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1
GATE2020EC: 1
If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$? It is not necessary that these vectors span $\mathbb{R}^{4}$ ... $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.
asked
Feb 13, 2020
in
Vector Analysis
by
jothee
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gate2020ec
vectoranalysis
engineeringmathematics
+1
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0
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2
GATE2020EC: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
asked
Feb 13, 2020
in
Vector Analysis
by
jothee
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gate2020ec
engineeringmathematics
vectoranalysis
0
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0
answers
3
GATE2020EC: 3
The partial derivative of the function $f(x, y, z) = e^{1x\cos y} + xze^{1/(1+y^{2})}$ with respect to $x$ at the point $(1,0,e)$ is $1$ $0$ $1 \\$ $\dfrac{1}{e}$
asked
Feb 13, 2020
in
Differential Equations
by
jothee
(
1.4k
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gate2020ec
partialdifferentialequations
engineeringmathematics
0
votes
0
answers
4
GATE2020EC: 4
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is $y=C_{1}e^{3x}+C_{2}e^{3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=C_{1}e^{3x}$
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
1.4k
points)
gate2020ec
engineeringmathematics
0
votes
0
answers
5
GATE2020EC: 5
The output $y[n]$ of a discretetime system for an input $x[n]$ is $y\left [ n \right ]=\underset{\infty \leq k\leq n}{\text{max}} \mid x\left [ k \right ] \mid$ The unit impulse response of the system is $0$ for all $n$. $1$ for all $n$. unit step signal $u\left [ n \right ].$ unit impulse signal $\delta \left [ n \right ].$
asked
Feb 13, 2020
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
impulseresponse
0
votes
0
answers
6
GATE2020EC: 6
A single crystal intrinsic semiconductor is at a temperature of $300$ $\text{K}$ with effective density of states for holes twice that of electrons. The thermal voltage is $26$ mV. The intrinsic Fermi level is shifted from midbandgap energy level by $18.02 \: meV$ $9.01 \: meV$ $13.45 \: meV$ $26.90 \: meV$
asked
Feb 13, 2020
in
Digital Circuits
by
jothee
(
1.4k
points)
gate2020ec
digitalcircuits
semiconductor
0
votes
0
answers
7
GATE2020EC: 7
Consider the recombination process via bulk traps in a forward biased $pn$ homojunction diode. The maximum recombination rate is $U_{\text{max}}$ ... applied bias. With all other parameters unchanged, $U_{\text{max}}$ increases if the thermal velocity of the carriers increases.
asked
Feb 13, 2020
in
Electronic Devices
by
jothee
(
1.4k
points)
gate2020ec
electronicdevices
0
votes
0
answers
8
GATE2020EC: 8
The components in the circuit shown below are ideal. If the opamp is in positive feedback and the input voltage $V_{i}$ is a sine wave of amplitude $1$ $\text{V}$, the output voltage $V_{o}$ is a noninverted sine wave of $2$ $\text{V}$ amplitude. an inverted sine wave ... amplitude. a square wave of $5$ $\text{V}$ amplitude. a constant of either $+5$ $\text{V}$ or $5$ $\text{V}$.
asked
Feb 13, 2020
in
Communications
by
jothee
(
1.4k
points)
gate2020ec
communications
amplitude
0
votes
0
answers
9
GATE2020EC: 9
In the circuit shown below, the Thevenin voltage $V_{TH}$is $2.4\:V$ $2.8\:V$ $3.6\:V$ $4.5\:V$
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
networksolutionmethods
thevenintheorem
0
votes
0
answers
10
GATE2020EC: 11
The polezero map of a rational function $G(s)$ is shown below. When the closed contour $\Gamma$ is mapped into the $G(s)$plane, then the mapping encircles the origin of the $G(s)$plane once in the counterclockwise direction. the origin of the $G(s)$ ... $1 + j0$ of the $G(s)$plane once in the clockwise direction.
asked
Feb 13, 2020
in
Continuoustime Signals
by
jothee
(
1.4k
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gate2020ec
continuoustimesignals
polesandzeros
0
votes
0
answers
11
GATE2020EC: 12
A digital communication system transmits a block of $N$ bits. The probability of error in decoding a bit is $\alpha$. The error event of each bit is independent of the error events of the other bits. The received block is declared erroneous if at least one of its bits is decoded wrongly. The ... $\alpha ^{N}$ $1\alpha ^{N}$ $1\left ( 1\alpha \right )^{N}$
asked
Feb 13, 2020
in
Communications
by
jothee
(
1.4k
points)
gate2020ec
digitalcommunications
communications
0
votes
0
answers
12
GATE2020EC: 13
The impedances $Z=jX,$ for all $X$ in the range $\left ( \infty ,\infty \right )$, map to the Smith chart as a circle of radius $1$ with centre at $(0, 0)$. a point at the centre of the chart. a line passing through the centre of the chart. a circle of radius $0.5$ with centre at $(0.5, 0)$.
asked
Feb 13, 2020
in
Electromagnetics
by
jothee
(
1.4k
points)
gate2020ec
impedance
electromagnetics
0
votes
0
answers
13
GATE2020EC: 14
Which one of the following polezero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the inputoutput difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( 1 \right )^{k}x\left [ nk \right ]$
asked
Feb 13, 2020
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
polesandzeros
continuoustimesignals
0
votes
0
answers
14
GATE2020EC: 15
In the given circuit, the twoport network has the impedance matrix $\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}$. The value of $Z_{L}$ for which maximum power is transferred to the load is _____________$\Omega$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
networksolutionmethods
twoportnetwork
0
votes
0
answers
15
GATE2020EC: 16
The current in the $\text{RL}$circuit shown below is $i\left ( t \right )=10\cos\left ( 5t\pi /4 \right )A$. The value of the inductor $\text{(rounded off to two decimal places)}$ is _______ $\text{H}$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
networksolutionmethods
0
votes
0
answers
16
GATE2020EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steadystate output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
networksolutionmethods
steadystate
sinusoidal
0
votes
0
answers
17
GATE2020EC: 18
In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the opamp is __________ $\text{mA}$.
asked
Feb 13, 2020
in
Analog Circuits
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
opamps
analogcircuits
0
votes
0
answers
18
GATE2020EC: 19
In an $8085$ microprocessor, the number of address lines required to access a $16$ K byte memory bank is ____________ .
asked
Feb 13, 2020
in
Digital Circuits
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
digitalcircuits
microprocessor8085
0
votes
0
answers
19
GATE2020EC: 20
A $10$bit D/A converter is calibrated over the full range from $0$ to $10$ V. If the input to the D/A converter is $13 \:A$ (in hex), the output ( rounded off to three decimal places) is __________ $V$.
asked
Feb 13, 2020
in
Digital Circuits
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
digitalcircuits
dataconverters
0
votes
0
answers
20
GATE2020EC: 21
A transmission line of length $3\lambda /4$ and having a characteristic impedance of $50$ $\Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is __________ $\Omega$.
asked
Feb 13, 2020
in
Electromagnetics
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
impedance
electromagnetics
0
votes
0
answers
21
GATE2020EC: 22
A binary random variable $X$ takes the value $+2$ or $2$. The probability $P(X=+2)=\alpha $. The value of $\alpha$ (rounded off to one decimal place), for which the entropy of $X$ is maximum, is __________.
asked
Feb 13, 2020
in
Communications
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
entropy
communications
0
votes
0
answers
22
GATE2020EC: 23
The loop transfer function of a negative feedback system is $G\left ( s \right )H\left ( s \right )=\frac{K(s+11)}{s(s+2)(s+8)}.$ The value of $K$, for which the system is marginally stable, is ___________.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
networksolutionmethods
transferfunction
0
votes
0
answers
23
GATE2020EC: 24
The random variable $Y=\int_{\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\ 0; & \text{otherwise} \end{cases}$ and $W(t)$ is a real white Gaussian noise process with twosided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
asked
Feb 13, 2020
in
Vector Analysis
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
vectoranalysis
engineeringmathematics
gaussstheorem
0
votes
0
answers
24
GATE2020EC: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
engineeringmathematics
0
votes
0
answers
25
GATE2020EC: 26
Consider the following system of linear equations. $\begin{array}{llll} x_{1}+2x_{2}=b_{1} ; & 2x_{1}+4x_{2}=b_{2}; & 3x_{1}+7x_{2}=b_{3} ; & 3x_{1}+9x_{2}=b_{4} \end{array}$ ... $b_{2}=2b_{1}$ and $3b_{1}6b_{3}+b_{4}=0$ $b_{3}=2b_{1}$ and $3b_{1}6b_{3}+b_{4}=0$
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
1.4k
points)
gate2020ec
engineeringmathematics
0
votes
0
answers
26
GATE2020EC: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y1 \right )x?$ $\ln\mid y1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y1 \mid=2x^{2}+C$ and $y=1$
asked
Feb 13, 2020
in
Differential Equations
by
jothee
(
1.4k
points)
gate2020ec
differentialequations
engineeringmathematics
0
votes
0
answers
27
GATE2020EC: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle 96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle23.63^{\circ}A$
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
networksolutionmethods
0
votes
0
answers
28
GATE2020EC: 29
A finite duration discretetime signal $x[n]$ is obtained by sampling the continuoustime signal $x\left ( t \right )=\cos\left ( 200\pi t \right )$ at sampling instants $t=n/400, n=0, 1, \dots ,7.$ The $8$point discrete Fourier transform $\text{(DFT)}$ of $x[n]$ is defined ... zero. Only $X[4]$ is nonzero. Only $X[2]$ and $X[6]$ are nonzero. Only $X[3]$ and $X[5]$ are nonzero.
asked
Feb 13, 2020
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
votes
0
answers
29
GATE2020EC: 30
For the given circuit, which one of the following is correct state equation? ...
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020ec
networksolutionmethods
stateequations
0
votes
0
answers
30
GATE2020EC: 31
A onesided abrupt $pn$ junction diode has a depletion capacitance $C_{D}$ of $50$ $\text{pF}$ at a reverse bias of $0.2 V$. The plot of $1/C^{2}_{D}$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is ___________ $\times 10^{20}F^{2}V^{1}$. $5.7$ $3.8$ $1.2$ $0.4$
asked
Feb 13, 2020
in
Electronic Devices
by
jothee
(
1.4k
points)
gate2020ec
electronicdevices
pnjunctiondiode
0
votes
0
answers
31
GATE2020EC: 32
The band diagram of a $p$type semiconductor with a bandgap of $1$ eV is shown. Using this semiconductor, a $\text{MOS}$ capacitor having $V_{TH}$ of $0.16 V$, ${C}'_{ox}$ of $100\:nF/cm^{2}$ and a metal work function of $3.87 \: eV$ is fabricated. There is no charge within the ... $C/cm^{2}$) is $1.70\times 10^{8}$ $0.52\times 10^{8}$ $1.41\times 10^{8}$ $0.93\times 10^{8}$
asked
Feb 13, 2020
in
Digital Circuits
by
jothee
(
1.4k
points)
gate2020ec
digitalcircuits
semiconductor
0
votes
0
answers
32
GATE2020EC: 33
The base of an $\text{npn BJT T1}$ has a linear doping profile $N_{B}\left ( x \right )$ as shown below. The base of another $\text{npn BJT T2}$ has a uniform doping $N_{B}$ of $10^{17}cm^{3}$. All other parameters are identical for both the devices. ... $\text{T1}$. approximately $2.5$ times that of $\text{T1}$. approximately $0.7$ times that of $\text{T1}$.
asked
Feb 13, 2020
in
Analog Circuits
by
jothee
(
1.4k
points)
gate2020ec
analogcircuits
bipolarjunctiontransistor
0
votes
0
answers
33
GATE2020EC: 34
A $pn$ junction solar cell of area $1.0\:cm^{2}$, illuminated uniformly with $100\:mW\:cm^{2}$, has the following parameters: Efficiency $= 15\%$, open circuit voltage $= 0.7\:V$, fill factor $= 0.8$, and thickness $=200 \mu m$ ... $0.84\times 10^{19}.$ $5.57\times 10^{19}.$ $1.04\times 10^{19}.$ $83.60\times 10^{19}.$
asked
Feb 13, 2020
in
Electronic Devices
by
jothee
(
1.4k
points)
gate2020ec
electronicdevices
pnjunction
0
votes
0
answers
34
GATE2020EC: 35
For the $\text{BJT}$ in the amplifier shown below, $V_{BE}=0.7V,\:kT/q=26\:mV$. Assume that $\text{BJT}$ output resistance $(r_{o})$ is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input ... . The low frequency voltage gain $v_{o}/v_{i}$ of the amplifier is $89.42$ $128.21$ $178.85$ $256.42$
asked
Feb 13, 2020
in
Analog Circuits
by
jothee
(
1.4k
points)
gate2020ec
analogcircuits
bipolarjunctiontransistor
0
votes
0
answers
35
GATE2020EC: 36
An enhancement $\text{MOSFET}$ of threshold voltage $3\:V$ is being used in the sample and hold circuit given below. Assume that the substrate of the $\text{MOS}$ device is connected to $10\:V$. If the input voltage $V_{1}$ lies between $\pm 10\:V,$ ... $\text{10 V and 10 V}$. $\text{13 V and 7 V}$. $\text{10 V and 13 V}$.
asked
Feb 13, 2020
in
Electronic Devices
by
jothee
(
1.4k
points)
gate2020ec
electronicdevices
mosfet
0
votes
0
answers
36
GATE2020EC: 37
Using the incremental low frequency smallsignal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is $r_{ds}+R+g_{m}r_{ds}R \\$ $\dfrac{r_{ds}+R}{1+g_{m}r_{ds}} \\$ $r_{ds}+\dfrac{1}{g_{m}}+R \\$ $r_{ds}+R$
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
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gate2020ec
networksolutionmethods
nortons
0
votes
0
answers
37
GATE2020EC: 38
$P, Q$, and $R$ are the decimal integers corresponding to the $4$bit binary number $1100$ considered in signed magnitude, $1$’s complement, and $2$’s complement representations, respectively. The $6$bit $2$’s complement representation of $(P+Q+R)$ is $110101$ $110010$ $111101$ $111001$
asked
Feb 13, 2020
in
Control Systems
by
jothee
(
1.4k
points)
gate2020ec
controlsystems
0
votes
0
answers
38
GATE2020EC: 39
The state diagram of a sequence detector is shown below. State $S_{0}$ is the initial state of the sequence detector. If the output is $1$, then the sequence $01010$ is detected. the sequence $01011$ is detected. the sequence $01110$ is detected. the sequence $01001$ is detected.
asked
Feb 13, 2020
in
Control Systems
by
jothee
(
1.4k
points)
gate2020ec
statediagram
sequencedetector
controlsystems
0
votes
0
answers
39
GATE2020EC: 40
The characteristic equation of a system is $s^{3}+3s^{2}+\left ( K+2 \right )s+3K=0.$ In the root locus plot for the given system, as $K$ varies from $0$ to $\infty$, the breakaway or breakin points(s) lie within $(1, 0)$ $(2, 1)$ $(3, 2)$ $(\infty, 3)$
asked
Feb 13, 2020
in
Control Systems
by
jothee
(
1.4k
points)
gate2020ec
controlsystems
bodeandrootlocusplots
0
votes
0
answers
40
GATE2020EC: 41
The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $3$ dB cutoff frequency of the circuit in Hz is $14.92$ $34.46$ $59.68$ $79.58$
asked
Feb 13, 2020
in
Control Systems
by
jothee
(
1.4k
points)
gate2020ec
controlsystems
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