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242
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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245
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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247
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...
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248
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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249
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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250
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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254
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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256
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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257
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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259
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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260
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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266
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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269
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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271
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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273
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$$i(t) =8 \cos \bigg( 377t + \frac{\pi}{6} \b...
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276
GATE Electrical 2019 | Question: 45
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________
A single-phase transformer of rating $25$ kVA, supplies a $12$ kW load at power factor of $0.6$ lagging. The additional load at unity power factor in kW (round off to two...
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278
GATE Electrical 2018 | Question: 7
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is $11$ $12$ $13$ $14$
The graph of a network has $8$ nodes and $5$ independent loops. The number of branches of the graph is$11$$12$$13$$14$
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279
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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