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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 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
two-ticks
answered
in
Vector Analysis
Mar 18
by
two-ticks
670
points
300
views
gateec-2021
vector-analysis
vector-in-planes
0
votes
1
answer
2
GATE ECE 2016 Set 3 | GA Question: 5
It takes $10$s and $15$s, respectively, for two trains traveling at a different constant speeds to completely pass a telegraph post. The length of the first train is $120$ m and that of the second train is $150$ m. The magnitude of the difference in the speeds of the two trains (in m/s) is _________ $2.0$ $10.0$ $12.0$ $22.0$
two-ticks
answered
in
Quantitative Aptitude
Mar 18
by
two-ticks
670
points
79
views
gate2016-ec-3
numerical-ability
speed-time-distance
1
vote
1
answer
3
GATE ECE 2020 | Question: 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 ___________.
Sweta910
answered
in
Probability and Statistics
Mar 18
by
Sweta910
150
points
154
views
gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
1
vote
1
answer
4
GATE ECE 2022 | GA Question: 5
An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) ... $\text{Q}$ $\text{Q}$ $\text{Q}$ and $\text{S}$ $\text{R}$ and $\text{S}$
Lakshman Patel RJIT
answered
in
Spatial Aptitude
Feb 26
by
Lakshman Patel RJIT
4.4k
points
76
views
gateece-2022
spatial-aptitude
patterns-in-two-dimensions
1
vote
1
answer
5
GATE ECE 2022 | GA Question: 9
In a class of five students $\text{P, Q, R, S}$ and $\text{T},$ ... given above, the person who has copied in the exam is $\text{R}$ $\text{P}$ $\text{Q}$ $\text{T}$
Lakshman Patel RJIT
answered
in
Analytical Aptitude
Feb 26
by
Lakshman Patel RJIT
4.4k
points
86
views
gateece-2022
analytical-aptitude
logical-reasoning
statements-follow
1
vote
1
answer
6
GATE ECE 2022 | GA Question: 10
Consider the following square with the four corners and the center marked as $\text{P, Q, R, S}$ and $\text{T}$ respectively. Let $\text{X, Y}$ and $\text{Z}$ represent the following operations: $\text{X:}$ rotation of the square by $180$ ... The sequence of operations $(2)$ and $(3)$ are equivalent The sequence of operations $(1), (2)$ and $(3)$ are equivalent
Lakshman Patel RJIT
answered
in
Spatial Aptitude
Feb 26
by
Lakshman Patel RJIT
4.4k
points
68
views
gateece-2022
spatial-aptitude
rotation
1
vote
1
answer
7
GATE ECE 2022 | GA Question: 1
Mr. $\text{X}$ speaks __________ Japanese ____________ Chinese. neither /or either / nor neither / nor also / but
Lakshman Patel RJIT
answered
in
Verbal Aptitude
Feb 21
by
Lakshman Patel RJIT
4.4k
points
89
views
gateece-2022
verbal-aptitude
most-appropriate-word
1
vote
1
answer
8
GATE ECE 2022 | GA Question: 4
The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a “hole in the interior” that can be formed within the $4 \times 4$ grid using the unit squares as building blocks? $15$ $20$ $21$ $26$
Lakshman Patel RJIT
answered
in
Spatial Aptitude
Feb 21
by
Lakshman Patel RJIT
4.4k
points
68
views
gateece-2022
spatial-aptitude
patterns-in-two-dimensions
counting-figure
1
vote
1
answer
9
GATE ECE 2022 | GA Question: 3
A trapezium has vertices marked as $\text{P, Q, R}$ and $\text{S}$ (in that order anticlockwise). The side $\text{PQ}$ is parallel to side $\text{SR}.$ Further, it is given that, $\text{PQ = 11 cm, QR = 4 cm, RS = 6 cm}$ and $\text{SP = 3 cm.}$ What is the shortest distance between $\text{PQ}$ and $\text{SR (in cm)}?$ $1.80$ $2.40$ $4.20$ $5.76$
Lakshman Patel RJIT
answered
in
Quantitative Aptitude
Feb 21
by
Lakshman Patel RJIT
4.4k
points
123
views
gateece-2022
quantitative-aptitude
geometry
1
vote
1
answer
10
GATE ECE 2022 | GA Question: 8
Four points $\text{P(0, 1), Q(0, – 3), R( – 2, – 1),}$ and $\text{S(2, – 1)}$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral? $4$ $4 \sqrt{2}$ $8$ $8 \sqrt{2}$
Lakshman Patel RJIT
answered
in
Quantitative Aptitude
Feb 21
by
Lakshman Patel RJIT
4.4k
points
58
views
gateece-2022
quantitative-aptitude
cartesian-coordinates
area
1
vote
1
answer
11
GATE ECE 2022 | GA Question: 2
A sum of money is to be distributed among $\text{P, Q, R,}$ and $\text{S}$ in the proportion $5:2:4:3,$ respectively. If $\text{R}$ gets $ ₹ \; 1000$ more than $\text{S},$ what is the share of $\text{Q (in ₹)}?$ $500$ $1000$ $1500$ $2000$
Lakshman Patel RJIT
answered
in
Quantitative Aptitude
Feb 21
by
Lakshman Patel RJIT
4.4k
points
82
views
gateece-2022
quantitative-aptitude
ratio-proportions
1
vote
1
answer
12
GATE ECE 2022 | GA Question: 7
Consider the following inequalities. $2x – 1 > 7$ $2x – 9 < 1$ Which one of the following expressions below satisfies the above two inequalities? $x \leq – 4$ $ – 4 < x \leq 4$ $4 < x < 5$ $x \geq 5$
Lakshman Patel RJIT
answered
in
Quantitative Aptitude
Feb 19
by
Lakshman Patel RJIT
4.4k
points
58
views
gateece-2022
quantitative-aptitude
inequality
0
votes
0
answers
13
GATE ECE 2022 | GA Question: 6
Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be ... may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence
Arjun
asked
in
Analytical Aptitude
Feb 15
by
Arjun
5.9k
points
62
views
gateece-2022
analytical-aptitude
logical-reasoning
passage-reading
0
votes
0
answers
14
GATE ECE 2022 | Question: 1
Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}$ denote the unit vectors along the $x - $axis and the $y - $ ... $0$ $1$ $8 + 2 \pi$ $ - 1$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
50
views
gateece-2022
0
votes
0
answers
15
GATE ECE 2022 | Question: 2
Consider a system of linear equations $Ax = b,$ where $A =\begin{bmatrix} 1 & – \sqrt{2} & 3 \\ – 1 & \sqrt{2} & – 3 \end{bmatrix}, \quad b = \begin{bmatrix} 1 \\ 3 \end{bmatrix}.$ This system of equations admits ______________. a unique solution for $x$ infinitely many solutions for $x$ no solutions for $x$ exactly two solutions for $x$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
62
views
gateece-2022
0
votes
0
answers
16
GATE ECE 2022 | Question: 3
The current $I$ in the circuit shown is ______________. $1.25 \times 10^{-3} \; \text{A}$ $0.75 \times 10^{-3} \; \text{A}$ $ – 0.5 \times 10^{-3} \; \text{A}$ $1.16 \times 10^{-3} \; \text{A}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
42
views
gateece-2022
0
votes
0
answers
17
GATE ECE 2022 | Question: 4
Consider the circuit shown in the figure. The current $I$ flowing through the $10 \; \Omega$ resistor is _____________. $1 \; \text{A}$ $0 \; \text{A}$ $0.1 \; \text{A}$ $ – 0.1 \; \text{A}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
33
views
gateece-2022
0
votes
0
answers
18
GATE ECE 2022 | Question: 5
The Fourier transform $X(j \omega)$ of the signal $x(t) = \frac{t}{(1+t^{2})^{2}}$ is ______________. $\frac{\pi}{2j} \omega e^{– |\omega|}$ $\frac{\pi}{2} \omega e^{– |\omega|}$ $\frac{\pi}{2j}e^{– |\omega|}$ $\frac{\pi}{2}e^{– |\omega|}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
33
views
gateece-2022
0
votes
0
answers
19
GATE ECE 2022 | Question: 6
Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10} \; \text{cm}^{-3}.$ Electron and hole diffusion lengths are $2 \; \mu\text{m}$ ... $3.7 \times 10^{14} \; \text{cm}^{-3}$ $10^{3} \; \text{cm}^{-3}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
29
views
gateece-2022
0
votes
0
answers
20
GATE ECE 2022 | Question: 7
In a non-degenerate bulk semiconductor with electron density $n = 10^{16} \; \text{cm}^{-3},$ the value of $E_{c} - E_{Fn} = 200 \; \text{meV},$ where $E_{c}$ and $E_{Fn}$ denote the bottom of the conduction band energy and electron Fermi level energy, ... given options, is ____________. $226 \; \text{meV}$ $174 \; \text{meV}$ $218 \; \text{meV}$ $182 \; \text{meV}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
63
views
gateece-2022
0
votes
0
answers
21
GATE ECE 2022 | Question: 8
Consider the $\text{CMOS}$ circuit shown in the figure (substrates are connected to their respective sources). The gate width $(W)$ to gate length $(L)$ ratios $\left( \frac{W}{L} \right)$ of the transistors are as shown. Both the transistors have the same gate oxide capacitance ... $2\; \text{V}$ less than $2 \; \text{V}$ equal to $2 \; \text{V}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
41
views
gateece-2022
0
votes
0
answers
22
GATE ECE 2022 | Question: 9
Consider the $ \text{2-bit}$ multiplexer $\text{(MUX)}$ shown in the figure. For $\text{OUTPUT}$ to be the $\text{XOR}$ of $\text{C}$ and $\text{D},$ the values for $A_{0}, A_{1}, A_{2},$ and $A_{3}$ are _______________. $A_{0} = 0, A_{1} = 0, A_{2} = 1, A_{3} = 1$ ... $A_{0} = 0, A_{1} = 1, A_{2} = 1, A_{3} = 0$ $A_{0} = 1, A_{1} = 1, A_{2} = 0, A_{3} = 0$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
35
views
gateece-2022
0
votes
0
answers
23
GATE ECE 2022 | Question: 10
The ideal long channel $n\text{MOSFET}$ and $p\text{MOSFET}$ devices shown in the circuits have threshold voltages of $1 \; \text{V}$ and $ - 1 \; \text{V},$ respectively. The $\text{MOSFET}$ substrates are connected to their respective sources. Ignore leakage currents and assume that the ... $V_{1} = 4 \; \text{V}, \quad V_{2} = - 5 \; \text{V}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
57
views
gateece-2022
0
votes
0
answers
24
GATE ECE 2022 | Question: 11
Consider a closed-loop control system with unity negative feedback and $KG(s)$ in the forward path. where the gain $K = 2.$ The complete Nyquist plot of the transfer function $G(s)$ is shown in the figure. Note that the Nyquist contour has been ... of the closed-loop transfer function in the closed right-half of the complex plane is ________________. $0$ $1$ $2$ $3$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
46
views
gateece-2022
0
votes
0
answers
25
GATE ECE 2022 | Question: 12
The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Note that $K$ is varied from $0$ to $\infty.$ Select the transfer function $G(s)$ that results in the root-locus plot of the closed-loop system as ... $G(s) = \frac{s - 1}{(s+1)^{6}}$ $G(s) = \frac{s + 1}{s^{6}+1}$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
49
views
gateece-2022
0
votes
0
answers
26
GATE ECE 2022 | Question: 13
The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure. Statement $\text{I}:$ The system is necessarily a pure delay system for inputs which are bandlimited to $ - \alpha \leq f \leq \alpha.$ Statement ... $\text{II}$ is correct Statement $\text{I}$ is incorrect, Statement $\text{II}$ is incorrect
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
37
views
gateece-2022
0
votes
0
answers
27
GATE ECE 2022 | Question: 14
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current $\text{(in Amperes)}$ through the resistor is $2\sin (t+\pi/2).$ The displacement current $\text{(in Amperes)}$ through the capacitor is ______________. $2 \sin (t)$ $2 \sin (t + \pi)$ $2 \sin(t + \pi/2)$ $0$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
38
views
gateece-2022
0
votes
0
answers
28
GATE ECE 2022 | Question: 15
Consider the following partial differential equation $\text{(PDE)}$ $a \frac{ \partial^{2} f(x ,y)}{\partial x^{2}} + b \frac{ \partial^{2} f(x ,y)}{\partial y^{2}} = f(x, y),$ where $a$ and $b$ are distinct positive real numbers. Select the combination(s) of values of the ... $\xi = 0, \eta = 0$ $\xi = \frac{1}{\sqrt{a}}, \eta = \frac{1}{\sqrt{b}}$
Arjun
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Others
Feb 15
by
Arjun
5.9k
points
30
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gateece-2022
multiple-selects
0
votes
0
answers
29
GATE ECE 2022 | Question: 16
An ideal $\text{OPAMP}$ circuit with a sinusoidal input is shown in the figure. The $3 \; \text{dB}$ frequency is the frequency at which the magnitude of the voltage gain decreases by $3 \; \text{dB}$ from the maximum value. Which of the options is/are correct? The circuit ... $1000 \; \text{rad/s}.$ The $3 \; \text{dB}$ frequency is $\frac{1000}{3} \; \text{rad/s}.$
Arjun
asked
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Others
Feb 15
by
Arjun
5.9k
points
39
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gateece-2022
0
votes
0
answers
30
GATE ECE 2022 | Question: 17
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation. $x + z + xy$ $(x + y)(x + z)$ $x + xy + yz$ $x + xz + xy$
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
34
views
gateece-2022
multiple-selects
0
votes
0
answers
31
GATE ECE 2022 | Question: 18
Select the correct statement(s) regarding $\text{CMOS}$ implementation of $\text{NOT}$ gates. Noise Margin High $(NM_{H})$ is always equal to the Noise Margin Low $(NM_{L}),$ irrespective of the sizing of transistors. Dynamic power consumption ... $\text{NOT}$ gate.
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
35
views
gateece-2022
0
votes
0
answers
32
GATE ECE 2022 | Question: 19
Let $H(X)$ denote the entropy of a discrete random variable $X$ taking $K$ possible distinct real values. Which of the following statements is/are necessarily true? $H(X) \leq \log_{2} K \; \text{bits}$ $H(X) \leq H (2X)$ $H(X) \leq H (X^{2})$ $H(X) \leq H (2^{X})$
Arjun
asked
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Others
Feb 15
by
Arjun
5.9k
points
41
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gateece-2022
multiple-selects
0
votes
0
answers
33
GATE ECE 2022 | Question: 20
Consider the following wave equation, $\frac{\partial^{2}f(x, t)}{\partial t^{2}} = 10000 \frac{\partial^{2}f(x, t)}{\partial x^{2}} $ Which of the given options is/are solution(s) to the given wave equation? $f(x, t) = e^{ - (x-100t)^{2}} + e^{ - (x+100t)^{2}}$ ... $f(x, t) = e^{ j 100 \pi (- 100x + t)} + e^{ j 100 \pi (100x + t)}$
Arjun
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Others
Feb 15
by
Arjun
5.9k
points
32
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gateece-2022
multiple-selects
0
votes
0
answers
34
GATE ECE 2022 | Question: 21
The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in $17$ of her matches, the bowler has taken $5$ wickets each. The median number of wickets taken by the bowler in a match is _______________ (rounded off to one decimal place).
Arjun
asked
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Others
Feb 15
by
Arjun
5.9k
points
57
views
gateece-2022
numerical-answers
0
votes
0
answers
35
GATE ECE 2022 | Question: 22
A simple closed path $C$ in the complex plane is shown in the figure. If $\oint_{c} \frac{2^{z}}{z^{2} – 1}dz = – i \pi A,$ where $i = \sqrt{-1},$ then the value of $A$ is _________ (rounded off to two decimal places).
Arjun
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Others
Feb 15
by
Arjun
5.9k
points
48
views
gateece-2022
numerical-answers
0
votes
0
answers
36
GATE ECE 2022 | Question: 23
Let $x_{1} (t) = e^{-t}u(t)$ and $x_{2}(t) = u(t) – u(t – 2),$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_{1}(t)$ and $x_{2}(t),$ then $\displaystyle \lim_{t \rightarrow \infty} y(t) =$ ______________ (rounded off to one decimal place).
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
34
views
gateece-2022
numerical-answers
0
votes
0
answers
37
GATE ECE 2022 | Question: 24
An ideal $\text{MOS}$ capacitor (p-type semiconductor) is shown in the figure. The $\text{MOS}$ capacitor is under strong inversion with $V_{G} = 2 \; \text{V}.$ The corresponding inversion charge density $(Q_{IN})$ is $2.2 \; \mu \text{C /cm}^{2}.$ ... $Q_{IN}$ is ______________ $\mu \text{C/cm}^{2}$ (rounded off to one decimal place).
Arjun
asked
in
Others
Feb 15
by
Arjun
5.9k
points
31
views
gateece-2022
numerical-answers
0
votes
0
answers
38
GATE ECE 2022 | Question: 25
A symbol stream contains alternate $\text{QPSK}$ and $\text{16-QAM}$ symbols. If symbols from this stream are transmitted at the rate of $1$ mega-symbols per second, the raw (uncoded) data rate is ____________ mega-bits per second (rounded off to one decimal place).
Arjun
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Others
Feb 15
by
Arjun
5.9k
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20
views
gateece-2022
numerical-answers
0
votes
0
answers
39
GATE ECE 2022 | Question: 26
The function $f(x) = 8 \log_{e} x – x^{2} + 3$ attains its minimum over the interval $[1, e]$ at $x = $____________. (Here $\log_{e}x$ is the natural logarithm of $x$.) $2$ $1$ $e$ $\frac{1+e}{2}$
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Others
Feb 15
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Arjun
5.9k
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18
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gateece-2022
0
votes
0
answers
40
GATE ECE 2022 | Question: 27
Let $\alpha, \beta$ be two non-zero real numbers and $v_{1}, v_{2}$ be two non-zero real vectors of size $3 \times 1.$ Suppose that $v_{1}$ and $v_{2}$ satisfy $v_{1}^{T} v_{2} = 0, v_{1}^{T} v_{1} = 1,$ and $v_{2}^{T} v_{2} = 1.$ Let $A$ be ... $0, \alpha+\beta, \alpha-\beta$ $0, \frac{\alpha+\beta}{2}, \sqrt{\alpha \beta}$ $0, 0, \sqrt{\alpha^{2} + \beta^{2}}$
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Feb 15
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27
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