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GATE ECE 2021 | GA Question: 1
The current population of a city is $11,02,500$ . If it has been increasing at the rate of $5\%$ per annum, what was its population $2$ years ago? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
Arjun
asked
in
Numerical Ability
Feb 20
by
Arjun
4.5k
points
161
views
gateec-2021
numerical-ability
simple-compound-interest
1
vote
2
answers
2
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
Arjun
asked
in
Numerical Ability
Feb 20
by
Arjun
4.5k
points
153
views
gateec-2021
numerical-ability
algebra
1
vote
1
answer
3
GATE ECE 2021 | GA Question: 3
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________ $4$ $3$ $6$ $7$
Arjun
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in
Spatial Aptitude
Feb 20
by
Arjun
4.5k
points
180
views
gateec-2021
spatial-aptitude
patterns-in-two-dimensions
1
vote
1
answer
4
GATE ECE 2021 | GA Question: 4
$\textit{Nostalgia}$ is to $\textit{anticipation}$ as ____________ is to _____________ Which one of the following options maintains a similar logical relation in the above sentence? Present, past Future, past Past, future Future, present
Arjun
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in
Verbal Ability
Feb 20
by
Arjun
4.5k
points
203
views
gateec-2021
verbal-ability
word-pairs
1
vote
1
answer
5
GATE ECE 2021 | GA Question: 5
Consider the following sentences: I woke up from sleep. I woked up from sleep. I was woken up from sleep. I was wokened up from sleep. Which of the above sentences are grammatically $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iv)}$
Arjun
asked
in
Verbal Ability
Feb 20
by
Arjun
4.5k
points
206
views
gateec-2021
verbal-ability
english-grammar
tense
1
vote
1
answer
6
GATE ECE 2021 | GA Question: 6
Given below are two statements and two conclusions. $\text{Statement 1}$: All purple are green. $\text{Statement 2}$: All black are green. $\text{Conclusion I}$: Some black are purple. $\text{Conclusion II}$: No black is purple. Based on the above ... correct Either conclusion $\text{I}$ or $\text{II}$ is correct Both conclusion $\text{I}$ and $\text{II}$ are correct
Arjun
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in
Analytical Aptitude
Feb 20
by
Arjun
4.5k
points
500
views
gateec-2021
analytical-aptitude
logical-reasoning
statements-follow
1
vote
1
answer
7
GATE ECE 2021 | GA Question: 7
Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence $\text{(AI)}$ is currently a hot topic. $\text{Al}$ enables computers to learn, given enough training data. For humans, sitting in front of a ... $\text{(ii) and (iv)}$ $\text{(i), (iii) and (iv)}$ $\text{(i) and (iii)}$
Arjun
asked
in
Verbal Ability
Feb 20
by
Arjun
4.5k
points
146
views
gateec-2021
verbal-ability
verbal-reasoning
passage-reading
1
vote
1
answer
8
GATE ECE 2021 | GA Question: 8
Consider a square sheet of side $1$ unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step. one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
Arjun
asked
in
Numerical Ability
Feb 20
by
Arjun
4.5k
points
775
views
gateec-2021
numerical-ability
mensuration
cones
1
vote
1
answer
9
GATE ECE 2021 | GA Question: 9
The number of minutes spent by two students, $X$ and $Y$, exercising every day in a given week are shown in the bar chart above. The number of days in the given week in which one of the students spent a minimum of $10\%$ more than the other student, on a given day, is $4$ $5$ $6$ $7$
Arjun
asked
in
Numerical Ability
Feb 20
by
Arjun
4.5k
points
210
views
gateec-2021
numerical-ability
data-interpretation
bar-graph
1
vote
1
answer
10
GATE ECE 2021 | GA Question: 10
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is $2:3$ $3:4$ $4:5$ $5:6$
Arjun
asked
in
Numerical Ability
Feb 20
by
Arjun
4.5k
points
182
views
gateec-2021
numerical-ability
geometry
triangles
area
0
votes
0
answers
11
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
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in
Vector Analysis
Feb 20
by
Arjun
4.5k
points
97
views
gateec-2021
vector-analysis
vector-in-planes
0
votes
0
answers
12
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 $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
Arjun
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in
Differential Equations
Feb 20
by
Arjun
4.5k
points
65
views
gateec-2021
differential-equations
first-order-differential-equation
0
votes
0
answers
13
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 $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
Arjun
asked
in
Probability and Statistics
Feb 20
by
Arjun
4.5k
points
50
views
gateec-2021
probability-and-statistics
random-variable
variance
0
votes
0
answers
14
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 $\text{15 kHz}$ $\text{30 kHz}$ $\text{60 kHz}$ $\text{20 kHz}$
Arjun
asked
in
Others
Feb 20
by
Arjun
4.5k
points
57
views
gateec-2021
0
votes
0
answers
15
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 ... $k=0,1,2,,15$ $k=0$ $k=15$ $\text{k=0 and k=15}$
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
79
views
gateec-2021
0
votes
0
answers
16
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 ... $2 \times 10^{20} \text{cm}^{-6}$ $10^{32} \text{cm}^{-6}$ $2 \times 10^{32} \text{cm}^{-6}$
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
102
views
gateec-2021
0
votes
0
answers
17
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 $\frac{\Delta }{qL}$ $\frac{2\Delta }{qL}$ $\frac{\Delta }{2qL}$ $\frac{3\Delta }{2qL}$
Arjun
asked
in
Others
Feb 20
by
Arjun
4.5k
points
65
views
gateec-2021
0
votes
0
answers
18
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 $g_{m1}$ ... $-g_{m2}\left ( \frac{1}{g_{m1}}\left | \right |r_{01}\left | \right |r_{02} \right )$
Arjun
asked
in
Others
Feb 20
by
Arjun
4.5k
points
50
views
gateec-2021
0
votes
0
answers
19
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 $3.285$ $2.860$ $3.825$ $5.555$
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
54
views
gateec-2021
0
votes
0
answers
20
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 ... $V_{\text{IN}}\:=\:2\:V_{\text{REF}}$ $V_{\text{IN}}\:=\:2\:+\:V_{\text{REF}}$
Arjun
asked
in
Others
Feb 20
by
Arjun
4.5k
points
62
views
gateec-2021
0
votes
0
answers
21
GATE ECE 2021 | Question: 11
If $(1235)_{x}\:=\:(3033)_{y}$, where $x$ and $y$ indicate the bases of the corresponding numbers, then $x\:=\:7$ and $y\:=\:5$ $x\:=\:8$ and $y\:=\:6$ $x\:=\:6$ and $y\:=\:4$ $x\:=\:9$ and $y\:=\:7$
Arjun
asked
in
Digital Circuits
Feb 20
by
Arjun
4.5k
points
125
views
gateec-2021
digital-circuits
number-system
number-representation
0
votes
0
answers
22
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 $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
Arjun
asked
in
Digital Circuits
Feb 20
by
Arjun
4.5k
points
59
views
gateec-2021
digital-circuits
combinational-circuits
decoders
0
votes
0
answers
23
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 $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
Arjun
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in
Control Systems
Feb 20
by
Arjun
4.5k
points
46
views
gateec-2021
control-systems
0
votes
0
answers
24
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 $0$ $1$ $4$ $3$
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
91
views
gateec-2021
0
votes
0
answers
25
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 ... $\frac{1}{3}$ $\frac{3}{5}$ $\frac{2}{5}$ $\frac{2}{3}$
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
56
views
gateec-2021
0
votes
0
answers
26
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 __________
Arjun
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in
Vector Analysis
Feb 20
by
Arjun
4.5k
points
72
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
votes
0
answers
27
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 _________________
Arjun
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Vector Analysis
Feb 20
by
Arjun
4.5k
points
81
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
votes
0
answers
28
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 ________ $A$.
Arjun
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Others
Feb 20
by
Arjun
4.5k
points
73
views
gateec-2021
numerical-answers
0
votes
0
answers
29
GATE ECE 2021 | Question: 19
Consider the circuit shown in the figure. The value of $v_{0}$ (rounded off to one decimal place) is _________ $V$.
Arjun
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Others
Feb 20
by
Arjun
4.5k
points
60
views
gateec-2021
numerical-answers
0
votes
0
answers
30
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 ___________ $V$.
Arjun
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Others
Feb 20
by
Arjun
4.5k
points
45
views
gateec-2021
numerical-answers
0
votes
0
answers
31
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 ________________
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Others
Feb 20
by
Arjun
4.5k
points
49
views
gateec-2021
numerical-answers
0
votes
0
answers
32
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 ______________
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
69
views
gateec-2021
numerical-answers
0
votes
0
answers
33
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 _____ $\text{kHz}$.
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Others
Feb 20
by
Arjun
4.5k
points
99
views
gateec-2021
numerical-answers
0
votes
0
answers
34
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 _____ $V$.
Arjun
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in
Others
Feb 20
by
Arjun
4.5k
points
63
views
gateec-2021
numerical-answers
0
votes
0
answers
35
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.
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Others
Feb 20
by
Arjun
4.5k
points
74
views
gateec-2021
numerical-answers
0
votes
0
answers
36
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 $-\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $-\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
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Complex Analysis
Feb 20
by
Arjun
4.5k
points
171
views
gateec-2021
complex-analysis
0
votes
0
answers
37
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 ... $4.37\times 10^{15}\:cm^{-3}$ $2.37\times 10^{15}\:cm^{-3}$ $9.37\times 10^{15}\:cm^{-3}$
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Others
Feb 20
by
Arjun
4.5k
points
33
views
gateec-2021
0
votes
0
answers
38
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 $3\:ns$ $5\:ns$ $6\:ns$ $7\:ns$
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Digital Circuits
Feb 20
by
Arjun
4.5k
points
127
views
gateec-2021
digital-circuits
combinational-circuits
multiplexers
0
votes
0
answers
39
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. $\text{PUSH } \{R_{1}\}$ $\text{PUSH } \{R_{2}\}$ $\text{PUSH } \{R_{3}\}$ $\text{POP } \{R_{1}\}$ $\text{POP } \{R_{2}\}$ ... $R_{1}=30H,\:R_{2}=40H,\:R_{3}=25H$ $R_{1}=40H,\:R_{2}=25H,\:R_{3}=30H$
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Others
Feb 20
by
Arjun
4.5k
points
27
views
gateec-2021
0
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0
answers
40
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
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Others
Feb 20
by
Arjun
4.5k
points
41
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gateec-2021
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