5$ leading $0.866$ leading $0.707$ lagging
A $3$-phase, star-connected, balanced load is supplied from a $3$-phase, $400 \mathrm{~V (rms),}$ balanced voltage source with phase sequence $\text{R-Y-B},$ as shown in ...
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GATE Electrical 2020 | Question: 36
Consider a negative unity feedback system with the forward path transfer function $\dfrac{s^{2}+s+1}{s^{3}+2s^{2}+2s+K},$ where $K$ is a positive real number. The value of $K$ for which the system will have some of its poles on the imaginary axis is ____________. $9$ $8$ $7$ $6$
Consider a negative unity feedback system with the forward path transfer function $\dfrac{s^{2}+s+1}{s^{3}+2s^{2}+2s+K},$ where $K$ is a positive real number. The value o...
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GATE Electrical 2019 | Question: 49
A three-phase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The line is under open circuit condition at the receiving end and energized with $400$ kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be _________
A three-phase $50$ Hz, $400$ kV transmission line is $300$ km long. The line inductance is $1$ mH/km per phase, and the capacitance is $0.01 \: \mu F/km$ per phase. The l...
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GATE Electrical 2017 Set 1 | Question: 20
A three-phase, $50$Hz, star-connected cylindrical rotor synchronous machine is running as a motor. The machine is operated from a $6.6$ kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is $30 \Omega$ ... $30^{\circ}$. The power delivered to the motor in kW is __________. (Give the answer up to one decimal place).
A three-phase, $50$Hz, star-connected cylindrical rotor synchronous machine is running as a motor. The machine is operated from a $6.6$ kV grid and draws current at unity...
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GATE Electrical 2023 | Question: 31
The three-bus power system shown in the figure has one alternator connected to bus $2$ which supplies $200 \mathrm{MW}$ and $40 \text{MVAr}$ power. Bus $3$ is infinite bus having a voltage of magnitude $\left|V_3\right|=1.0$ p.u. and angle of $-15^{\circ}$. A ... $3 \quad$ Slack bus Bus $1 \quad P-|V|$ bus Bus $2 \quad P-Q$ bus Bus $3 \quad$ Slack bus
The three-bus power system shown in the figure has one alternator connected to bus $2$ which supplies $200 \mathrm{MW}$ and $40 \text{MVAr}$ power. Bus $3$ is infinite bu...
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GATE Electrical 2018 | Question: 46
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ___________ (up to $2$ decimal places).
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s)= \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is _...
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GATE Electrical 2023 | Question: 16
A semiconductor switch needs to block voltage $\text{V}$ of only one polarity $\text{(V>0)}$ during OFF state as shown in figure (i) and carry current in both directions during $\text{ON}$ state as shown in figure (ii). Which of the following switch combination(s) will realize the same?
A semiconductor switch needs to block voltage $\text{V}$ of only one polarity $\text{(V>0)}$ duringOFF state as shown in figure (i) and carry current in both directions d...
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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: 55
A single-phase full-bridge inverter fed by a $\text{325 V DC}$ produces a symmetric quasi-square waveform across '$ab$' as shown. To achieve a modulation index of $0.8$, the angle $\theta$ expressed in degrees should be _______________. ( ... is defined as the ratio of the peak of the fundamental component of $V_{ab}$ to the applied $\text{DC}$ value.)
A single-phase full-bridge inverter fed by a $\text{325 V DC}$ produces a symmetric quasi-square waveform across '$ab$' as shown. To achieve a modulation index of $0.8$, ...
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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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GATE Electrical 2020 | Question: 50
In the $\text{dc-dc}$ converter circuit shown, switch $\text{Q}$ is switched at a frequency of $10 \: kHz$ with a duty ratio of $0.6$. All components of the circuit are ideal, and the initial current in the inductor is zero. Energy stored in the inductor in $\text{mJ}$ (rounded off to $2$ decimal places) at the end of $10$ complete switching cycles is _________.
In the $\text{dc-dc}$ converter circuit shown, switch $\text{Q}$ is switched at a frequency of $10 \: kHz$ with a duty ratio of $0.6$. All components of the circuit are i...
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GATE Electrical 2023 | Question: 44
The circuit shown in the figure is initially in the steady state with the switch $K$ in open condition and $\bar{K}$ in closed condition. The switch $ K$ is closed and $\bar{K}$ is opened simultaneously at the instant $t=t_{1},$ where ... there is no transient in the voltage across the $ 100 \mu \mathrm{F}$ capacitor, is_________(Round off to $2$ decimal places).
The circuit shown in the figure is initially in the steady state with the switch $K$ in open condition and $\bar{K}$ in closed condition. The switch $ K$ is closed and $...
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GATE Electrical 2020 | Question: 30
Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic $I_{D}=I_{S}\left ( exp\left ( \dfrac{V_{D}}{nV_{T}} \right )-1 \right )$, where $n> 1, V_{T}> 0, V_{D}$ is the voltage across the diode and $I_{D}$ is the ... $R_{1}$ and small $R_{2}$. Large $R_{1}$ and small $R_{2}$. Small $R_{1}$ and large $R_{2}$.
Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic $I_{D}=I_{S}\left ( exp\left ( \dfrac{V_{D}}{nV_{T}} \right )-1 \right )$, ...
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GATE Electrical 2020 | Question: 45
A resistor and a capacitor are connected in series to a $\text{10 V dc}$ supply through a switch. The switch is closed at $\text{t = 0}$, and the capacitor voltage is found to cross $\text{0 V}$ at $t=0.4\tau$, where ... the initial capacitor voltage if the zero crossing has to happen at $t=0.2\tau$ is _______________________ (rounded off to $2$ decimal places).
A resistor and a capacitor are connected in series to a $\text{10 V dc}$ supply through a switch. The switch is closed at $\text{t = 0}$, and the capacitor voltage is fou...
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GATE Electrical 2019 | Question: 51
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is _________
In the single machine infinite bus system shown below, the generator is delivering the real power of $0.8$ pu at $0.8$ power factor lagging to the infinite bus. The power...
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GATE Electrical 2017 Set 2 | Question: 31
The output $y(t)$ of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is $1000$ samples/s $1500$ samples/s $2000$ samples/s $3000$ samples/s
The output $y(t)$ of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is$1000$ samples/s$1500$...
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GATE Electrical 2017 Set 1 | Question: 55
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $1.5 \sin \delta$, where $\delta$ is the rotor angle. The system is operating at the stable equilibrium point with ... $P_{\max}$, in pu is ______. (Give the answer up to three decimal places.)
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $1.5 \sin \delta$, where $\delt...
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GATE Electrical 2019 | Question: 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 $60$ $-45$ $90$ $-30$
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 s...
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GATE Electrical 2019 | Question: 32
A moving coil instrument having a resistance of $10 \: \Omega$, gives a full-scale 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? $9 \: \Omega$ $99 \: \Omega$ $990 \: \Omega$ $9990 \: \Omega$
A moving coil instrument having a resistance of $10 \: \Omega$, gives a full-scale deflection when the current is $10$ mA. What should be the value of the series resistan...
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GATE Electrical 2019 | Question: 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 _________.
The voltage across and the current through a load are expressed as follows$v(t)=-170 \sin \bigg( 377t- \frac{\pi}{6} \bigg) V$$i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \b...
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GATE Electrical 2019 | Question: 48
A $220$ V(line), three-phase, Y-connected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10$ A at $0.8$ pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _________
A $220$ V(line), three-phase, Y-connected, synchronous motor has a synchronous impedance of $(0.25+j2.5) \: \Omega/\text{phase}$. The motor draws the rated current of $10...
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GATE Electrical 2021 | Question: 10
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are $\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$ $\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}$ They need to deliver a combined load of $260$ $\text{MW}$. Ignoring the network losses, for ... $P_{1}=P_{2}=130$ $P_{1}=160, P_{2}=100$ $P_{1}=140, P_{2}=120$ $P_{1}=120, P_{2}=140$
Two generators have cost functions $F_{1}$ and $F_{2}$ . Their incremental-cost characteristics are$\dfrac{dF_{1}}{dP_{1}}=40+0.2P_{1}$$\dfrac{dF_{2}}{dP_{2}}=32+0.4P_{2}...
Arjun
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GATE Electrical 2019 | Question: 45
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two...
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GATE Electrical 2018 | Question: 29
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator $G_1$ and $G_2$ are $Q_{G1}$ and $Q_{G2}$ respectively. The per unit values of $Q_{G1}$, $Q_{G2}$, and line ... $6.34, \: 11.34, \: 2.68$ $5.00, \: 11.34, \: 1.34$
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by gene...
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GATE Electrical 2023 | Question: 24
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-\alpha t}}{2+\alpha t}, \quad \alpha=0.01$ and $y(0)=0$
In the following differential equation, the numerically obtained value of $y(t),$ at $t=1,$ is ___________ (Round off to $2$ decimal places). $\frac{d y}{d t}=\frac{e^{-...
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GATE Electrical 2020 | Question: 49
A cylindrical rotor synchronous generator has steady state synchronous reactance of $0.7 \: pu$ and subtransient reactance of $0.2 \: pu$. It is operating at $\left ( 1+j0 \right ) pu$ terminal voltage with an internal $\text{emf}$ ... the generator, the magnitude of the subtransient internal $\text{emf}$ (rounded off to $2$ decimal places) is ____________ $pu$.
A cylindrical rotor synchronous generator has steady state synchronous reactance of $0.7 \: pu$ and subtransient reactance of $0.2 \: pu$. It is operating at $\left ( 1+j...
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GATE Electrical 2019 | Question: 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 $\sqrt{\frac{3}{T^2}}$ $\sqrt{\frac{1}{3T^2}}$ $\sqrt{3T}$ $\sqrt{3T^2}$
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), a...
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GATE Electrical 2012 | Question: 54
The transfer function of a compensator is given as $G_c(s) = \frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $a=1, \: b=2$ $a=3, \: b=2$ $a=-3, \: b=-1$ $a=3, \: b=1$
The transfer function of a compensator is given as $$G_c(s) = \frac{s+a}{s+b}$$$G_c(s)$ is a lead compensator if$a=1, \: b=2$$a=3, \: b=2$$a=-3, \: b=-1$$a=3, \: b=1$
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