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1881
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 $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
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...
Arjun
6.6k
points
285
views
Arjun
asked
Feb 19, 2021
Differential Equations
gateec-2021
differential-equations
first-order-differential-equation
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1882
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 $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
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 vari...
Arjun
6.6k
points
222
views
Arjun
asked
Feb 19, 2021
Probability and Statistics
gateec-2021
probability-and-statistics
random-variable
variance
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0
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1883
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 $\text{15 kHz}$ $\text{30 kHz}$ $\text{60 kHz}$ $\text{20 kHz}$
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...
Arjun
6.6k
points
183
views
Arjun
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Feb 19, 2021
Others
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1884
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 ... $k=0,1,2,,15$ $k=0$ $k=15$ $\text{k=0 and k=15}$
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 denot...
Arjun
6.6k
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276
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Arjun
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Feb 19, 2021
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1885
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 ... $2 \times 10^{20} \text{cm}^{-6}$ $10^{32} \text{cm}^{-6}$ $2 \times 10^{32} \text{cm}^{-6}$
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 electro...
Arjun
6.6k
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334
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Arjun
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Feb 19, 2021
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1886
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 $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$
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 th...
Arjun
6.6k
points
225
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Arjun
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Feb 19, 2021
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1887
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 $g_{m1}$ ... $-g_{m2}\left ( \frac{1}{g_{m1}}\left | \right |r_{01}\left | \right |r_{02} \right )$
In the circuit shown in the figure, the transistors $M_{1}$ and $M_{2}$ are operating in saturation. The channel length modulation coefficients of bo...
Arjun
6.6k
points
195
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Arjun
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Feb 19, 2021
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1888
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 $3.285$ $2.860$ $3.825$ $5.555$
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 $V_{\text{OUT}}=6$...
Arjun
6.6k
points
189
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Arjun
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Feb 19, 2021
Others
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1889
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 ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
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{RE...
Arjun
6.6k
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226
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Arjun
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Feb 19, 2021
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1890
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 $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
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$2^{8}$...
Arjun
6.6k
points
194
views
Arjun
asked
Feb 19, 2021
Digital Circuits
gateec-2021
digital-circuits
combinational-circuits
decoders
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1891
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 $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
The block diagram of a feedback control system is shown in the figureThe transfer function $\dfrac{Y{\left ( s \right )}}{X {\left ( s \right )}}$ of the system is$\frac{...
Arjun
6.6k
points
278
views
Arjun
asked
Feb 19, 2021
Control Systems
gateec-2021
control-systems
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1892
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 $0$ $1$ $4$ $3$
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 $s$...
Arjun
6.6k
points
595
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Arjun
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Feb 19, 2021
Others
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1893
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 ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
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...
Arjun
6.6k
points
171
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Arjun
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Feb 19, 2021
Others
gateec-2021
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1894
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 __________
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
6.6k
points
274
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Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
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1895
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 _________________
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 ...
Arjun
6.6k
points
207
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Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
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1896
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 ________ $A$.
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
6.6k
points
227
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Arjun
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Feb 19, 2021
Others
gateec-2021
numerical-answers
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1897
GATE ECE 2021 | Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
Consider the circuit shown in the figure.The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
Arjun
6.6k
points
256
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Arjun
asked
Feb 19, 2021
Others
gateec-2021
numerical-answers
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1898
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 ___________ $V$.
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 di...
Arjun
6.6k
points
189
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Arjun
asked
Feb 19, 2021
Others
gateec-2021
numerical-answers
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1899
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 ________________
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 _________...
Arjun
6.6k
points
202
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Arjun
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Feb 19, 2021
Others
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numerical-answers
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1900
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 ______________
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 sideban...
Arjun
6.6k
points
181
views
Arjun
asked
Feb 19, 2021
Others
gateec-2021
numerical-answers
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1901
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 _____ $\text{kHz}$.
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 d...
Arjun
6.6k
points
256
views
Arjun
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Feb 19, 2021
Others
gateec-2021
numerical-answers
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1902
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 _____ $V$.
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 re...
Arjun
6.6k
points
197
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Arjun
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Feb 19, 2021
Others
gateec-2021
numerical-answers
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1903
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.
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 a...
Arjun
6.6k
points
233
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Arjun
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Feb 19, 2021
Others
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numerical-answers
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1904
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 $-\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $-\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
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 \...
Arjun
6.6k
points
323
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Arjun
asked
Feb 19, 2021
Complex Analysis
gateec-2021
complex-analysis
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1905
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 $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
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 fa...
Arjun
6.6k
points
437
views
Arjun
asked
Feb 19, 2021
Probability and Statistics
gateec-2021
probability-and-statistics
probability
conditional-probability
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1906
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 $0\:V/s$ $3\:V/s$ $-3\:V/s$ $-5\:V/s$
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...
Arjun
6.6k
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182
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Arjun
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Feb 19, 2021
Others
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1907
GATE ECE 2021 | Question: 29
Consider the two-port network shown in the figure. The admittance parameters, in siemens, are $y_{11}=2,\:y_{12}=-4,\:y_{21}=-4,\:y_{22}=2$ $y_{11}=1,\:y_{12}=-2,\:y_{21}=-1,\:y_{22}=3$ $y_{11}=2,\:y_{12}=-4,\:y_{21}=-1,\:y_{22}=2$ $y_{11}=2,\:y_{12}=-4,\:y_{21}=-4,\:y_{22}=3$
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...
Arjun
6.6k
points
113
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Arjun
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Feb 19, 2021
Others
gateec-2021
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1908
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}$
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 )...
Arjun
6.6k
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127
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Arjun
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Feb 19, 2021
Others
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1909
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$
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\...
Arjun
6.6k
points
675
views
Arjun
asked
Feb 19, 2021
Digital Circuits
gateec-2021
digital-circuits
combinational-circuits
multiplexers
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1910
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$
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_{...
Arjun
6.6k
points
121
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Arjun
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Feb 19, 2021
Others
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1911
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
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 $v_{c}(t)$...
Arjun
6.6k
points
213
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Arjun
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Feb 19, 2021
Others
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1912
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? $1101001$ $1011010$ $0001011$ $0110100$
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 cod...
Arjun
6.6k
points
278
views
Arjun
asked
Feb 19, 2021
Others
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1913
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 $112.5\:\Omega$ $75.0\:\Omega$ $50.0\:\Omega$ $33.3\:\Omega$
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 quarte...
Arjun
6.6k
points
212
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Arjun
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Feb 19, 2021
Others
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1914
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 ________________
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....
Arjun
6.6k
points
182
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Arjun
asked
Feb 19, 2021
Linear Algebra
gateec-2021
numerical-answers
linear-algebra
eigen-values
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1915
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 ________________
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...
Arjun
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Arjun
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Vector Analysis
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vector-analysis
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1916
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 ________________ $\text{ms}$.
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 th...
Arjun
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145
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Arjun
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Feb 19, 2021
Others
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1917
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 ______________
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 _...
Arjun
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113
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Arjun
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Others
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1918
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 _________________
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 ...
Arjun
6.6k
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85
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Others
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1919
GATE ECE 2021 | Question: 41
Consider the signals $x\left [ n \right ]=2^{n-1}u\left [ -n+2 \right ]$ and $y\left [ n \right ]=2^{-n+2}u\left [ n+1 \right ]$, where $u[n]$ is the unit step sequence. Let $X(e^{jw})$ and $Y(e^{jw})$ be the discrete-time Fourier ... (rounded off to one decimal place) is ___________
Consider the signals $x\left [ n \right ]=2^{n-1}u\left [ -n+2 \right ]$ and $y\left [ n \right ]=2^{-n+2}u\left [ n+1 \right ]$, where $u[n]$ is the unit step sequence. ...
Arjun
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74
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Arjun
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Others
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1920
GATE ECE 2021 | Question: 42
A silicon $P-N$ junction is shown in the figure. The doping in the $P$ region is $5\times10^{16}\:cm^{-3}$ and doping in the $N$ region is $10\times10^{16}\:cm^{-3}$ ... completely deplete one of the two regions ($P$ or $N$) prior to the other (rounded off to one decimal place) is ______________________ $V$.
A silicon $P-N$ junction is shown in the figure. The doping in the $P$ region is $5\times10^{16}\:cm^{-3}$ and doping in the $N$ region is $10\times10^{16}\:cm^{-3}$. The...
Arjun
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105
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Arjun
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Feb 19, 2021
Others
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