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GATE2020EE1
$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true? $\text{d}$ can be chosen to ensure that $\text{x = 0}$ is a root for any given set ... identical. $\text{a, b, c, d}$ can be chosen to ensure that all roots are complex. $\text{c}$ alone cannot ensure that all roots are real.
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GATE2020EE2
Which of the following is true for all possible nonzero choices of integers $m,n;m\neq n,$ or all possible nonzero choices of real numbers $p,q;p\neq q,$ as applicable? $\dfrac{1}{\pi }\int_{0}^{\pi }\sin m\theta \:\sin n\theta d\theta =0 \\$ ... $\lim_{\alpha \rightarrow \infty }\dfrac{1}{2\alpha }\int_{\alpha }^{\alpha }\sin p\theta \:\sin q\theta d\theta =0$
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GATE2020EE3
Which of the following statements is true about the two sided Laplace transform? It exists for every signal that may or may not have a Fourier transform. It has no poles for any bounded signal that is nonzero only inside a finite time interval. The ... If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.
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GATE2020EE4
Consider a signal $x\left [ n \right ]=\left ( \dfrac{1}{2} \right )^{n}1\left [ n \right ],$ where $1\left [ n \right ]=0$ if $n< 0$, and $1\left [ n \right ]= 1$ if $n \geq 0.$ The ztransform of $x\left [ nk \right ],\:k> 0$ ... region of convergence being $\mid z \mid< 2$ $\mid z \mid> 2$ $\mid z \mid < \dfrac{1}{2}$ $\mid z \mid > \dfrac{1}{2}$
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GATE2020EE5
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is: $\int _{C}\frac{z^{2}+1}{z^{2}2z}\:dz$ $8\pi i$ $8\pi i$ $\pi i$ $\pi i$
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GATE2020EE6
$x_{R}$ and $x_{A}$ are, respectively, the rms and average values of $x\left ( t \right )=x\left ( tT \right ),$ and similarly, $y_{R}$ and $y_{A}$ are, respectively, the rms and average values of $y\left ( t \right )=kx\left ( t \right ).\:k,T$ are independent of $\text{t}$. ... $y_{A}\neq kx_{A} ;\:y_{R}= kx_{R}$ $y_{A}\neq kx_{A} ;\:y_{R}\neq kx_{R}$
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GATE2020EE7
A threephase cylindrical rotor synchronous generator has a synchronous reactance $X_{s}$ and a negligible armature resistance. The magnitude of per phase terminal voltage is $V_{A}$ and the magnitude of per phase induced emf is $E_{A}$. Considering the following two statements, $P$ and $Q$ ... true $P$ is true and $Q$ is false $P$ is false and $Q$ is false $P$ is true and $Q$ is true
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GATE2020EE8
A lossless transmission line with $0.2$ $\text{pu}$ reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to $80 \%$ of its length by a distance relay placed at the generator bus. The generator ... for a solid three phasetoground fault on the transmission line is closest to: $1.00$ $3.61$ $5.00$ $6.25$
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GATE2020EE9
Out of the following options, the most relevant information needed to specify the real power $\text{(P)}$ at the $\text{PV}$ buses in a load flow analysis is solution of economic load dispatch rated power output of the generator rated voltage of the generator base power of the generator
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GATE2020EE10
Consider a linear timeinvariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation: $\frac{d^{2}y\left ( t \right )}{dt^{2}}+4y\left ( t \right )=6r\left ( t \right )$ The poles of this system are at $+2j,2j$ $+2,2$ $+4,4$ $+4j,4j$
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lineartimeinvariantsystem
signalsandsystems
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GATE2020EE11
A singlephase, fullbridge diode rectifier fed from a $230$ $\text{V}$, $50$ $\text{Hz}$ sinusoidal source supplies a series combination of finite resistance, $\text{R}$, and a very large inductance, $\text{L}$. The two most dominant frequency components in the source current are: $50\:Hz,\:0\:Hz$ $50\:Hz,\:100\:Hz$ $50\:Hz,\:150\:Hz$ $150\:Hz,\:250\:Hz$
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GATE2020EE12
Thyristor $T_{1}$ is triggered at an angle $\alpha$ (in degree), and $T_{2}$ at angle $180^{\circ}+\alpha$, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range $0$ to $\text{2 k W}$, the minimum range of ... $0^{\circ}$ to $120^{\circ}$ $60^{\circ}$ to $120^{\circ}$ $60^{\circ}$ to $180^{\circ}$
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GATE2020EE13
Which of the options is an equivalent representation of the signal flow graph shown here?
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GATE2020EE14
A commonsource amplifier with a drain resistance, $R_{D}=4.7\:k\Omega$, is powered using a $10\:V$ power supply. Assuming that the transconductance, $g_{m}$, is $520\:\mu A/V$, the voltage gain of the amplifier is closest to: $2.44$ $1.22$ $1.22$ $2.44$
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GATE2020EE15
A sequence detector is designed to detect precisely $3$ digital inputs, with overlapping sequences detectable. For the sequence $\text{(1,0,1)}$ and input data $(1,1,0,1,0,0,1,1,0,1,0,1,1,0)$, what is the output of this detector? $1,1,0,0,0,0,1,1,0,1,0,0$ $0,1,0,0,0,0,0,1,0,1,0,0$ $0,1,0,0,0,0,0,1,0,1,1,0$ $0,1,0,0,0,0,0,0,1,0,0,0$
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GATE2020EE16
Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is_____________________. $\frac{\mathrm{d} y}{\mathrm{d} x}=2xy,\:\:y\left ( 0 \right )=1$
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numericalanswers
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GATE2020EE17
A threephase, $\text{50 Hz}$, $4$pole induction motor runs at noload with a slip of $1\%$. With full load, the slip increases to $5 \%$. The $\%$ speed regulation of the motor (rounded off to $2$ decimal places) is _____________________.
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GATE2020EE18
Currents through ammeters $\text{A2}$ and $\text{A3}$ in the figure are $1\angle 10^{\circ}\:and\:1\angle 70^{\circ}$, respectively. The reading of the ammeter $\text{A1}$ (rounded off to $3$ decimal places) is_______$\text{A}$.
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GATE2020EE19
The Thevenin equivalent voltage, $V_{TH}$, in $\text{V}$ (rounded off to $2$ decimal places) of the network shown below, is _______
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GATE2020EE20
A double pulse measurement for an inductively loaded circuit controlled by the $\text{IGBT}$ switch is carried out to evaluate the reverse recovery characteristics of the diode, $\text{D}$, represented approximately as a piecewise linear plot of current vs time at diode turn ... $1, 2, 3$, or $4$) at which the $\text{IGBT}$ experiences the highest current stress is _________.
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GATE2020EE21
A singlephase, $\text{4 kVA}$, $200\: V/100 \: V$, $50 \: Hz$ transformer with laminated $\text{CRGO}$ steel core has rated noload loss of $450 \: W$. When the highvoltage winding is excited with $160 \: V$, $40 \: Hz$ sinusoidal ac supply ... $\text{25 Hz}$ sinusoidal ac source, the noload losses will be _____________________$\text{W}$ (rounded off to $2$ decimal places).
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GATE2020EE22
A singlephase inverter is fed from a $100 \: V$ dc source and is controlled using a quasisquare wave modulation scheme to produce an output waveform, $\nu\left ( t \right )$, as shown. The angle $\sigma$ is adjusted to entirely eliminate ... $2$ decimal places).
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GATE2020EE23
A single $50 \: Hz$ synchronous generator on droop control was delivering $100 \: MW$ power to a system. Due to increase in load, generator power had to be increased by $10 \: MW$, as a result of which, system frequency dropped to $49.75 \: Hz$. ... $\text{MW}$ supplied by the generator is _________________ (rounded off to $2$ decimal places).
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GATE2020EE24
Consider a negative unity feedback system with forward path transfer function $G\left ( s \right )=\dfrac{K}{\left ( s+a \right )\left ( sb \right )\left ( s+c \right )}$, where $\text{K, a, b, c}$ are positive real numbers. For a Nyquist path enclosing the ... $\dfrac{G\left ( s \right )}{1+G\left ( s \right )}$ lying in the open right half of the $\text{s}$plane is__________.
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GATE2020EE25
The crosssection of a metaloxidesemiconductor structure is shown schematically. Starting from an uncharged condition, a bias of $\text{+3 V}$ is applied to the gate contact with respect to the body contact. The charge inside the silicon dioxide layer is ... of bias, expressed as a multiple of $\text{Q}$ (absolute value in Coulombs, rounded off to the nearest integer) is___________
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GATE2020EE26
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ 2,0 \right ]$ are respectively, ______. $7$ and $1/4$ $7$ and $1$ $2$ and $1/2$ $1$ and $1/4$
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GATE2020EE27
The vector function expressed by $F=a_{x}\left ( 5yk_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y4x\right )$ represents a conservative field, where $a_{x}, a_{y},a_{z}$ are unit vectors along $x, y$ and $z$ ... $k_{1}=3, k_{2}=8,k_{3}=5$ $k_{1}=4, k_{2}=5,k_{3}=3$ $k_{1}=0, k_{2}=0,k_{3}=0$
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GATE2020EE28
A $250 V$ dc shunt motor has an armature resistance of $0.2\:\Omega$ and a field resistance of $100\:\Omega$. When the motor is operated on noload at rated voltage, it draws an armature current of $5 \: A$ and runs at $1200 \: rpm$. When a load ... all operating conditions. The speed of the motor, in $\text{rpm}$ under this loaded condition, is closest to: $1200$ $1000$ $1220$ $900$
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GATE2020EE29
Two buses, $\text{i and j}$, are connected with a transmission line admittance $y.$ ...
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GATE2020EE30
Consider the diode circuit shown below. The diode, D, obeys the currentvoltage 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 current through it. ... $R_{1}$ and small $R_{2}$. Large $R_{1}$ and small $R_{2}$. Small $R_{1}$ and large $R_{2}$.
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GATE2020EE31
A nonideal diode is biased with a voltage of $0.03 \: V$, and a diode current of $I_{1}$ is measured. The thermal voltage is $26 \: mV$ and the ideality factor for the diode is $15/13$. The voltage, in $V$, at which the measured current increases to $1.5 \: I_{1}$ is closest to: $0.02$ $0.09$ $1.50$ $4.50$
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GATE2020EE32
A benchtop dc power supply acts as an ideal $4 \: A$ current source as long as its terminal voltage is below $10 \: V$. Beyond this point, it begins to behave as an ideal $10 \: V$ voltage source for all load currents going down to $0 \: A$. When connected to an ideal rheostat, find the load resistance ... $2.5 \Omega, 4 \: A, 10 \: V$ $2.5 \Omega, 4 \: A , 5 \: V$
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GATE2020EE33
The static electric field inside a dielectric medium with relative permittivity, $\varepsilon _{r}=2.25$, expressed in cylindrical coordinate system is given by the following expression $E=a_{r}2r+a_{\varphi }\left ( \frac{3}{r} \right )+a_{z}6$ ... $3\varepsilon _{0}$ $4\varepsilon _{0}$ $5\varepsilon _{0}$ $9\varepsilon _{0}$
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GATE2020EE34
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 $0.5 \: s$ and finally settles to $10 \text{ rad/s}$. Assuming ... motor is $\dfrac{10}{0.5s+1} \\$ $\dfrac{2}{0.5s+1} \\$ $\dfrac{2}{s+0.5} \\$ $\dfrac{10}{s+0.5}$
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35
GATE2020EE35
Which of the following options is correct for the system shown below? $4^{th}$ order and stable $3^{rd}$ order and stable $4^{th}$ order and unstable $3^{rd}$ order and unstable
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36
GATE2020EE36
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 ____________. $9$ $8$ $7$ $6$
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37
GATE2020EE37
Suppose for input $x(t)$ a linear timeinvariant system with impulse response $h(t)$ produces output $y(t)$,so that $x\left ( t \right )*h\left ( t \right )=y\left ( t \right )$ ... $t\:\in \left ( \infty, \infty \right ),z\left ( t \right )\geq y\left ( t \right )$
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38
GATE2020EE38
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
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39
GATE2020EE39
Which of the following options is true for a linear timeinvariant discrete time system that obeys the difference equation: $y\left [ n \right ]ay\left [ n1 \right ]=b_{0}x\left [ n \right ]b_{1}x\left [ n1 \right ]$ $y[n]$ ... $y\left [ n \right];n > 0$ is solely determined by the function $x[n]$.
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40
GATE2020EE40
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 given by $D=\left ( a_{r}15+a_{\phi } 2r  a_{z} 3rz \right ) \text{ Coulomb}/m^{2}$, the total ... height $5\:m$ oriented along the $z$axis with its base at the origin is: $54\:\pi$ $90\:\pi$ $108\:\pi$ $180\:\pi$
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