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Most viewed questions in Engineering Mathematics
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1
GATE ECE 2013 | Question: 19
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
The minimum eigenvalue of the following matrix is$$\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$$$0$$1$$2$$3$
Milicevic3306
16.0k
points
934
views
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-ec
linear-algebra
matrices
eigen-values
+
–
1
votes
1
answer
2
GATE ECE 2014 Set 1 | Question: 2
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at r...
Milicevic3306
16.0k
points
742
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
+
–
0
votes
1
answer
3
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}$
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...
Arjun
6.6k
points
724
views
Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
4
GATE ECE 2017 Set 1 | Question: 3
Consider the following statements about the linear dependence of the real valued function $y_{1}=1,y_{2}=x$ and $y_{3}=x^{2}$ over the field of real numbers. $y_{1},y_{2}$ and $y_{3} $ are linearly independent on $-1\leq x\leq 0$ ... among the following is correct? Both I and II are true Both I and III are true Both II and IV are true Both III and IV are true
Consider the following statements about the linear dependence of the real valued function $y_{1}=1,y_{2}=x$ and $y_{3}=x^{2}$ over the field of real numbers.$y_{1},y_{2}$...
admin
46.4k
points
644
views
admin
asked
Nov 17, 2017
Vector Analysis
gate2017-ec-1
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
5
GATE ECE 2017 Set 1 | Question: 2
The rank of the matrix $\textbf{M} = \begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$ is $0$ $1$ $2$ $3$
The rank of the matrix $$\textbf{M} = \begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$$ is$0$$1$$2$$3$
admin
46.4k
points
522
views
admin
asked
Nov 17, 2017
Linear Algebra
gate2017-ec-1
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
6
GATE ECE 2021 | Question: 27
A box contains the following three coins. A fair coin with head on one face and tail on the other face. A coin with heads on both the faces. A coin with tails on both the faces. A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one ... getting a head in the second toss is $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
A box contains the following three coins.A fair coin with head on one face and tail on the other face.A coin with heads on both the faces.A coin with tails on both the fa...
Arjun
6.6k
points
434
views
Arjun
asked
Feb 19, 2021
Probability and Statistics
gateec-2021
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
7
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
433
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
vector-analysis
+
–
1
votes
0
answers
8
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.$$\t...
go_editor
1.9k
points
414
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
vector-analysis
+
–
0
votes
0
answers
9
GATE ECE 2018 | Question: 51
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{-1}.$ The value of the integral $\displaystyle{}\dfrac{1}{\pi j}\oint _{C}\dfrac{dz}{z^{2}-1}$ is _______.
The contour $C$ given below is on the complex plane $z=x+j y,$ where $j=\sqrt{-1}.$ The value of the integral $\disp...
gatecse
1.6k
points
411
views
gatecse
asked
Feb 19, 2018
Complex Analysis
gate2018-ec
numerical-answers
complex-analysis
+
–
0
votes
0
answers
10
GATE ECE 2017 Set 1 | Question: 1
Consider the 5 $\times$ 5 matrix $\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$ It is given that A has only one real eigenvalue. Then the real eigenvalue of A is $-2.5$ $0$ $15$ $25$
Consider the 5 $\times$ 5 matrix$$\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$$It is given that A has only one real eigenv...
admin
46.4k
points
385
views
admin
asked
Nov 17, 2017
Linear Algebra
gate2017-ec-1
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
11
GATE ECE 2019 | Question: 27
Consider the line integral $\int_{c} (xdy-ydx)$ the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $R$ shown in the figure below. The region $R$ is the area enclosed by the union of a $2 \times 3$ ... circle of radius $1$. The line integral evaluates to $6+ \dfrac{\pi}{2}$ $8+\pi$ $12+\pi$ $16+2\pi$
Consider the line integral$$\int_{c} (xdy-ydx)$$the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $...
Arjun
6.6k
points
371
views
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ec
integrals
calculus
+
–
1
votes
1
answer
12
GATE ECE 2020 | Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of th...
go_editor
1.9k
points
365
views
go_editor
asked
Feb 13, 2020
Probability and Statistics
gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
+
–
0
votes
0
answers
13
GATE ECE 2016 Set 2 | Question: 5
Consider the time-varying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega> 0$ is a constant. When the vector magnitude $\mid \textbf{I} \mid$ is at its minimum value, the angle $\theta$ that $\textbf{I}$ makes with the $x$ axis (in degrees, such that $ 0\leq \theta \leq 180)$ ________
Consider the time-varying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega 0$ is a constant. When the vector mag...
Milicevic3306
16.0k
points
342
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-2
numerical-answers
vector-analysis
+
–
2
votes
0
answers
14
GATE ECE 2019 | Question: 1
Which one of the following functions is analytic over the entire complex plane? $\ln(z)$ $e^{1/z}$ $\frac{1}{1-z}$ $\cos(z)$
Which one of the following functions is analytic over the entire complex plane?$\ln(z)$$e^{1/z}$$\frac{1}{1-z}$$\cos(z)$
Arjun
6.6k
points
341
views
Arjun
asked
Feb 12, 2019
Complex Analysis
gate2019-ec
complex-analysis
+
–
1
votes
0
answers
15
GATE ECE 2017 Set 1 | Question: 27
A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal places) is _________
A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal...
admin
46.4k
points
341
views
admin
asked
Nov 17, 2017
Vector Analysis
gate2017-ec-1
vector-analysis
numerical-answers
+
–
0
votes
0
answers
16
GATE ECE 2020 | Question: 3
The partial derivative of the function $f(x, y, z) = e^{1-x\cos y} + xze^{-1/(1+y^{2})}$ with respect to $x$ at the point $(1,0,e)$ is $-1$ $0$ $1 \\$ $\dfrac{1}{e}$
The partial derivative of the function$$f(x, y, z) = e^{1-x\cos y} + xze^{-1/(1+y^{2})}$$with respect to $x$ at the point $(1,0,e)$ is$-1$$0$$1 \\$$\dfrac{1}{e}$
go_editor
1.9k
points
328
views
go_editor
asked
Feb 13, 2020
Calculus
gate2020-ec
calculus
derivatives
partial-derivatives
+
–
0
votes
0
answers
17
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 $-\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $-\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
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 \...
Arjun
6.6k
points
319
views
Arjun
asked
Feb 19, 2021
Complex Analysis
gateec-2021
complex-analysis
+
–
1
votes
0
answers
18
GATE ECE 2017 Set 2 | Question: 29
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation...
admin
46.4k
points
318
views
admin
asked
Nov 23, 2017
Probability and Statistics
gate2017-ec-2
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
19
TIFR ECE 2023 | Question: 1
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and second $\mathrm{D}_{2}$ that has three faces numbered $2,4,6$ ... dice in the experiment. What is $\mathbb{E}[X]$ ? $\frac{7}{2}$ $4$ $3$ $\frac{9}{2}$ None of the above
Consider a fair coin with probability of heads and tails equal to $1 / 2$. Moreover consider two dice, first $\mathrm{D}_{1}$ that has three faces numbered $1,3,5$ and se...
admin
46.4k
points
307
views
admin
asked
Mar 14, 2023
Probability and Statistics
tifrece2023
probability
+
–
1
votes
1
answer
20
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}$e_3$
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...
Milicevic3306
16.0k
points
291
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-3
vector-analysis
+
–
1
votes
0
answers
21
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 $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
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...
Arjun
6.6k
points
279
views
Arjun
asked
Feb 19, 2021
Differential Equations
gateec-2021
differential-equations
first-order-differential-equation
+
–
0
votes
0
answers
22
GATE ECE 2020 | Question: 51
For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.
For the solid $S$ shown below, the value of $\underset{S}{\iiint} xdxdydz$ (rounded off to two decimal places) is _______________.
go_editor
1.9k
points
274
views
go_editor
asked
Feb 13, 2020
Calculus
gate2020-ec
numerical-answers
calculus
definite-integrals
+
–
0
votes
0
answers
23
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
6.6k
points
270
views
Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
+
–
0
votes
0
answers
24
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 $$Y=\int_{-\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\...
go_editor
1.9k
points
257
views
go_editor
asked
Feb 13, 2020
Vector Analysis
gate2020-ec
numerical-answers
vector-analysis
gausss-theorem
+
–
0
votes
0
answers
25
GATE ECE 2012 | Question: 38
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probability of error for an optimum receiver will be $\frac{7}{80}$ $\frac{63}{80}$ $\frac{9}{10}$ $\frac{1}{10}$
A binary symmetric channel (BSC) has a transition probability of $\frac{1}{8}$. If the binary transmit symbol $X$ is such that $P(X=0)\:=\:\frac{9}{10}$, then the probabi...
Milicevic3306
16.0k
points
237
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ec
probability-and-statistics
probability
+
–
0
votes
0
answers
26
GATE ECE 2019 | Question: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by $F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by$$F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text...
Arjun
6.6k
points
235
views
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
27
GATE ECE 2013 | Question: 38
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. Then, for all values of $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. ...
Milicevic3306
16.0k
points
230
views
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ec
probability-and-statistics
probability
random-variable
+
–
0
votes
1
answer
28
GATE ECE 2019 | Question: 17
The number of distinct eigenvalues of the matrix $A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$ is equal to ____________.
The number of distinct eigenvalues of the matrix$$A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$$is equal to ____________.
Arjun
6.6k
points
227
views
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ec
numerical-answers
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
29
GATE ECE 2020 | Question: 4
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is $y=C_{1}e^{3x}+C_{2}e^{-3x}$ $y=(C_{1}+C_{2}x)e^{-3x}$ $y=(C_{1}+C_{2}x)e^{3x}$ $y=C_{1}e^{3x}$
The general solution of $\dfrac{\mathrm{d^{2}} y}{\mathrm{d} x^{2}}-6\dfrac{\mathrm{d} y}{\mathrm{d} x}+9y=0$ is$y=C_{1}e^{3x}+C_{2}e^{-3x}$$y=(C_{1}+C_{2}x)e^{-3x}$$y=(C...
go_editor
1.9k
points
226
views
go_editor
asked
Feb 13, 2020
Differential Equations
gate2020-ec
differential-equations
second-order-differential-equation
+
–
0
votes
0
answers
30
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
226
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-3
numerical-answers
vector-analysis
+
–
0
votes
0
answers
31
GATE ECE 2014 Set 1 | Question: 29
Consider the matrix ... $\alpha$ is a non-negative real number. The value of $\alpha$ for which $\text{det(P)} = 0$ is _______.
Consider the matrix $$J_{6} = \begin{bmatrix} 0&0 &0 &0 &0 &1 \\ 0& 0& 0& 0& 1&0 \\ 0& 0& 0& 1& 0&0 \\ 0&0 & 1& 0&0 &0 \\0 &1 &0 &0 &0 &0 \\1 &0 &0 &0 & 0& 0\end{bmatrix}...
Milicevic3306
16.0k
points
226
views
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-ec-1
numerical-answers
linear-algebra
matrices
determinant
+
–
0
votes
0
answers
32
GATE ECE 2017 Set 1 | Question: 48
Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane? Four left half plane(LHP) roots One right half plane(RHP) root,one LHP root and two roots on the imaginary axis Two RHP roots and two LHP roots All four roots are on the imaginary axis
Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane?Four left half plane(LHP) rootsOn...
admin
46.4k
points
225
views
admin
asked
Nov 17, 2017
Complex Analysis
gate2017-ec-1
complex-analysis
+
–
0
votes
0
answers
33
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
224
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-4
numerical-answers
vector-analysis
+
–
0
votes
0
answers
34
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}$
Two continuous random variables $X$ and $Y$ are related as$$Y=2X+3$$Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The vari...
Arjun
6.6k
points
220
views
Arjun
asked
Feb 19, 2021
Probability and Statistics
gateec-2021
probability-and-statistics
random-variable
variance
+
–
0
votes
0
answers
35
GATE ECE 2019 | Question: 26
Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $ \mid f’(x) \mid \leq 2.$ Given these conditions, which one of the following inequalities is necessarily true for all $x \in[-2,2]?$ $f(x)\leq \frac{1}{2} \mid x+1 \mid$ $f(x)\leq 2 \mid x+1 \mid $ $f(x)\leq \frac{1}{2} \mid x \mid$ $f(x)\leq 2 \mid x \mid$
Consider a differentiable function $f(x)$ on the set of real numbers, such that $f(-1)=0$ and $ \mid f’(x) \mid \leq 2.$ Given these conditions, which one of the follow...
Arjun
6.6k
points
217
views
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ec
calculus
maxima-minima
+
–
0
votes
0
answers
36
GATE ECE 2016 Set 3 | Question: 3
The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _______
The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, ...
Milicevic3306
16.0k
points
214
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-3
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
37
GATE ECE 2009 | Question: 1
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is $1$ $2$ $3$ $4$
The order of the differential equation $\dfrac{d^{2} y}{d t^{2}}+\left(\dfrac{d y}{d t}\right)^{3}+y^{4}=e^{-t} \quad$ is$1$$2$$3$$4$
admin
46.4k
points
213
views
admin
asked
Sep 15, 2022
Differential Equations
gate2009-ec
differential-equations
second-order-differential-equation
+
–
0
votes
0
answers
38
GATE ECE 2016 Set 3 | Question: 51
The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be in error is _______
The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bi...
Milicevic3306
16.0k
points
211
views
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ec-3
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
39
GATE ECE 2015 Set 3 | Question: 28
Consider the differential equation $\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0. $ Given $x(0) = 20$ and $x(1) = 10/e,$ where $e = 2.718,$ the value of $x(2)$ is ________.
Consider the differential equation$$\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0. $$Given $x(0) = 20$ and $x(1) = 10/e,...
Milicevic3306
16.0k
points
209
views
Milicevic3306
asked
Mar 27, 2018
Differential Equations
gate2015-ec-3
numerical-answers
differential-equations
+
–
0
votes
0
answers
40
GATE ECE 2018 | Question: 40
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ where $Z$ ... $\alpha$ (accurate to two decimal places) is ________.
A random variable $X$ takes values $-0.5$ and $0.5$ with probabilities $\dfrac{1}{4}$ and $\dfrac{3}{4}$, respectively. The noisy observation of $X\:\text{is}\:Y=X+Z,$ wh...
gatecse
1.6k
points
206
views
gatecse
asked
Feb 19, 2018
Probability and Statistics
gate2018-ec
numerical-answers
probability-and-statistics
propability
random-variable
+
–
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