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1
GATE ECE 2021  Question: 1
The vector function $F\left ( r \right )=x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure. The line integral of $\int _{C} F\left ( r \right ).dr$ is $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.5k
points)

67
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gateec2021
vectoranalysis
vectorinplanes
0
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0
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2
GATE ECE 2021  Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1x^{2} \right )^{3/4}$ $\left ( 1x^{2} \right )^{1/4}$ $\left ( 1x^{2} \right )^{3/2}$ $\left ( 1x^{2} \right )^{1/2}$
asked
Feb 20
in
Differential Equations
by
Arjun
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4.5k
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43
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gateec2021
differentialequations
firstorderdifferentialequation
0
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0
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3
GATE ECE 2021  Question: 3
Two continuous random variables $X$ and $Y$ are related as $Y=2X+3$ Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The variances are related as $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
asked
Feb 20
in
Probability and Statistics
by
Arjun
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4.5k
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38
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gateec2021
probabilityandstatistics
randomvariable
variance
0
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0
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4
GATE ECE 2021  Question: 4
Consider a realvalued baseband signal $x(t)$, band limited to $\text{10 kHz}$. The Nyquist rate for the signal $y\left ( t \right )=x\left ( t \right )x\left ( 1+\dfrac{t}{2} \right )$ is $\text{15 kHz}$ $\text{30 kHz}$ $\text{60 kHz}$ $\text{20 kHz}$
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Feb 20
in
Others
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39
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gateec2021
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5
GATE ECE 2021  Question: 5
Consider two $16$point sequences $x\left [ n \right ]$ and $h\left [ n \right ]$. Let the linear convolution of $x\left [ n \right ]$ and $h\left [ n \right ]$ be denoted by $y\left [ n \right ]$, while $z\left [ n \right ]$ denotes the $16$point inverse discrete Fourier ... $k=0,1,2,,15$ $k=0$ $k=15$ $\text{k=0 and k=15}$
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Feb 20
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Others
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43
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gateec2021
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6
GATE ECE 2021  Question: 6
A bar of silicon is doped with boron concentration of $10^{16} \text{cm}^{3}$ and assumed to be fully ionized. It is exposed to light such that electronhole pairs are generated throughout the volume of the bar at the rate of $10^{20} \text{cm}^{3} s^{1}$. If the ... $2 \times 10^{20} \text{cm}^{6}$ $10^{32} \text{cm}^{6}$ $2 \times 10^{32} \text{cm}^{6}$
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Feb 20
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Others
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4.5k
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47
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gateec2021
0
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7
GATE ECE 2021  Question: 7
The energy band diagram of a $\text{ptype}$ semiconductor bar of length $L$ under equilibrium condition (i.e.. the Fermi energy level $E_{F}$ is constant) is shown in the figure. The valance band $E_{V}$ is sloped since doping is nonuniform along the bar. The difference ... bar is $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$
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Feb 20
in
Others
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4.5k
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31
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gateec2021
0
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8
GATE ECE 2021  Question: 8
In the circuit shown in the figure, the transistors $M_{1}$ and $M_{2}$ are operating in saturation. The channel length modulation coefficients of both the transistors are nonzero. The transconductance of the $\text{MOSFETs}$ $M_{1}$ and $M_{2}$ are $g_{m1}$ ... $g_{m2}\left ( \frac{1}{g_{m1}}\left  \right r_{01}\left  \right r_{02} \right )$
asked
Feb 20
in
Others
by
Arjun
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4.5k
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32
views
gateec2021
0
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0
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9
GATE ECE 2021  Question: 9
For the circuit with an ideal $\text{OPAMP}$ shown in the figure. $V_{\text{REF}}$ is fixed. If $V_{\text{OUT}}=1$ volt for $V_{\text{IN}}0.1$ volt and $V_{\text{OUT}}=6$ volt for $V_{\text{IN}}=1$ volt, where $V_{\text{OUT}}$ is measured across $R_{L}$ connected at the output of this $\text{OPAMP}$, the value of $R_{F}/R_{\text{IN}}$ is $3.285$ $2.860$ $3.825$ $5.555$
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Feb 20
in
Others
by
Arjun
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4.5k
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35
views
gateec2021
0
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0
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10
GATE ECE 2021  Question: 10
Consider the circuit with an ideal $\text{OPAMP}$ shown in the figure. Assuming $\left  V_{\text{IN}} \right \ll \left  V_{\text{CC}} \right $ and $\left  V_{\text{REF}} \right \ll \left  V_{\text{CC}} \right  $, the condition at which $V_{\text{OUT}}$ equals ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
asked
Feb 20
in
Others
by
Arjun
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4.5k
points)

44
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gateec2021
0
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11
GATE ECE 2021  Question: 11
If $(1235)_{x}\:=\:(3033)_{y}$, where $x$ and $y$ indicate the bases of the corresponding numbers, then $x\:=\:7$ and $y\:=\:5$ $x\:=\:8$ and $y\:=\:6$ $x\:=\:6$ and $y\:=\:4$ $x\:=\:9$ and $y\:=\:7$
asked
Feb 20
in
Digital Circuits
by
Arjun
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4.5k
points)

87
views
gateec2021
digitalcircuits
numbersystem
numberrepresentation
0
votes
0
answers
12
GATE ECE 2021  Question: 12
Addressing of a $32K\:\times\:16$ memory is realized using a single decoder. The minimum number of $\text{AND}$ gates required for the decoder is $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
asked
Feb 20
in
Digital Circuits
by
Arjun
(
4.5k
points)

50
views
gateec2021
digitalcircuits
combinationalcircuits
decoders
0
votes
0
answers
13
GATE ECE 2021  Question: 13
The block diagram of a feedback control system is shown in the figure The transfer function $\dfrac{Y{\left ( s \right )}}{X {\left ( s \right )}}$ of the system is $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
asked
Feb 20
in
Control Systems
by
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4.5k
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33
views
gateec2021
controlsystems
0
votes
0
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14
GATE ECE 2021  Question: 14
The complete Nyquist plot of the openloop transfer function $G(s)H(s)$ of a feedback control system in the figure. If $G(s)H(s)$ has one zero in the righthalf of the $s$plane, the number of poles that the closedloop system will have in the righthalf of the $s$plane is $0$ $1$ $4$ $3$
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

51
views
gateec2021
0
votes
0
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15
GATE ECE 2021  Question: 15
Consider a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x}\:a_{y}$ and $a_{z}$. A plane wave traveling in the region $z\geq 0$ with electric field vector $E=10\cos\left ( 2\times 10^{8}t\:+\:\beta z\right )a_{y}$ is incident normally on the ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
asked
Feb 20
in
Others
by
Arjun
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4.5k
points)

38
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gateec2021
0
votes
0
answers
16
GATE ECE 2021  Question: 16
If the vectors $(1.0,\:1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.5k
points)

45
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
17
GATE ECE 2021  Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4yc_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ in a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x},\:a_{y}$ and $a_{z}$. If the field $F$ is irrotational (conservative), then the constant $c_{1}$ (in integer) is _________________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.5k
points)

61
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
18
GATE ECE 2021  Question: 18
Consider the circuit shown in the figure. The current $I$ flowing through the $7\:\Omega$ resistor between $P$ and $Q$ (rounded off to one decimal place) is ________ $A$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

51
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gateec2021
numericalanswers
0
votes
0
answers
19
GATE ECE 2021  Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
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Feb 20
in
Others
by
Arjun
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4.5k
points)

46
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gateec2021
numericalanswers
0
votes
0
answers
20
GATE ECE 2021  Question: 20
An $8$bit unipolar (all analog output values are positive) digitaltoanalog converter $\text{(DAC)}$ has a fullscale voltage range from $0\; V$ to $7.68\:V$. If the digital input code is $10010110$ (the leftmost bit is $\text{MSB}$), then the analog output voltage of the $\text{DAC}$ (rounded off to one decimal place) is ___________ $V$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

28
views
gateec2021
numericalanswers
0
votes
0
answers
21
GATE ECE 2021  Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a widesense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

37
views
gateec2021
numericalanswers
0
votes
0
answers
22
GATE ECE 2021  Question: 22
Consider a carrier signal which is amplitude modulated by a singletone sinusoidal message signal with a modulation index of $50\%$. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is ______________
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

48
views
gateec2021
numericalanswers
0
votes
0
answers
23
GATE ECE 2021  Question: 23
A speech signal, band limited to $4\:\text{kHz}$, is sampled at $1.25$ times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range $5\:V$ to $+5\:V$, are ... transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is _____ $\text{kHz}$.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

68
views
gateec2021
numericalanswers
0
votes
0
answers
24
GATE ECE 2021  Question: 24
A $4\:kHz$ sinusoidal message signal having amplitude $4\:V$ is fed to a delta modulator ($DM$) operating at a sampling rate of $32\:\text{kHz}$. The minimum step size required to avoid slope overload noise in the $DM$ (rounded off to two decimal places) is _____ $V$.
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Feb 20
in
Others
by
Arjun
(
4.5k
points)

45
views
gateec2021
numericalanswers
0
votes
0
answers
25
GATE ECE 2021  Question: 25
The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.
asked
Feb 20
in
Others
by
Arjun
(
4.5k
points)

51
views
gateec2021
numericalanswers
0
votes
0
answers
26
GATE ECE 2021  Question: 26
Consider the integral $\oint _{c}\frac{sin\left ( x \right )}{x^{2}\left ( x^{2}+4 \right )}dx$ where $C$ is a counterclockwise oriented circle defined as $\left  xi \right =2$. The value of the integral is $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
asked
Feb 20
in
Complex Analysis
by
Arjun
(
4.5k
points)

147
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gateec2021
complexanalysis
0
votes
0
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27
GATE ECE 2021  Question: 27
A box contains the following three coins. A fair coin with head on one face and tail on the other face. A coin with heads on both the faces. A coin with tails on both the faces. A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one ... getting a head in the second toss is $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
asked
Feb 20
in
Probability and Statistics
by
Arjun
(
4.5k
points)

64
views
gateec2021
probabilityandstatistics
probability
conditionalprobability
0
votes
0
answers
28
GATE ECE 2021  Question: 28
The switch in the circuit in the figure is in position $P$ for a long time and then moved to position $Q$ at time $t=0$. The value of $\dfrac{dv\left ( t \right )}{dt}$ at $t=0^{+}$ is $0\:V/s$ $3\:V/s$ $3\:V/s$ $5\:V/s$
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Feb 20
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Others
by
Arjun
(
4.5k
points)

33
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gateec2021
0
votes
0
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29
GATE ECE 2021  Question: 29
Consider the twoport network shown in the figure. The admittance parameters, in siemens, are $y_{11}=2,\:y_{12}=4,\:y_{21}=4,\:y_{22}=2$ $y_{11}=1,\:y_{12}=2,\:y_{21}=1,\:y_{22}=3$ $y_{11}=2,\:y_{12}=4,\:y_{21}=1,\:y_{22}=2$ $y_{11}=2,\:y_{12}=4,\:y_{21}=4,\:y_{22}=3$
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Feb 20
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Others
by
Arjun
(
4.5k
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36
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gateec2021
0
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0
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30
GATE ECE 2021  Question: 30
For an $n$channel silicon $\text{MOSFET}$ with $10\:nm$ gate oxide thickness, the substrate sensitivity $\left ( \partial V_{T}/\partial \left  V_{BS} \right  \right )$ is found to be $50\:mV/V$ at a substrate voltage $\left  V_{BS} \right =2V$, where $V_{T}$ is the ... $4.37\times 10^{15}\:cm^{3}$ $2.37\times 10^{15}\:cm^{3}$ $9.37\times 10^{15}\:cm^{3}$
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Feb 20
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Others
by
Arjun
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4.5k
points)

29
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gateec2021
0
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31
GATE ECE 2021  Question: 31
The propagation delays of the $\text{XOR}$ gate, $\text{AND}$ gate and multiplexer $\text{(MUX)}$ in the circuit shown in the figure are $4\:ns$, $2\:ns$ and $1\:ns$, respectively. If all the inputs $\text{P, Q, R, S and T}$ are applied simultaneously and held constant, the maximum propagation delay of the circuit is $3\:ns$ $5\:ns$ $6\:ns$ $7\:ns$
asked
Feb 20
in
Digital Circuits
by
Arjun
(
4.5k
points)

67
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gateec2021
digitalcircuits
combinationalcircuits
multiplexers
0
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0
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32
GATE ECE 2021  Question: 32
The content of the registers are $R_{1} = 25H, R_{2} = 30H$ and $R_{3} = 40H$. The following machine instructions are executed. $\text{PUSH } \{R_{1}\}$ $\text{PUSH } \{R_{2}\}$ $\text{PUSH } \{R_{3}\}$ $\text{POP } \{R_{1}\}$ $\text{POP } \{R_{2}\}$ ... $R_{1}=30H,\:R_{2}=40H,\:R_{3}=25H$ $R_{1}=40H,\:R_{2}=25H,\:R_{3}=30H$
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Feb 20
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4.5k
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22
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33
GATE ECE 2021  Question: 33
The electrical system shown in the figure converts input source current $i_{s}(t)$ to output voltage $v_{o}(t)$ Current i $i_{L}(t)$ in the inductor and voltage $v_{c}(t)$ across the capacitor ... as well as completely observable completely state controllable but not observable completely observable but not state controllable neither state controllable nor observable
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Feb 20
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29
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34
GATE ECE 2021  Question: 34
A digital transmission system uses a ($7,4$) systematic linear Hamming code for transmitting data over a noisy channel. If three of the messagecodeword pairs in this code ($\text{m}_{i}$ ; $\text{c}_{i}$), where $\text{c}_{i}$ is the ... $\text{valid codeword}$ in this code? $1101001$ $1011010$ $0001011$ $0110100$
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Feb 20
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4.5k
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29
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35
GATE ECE 2021  Question: 35
The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarterwave line having a characteristic impedance $Z_1=75\:\Omega$ is connected to $Z_{L}$. Two stubs having ... the real part of $Z_{L}$ is $112.5\:\Omega$ $75.0\:\Omega$ $50.0\:\Omega$ $33.3\:\Omega$
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Feb 20
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23
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36
GATE ECE 2021  Question: 36
A real $2\times2$ nonsingular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & 3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________
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Feb 20
in
Linear Algebra
by
Arjun
(
4.5k
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32
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gateec2021
numericalanswers
linearalgebra
eigenvalues
0
votes
0
answers
37
GATE ECE 2021  Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________
asked
Feb 20
in
Vector Analysis
by
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4.5k
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25
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gateec2021
numericalanswers
vectoranalysis
0
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0
answers
38
GATE ECE 2021  Question: 38
In the circuit shown in the figure, the switch is closed at time $t=0$, while the capacitor is initially charged to $5\:V$ (i.e., $v_{c}(0)=5V$). The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is ________________ $\text{ms}$.
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Feb 20
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28
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39
GATE ECE 2021  Question: 39
The exponential Fourier series representation of a continuoustime periodic signal $x(t)$ is defined as $x\left ( t \right )=\sum_{k=\infty }^{\infty }a_{k}e^{jk\omega _{0}t}$ where $\omega _0$ ... $x(t)$ (rounded off to one decimal place) is ______________
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Feb 20
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40
GATE ECE 2021  Question: 40
For a unit step input $u[n]$, a discretetime $\text{LTI}$ system produces an output signal $\left ( 2\delta \left [ n+1 \right ] +\delta \left [ n \right ]+\delta \left [ n1 \right ]\right )$. Let $y[n]$ be the output of the system for an input $\left ( \left ( \dfrac{1}{2} \right )^n u\left [ n \right ]\right )$. The value of $y[0]$ is _________________
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