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281
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 2020 | Question: 37
Suppose for input $x(t)$ a linear time-invariant system with impulse response $h(t)$ produces output $y(t)$,so that $x\left ( t \right )*h\left ( t \right )=y\left ( t \right )$ ... $t\:\in \left ( -\infty, \infty \right ),z\left ( t \right )\geq y\left ( t \right )$
Suppose for input $x(t)$ a linear time-invariant system with impulse response $h(t)$ produces output $y(t)$,so that $x\left ( t \right )*h\left ( t \right )=y\left ( t \r...
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GATE Electrical 2020 | Question: 38
The causal realization of a system transfer function $H(s)$ having poles at $(2,-1), (-2,1)$ and zeroes at $(2,1), (-2,-1)$ will be stable, real, allpass unstable, complex, allpass unstable, real, highpass stable, complex, lowpass
The causal realization of a system transfer function $H(s)$ having poles at $(2,-1), (-2,1)$ and zeroes at $(2,1), (-2,-1)$ will be stable, real, allpassunstable, complex...
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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:$$y\left [ n \right ]-ay\left [ n-1 \right ]=b_...
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285
GATE Electrical 2020 | Question: 40
Let $a_{r},\:a_{\phi }$ and $a_{z}$ be unit vectors along $r,\:\phi$ and $z$ ... $z$-axis with its base at the origin is: $54\:\pi$ $90\:\pi$ $108\:\pi$ $180\:\pi$
Let $a_{r},\:a_{\phi }$ and $a_{z}$ be unit vectors along $r,\:\phi$ and $z$ directions, respectively in the cylindrical coordinate system. For the electric flux density ...
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GATE Electrical 2020 | Question: 41
A stable real linear time-invariant system with single pole at $\text{p}$, has a transfer function $H\left ( s \right )=\dfrac{s^{2}+100}{s-p}$ with a $\text{dc}$ gain of $5$. The smallest positive frequency, in $\text{rad/s}$, at unity gain is closest to: $8.84$ $11.08$ $78.13$ $122.87$
A stable real linear time-invariant system with single pole at $\text{p}$, has a transfer function $H\left ( s \right )=\dfrac{s^{2}+100}{s-p}$ with a $\text{dc}$ gain of...
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287
GATE Electrical 2020 | Question: 42
The number of purely real elements in a lower triangular representation of the given $3\times 3$ ... $5$ $6$ $8$ $9$
The number of purely real elements in a lower triangular representation of the given $3\times 3$ matrix, obtained through the given decomposition is ______________.$$\beg...
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Feb 28, 2020
Linear Algebra
gate2020-ee
linear-algebra
matrices
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288
GATE Electrical 2020 | Question: 43
The figure below shows the per-phase Open Circuit Characteristics (measured in $\text{V}$) and Short Circuit Characteristics (measured in $\text{A}$) of a $14 \: kVA$, $400 \: V$, $50 \: Hz$, $4$-pole, $3$ ... $2.100$ $2.025$ $2.000$ $1.000$
The figure below shows the per-phase Open Circuit Characteristics (measured in $\text{V}$) and Short Circuit Characteristics (measured in $\text{A}$) of a $14 \: kVA$, $4...
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GATE Electrical 2020 | Question: 44
Let $a_{x}$ and $a_{y}$ be unit vectors along $x$ and $y$ directions, respectively. A vector function is given by $F=a_{x}y-a_{y}x$ The line integral of the above function $\int _{C}F.dl$ along the curve $\textbf{C}$, which follows the parabola $y=x^{2}$ as shown below is ___________ (rounded off to $2$ decimal places).
Let $a_{x}$ and $a_{y}$ be unit vectors along $x$ and $y$ directions, respectively. A vector function is given by $$F=a_{x}y-a_{y}x$$The line integral of the above functi...
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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 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 2020 | Question: 47
Bus $1$ with voltage magnitude $V_{1}=1.1 \: pu$ is sending reactive power $Q_{12}$ towards bus $2$ with voltage magnitude $\text{$V_{2}=1$ pu}$ through a lossless transmission line of reactance $X$. Keeping the voltage at bus $ ... value of the voltage magnitude, $V_{1}$, in $pu$ ( rounded off to $2$ decimal places), at bus $1$ is___________________.
Bus $1$ with voltage magnitude $V_{1}=1.1 \: pu$ is sending reactive power $Q_{12}$ towards bus $2$ with voltage magnitude $\text{$V_{2}=1$ pu}$ through a lossless transm...
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GATE Electrical 2020 | Question: 48
Windings $\text{ A','B'}$ and $\text{ C'}$ have $20$ turns each and are wound on the same iron core as shown, along with winding $\text{ X'}$ which has $2$ turns. The figure shows the sense (clockwise/anti-clockwise) of each of the windings ... $\text{RMS}$ voltage (in $\text{V}$, rounded off to $2$ decimal places) across winding $\text{ X'}$ is _______________.
Windings $\text{‘A’,’B’}$ and $\text{‘C’}$ have $20$ turns each and are wound on the same iron core as shown, along with winding $\text{‘X’}$ which has $2...
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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 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 2020 | Question: 51
A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a $10 \: \Omega$ resistance in series with a very large inductance. The rectifier is fed from an ideal $230 \: V$, $50 \: Hz$ sinusoidal source through ... $\alpha =45^{\circ}$, the commutation overlap angle in degree (rounded off to $2$ decimal places) is _______________.
A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a $10 \: \Omega$ resistance in series with a very large inductance. The rectifie...
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GATE Electrical 2020 | Question: 52
A non-ideal $\text{Si}$-based $\text{pn}$ junction diode is tested by sweeping the bias applied across its terminals from $-5\:V$ to $5\:V$. The effective thermal voltage, $V_{T}$ ... percentage uncertainty (rounded off to $2$ decimal places) in the measured current at a bias voltage of $\text{0.02 V}$ is ____________.
A non-ideal $\text{Si}$-based $\text{pn}$ junction diode is tested by sweeping the bias applied across its terminals from $-5\:V$ to $5\:V$. The effective thermal voltage...
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GATE Electrical 2020 | Question: 53
The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, $R_{thermistor}=2\left ( 1+\alpha\:T \right )k\Omega$, where $\text{T}$ is the temperature in ... the output signal (in $\text{V}$ , rounded off to $2$ decimal places) at $150^{\circ}C$ is ____________.
The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, $R_{ther...
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GATE Electrical 2020 | Question: 54
An $8085$ microprocessor acesses two memory locations $\text{(2001H)}$ and $\text{(2002H)}$, that contain $8$-bit numbers $\text{98H}$ and $\text{B1H}$, respectively. The following program is executed: LXI H,2001H MVI A, 21 H INX H ... the end of this program, the memory location $\text{2003H}$ contains the number in decimal $\text{(base 10)}$ form _____________.
An $8085$ microprocessor acesses two memory locations $\text{(2001H)}$ and $\text{(2002H)}$, that contain $8$-bit numbers $\text{98H}$ and $\text{B1H}$, respectively. The...
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GATE Electrical 2020 | Question: 55
A conducting square loop of side length $1\:m$ is placed at a distance of $1\:m$ from a long straight wire carrying a current $I = 2 A$ as shown below. The mutual inductance, in $nH$ (rounded off to $2$ decimal places), between the conducting loop and the long wire is __________.
A conducting square loop of side length $1\:m$ is placed at a distance of $1\:m$ from a long straight wire carrying a current $I = 2 A$ as shown below. The mutual inducta...
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Gate2006-EE
...
$\\ P=\begin{pmatrix} -10\\ -1\\ 3 \end{pmatrix}^{T} Q=\begin{pmatrix} -2\\ -5\\ 9 \end{pmatrix}^{T} R=\begin{pmatrix} 2\\ -7\\ 12 \end{pmatrix}^{T} are\ three\ vectors.\...
KUSHAGRA गुप्ता
120
points
KUSHAGRA गुप्ता
asked
Sep 29, 2019
Linear Algebra
gate2006-ee
linear-algebra
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302
GATE Electrical 2019 | GA Question: 1
I am not sure if the bus that has been booked will be able to ______ all the students. sit deteriorate fill accommodate
I am not sure if the bus that has been booked will be able to ______ all the students.sitdeterioratefillaccommodate
Arjun
15.9k
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Arjun
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Feb 12, 2019
Verbal Aptitude
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verbal-ability
most-appropriate-word
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303
GATE Electrical 2019 | GA Question: 2
The passengers were angry ______ the airline staff about the delay. on about with towards
The passengers were angry ______ the airline staff about the delay.onaboutwithtowards
Arjun
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Feb 12, 2019
Verbal Aptitude
gate2019-ee
verbal-ability
prepositions
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304
GATE Electrical 2019 | GA Question: 3
The missing number in the given sequence $343,1331,$_____$,4913$ is $3375$ $2744$ $2197$ $4096$
The missing number in the given sequence $343,1331,$_____$,4913$ is$3375$$2744$$2197$$4096$
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Feb 12, 2019
Analytical Aptitude
gate2019-ee
analytical-aptitude
logical-reasoning
sequence-series
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305
GATE Electrical 2019 | GA Question: 4
It takes two hours for a person $X$ to mow the lawn. $Y$ can mow the same lawn in four hours. How long (in minutes) will it take $X$ and $Y,$ if they work together to mow the lawn$?$ $60$ $80$ $90$ $120$
It takes two hours for a person $X$ to mow the lawn. $Y$ can mow the same lawn in four hours. How long (in minutes) will it take $X$ and $Y,$ if they work together to mow...
Arjun
15.9k
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Arjun
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Feb 12, 2019
Quantitative Aptitude
gate2019-ee
numerical-ability
work-time
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306
GATE Electrical 2019 | GA Question: 5
Newspapers are a constant source of delight and recreation for me. The ________ trouble is that I read _______ many of them. even, quite even, too only, quite only, too
Newspapers are a constant source of delight and recreation for me. The ________ trouble is that I read _______ many of them.even, quiteeven, tooonly, quiteonly, too
Arjun
15.9k
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Feb 12, 2019
Verbal Aptitude
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verbal-ability
most-appropriate-word
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307
GATE Electrical 2019 | GA Question: 6
How many integers are there between $100$ and $1000$ all of whose digits are even? $60$ $80$ $100$ $90$
How many integers are there between $100$ and $1000$ all of whose digits are even?$60$$80$$100$$90$
Arjun
15.9k
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Feb 12, 2019
Quantitative Aptitude
gate2019-ee
numerical-ability
arithmetic-series
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308
GATE Electrical 2019 | GA Question: 7
The ration of the number of boys and girls who participated in an examination is $4:3.$ The total percentage of candidates who passed the examination is $80$ and the percentage of girls who passed the exam is $90.$ The percentage of boys who passed is _______. $55.50$ $72.50$ $80.50$ $90.00$
The ration of the number of boys and girls who participated in an examination is $4:3.$ The total percentage of candidates who passed the examination is $80$ and the perc...
Arjun
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Feb 12, 2019
Quantitative Aptitude
gate2019-ee
numerical-ability
percentage
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309
GATE Electrical 2019 | GA Question: 8
An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women but women feel more guilty about shopping. which one of the following statements can be inferred from the given text? Some men and ... in buying on impulse Few men and women indulge in buying on impulse Many men and women indulge in buying on impulse
An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women but women feel more guilty about shopping.which one of the ...
Arjun
15.9k
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Arjun
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Feb 12, 2019
Verbal Aptitude
gate2019-ee
verbal-ability
verbal-reasoning
statements-follow
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310
GATE Electrical 2019 | GA Question: 9
Given two sets $X=\{1,2,3\}$ and $Y=\{2,3,4\},$ we construct a set $Z$ of all possible fractions where the numerators belong to set $X$ and the denominators belong to set $Y.$ The product of elements having minimum and maximum values in the set $Z$ is _____. $1/12$ $1/8$ $1/6$ $3/8$
Given two sets $X=\{1,2,3\}$ and $Y=\{2,3,4\},$ we construct a set $Z$ of all possible fractions where the numerators belong to set $X$ and the denominators belong to set...
Arjun
15.9k
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Arjun
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Feb 12, 2019
Quantitative Aptitude
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numerical-ability
numerical-computation
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311
GATE Electrical 2019 | GA Question: 10
Consider five people- Mita, Ganga, Rekha, Lakshmi, and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga. Which of the following conclusions are true? Lakshmi is taller than Rekha Rekha is shorter than Mita Rekha is taller than Sana Sana is shorter than Ganga $1$ and $3$ $3$ only $2$ and $4$ $1$ only
Consider five people- Mita, Ganga, Rekha, Lakshmi, and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.Which of ...
Arjun
15.9k
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Arjun
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Feb 12, 2019
Analytical Aptitude
gate2019-ee
analytical-aptitude
logical-reasoning
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312
GATE Electrical 2019 | Question: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$ $3te^{-t}+e^{-t}$ $3e^{-t}$ $2te^{-t}+e^{-t}$ $4te^{-t}+e^{-t}$
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$$3te^{-t}+e^{-t}$$3e^{-t}$$2te^{-t}+e^{-t}$$4te^{-t}+e^{-t}$
Arjun
15.9k
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Arjun
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Feb 12, 2019
Transform Theory
gate2019-ee
transform-theory
laplace-transform
inverse-laplace-transform
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313
GATE Electrical 2019 | Question: 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
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;...
Arjun
15.9k
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Arjun
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Feb 12, 2019
Differential Equations
gate2019-ee
differential-equations
partial-differential-equation
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314
GATE Electrical 2019 | Question: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}-1}{z} \\ $ $\frac{z^{2}-1}{z+2} \\ $ $\frac{z^{2}-1}{z-0.5} \\ $ $\frac{z^{2}-1}{z+j0.5} $
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ?$\frac{z^{2}-1}{z} \\ $$\frac{z^{2}-1}{z+2} \\ $$\frac{z^{2}-1}{z-0.5} \\ $$\frac{z^...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Complex Variables
gate2019-ee
complex-variables
analytic-functions
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315
GATE Electrical 2019 | Question: 5
The mean-square of a zero-mean random process is $\frac{kT}{c},$ where $k$ is Boltzmann’s constant, $T$ is the absolute temperature, and $C$ is a capacitance. The standard deviation of the random process is $\frac{kT}{c} \\ $ $\sqrt{\frac{kT}{c}} \\ $ $\frac{c}{kT} \\ $ $\frac{\sqrt{kT}}{c}$
The mean-square of a zero-mean random process is $\frac{kT}{c},$ where $k$ is Boltzmann’s constant, $T$ is the absolute temperature, and $C$ is a capacitance. The stand...
Arjun
15.9k
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Arjun
asked
Feb 12, 2019
new
gate2019-ee
probability-and-statistics
probability
standard-deviation
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316
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...
Arjun
15.9k
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Arjun
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Feb 12, 2019
new
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317
GATE Electrical 2019 | Question: 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 time-invariant system? $e^{+at}u(t)$ $e^{-a(t+T)}u(t)$ $1+e^{-at}u(t)$ $e^{-a(t-T)}u(t)$
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 ...
Arjun
15.9k
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Arjun
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Feb 12, 2019
new
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318
GATE Electrical 2019 | Question: 8
A $5kVA, 50V/100V,$ single-phase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is $4.5\%$ $9\%$ $5\%$ $1\%$
A $5kVA, 50V/100V,$ single-phase transformer has a secondary terminal voltage of $95V$ when loaded. The regulation of the transformer is$4.5\%$$9\%$$5\%$$1\%$
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
new
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319
GATE Electrical 2019 | Question: 9
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, $50Hz$ AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is $100 Hz$ $150 Hz$ $250 Hz$ $300 Hz$
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, $50Hz$ AC source. Assuming that the DC output current of the rectifier is constant, the low...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
new
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320
GATE Electrical 2019 | Question: 10
The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is rotor resistance rotor leakage reactance magnetizing reactance stator resistance
The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency isrotor resistance...
Arjun
15.9k
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Arjun
asked
Feb 12, 2019
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gate2019-ee
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