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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 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
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Vector Analysis
Feb 20, 2021
by
Arjun
4.5k
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184
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gateec-2021
vector-analysis
vector-in-planes
0
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0
answers
2
GATE ECE 2021 | Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
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Differential Equations
Feb 20, 2021
by
Arjun
4.5k
points
100
views
gateec-2021
differential-equations
first-order-differential-equation
0
votes
0
answers
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 $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
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Probability and Statistics
Feb 20, 2021
by
Arjun
4.5k
points
69
views
gateec-2021
probability-and-statistics
random-variable
variance
0
votes
0
answers
4
GATE ECE 2021 | Question: 4
Consider a real-valued base-band 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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Others
Feb 20, 2021
by
Arjun
4.5k
points
86
views
gateec-2021
0
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0
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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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Others
Feb 20, 2021
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4.5k
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118
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gateec-2021
0
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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 electron-hole 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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Others
Feb 20, 2021
by
Arjun
4.5k
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136
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gateec-2021
0
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0
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7
GATE ECE 2021 | Question: 7
The energy band diagram of a $\text{p-type}$ 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 non-uniform 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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Others
Feb 20, 2021
by
Arjun
4.5k
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85
views
gateec-2021
0
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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 non-zero. The transconductance of the $\text{MOSFETs}$ $M_{1}$ and $M_{2}$ are $g_{m1}$ ... $-g_{m2}\left ( \frac{1}{g_{m1}}\left | \right |r_{01}\left | \right |r_{02} \right )$
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Others
Feb 20, 2021
by
Arjun
4.5k
points
69
views
gateec-2021
0
votes
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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Others
Feb 20, 2021
by
Arjun
4.5k
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69
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gateec-2021
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 ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
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Others
Feb 20, 2021
by
Arjun
4.5k
points
75
views
gateec-2021
0
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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 $y\:=\:7$
Arjun
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in
Digital Circuits
Feb 20, 2021
by
Arjun
4.5k
points
170
views
gateec-2021
digital-circuits
number-system
number-representation
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 $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
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in
Digital Circuits
Feb 20, 2021
by
Arjun
4.5k
points
88
views
gateec-2021
digital-circuits
combinational-circuits
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 $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
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Control Systems
Feb 20, 2021
by
Arjun
4.5k
points
60
views
gateec-2021
control-systems
0
votes
0
answers
14
GATE ECE 2021 | Question: 14
The complete Nyquist plot of the open-loop transfer function $G(s)H(s)$ of a feedback control system in the figure. If $G(s)H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is $0$ $1$ $4$ $3$
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Others
Feb 20, 2021
by
Arjun
4.5k
points
196
views
gateec-2021
0
votes
0
answers
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 ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
Arjun
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Others
Feb 20, 2021
by
Arjun
4.5k
points
69
views
gateec-2021
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 __________
Arjun
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in
Vector Analysis
Feb 20, 2021
by
Arjun
4.5k
points
107
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
votes
0
answers
17
GATE ECE 2021 | Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4y-c_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ 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 _________________
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Vector Analysis
Feb 20, 2021
by
Arjun
4.5k
points
98
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
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 ________ $A$.
Arjun
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Others
Feb 20, 2021
by
Arjun
4.5k
points
98
views
gateec-2021
numerical-answers
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 _________ $V$.
Arjun
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Others
Feb 20, 2021
by
Arjun
4.5k
points
88
views
gateec-2021
numerical-answers
0
votes
0
answers
20
GATE ECE 2021 | Question: 20
An $8$-bit unipolar (all analog output values are positive) digital-to-analog converter $\text{(DAC)}$ has a full-scale 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 ___________ $V$.
Arjun
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Others
Feb 20, 2021
by
Arjun
4.5k
points
67
views
gateec-2021
numerical-answers
0
votes
0
answers
21
GATE ECE 2021 | Question: 21
The autocorrelation function $R_{X}\left ( \tau \right )$ of a wide-sense stationary random process $X(t)$ is shown in the figure. The average power of $X(t)$ is ________________
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Others
Feb 20, 2021
by
Arjun
4.5k
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68
views
gateec-2021
numerical-answers
0
votes
0
answers
22
GATE ECE 2021 | Question: 22
Consider a carrier signal which is amplitude modulated by a single-tone 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 ______________
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Others
Feb 20, 2021
by
Arjun
4.5k
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90
views
gateec-2021
numerical-answers
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 _____ $\text{kHz}$.
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Others
Feb 20, 2021
by
Arjun
4.5k
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120
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gateec-2021
numerical-answers
0
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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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Others
Feb 20, 2021
by
Arjun
4.5k
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79
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gateec-2021
numerical-answers
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.
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Others
Feb 20, 2021
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Arjun
4.5k
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96
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gateec-2021
numerical-answers
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 counter-clockwise oriented circle defined as $\left | x-i \right |=2$. The value of the integral is $-\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $-\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
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Complex Analysis
Feb 20, 2021
by
Arjun
4.5k
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186
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gateec-2021
complex-analysis
0
votes
0
answers
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 $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
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Probability and Statistics
Feb 20, 2021
by
Arjun
4.5k
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143
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gateec-2021
probability-and-statistics
probability
conditional-probability
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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Others
Feb 20, 2021
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58
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0
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29
GATE ECE 2021 | Question: 29
Consider the two-port 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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Others
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4.5k
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47
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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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Others
Feb 20, 2021
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41
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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 $3\:ns$ $5\:ns$ $6\:ns$ $7\:ns$
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Digital Circuits
Feb 20, 2021
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Arjun
4.5k
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186
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gateec-2021
digital-circuits
combinational-circuits
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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Others
Feb 20, 2021
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35
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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, 2021
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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 message-codeword 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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Others
Feb 20, 2021
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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 quarter-wave 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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Others
Feb 20, 2021
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49
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36
GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular 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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Linear Algebra
Feb 20, 2021
by
Arjun
4.5k
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67
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gateec-2021
numerical-answers
linear-algebra
eigen-values
0
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0
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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 ________________
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Vector Analysis
Feb 20, 2021
by
Arjun
4.5k
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43
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gateec-2021
numerical-answers
vector-analysis
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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Others
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numerical-answers
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39
GATE ECE 2021 | Question: 39
The exponential Fourier series representation of a continuous-time 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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Others
Feb 20, 2021
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numerical-answers
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40
GATE ECE 2021 | Question: 40
For a unit step input $u[n]$, a discrete-time $\text{LTI}$ system produces an output signal $\left ( 2\delta \left [ n+1 \right ] +\delta \left [ n \right ]+\delta \left [ n-1 \right ]\right )$. 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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