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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 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
Arjun
answer selected
in
Vector Analysis
Mar 29
by
Arjun
5.9k
points
300
views
gateec-2021
vector-analysis
vector-in-planes
0
votes
0
answers
2
GATE ECE 2022 | Question: 39
Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation. The Boolean inputs $'0'$ and $'1'$ are also ... $\text{OR}$ logic cannot be implemented $\text{NOR}$ logic can be implemented $\text{AND}$ logic cannot be implemented
Lakshman Patel RJIT
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Others
Mar 21
by
Lakshman Patel RJIT
4.4k
points
13
views
gateece-2022
multiple-selects
0
votes
0
answers
3
GATE ECE 2022 | Question: 38
A state transition diagram with states $A, B,$ and $C,$ and transition probabilities $p_{1}, p_{2}, \dots, p_{7}$ is shown in the figure (e.g., $\text{p}_{1}$ denotes the probability of transition from state $A$ to $B$). For this state diagram, select the statement(s) which is/are ... $p_{1} + p_{4} + p_{7} = 1$ $p_{2} + p_{5} + p_{7} = 1$
Lakshman Patel RJIT
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Others
Mar 21
by
Lakshman Patel RJIT
4.4k
points
11
views
gateece-2022
multiple-selects
0
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0
answers
4
GATE ECE 2022 | Question: 37
Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices. Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium. Collector region is generally more heavily doped than Base region in a $\text{BJT}.$ ... under steady state condition. Mobility of electrons always increases with temperature in Silicon beyond $300 \; \text{K}.$
Lakshman Patel RJIT
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Others
Mar 21
by
Lakshman Patel RJIT
4.4k
points
23
views
gateece-2022
multiple-selects
0
votes
0
answers
5
GATE ECE 2022 | Question: 36
The outputs of four systems $(S_{1}, S_{2}, S_{3},$ and $\text{S}_{4})$ corresponding to the input signal $\sin(t),$ for all time $t,$ are shown in the figure. Based on the given information, which of the four systems is/are definitely $\text{NOT LTI}$ (linear and time-invariant)? $S_{1}$ $S_{2}$ $S_{3}$ $S_{4}$
Lakshman Patel RJIT
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Mar 21
by
Lakshman Patel RJIT
4.4k
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11
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gateece-2022
multiple-selects
0
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0
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6
GATE ECE 2022 | Question: 35
Consider the following series: $ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$ For which of the following combinations of $c, d$ values does this series converge? $ c= 1, d = – 1$ $ c= 2, d = 1$ $ c= 0.5, d = – 10$ $ c= 1, d = – 2$
Lakshman Patel RJIT
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in
Others
Mar 21
by
Lakshman Patel RJIT
4.4k
points
11
views
gateece-2022
multiple-selects
0
votes
0
answers
7
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? $f(x, t) = e^{ - (x-100t)^{2}} + e^{ - (x+100t)^{2}}$ ... $f(x, t) = e^{ j 100 \pi (- 100x + t)} + e^{ j 100 \pi (100x + t)}$
Lakshman Patel RJIT
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Mar 21
by
Lakshman Patel RJIT
4.4k
points
32
views
gateece-2022
multiple-selects
0
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0
answers
8
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? $H(X) \leq \log_{2} K \; \text{bits}$ $H(X) \leq H (2X)$ $H(X) \leq H (X^{2})$ $H(X) \leq H (2^{X})$
Lakshman Patel RJIT
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Others
Mar 21
by
Lakshman Patel RJIT
4.4k
points
41
views
gateece-2022
multiple-selects
0
votes
0
answers
9
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. $x + z + xy$ $(x + y)(x + z)$ $x + xy + yz$ $x + xz + xy$
Lakshman Patel RJIT
retagged
in
Others
Mar 21
by
Lakshman Patel RJIT
4.4k
points
34
views
gateece-2022
multiple-selects
0
votes
0
answers
10
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 ... $\xi = 0, \eta = 0$ $\xi = \frac{1}{\sqrt{a}}, \eta = \frac{1}{\sqrt{b}}$
Lakshman Patel RJIT
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Mar 21
by
Lakshman Patel RJIT
4.4k
points
30
views
gateece-2022
multiple-selects
0
votes
1
answer
11
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
12
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
13
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
14
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
answer edited
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
15
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
0
votes
0
answers
16
GATE ECE 2022 | Question: 31
For the following circuit with an ideal $\text{OPAMP},$ the difference between the maximum and the minimum values of the capacitor voltage $(V_{c})$ is ____________. $15 \; \text{V}$ $27 \; \text{V}$ $13 \; \text{V}$ $14 \; \text{V}$
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
14
views
gateece-2022
0
votes
0
answers
17
GATE ECE 2022 | Question: 32
A circuit with an ideal $\text{OPAMP}$ is shown. The Bode plot for the magnitude $\text{(in dB)}$ of the gain transfer function $(A_{V} (j \omega) = V_{\text{out}} (j \omega) / V_{\text{in}} (j \omega))$ of the circuuit is also provided (here, $\omega$ is the angular frequency ... $R = 3 \; \text{k} \Omega, C = 2 \; \mu \text{F}$
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
13
views
gateece-2022
0
votes
0
answers
18
GATE ECE 2022 | Question: 33
For the circuit shown, the clock frequency is $f_{0}$ and the duty cycle is $25 \%.$ For the signal at the $\text{Q}$ output of the Flip-Flop, _______________. frequency is $f_{0}/4$ and duty cycle is $50 \%$ frequency is $f_{0}/4$ and duty cycle is $25 \%$ frequency is $f_{0}/2$ and duty cycle is $50 \%$ frequency is $f_{0}$ and duty cycle is $25 \%$
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
13
views
gateece-2022
0
votes
0
answers
19
GATE ECE 2022 | Question: 34
Consider an even polynomial $p(s)$ given by $p(s) = s^{4} + 5s^{2} + 4 + K,$ where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all its roots on the imaginary axis is _____________. $ – 4 \leq K \leq \frac{9}{4}$ $ – 3 \leq K \leq \frac{9}{2}$ $ – 6 \leq K \leq \frac{5}{4}$ $ – 5 \leq K \leq 0$
soujanyareddy13
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in
Others
Feb 23
by
soujanyareddy13
100
points
15
views
gateece-2022
0
votes
0
answers
20
GATE ECE 2022 | Question: 40
Two linear time-invariant systems with transfer functions $G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$ have unit step responses $y_{1}(t)$ and $y_{2}(t),$ respectively. Which of the following ... and $y_{2}(t)$ have the same damped frequency of oscillation. $y_{1}(t)$ and $y_{2}(t)$ have the same $2\%$ settling time.
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
10
views
gateece-2022
0
votes
0
answers
21
GATE ECE 2022 | Question: 41
Consider an $\text{FM}$ broadcast that employs the pre-emphasis filter with frequency response $H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}},$ where $\omega_{0} = 10^{4} \; \text{rad/sec}.$ For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate ... $R = 1 \; k \Omega, C = 2 \; \mu F$ $R = 2 \; k \Omega, C = 0.5 \; \mu F$
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
22
views
gateece-2022
0
votes
0
answers
22
GATE ECE 2022 | Question: 42
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light in air to be $3 \times 10^{8} \; \text{m/s}.$ The frequency/frequencies of $\text{TM}$ waves which can ... $8 \times 10^{14} \; \text{Hz}$ $1 \times 10^{13} \; \text{Hz}$
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
11
views
gateece-2022
0
votes
0
answers
23
GATE ECE 2022 | Question: 43
The value of the integral $ \iint_{D} 3(x^{2} + y^{2})dxdy,$ where $D$ is the shaded triangular region shown in the diagram, is ___________ (rounded off to the nearest integer).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
16
views
gateece-2022
numerical-answers
0
votes
0
answers
24
GATE ECE 2022 | Question: 44
A linear $\text{2-port}$ network is shown in $\text{Fig.(a)}.$ An ideal $\text{DC}$ voltage source of $10 \; \text{V}$ is connected across Port $1.$ A variable resistance $R$ is connected across Port $2.$ As $R$ is varied, the measured voltage ... by the load shown in $\text{Fig.(c)},$ the current $I_{2}$ is ___________ $\text{mA}$ (rounded off to one decimal place).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
11
views
gateece-2022
numerical-answers
0
votes
0
answers
25
GATE ECE 2022 | Question: 45
For a vector $\overline{x} = \left[ x [0], x[1], \dots, x[7] \right],$ the $\text{8-point}$ discrete Fourier transform $\text{(DFT)}$ is denoted by $\overline{X} = DFT (\overline{x}) = \left[ X [0], X[1], \dots, X[7] \right],$ ... $\overline{y} = DFT (DFT(\overline{x})),$ then the value of $y[0]$ is _____________ (rounded off to one decimal place).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
11
views
gateece-2022
numerical-answers
0
votes
0
answers
26
GATE ECE 2022 | Question: 46
A $p-$type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at $x = \pm 2l_{n},$ where $l_{n} = 10 ^{-4} \; \text{cm}$ is the diffusion length of ... photo-generated electrons at $x = + 2l_{n}$ is ______________ $\text{mA/cm}^{2}$ (rounded off to two decimal places).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
18
views
gateece-2022
numerical-answers
0
votes
0
answers
27
GATE ECE 2022 | Question: 50
The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and $d(t),$ ... $e (\infty),$ due to a unit step disturbance $d(t),$ is __________ (rounded off to two decimal places).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
22
views
gateece-2022
numerical-answers
0
votes
0
answers
28
GATE ECE 2022 | Question: 51
The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked. The parameter $\alpha$ lies in the interval $[0.25, 1].$ The value of $\alpha$ for which the capacity of this channel is maximized, is ___________ (rounded off to two decimal places).
soujanyareddy13
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in
Others
Feb 23
by
soujanyareddy13
100
points
21
views
gateece-2022
numerical-answers
0
votes
0
answers
29
GATE ECE 2022 | Question: 52
Consider communication over a memoryless binary symmetric channel using a $(7, 4)$ Hamming code. Each transmitted bit is received correctly with probability $(1 - \in),$ and flipped with probability $\in.$ For each codeword transmission, the ... the probability that a transmitted codeword is decoded correctly is ___________(rounded off to two decimal places).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
17
views
gateece-2022
numerical-answers
0
votes
0
answers
30
GATE ECE 2022 | Question: 49
Consider the circuit shown with an ideal long channel $n \text{MOSFET}$ (enhancement-mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with $V_{GG}$ and $V_{DD}$ such that it acts as a linear amplifier ... $\dfrac{v_{A}}{v_{B}}$ is _____________ (rounded off to one decimal place).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
15
views
gateece-2022
numerical-answers
0
votes
0
answers
31
GATE ECE 2022 | Question: 47
A circuit and the characteristics of the diode $\text{(D)}$ in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{\text{out}}}{\partial V_{\text{in}}}$ is ____________ (rounded off to two decimal places).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
13
views
gateece-2022
numerical-answers
0
votes
0
answers
32
GATE ECE 2022 | Question: 48
Consider the circuit shown with an ideal $\text{OPAMP}.$ The output voltage $V_{0}$ is ____________ $V$ (rounded off to two decimal places).
soujanyareddy13
edited
in
Others
Feb 23
by
soujanyareddy13
100
points
12
views
gateece-2022
numerical-answers
1
vote
1
answer
33
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? $4$ $4 \sqrt{2}$ $8$ $8 \sqrt{2}$
soujanyareddy13
edited
in
Quantitative Aptitude
Feb 23
by
soujanyareddy13
100
points
58
views
gateece-2022
quantitative-aptitude
cartesian-coordinates
area
1
vote
1
answer
34
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$ $4 < x < 5$ $x \geq 5$
soujanyareddy13
edited
in
Quantitative Aptitude
Feb 23
by
soujanyareddy13
100
points
58
views
gateece-2022
quantitative-aptitude
inequality
0
votes
0
answers
35
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
soujanyareddy13
edited
in
Analytical Aptitude
Feb 23
by
soujanyareddy13
100
points
62
views
gateece-2022
analytical-aptitude
logical-reasoning
passage-reading
1
vote
1
answer
36
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? $15$ $20$ $21$ $26$
soujanyareddy13
edited
in
Spatial Aptitude
Feb 23
by
soujanyareddy13
100
points
68
views
gateece-2022
spatial-aptitude
patterns-in-two-dimensions
counting-figure
1
vote
1
answer
37
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 $\text{SR (in cm)}?$ $1.80$ $2.40$ $4.20$ $5.76$
soujanyareddy13
edited
in
Quantitative Aptitude
Feb 23
by
soujanyareddy13
100
points
123
views
gateece-2022
quantitative-aptitude
geometry
1
vote
1
answer
38
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 $\text{Q (in ₹)}?$ $500$ $1000$ $1500$ $2000$
soujanyareddy13
edited
in
Quantitative Aptitude
Feb 23
by
soujanyareddy13
100
points
82
views
gateece-2022
quantitative-aptitude
ratio-proportions
1
vote
1
answer
39
GATE ECE 2022 | GA Question: 1
Mr. $\text{X}$ speaks __________ Japanese ____________ Chinese. neither /or either / nor neither / nor also / but
soujanyareddy13
edited
in
Verbal Aptitude
Feb 23
by
soujanyareddy13
100
points
89
views
gateece-2022
verbal-aptitude
most-appropriate-word
0
votes
0
answers
40
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 $2 \; \mu\text{m}$ ... $3.7 \times 10^{14} \; \text{cm}^{-3}$ $10^{3} \; \text{cm}^{-3}$
soujanyareddy13
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in
Others
Feb 23
by
soujanyareddy13
100
points
29
views
gateece-2022
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