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1
GATE2020-EC: 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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gate2020-ec
vector-analysis
engineering-mathematics
+1
vote
0
answers
2
GATE2020-EC: 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
(
1.4k
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gate2020-ec
engineering-mathematics
vector-analysis
0
votes
0
answers
3
GATE2020-EC: 3
The partial derivative of the function $f(x, y, z) = e^{1-x\cos y} + xze^{-1/(1+y^{2})}$ 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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gate2020-ec
partial-differential-equations
engineering-mathematics
0
votes
0
answers
4
GATE2020-EC: 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)
gate2020-ec
engineering-mathematics
0
votes
0
answers
5
GATE2020-EC: 5
The output $y[n]$ of a discrete-time 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
Continuous-time Signals
by
jothee
(
1.4k
points)
gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
impulse-response
0
votes
0
answers
6
GATE2020-EC: 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 mid-bandgap 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)
gate2020-ec
digital-circuits
semiconductor
0
votes
0
answers
7
GATE2020-EC: 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)
gate2020-ec
electronic-devices
0
votes
0
answers
8
GATE2020-EC: 8
The components in the circuit shown below are ideal. If the op-amp 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 non-inverted 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)
gate2020-ec
communications
amplitude
0
votes
0
answers
9
GATE2020-EC: 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)
gate2020-ec
network-solution-methods
thevenin-theorem
0
votes
0
answers
10
GATE2020-EC: 11
The pole-zero 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 counter-clockwise direction. the origin of the $G(s)$- ... $-1 + j0$ of the $G(s)$-plane once in the clockwise direction.
asked
Feb 13, 2020
in
Continuous-time Signals
by
jothee
(
1.4k
points)
gate2020-ec
continuous-time-signals
poles-and-zeros
0
votes
0
answers
11
GATE2020-EC: 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)
gate2020-ec
digital-communications
communications
0
votes
0
answers
12
GATE2020-EC: 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)
gate2020-ec
impedance
electromagnetics
0
votes
0
answers
13
GATE2020-EC: 14
Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]$
asked
Feb 13, 2020
in
Continuous-time Signals
by
jothee
(
1.4k
points)
gate2020-ec
poles-and-zeros
continuous-time-signals
0
votes
0
answers
14
GATE2020-EC: 15
In the given circuit, the two-port 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)
gate2020-ec
numerical-answers
network-solution-methods
two-port-network
0
votes
0
answers
15
GATE2020-EC: 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)
gate2020-ec
numerical-answers
network-solution-methods
0
votes
0
answers
16
GATE2020-EC: 17
In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decimal places) is ______ $V$.
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020-ec
numerical-answers
network-solution-methods
steady-state
sinusoidal
0
votes
0
answers
17
GATE2020-EC: 18
In the circuit shown below, all the components are ideal. If $V_{i}$ is $+2\:V$, the current $I_{o}$ sourced by the op-amp is __________ $\text{mA}$.
asked
Feb 13, 2020
in
Analog Circuits
by
jothee
(
1.4k
points)
gate2020-ec
numerical-answers
op-amps
analog-circuits
0
votes
0
answers
18
GATE2020-EC: 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)
gate2020-ec
numerical-answers
digital-circuits
microprocessor-8085
0
votes
0
answers
19
GATE2020-EC: 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)
gate2020-ec
numerical-answers
digital-circuits
data-converters
0
votes
0
answers
20
GATE2020-EC: 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)
gate2020-ec
numerical-answers
impedance
electromagnetics
0
votes
0
answers
21
GATE2020-EC: 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)
gate2020-ec
numerical-answers
entropy
communications
0
votes
0
answers
22
GATE2020-EC: 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)
gate2020-ec
numerical-answers
network-solution-methods
transfer-function
0
votes
0
answers
23
GATE2020-EC: 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 two-sided 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)
gate2020-ec
numerical-answers
vector-analysis
engineering-mathematics
gausss-theorem
0
votes
0
answers
24
GATE2020-EC: 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)
gate2020-ec
numerical-answers
engineering-mathematics
0
votes
0
answers
25
GATE2020-EC: 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)
gate2020-ec
engineering-mathematics
0
votes
0
answers
26
GATE2020-EC: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y-1 \right )x?$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=-1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=-1$
asked
Feb 13, 2020
in
Differential Equations
by
jothee
(
1.4k
points)
gate2020-ec
differential-equations
engineering-mathematics
0
votes
0
answers
27
GATE2020-EC: 28
The current $I$ in the given network is $0 \: A$ $2.38\angle -96.37^{\circ}A$ $2.38\angle143.63^{\circ}A$ $2.38\angle-23.63^{\circ}A$
asked
Feb 13, 2020
in
Network Solution Methods
by
jothee
(
1.4k
points)
gate2020-ec
network-solution-methods
0
votes
0
answers
28
GATE2020-EC: 29
A finite duration discrete-time signal $x[n]$ is obtained by sampling the continuous-time 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 non-zero. Only $X[2]$ and $X[6]$ are non-zero. Only $X[3]$ and $X[5]$ are non-zero.
asked
Feb 13, 2020
in
Continuous-time Signals
by
jothee
(
1.4k
points)
gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
0
votes
0
answers
29
GATE2020-EC: 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)
gate2020-ec
network-solution-methods
state-equations
0
votes
0
answers
30
GATE2020-EC: 31
A one-sided 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)
gate2020-ec
electronic-devices
p-n-junction-diode
0
votes
0
answers
31
GATE2020-EC: 32
The band diagram of a $p$-type semiconductor with a band-gap 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)
gate2020-ec
digital-circuits
semiconductor
0
votes
0
answers
32
GATE2020-EC: 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)
gate2020-ec
analog-circuits
bipolar-junction-transistor
0
votes
0
answers
33
GATE2020-EC: 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)
gate2020-ec
electronic-devices
p-n-junction
0
votes
0
answers
34
GATE2020-EC: 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)
gate2020-ec
analog-circuits
bipolar-junction-transistor
0
votes
0
answers
35
GATE2020-EC: 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)
gate2020-ec
electronic-devices
mosfet
0
votes
0
answers
36
GATE2020-EC: 37
Using the incremental low frequency small-signal 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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gate2020-ec
network-solution-methods
nortons
0
votes
0
answers
37
GATE2020-EC: 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)
gate2020-ec
control-systems
0
votes
0
answers
38
GATE2020-EC: 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)
gate2020-ec
state-diagram
sequence-detector
control-systems
0
votes
0
answers
39
GATE2020-EC: 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 break-away or break-in points(s) lie within $(-1, 0)$ $(-2, -1)$ $(-3, -2)$ $(-\infty, -3)$
asked
Feb 13, 2020
in
Control Systems
by
jothee
(
1.4k
points)
gate2020-ec
control-systems
bode-and-root-locus-plots
0
votes
0
answers
40
GATE2020-EC: 41
The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $-3$ dB cut-off 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)
gate2020-ec
control-systems
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