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1
The value of the integral ∫ ∞ − ∞ 12 cos ( 2 π ) sin ( 4 π t ) 4 π t d t is
akalok808
asked
in
Continuous-time Signals
Aug 24
by
akalok808
120
points
17
views
0
votes
1
answer
2
GATE ECE 2016 Set 3 | Question: 27
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(-2,0,1)$ form an orthogonal basis of the three-dimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4,3,-3)\in \mathbb{R}^3 $ can be expressed as $\textbf{u}=-$ ... \frac{2}{5}$e_1+3e_2+$\large\frac{11}{5}$e_3 \\$ $\textbf{u}=-$\large\frac{2}{5}$e_1+3e_2-$\large\frac{11}{5}$e_3$
Divyanshu Shukla
answered
in
Vector Analysis
Jun 20
by
Divyanshu Shukla
140
points
87
views
gate2016-ec-3
vector-analysis
1
vote
1
answer
3
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
answered
in
Verbal Ability
Apr 11
by
Arjun
4.5k
points
131
views
gateec-2021
verbal-ability
verbal-reasoning
passage-reading
1
vote
1
answer
4
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
answered
in
Verbal Ability
Apr 11
by
Arjun
4.5k
points
184
views
gateec-2021
verbal-ability
english-grammar
tense
1
vote
1
answer
5
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
Dhruov
answered
in
Verbal Ability
Apr 11
by
Dhruov
480
points
179
views
gateec-2021
verbal-ability
word-pairs
1
vote
2
answers
6
GATE ECE 2020 | GA Question: 4
The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in- ... the French ones. the English announcements being longer than the French ones. equal importance being given to English and French.
Arjun
answered
in
Verbal Ability
Apr 11
by
Arjun
4.5k
points
245
views
gate2020-ec
verbal-ability
verbal-reasoning
passage-reading
1
vote
2
answers
7
GATE ECE 2020 | GA Question: 6
The global financial crisis in $2008$ is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in $\text{USA}$ in $2007$. The sub-prime lending crisis led to the ... $\rightarrow$ East Asian crisis$\rightarrow$ banking crisis$\rightarrow$ subprime lending crisis.
Arjun
answered
in
Verbal Ability
Apr 10
by
Arjun
4.5k
points
227
views
gate2020-ec
verbal-ability
verbal-reasoning
passage-reading
1
vote
2
answers
8
GATE ECE 2020 | GA Question: 2
He was not only accused of theft _____ of conspiracy. rather but also but even rather than
Arjun
answered
in
Verbal Ability
Apr 10
by
Arjun
4.5k
points
478
views
gate2020-ec
verbal-ability
english-grammar
1
vote
2
answers
9
GATE ECE 2020 | GA Question: 5
A superadditive function $f(\cdot)$ satisfies the following property $f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$ Which of the following functions is a superadditive function for $x > 1$? $e^{x}$ $\sqrt{x}$ $1/x$ $e^{-x}$
Lakshman Patel RJIT
answered
in
Numerical Ability
Apr 10
by
Lakshman Patel RJIT
3.8k
points
476
views
gate2020-ec
numerical-ability
functions
1
vote
2
answers
10
GATE ECE 2020 | GA Question: 10
The following figure shows the data of students enrolled in $5$ years $(2014\;\text{to}\; 2018)$ for two schools $P$ and $Q$. During this period, the ratio of the average number of the students enrolled in school $P$ to the average of the difference of the number of students enrolled in schools $P$ and $Q$ is _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
Lakshman Patel RJIT
answered
in
Numerical Ability
Mar 31
by
Lakshman Patel RJIT
3.8k
points
720
views
gate2020-ec
numerical-ability
data-interpretation
bar-graph
1
vote
1
answer
11
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 $2:3$ $3:4$ $4:5$ $5:6$
Lakshman Patel RJIT
answered
in
Numerical Ability
Mar 22
by
Lakshman Patel RJIT
3.8k
points
164
views
gateec-2021
numerical-ability
geometry
triangles
area
1
vote
1
answer
12
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 $4$ $5$ $6$ $7$
Lakshman Patel RJIT
answered
in
Numerical Ability
Mar 22
by
Lakshman Patel RJIT
3.8k
points
189
views
gateec-2021
numerical-ability
data-interpretation
bar-graph
1
vote
1
answer
13
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
Lakshman Patel RJIT
answered
in
Analytical Aptitude
Mar 22
by
Lakshman Patel RJIT
3.8k
points
479
views
gateec-2021
analytical-aptitude
logical-reasoning
statements-follow
1
vote
1
answer
14
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 ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
Lakshman Patel RJIT
answered
in
Numerical Ability
Mar 22
by
Lakshman Patel RJIT
3.8k
points
701
views
gateec-2021
numerical-ability
mensuration
cones
1
vote
1
answer
15
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 ____________ $4$ $3$ $6$ $7$
Lakshman Patel RJIT
answered
in
Spatial Aptitude
Mar 22
by
Lakshman Patel RJIT
3.8k
points
162
views
gateec-2021
spatial-aptitude
patterns-in-two-dimensions
2
votes
1
answer
16
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? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
Lakshman Patel RJIT
answered
in
Numerical Ability
Mar 22
by
Lakshman Patel RJIT
3.8k
points
143
views
gateec-2021
numerical-ability
simple-compound-interest
1
vote
2
answers
17
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
Lakshman Patel RJIT
answered
in
Numerical Ability
Mar 22
by
Lakshman Patel RJIT
3.8k
points
139
views
gateec-2021
numerical-ability
algebra
0
votes
0
answers
18
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
asked
in
Vector Analysis
Feb 20
by
Arjun
4.5k
points
92
views
gateec-2021
vector-analysis
vector-in-planes
0
votes
0
answers
19
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
asked
in
Differential Equations
Feb 20
by
Arjun
4.5k
points
61
views
gateec-2021
differential-equations
first-order-differential-equation
0
votes
0
answers
20
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
47
views
gateec-2021
probability-and-statistics
random-variable
variance
0
votes
0
answers
21
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
54
views
gateec-2021
0
votes
0
answers
22
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
68
views
gateec-2021
0
votes
0
answers
23
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
87
views
gateec-2021
0
votes
0
answers
24
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
59
views
gateec-2021
0
votes
0
answers
25
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
41
views
gateec-2021
0
votes
0
answers
26
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
44
views
gateec-2021
0
votes
0
answers
27
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
57
views
gateec-2021
0
votes
0
answers
28
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
111
views
gateec-2021
digital-circuits
number-system
number-representation
0
votes
0
answers
29
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
57
views
gateec-2021
digital-circuits
combinational-circuits
decoders
0
votes
0
answers
30
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
asked
in
Control Systems
Feb 20
by
Arjun
4.5k
points
42
views
gateec-2021
control-systems
0
votes
0
answers
31
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
77
views
gateec-2021
0
votes
0
answers
32
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
51
views
gateec-2021
0
votes
0
answers
33
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
asked
in
Vector Analysis
Feb 20
by
Arjun
4.5k
points
63
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
votes
0
answers
34
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
asked
in
Vector Analysis
Feb 20
by
Arjun
4.5k
points
75
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
votes
0
answers
35
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
65
views
gateec-2021
numerical-answers
0
votes
0
answers
36
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
asked
in
Others
Feb 20
by
Arjun
4.5k
points
54
views
gateec-2021
numerical-answers
0
votes
0
answers
37
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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in
Others
Feb 20
by
Arjun
4.5k
points
44
views
gateec-2021
numerical-answers
0
votes
0
answers
38
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 ________________
Arjun
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Others
Feb 20
by
Arjun
4.5k
points
44
views
gateec-2021
numerical-answers
0
votes
0
answers
39
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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Others
Feb 20
by
Arjun
4.5k
points
62
views
gateec-2021
numerical-answers
0
votes
0
answers
40
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 _____ $\text{kHz}$.
Arjun
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Others
Feb 20
by
Arjun
4.5k
points
89
views
gateec-2021
numerical-answers
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