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Questions without answers in Vector Analysis
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1
TIFR ECE 2023 | Question: 14
Suppose that $Z \sim \mathcal{N}(0,1)$ is a Gaussian random variable with mean zero and variance $1$. Let $F(z) \equiv \mathbb{P}(Z \leq z)$ be the cumulative distribution function $\operatorname{(CDF)}$ of $Z$. Define a new random variable $Y$ as $Y=F(Z)$. This means that the ... of $\mathbb{E}[Y]$ is: $F(1)$ $1$ $\frac{1}{2}$ $\frac{1}{\sqrt{2 \pi}}$ $\frac{\pi}{4}$
Suppose that $Z \sim \mathcal{N}(0,1)$ is a Gaussian random variable with mean zero and variance $1$. Let $F(z) \equiv \mathbb{P}(Z \leq z)$ be the cumulative distributio...
admin
46.4k
points
132
views
admin
asked
Mar 14, 2023
Vector Analysis
tifrece2023
engineering-mathematics
gausss-theorem
+
–
1
votes
0
answers
2
TIFR ECE 2022 | Question: 5
Let $Q$ be a unit square in the plane with corners at $(0,0),(0,1),(1,0)$ and $(1,1)$. Let $B$ be a ball of radius $1$ in the plane centered at the origin $(0,0)$. Let $Q+B$ denote the set of all vectors in the plane of the form $v+w,$ where $v \in Q$ and $w \in B$. The area of $Q+B$ is: $5+\pi$ $4+\pi$ $3+\pi$ $2+\pi$ $1+\pi$
Let $Q$ be a unit square in the plane with corners at $(0,0),(0,1),(1,0)$ and $(1,1)$. Let $B$ be a ball of radius $1$ in the plane centered at the origin $(0,0)$. Let $Q...
admin
46.4k
points
142
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2022
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
3
TIFR ECE 2022 | Question: 10
Find the vector which is closest (in Euclidean distance) to $\left(\begin{array}{lll}-1 & 1 & 1\end{array}\right)$ which can be written in the form \[a\left(\begin{array}{lll} 1 & 1 & 1 \end{array}\right)+b\left(\begin{array}{lll} 0 ... None of the above
Find the vector which is closest (in Euclidean distance) to $\left(\begin{array}{lll}-1 & 1 & 1\end{array}\right)$ which can be written in the form\[a\left(\begin{array}{...
admin
46.4k
points
85
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2022
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
4
TIFR ECE 2020 | Question: 15
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors such that $\vec{v}_{1}^{T} \vec{v}_{2}=0$. Let the pair of real numbers $\left(a_{1}^{*}, a_{2}^{*}\right)$ be such that they solve the following optimization problem \[ ... $\left\|\vec{v}_{*}\right\|^{2}-\|\vec{u}\|^{2}$ $0$ None of the above
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors such that $\vec{v}_{1}^{T} \vec{v}_{2}=0$. Let the pair of real numbers $\...
admin
46.4k
points
40
views
admin
asked
Nov 30, 2022
Vector Analysis
tifrece2020
vector-analysis
vector-in-planes
+
–
1
votes
0
answers
5
TIFR ECE 2018 | Question: 5
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors. Let the pair of real numbers $\left(a_{1}^{*}, a_{2}^{*}\right)$ be such that they solve the following optimization problem \[d=\min _{a_{1}, a_{2} \in \mathbb{R}}\left\ ... $\left\|\vec{v}_{*}\right\|^{2}-\|\vec{u}\|^{2}$ None of the above
Suppose $\vec{u}, \vec{v}_{1}, \vec{v}_{2} \in \mathbb{R}^{n}$ are linearly independent vectors. Let the pair of real numbers $\left(a_{1}^{*}, a_{2}^{*}\right)$ be such ...
admin
46.4k
points
87
views
admin
asked
Nov 29, 2022
Vector Analysis
tifrece2018
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
6
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 __________
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
6.5k
points
254
views
Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
7
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 _________________
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 ...
Arjun
6.5k
points
189
views
Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
8
GATE ECE 2021 | Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with...
Arjun
6.5k
points
108
views
Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
+
–
0
votes
0
answers
9
GATE ECE 2020 | Question: 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 $\mathbb{R}^{4}$. These vectors are not linearly independent. Any four of these vectors form a basis ... $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.
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 $...
go_editor
1.9k
points
402
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
vector-analysis
+
–
1
votes
0
answers
10
GATE ECE 2020 | Question: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$?$\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$$\t...
go_editor
1.9k
points
404
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
vector-analysis
+
–
0
votes
0
answers
11
GATE ECE 2020 | Question: 24
The random variable $Y=\int_{-\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\ 0; & \text{otherwise} \end{cases}$ and $W(t)$ is ... noise process with two-sided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
The random variable $$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 &\\...
go_editor
1.9k
points
248
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
numerical-answers
vector-analysis
gausss-theorem
+
–
0
votes
0
answers
12
GATE ECE 2016 Set 3 | Question: 28
A triangle in the $xy$-plane is bounded by the straight lines $2x=3y, \: y=0$ and $x=3$. The volume above the triangle and under the plane $x+y+z=6$ is _______
A triangle in the $xy$-plane is bounded by the straight lines $2x=3y, \: y=0$ and $x=3$. The volume above the triangle and under the plane $x+y+z=6$ is _______
Milicevic3306
16.0k
points
169
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-3
numerical-answers
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
13
GATE ECE 2016 Set 3 | Question: 50
A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0\:kHz$ and two-sided noise power spectral density ${\large\frac{\eta}{2}}=2.5\times10^{-5}Watt\:per\:Hz$. If information at the rate ... transmitted over this channel with arbitrarily small bit error rate, then the minimum bit-energy $E_b$ (in mJ/bit) necessary is _______
A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0\:kHz$ and two-sided noise power spectral density ${\large\frac{\eta}{2}}=2.5\...
Milicevic3306
16.0k
points
118
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-3
numerical-answers
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
14
GATE ECE 2016 Set 2 | Question: 5
Consider the time-varying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega> 0$ is a constant. When the vector magnitude $\mid \textbf{I} \mid$ is at its minimum value, the angle $\theta$ that $\textbf{I}$ makes with the $x$ axis (in degrees, such that $ 0\leq \theta \leq 180)$ ________
Consider the time-varying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega 0$ is a constant. When the vector mag...
Milicevic3306
16.0k
points
334
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-2
numerical-answers
vector-analysis
+
–
0
votes
0
answers
15
GATE ECE 2016 Set 2 | Question: 55
A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=-d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. The charge is at rest at $t=0$, when a voltage $+V$ is applied to the plate at $-d$ and ... that the charge $q$ takes to reach the right plate is proportional to $d/V$ $\sqrt{d}/V$ $d/\sqrt{V}$ $\sqrt{d/V}$
A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=-d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. ...
Milicevic3306
16.0k
points
87
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-2
vector-analysis
+
–
0
votes
0
answers
16
GATE ECE 2016 Set 1 | Question: 29
The region specified by $\{ (\rho,\varphi,z):3 \leq\rho\leq 5,\frac{\pi}{8}\leq\varphi\leq\frac{\pi}{4}, \: 3\leq z\leq4.5\}$ in cylindrical coordinates has volume of _________
The region specified by $\{ (\rho,\varphi,z):3 \leq\rho\leq 5,\frac{\pi}{8}\leq\varphi\leq\frac{\pi}{4}, \: 3\leq z\leq4.5\}$ in cylindrical coordinates has volume of ___...
Milicevic3306
16.0k
points
121
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-1
numerical-answers
vector-analysis
+
–
0
votes
0
answers
17
GATE ECE 2016 Set 1 | Question: 50
An analog pulse $s(t)$ is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is $r(t) = s(t) + n(t)$, where $n(t)$ is additive white Gaussian noise with power spectral density $\frac{N_0}{2}$. The received signal is passed ... $E_s > E_h$ ; $SNR_{max}>\frac{2E_s}{N_0} \\ $ $E_s < E_h$ ; $SNR_{max}=\frac{2E_h}{N_0}$
An analog pulse $s(t)$ is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is $r(t) = s(t) + n(t)$, where $n(t)$ is additive white Ga...
Milicevic3306
16.0k
points
148
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-1
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
18
GATE ECE 2015 Set 3 | Question: 4
Consider the function $g(t) = e^{-t}\sin(2\pi t)u(t)$ where $u(t)$ is the unit step function. The area under $g(t)$ is ______.
Consider the function $g(t) = e^{-t}\sin(2\pi t)u(t)$ where $u(t)$ is the unit step function. The area under $g(t)$ is ______.
Milicevic3306
16.0k
points
217
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-3
numerical-answers
vector-analysis
+
–
0
votes
0
answers
19
GATE ECE 2015 Set 3 | Question: 29
A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ Let $S$ be the surface bounding this cylindrical region. The surface integral of this field on $S(∯_{S} \textbf{D.ds})$ is _______.
A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ ...
Milicevic3306
16.0k
points
125
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-3
numerical-answers
vector-analysis
+
–
0
votes
0
answers
20
GATE ECE 2015 Set 2 | Question: 49
A zero mean white Gaussian noise having power spectral density $\dfrac{N_{0}}{2}$ is passed through an LTI filter whose impulse response $h(t)$ is shown in the figure. The variance of the filtered noise at $t = 4$ is $\dfrac{3}{2}A^{2}N_{0} \\$ $\dfrac{3}{4}A^{2}N_{0} \\$ $A^{2}N_{0} \\$ $\dfrac{1}{2}A^{2}N_{0}$
A zero mean white Gaussian noise having power spectral density $\dfrac{N_{0}}{2}$ is passed through an LTI filter whose impulse response $h(t)$ is shown in the figure. Th...
Milicevic3306
16.0k
points
114
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-2
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
21
GATE ECE 2015 Set 1 | Question: 25
A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x - x^2y^2\overrightarrow{a}_y - x^2 yz \overrightarrow{a}_z$. Which one of the statements is TRUE? $\overrightarrow{P}$ is ... irrotational, but not solenoidal $\overrightarrow{P}$ is neither solenoidal, nor irrotational $\overrightarrow{P}$ is both solenoidal and irrotational
A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x – x^2y^2\overrightarrow{a}_y – x^2 yz \overrightarrow{a}_z$. Which one of the...
Milicevic3306
16.0k
points
106
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-1
vector-analysis
+
–
0
votes
0
answers
22
GATE ECE 2015 Set 1 | Question: 54
The electric field intensity of a plane wave traveling in free space is given by the following expression $\textbf{E}(x,t)=\textbf{a}_y \: 24 \: \pi \: \: \cos(\omega t - k_0 x) \: \: (V/m)$ ... $x+y=1$. The total time-averaged power (in mW) passing through the square area is _____________.
The electric field intensity of a plane wave traveling in free space is given by the following expression $$\textbf{E}(x,t)=\textbf{a}_y \: 24 \: \pi \: \: \cos(\omega t ...
Milicevic3306
16.0k
points
82
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-1
numerical-answers
vector-analysis
+
–
0
votes
0
answers
23
GATE ECE 2015 Set 1 | Question: 55
Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $(\varepsilon _r)$ ... electric field component (in V/m) after it has travelled a distance of $10$ cm inside the dielectric region is ____________.
Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex r...
Milicevic3306
16.0k
points
101
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-1
numerical-answers
vector-analysis
+
–
0
votes
0
answers
24
GATE ECE 2014 Set 4 | Question: 2
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
Milicevic3306
16.0k
points
82
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
numerical-answers
vector-analysis
gradient
+
–
0
votes
0
answers
25
GATE ECE 2014 Set 4 | Question: 3
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
Milicevic3306
16.0k
points
105
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
numerical-answers
vector-analysis
gausss-theorem
random-variable
+
–
0
votes
0
answers
26
GATE ECE 2014 Set 4 | Question: 5
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by _________.
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by...
Milicevic3306
16.0k
points
84
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
vector-analysis
numerical-answers
+
–
0
votes
0
answers
27
GATE ECE 2014 Set 4 | Question: 22
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be Poisson Gaussian Exponential Gamma
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distri...
Milicevic3306
16.0k
points
165
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
28
GATE ECE 2014 Set 4 | Question: 49
Consider a communication scheme where the binary valued signal $X$ satisfies $P\{X=+1\}=0.75$ and $P\{X=-1 \}=0.25$. The received signal $Y=X+Z$, where $Z$ is a Gaussian random variable with zero mean and variance ... $\sigma ^2$
Consider a communication scheme where the binary valued signal $X$ satisfies $P\{X=+1\}=0.75$ and $P\{X=-1 \}=0.25$. The received signal $Y=X+Z$, where $Z$ is a Gaussian ...
Milicevic3306
16.0k
points
95
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
29
GATE ECE 2014 Set 4 | Question: 52
Consider a discrete-time channel $Y=X +Z$, where the additive noise $Z$ is signal-dependent. In particular, given the transmitted symbol $ X \in \{-a , +a\}$ at any instant, the noise sample $Z$ is chosen independently from a Gaussian distribution with mean $\beta X$ and unit ... $\beta = -0.3$, the BER is closest to $10^{-7}$ $10^{-6}$ $10^{-4}$ $10^{-2}$
Consider a discrete-time channel $Y=X +Z$, where the additive noise $Z$ is signal-dependent. In particular, given the transmitted symbol $ X \in \{-a , +a\}$ at any insta...
Milicevic3306
16.0k
points
90
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
vector-analysis
gausss-theorem
+
–
0
votes
0
answers
30
GATE ECE 2014 Set 4 | Question: 54
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \times \overrightarrow{F} \cdot \overrightarrow{ds}$ is __________.
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \ti...
Milicevic3306
16.0k
points
212
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
numerical-answers
vector-analysis
+
–
0
votes
0
answers
31
GATE ECE 2014 Set 3 | Question: 53
Given the vector $\textbf{A}= ( \cos x ) ( \sin y )\hat{a_{x}}+( \sin x )( \cos y )\hat{a_{y}},$ where $\hat{a_{x}},$ $\hat{a_{y}}$ denote unit vectors along $x$, $y$ directions, respectively. The magnitude of curl of $\textbf{A}$ is __________
Given the vector $\textbf{A}= ( \cos x ) ( \sin y )\hat{a_{x}}+( \sin x )( \cos y )\hat{a_{y}},$ where $\hat{a_{x}},$ $\hat{a_{y}}$ denote unit vectors along $x$, $y$ di...
Milicevic3306
16.0k
points
119
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-3
numerical-answers
vector-analysis
+
–
0
votes
0
answers
32
GATE ECE 2014 Set 2 | Question: 22
The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by $C = W \log_{2}\left ( 1+\frac{p} {\sigma ^{2}w} \right )$ bits per second (bps), where $W$ is the channel bandwidth, $P$ is the average power received ... channel capacity (in kbps) with infinite bandwidth $(W\rightarrow \infty )$ is approximately $1.44$ $1.08$ $0.72$ $0.36$
The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by $C = W \log_{2}\left ( 1+\frac{p} {\sigma ^{2}w} \right )$ bits per second (bps), ...
Milicevic3306
16.0k
points
152
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-2
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
33
GATE ECE 2014 Set 2 | Question: 29
If $\overrightarrow {r}= x\hat{a_{x}}+y\hat{a_{y}}+z\hat{a_{z}}$ and $\mid \overrightarrow{r} \mid= r$ , then $\text{div} ( r^{2} \nabla ( \text{ln }r ) )$ = _______ .
If $\overrightarrow {r}= x\hat{a_{x}}+y\hat{a_{y}}+z\hat{a_{z}}$ and $\mid \overrightarrow{r} \mid= r$ , then $\text{div} ( r^{2} \nabla ( \text{ln }r ) )$ = _______ .
Milicevic3306
16.0k
points
87
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-2
vector-analysis
numerical-answers
+
–
0
votes
0
answers
34
GATE ECE 2014 Set 1 | Question: 28
The volume under the surface $z(x,y) = x + y$ and above the triangle in the $x – y$ plane defined by $\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\}$ is _______.
The volume under the surface $z(x,y) = x + y$ and above the triangle in the $x – y$ plane defined by $\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\}$ is _______....
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GATE ECE 2014 Set 1 | Question: 46
Consider the state space model of a system, as given below ... The system is controllable and observable uncontrollable and observable uncontrollable and unobservable controllable and unobservable
Consider the state space model of a system, as given below$\begin{bmatrix} x_{1}\\x_{2} \\x_{3} \end{bmatrix} \begin{bmatrix} -1 &1 &0 \\ 0& -1 &0 \\ 0 & 0 & -2 \end{bmat...
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GATE ECE 2014 Set 1 | Question: 53
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions. $\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t - \beta r)\hat{a_{\theta}}\: V/m$ ... free space. The average power $(W)$ crossing the hemispherical shell located at $r = 1\:km,0\leq \theta \leq \pi/2$ is ______.
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions.$$\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omeg...
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GATE ECE 2013 | Question: 53
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
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GATE ECE 2013 | Question: 52
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
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GATE ECE 2013 | Question: 39
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ consider the...
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GATE ECE 2013 | Question: 7
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$$1/3$ $1$ $3$
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