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Most viewed questions in Engineering Mathematics
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121
GATE ECE 2016 Set 3 | Question: 1
Consider a $2\times2$ sqaure matrix $\textbf{A}= \begin{bmatrix} \sigma &x\\ \omega &\sigma \end{bmatrix},$ where $x$ is unknown. If the eigen values of the matrix $\textbf{A}$ are $(\sigma + j\omega)$ and $(\sigma - j\omega)$, then $x$ is equal to $+j\omega$ $-j\omega$ $+\omega$ $-\omega$
Consider a $2\times2$ sqaure matrix $$\textbf{A}= \begin{bmatrix} \sigma &x\\ \omega &\sigma \end{bmatrix},$$ where $x$ is unknown. If the eigen values of the matrix $\te...
Milicevic3306
16.0k
points
130
views
Milicevic3306
asked
Mar 27, 2018
Linear Algebra
gate2016-ec-3
linear-algebra
matrices
+
–
0
votes
0
answers
122
GATE ECE 2018 | Question: 4
Let the input be $u$ and the output be $y$ ... $y=au+b,b\neq 0$ $y=au$
Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:$\d...
gatecse
1.6k
points
130
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
123
GATE ECE 2018 | Question: 34
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{x}.$ The equation that describes the curve is $\ln\left (1+\dfrac{y^{2}}{x^{2}}\right)=x-1$ ... $\ln\left (1+\dfrac{y}{x}\right)=x-1$ $\dfrac{1}{2}\ln\left (1+\dfrac{y}{x}\right)=x-1$
A curve passes through the point $\left ( x=1,y=0 \right )$ and satisfies the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x^{2}+y^{2}}{2y}+\dfrac{y}{...
gatecse
1.6k
points
129
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
differential-equations
+
–
0
votes
0
answers
124
TIFR ECE 2023 | Question: 9
Consider an $n \times n$ matrix $A$ with the property that each element of $A$ is non-negative and the sum of elements of each row is $1$. Consider the following statements. $1$ is an eigenvalue of $A$ The magnitude of any eigenvalue of $A$ is at ... statements $1$ and $3$ are correct Only statements $2$ and $3$ are correct All statements $1,2$ , and $3$ are correct
Consider an $n \times n$ matrix $A$ with the property that each element of $A$ is non-negative and the sum of elements of each row is $1$.Consider the following statement...
admin
46.4k
points
128
views
admin
asked
Mar 14, 2023
Linear Algebra
tifrece2023
engineering-mathematics
linear-algebra
+
–
0
votes
0
answers
125
GATE ECE 2014 Set 3 | Question: 5
If $z= xy \text{ ln} (xy)$, then $x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= 0 \\$ $y\frac{\partial z}{\partial x}= x\frac{\partial z}{\partial y} \\$ $x\frac{\partial z}{\partial x}= y\frac{\partial z}{\partial y} \\$ $y\frac{\partial z}{\partial x}+x\frac{\partial z}{\partial y}= 0$
If $z= xy \text{ ln} (xy)$, then$x\frac{\partial z}{\partial x}+y\frac{\partial z}{\partial y}= 0 \\$$y\frac{\partial z}{\partial x}= x\frac{\partial z}{\partial y} \\$$x...
Milicevic3306
16.0k
points
128
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-3
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
126
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.$$\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omeg...
Milicevic3306
16.0k
points
128
views
Milicevic3306
asked
Mar 25, 2018
Vector Analysis
gate2014-ec-1
numerical-answers
vector-analysis
+
–
0
votes
0
answers
127
GATE ECE 2016 Set 1 | Question: 28
In the following integral, the contour $C$ encloses the points $2 \pi j$ and $- 2\pi j$ $-\frac{1}{2\pi}\oint_C\frac{\sin z}{(z-2\pi j)^3} \,dz$ The value of the integral is _________
In the following integral, the contour $C$ encloses the points $2 \pi j$ and $- 2\pi j$ $$-\frac{1}{2\pi}\oint_C\frac{\sin z}{(z-2\pi j)^3} \,dz$$The value of the integra...
Milicevic3306
16.0k
points
127
views
Milicevic3306
asked
Mar 27, 2018
Complex Analysis
gate2016-ec-1
numerical-answers
complex-analysis
+
–
0
votes
0
answers
128
GATE ECE 2014 Set 4 | Question: 27
Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is _________
Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independent...
Milicevic3306
16.0k
points
127
views
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2014-ec-4
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
129
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
127
views
Milicevic3306
asked
Mar 26, 2018
Vector Analysis
gate2014-ec-3
numerical-answers
vector-analysis
+
–
1
votes
0
answers
130
TIFR ECE 2014 | Question: 1
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0,1]$. For $\alpha \in[0,1]$, the probability that $\alpha \max (X, Y)<\min (X, Y)$ is $1 /(2 \alpha)$. $\exp (1-\alpha)$ $1-\alpha$ $(1-\alpha)^{2}$ $1-\alpha^{2}$
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0,1]$. For $\alpha \in[0,1]$, the probability that $\alpha \m...
admin
46.4k
points
126
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
131
TIFR ECE 2014 | Question: 12
Assume that $Y, Z$ are independent, zero-mean, continuous random variables with variances $\sigma_{Y}^{2}$ and $\sigma_{Z}^{2},$ respectively. Let $X=Y+Z$. The optimal value of $\alpha$ which minimizes $\mathbb{E}\left[(X-\alpha Y)^{2}\right]$ ... $1$ $\frac{\sigma_{Y}^{2}}{\sigma_{Z}^{2}}$ None of the above.
Assume that $Y, Z$ are independent, zero-mean, continuous random variables with variances $\sigma_{Y}^{2}$ and $\sigma_{Z}^{2},$ respectively. Let $X=Y+Z$. The optimal va...
admin
46.4k
points
126
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
random-variable
+
–
0
votes
0
answers
132
GATE ECE 2015 Set 1 | Question: 2
A function $f(x)=1-x^2+x^3$ is defined in the closed interval $[-1,1]$. The value of $x$, in the open interval $(-1,1)$ for which the mean value theorem is satisfied, is $-1/2$ $-1/3$ $1/3$ $1/2$
A function $f(x)=1-x^2+x^3$ is defined in the closed interval $[-1,1]$. The value of $x$, in the open interval $(-1,1)$ for which the mean value theorem is satisfied, is$...
Milicevic3306
16.0k
points
126
views
Milicevic3306
asked
Mar 27, 2018
Calculus
gate2015-ec-1
calculus
mean-value-theorem
+
–
0
votes
0
answers
133
GATE ECE 2015 Set 1 | Question: 4
Let $z=x+iy$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE? The residue of $\frac{z}{z^2-1}$ at $z=1$ is $1/2$ $\oint_C z^2 dz=0$ $\frac{1}{2 \pi i} \oint_C \frac{1}{z} dz =1$ $\overline{z}$ (complex conjugate of $z$ is an analytical function
Let $z=x+iy$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements...
Milicevic3306
16.0k
points
126
views
Milicevic3306
asked
Mar 27, 2018
Complex Analysis
gate2015-ec-1
complex-analysis
analytic-functions
+
–
0
votes
0
answers
134
TIFR ECE 2023 | Question: 7
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\infty}^{\infty} f(x) \ln f(x) d x$. In which case does $X$ have the least differential entropy? You may use these facts: The ... $f(x):=(1 / 4) e^{-|x| / 2}$. $f(x):=e^{-2|x|}$.
Let $f(x)$ be a positive continuous function on the real line that is the density of a random variable $X$. The differential entropy of $X$ is defined to be $-\int_{-\inf...
admin
46.4k
points
125
views
admin
asked
Mar 14, 2023
Probability and Statistics
tifrece2023
engineering-mathematics
probability-and-statistics
+
–
0
votes
0
answers
135
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
125
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2015-ec-1
vector-analysis
+
–
1
votes
0
answers
136
TIFR ECE 2022 | Question: 8
Let $a, b, c$ be real numbers such that the following system of equations has a solution \[\begin{aligned} x+2 y+3 z &=a & & (1)\\ 8 x+10 y+12 z &=b & & (2)\\ 7 x+8 y+9 z &=c-1 & & (3) \end{aligned}\] Let $A$ be a ... 1 & 0 \\ -1 & 0 & 1 \end{array}\right]\] What is the value of $\operatorname{det}(A)$? $1$ $2$ $3$ $4$ $5$
Let $a, b, c$ be real numbers such that the following system of equations has a solution\[\begin{aligned}x+2 y+3 z &=a & & (1)\\8 x+10 y+12 z &=b & & (2)\\7 x+8 y+9 z &=c...
admin
46.4k
points
124
views
admin
asked
Nov 30, 2022
Linear Algebra
tifrece2022
linear-algebra
system-of-equations
+
–
1
votes
0
answers
137
TIFR ECE 2018 | Question: 3
Let $\lim _{n \rightarrow \infty} f(n)=\infty$ and $\lim _{n \rightarrow \infty} g(n)=\infty$. Then which of the following is necessarily $\text{TRUE.}$ $\lim _{n \rightarrow \infty}|f(n)-g(n)|=\infty$ $\lim _{n \rightarrow \infty}|f(n)-g(n)|=0$ $\lim _{n \rightarrow \infty}|f(n) / g(n)|=\infty$ $\lim _{n \rightarrow \infty}|f(n) / g(n)|=1$ None of the above
Let $\lim _{n \rightarrow \infty} f(n)=\infty$ and $\lim _{n \rightarrow \infty} g(n)=\infty$. Then which of the following is necessarily $\text{TRUE.}$$\lim _{n \rightar...
admin
46.4k
points
124
views
admin
asked
Nov 29, 2022
Calculus
tifrece2018
calculus
limits
+
–
0
votes
0
answers
138
GATE ECE 2020 | Question: 27
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y-1 \right )x?$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=1$ $\ln\mid y-1 \mid=0.5x^{2}+C$ and $y=-1$ $\ln\mid y-1 \mid=2x^{2}+C$ and $y=-1$
Which one of the following options contains two solutions of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x}=\left ( y-1 \right )x?$$\ln\mid y-1 \mid=0.5x^{...
go_editor
1.9k
points
124
views
go_editor
asked
Feb 13, 2020
Differential Equations
gate2020-ec
differential-equations
+
–
0
votes
0
answers
139
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
124
views
Milicevic3306
asked
Mar 27, 2018
Vector Analysis
gate2016-ec-3
numerical-answers
vector-analysis
gauss's-theorem
+
–
0
votes
0
answers
140
GATE ECE 2017 Set 1 | Question: 30
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.
admin
46.4k
points
124
views
admin
asked
Nov 17, 2017
Numerical Methods
gate2017-ec-1
numerical-answers
numerical-methods
+
–
0
votes
0
answers
141
GATE ECE 2016 Set 3 | Question: 2
For $f(z)= \large\frac{\sin(z)}{z^2}$, the residue of the pole at $z = 0$ is _______
For $f(z)= \large\frac{\sin(z)}{z^2}$, the residue of the pole at $z = 0$ is _______
Milicevic3306
16.0k
points
123
views
Milicevic3306
asked
Mar 27, 2018
Complex Analysis
gate2016-ec-3
numerical-answers
complex-analysis
+
–
0
votes
0
answers
142
GATE ECE 2014 Set 1 | Question: 1
For matrices of same dimension $M, N$ and scalar $c$, which one of these properties DOES NOT ALWAYS hold? $(M^{T})^{T} = M$ $(cM)^{T} = c(M)^{T}$ $(M+N)^{T} = M^{T} + N^{T}$ $MN = NM$
For matrices of same dimension $M, N$ and scalar $c$, which one of these properties DOES NOT ALWAYS hold?$(M^{T})^{T} = M$$(cM)^{T} = c(M)^{T}$$(M+N)^{T} = M^{T} + N^{T}...
Milicevic3306
16.0k
points
123
views
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-ec-1
linear-algebra
matrices
+
–
0
votes
0
answers
143
GATE ECE 2018 | Question: 52
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to two decimal places) of $\dfrac{\partial r}{\partial x}$ is _________ .
Let $r=x^{2}+y-z$ and $z^{3}-xy+yz+y^{3}=1.$ Assume that $x$ and $y$ are independent variables. At $\left( x,y,z \right)=\left ( 2,-1,1 \right ),$ the value (correct to t...
gatecse
1.6k
points
123
views
gatecse
asked
Feb 19, 2018
Calculus
gate2018-ec
numerical-answers
calculus
partial-derivatives
+
–
0
votes
0
answers
144
GATE ECE 2018 | Question: 11
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements: $S1: M $ has $4$ linearly independent eigenvectors. $S2: M$ has $4$ distinct eigenvalues. $S3: M$ is non-singular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements:$S1: M $ has $4$ linearly independent eigenvectors.$S2: M$ has $4$ distinct eigenvalues. $S...
gatecse
1.6k
points
122
views
gatecse
asked
Feb 19, 2018
Linear Algebra
gate2018-ec
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
145
GATE ECE 2017 Set 1 | Question: 26
Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$. $1 + x + x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $ $1 + x +3 x^{2} + 7x^{3} $
Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than...
admin
46.4k
points
122
views
admin
asked
Nov 17, 2017
Calculus
gate2017-ec-1
calculus
taylor-series
+
–
0
votes
0
answers
146
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
6.6k
points
121
views
Arjun
asked
Feb 19, 2021
Vector Analysis
gateec-2021
numerical-answers
vector-analysis
+
–
0
votes
0
answers
147
GATE ECE 2014 Set 3 | Question: 2
Which $ONE$ of the following is a linear non-homogeneous differential equation, where $x$ and $y$ are the independent and dependent variables respectively? $\frac{dy}{dx}+xy= e^{-x}$ $\frac{dy}{dx}+xy= 0$ $\frac{dy}{dx}+xy= e^{-y}$ $\frac{dy}{dx}+ e^{-y}= 0$
Which $ONE$ of the following is a linear non-homogeneous differential equation, where $x$ and $y$ are the independent and dependent variables respectively?$\frac{dy}{dx}+...
Milicevic3306
16.0k
points
121
views
Milicevic3306
asked
Mar 26, 2018
Differential Equations
gate2014-ec-3
differential-equations
+
–
0
votes
0
answers
148
GATE ECE 2018 | Question: 50
The position of a particle $y\left ( t \right )$ is described by the differential equation: $\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$ The initial conditions are $y\left ( 0 \right )=1$ and $\frac{dy}{dt}\mid_{t=0}=0$. The position (accurate to two decimal places) of the particle at $t=\pi$ is _________.
The position of a particle $y\left ( t \right )$ is described by the differential equation:$$\frac{d^{2}y}{dt^{2}}=-\frac{dy}{dt}-\frac{5y}{4}.$$The initial conditions ar...
gatecse
1.6k
points
121
views
gatecse
asked
Feb 19, 2018
Differential Equations
gate2018-ec
numerical-answers
differential-equations
second-order-differential-equation
+
–
1
votes
0
answers
149
TIFR ECE 2022 | Question: 14
Let a bag contain ten balls numbered $1,2, \ldots, 10$. Let three balls be drawn at random in sequence without replacement, and the number on the ball drawn on the $i^{\text {th }}$ choice be $n_{i} \in\{1,2, \ldots, 10\}.$ What is the probability that $n_{1} < n_{2} < n_{3} ?$ $\frac{1}{3}$ $\frac{1}{12}$ $\frac{1}{4}$ $\frac{1}{6}$ None of the above
Let a bag contain ten balls numbered $1,2, \ldots, 10$. Let three balls be drawn at random in sequence without replacement, and the number on the ball drawn on the $i^{\t...
admin
46.4k
points
120
views
admin
asked
Nov 30, 2022
Probability and Statistics
tifrece2022
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
150
GATE ECE 2014 Set 1 | Question: 43
Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$ is $\mid z \mid > \frac{1}{9} \\$ is $\mid z \mid < \frac{1}{3} \\$ is $\frac{1}{3}>\mid z \mid > \frac{1}{9} \\$ does not exist
Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$is $\mid ...
Milicevic3306
16.0k
points
120
views
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2014-ec-1
convergence-criteria
numerical-methods
+
–
0
votes
0
answers
151
GATE ECE 2013 | Question: 36
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$ Let $x(t)$ be a rectangular pulse given by $x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$ ... $\frac{e^{-2s}}{(s+2)(s+3)} \\$ $\frac{1-e^{-2s}}{s(s+2)(s+3)} $
A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$Let $x(t)$ be a rectangul...
Milicevic3306
16.0k
points
120
views
Milicevic3306
asked
Mar 25, 2018
Differential Equations
gate2013-ec
differential-equations
laplace-transform
+
–
1
votes
0
answers
152
TIFR ECE 2021 | Question: 4
The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider the following statements? System is memoryless. System is causal. System is stable. Which of the ... correct. All $(1), (2)$ and $(3)$ are correct. Only $(2)$ and $(3)$ are correct. None of the above
The first-order differential equation $\frac{d y(t)}{d t}+2 y(t)=x(t)$ describes a particular continuous-time system initially at rest at origin i.e., $x(0)=0$. Consider ...
admin
46.4k
points
119
views
admin
asked
Nov 30, 2022
Differential Equations
tifrece2021
differential-equations
first-order-differential-equation
+
–
0
votes
0
answers
153
GATE ECE 2014 Set 1 | Question: 5
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is the largest}\}$ is ________.
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is ...
Milicevic3306
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Mar 25, 2018
Probability and Statistics
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
uniform-distribution
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0
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0
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154
GATE ECE 2014 Set 1 | Question: 45
A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system. $y(t) + 5y(t) = u(t)$ When $y(0) = 1$ and $u(t)$ is a unit step function, $y(t)$ is $0.2 + 0.8e^{-5t}$ $0.2 - 0.2e^{-5t}$ $0.8 + 0.2e^{-5t}$ $0.8 - 0.8e^{-5t}$
A system is described by the following differential equation, where $u(t)$ is the input to the system and $y(t)$ is the output of the system.$$y(t) + 5y(t) = u(t)$$When $...
Milicevic3306
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Mar 25, 2018
Differential Equations
gate2014-ec-1
differential-equations
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0
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0
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155
GATE ECE 2017 Set 2 | Question: 4
The residues of a function $f(z)=\frac1{(z-4)(z+1)^3 }$ are $\frac{-1}{27}$ and $\frac{-1}{125} \\$ $\frac{1}{125}$ and $\frac{-1}{125} \\$ $\frac{-1}{27}$ and $\frac{1}{5} \\$ $\frac{1}{125}$and $\frac{-1}{5}$
The residues of a function $$f(z)=\frac1{(z-4)(z+1)^3 }$$are$\frac{-1}{27}$ and $\frac{-1}{125} \\$$\frac{1}{125}$ and $\frac{-1}{125} \\$$\frac{-1}{27}$ and $\frac{1}...
admin
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admin
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Nov 23, 2017
Complex Analysis
gate2017-ec-2
complex-analysis
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1
votes
0
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156
TIFR ECE 2015 | Question: 7
Let $A$ be an $8 \times 8$ matrix of the form \[ \left[\begin{array}{cccc} 2 & 1 & \ldots & 1 \\ 1 & 2 & \ldots & 1 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & \ldots & 2 \end{array}\ ... $\operatorname{det}(A)=9$ $\operatorname{det}(A)=18$ $\operatorname{det}(A)=14$ $\operatorname{det}(A)=27$ None of the above
Let $A$ be an $8 \times 8$ matrix of the form\[\left[\begin{array}{cccc}2 & 1 & \ldots & 1 \\1 & 2 & \ldots & 1 \\\vdots & \vdots & \ddots & \vdots \\1 & 1 & \ldots & 2\e...
admin
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Dec 15, 2022
Linear Algebra
tifr2015
linear-algebra
determinant
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1
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0
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157
TIFR ECE 2012 | Question: 1
The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is $\ln \left(1+e^{-1 / 4}\right)$ $\ln (5 / 3)$ $0$ $\ln \left(1+e^{2}\right)$ None of the above
The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is$\ln \left(1+e^{-1 / 4}\...
admin
46.4k
points
117
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Dec 8, 2022
Calculus
tifr2012
calculus
maxima-minima
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1
votes
0
answers
158
TIFR ECE 2018 | Question: 9
Let $X$ and $Y$ be two independent and identically distributed binary random variables that take values $\{-1,+1\}$ each with probability $1 / 2$. Let $Z_{1}=\max (X, Y)$, and $Z_{2}=\min (X, Y)$. Consider the following statements. $Z_{1}$ and $Z_{2}$ are uncorrelated ... $\text{(iii)}$ Both $\text{(i) and (ii), but not (iii)}$ All of $\text{(i), (ii) and (iii)}$
Let $X$ and $Y$ be two independent and identically distributed binary random variables that take values $\{-1,+1\}$ each with probability $1 / 2$. Let $Z_{1}=\max (X, Y)$...
admin
46.4k
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117
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Nov 29, 2022
Probability and Statistics
tifrece2018
probability-and-statistics
probability
random-variable
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0
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0
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159
GATE ECE 2018 | Question: 6
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is $0$ $1$ $2$ $3$
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)...
gatecse
1.6k
points
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gatecse
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Feb 19, 2018
Calculus
gate2018-ec
calculus
derivatives
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0
votes
0
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160
GATE ECE 2016 Set 1 | Question: 6
Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems ($u(t)$ denotes the unit-step function)? $e^{j\omega_0t}u(t)$ $\cos(\omega_0t)$ $e^{j\omega_0t}$ $\sin(\omega_0t)$
Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems ($u(t)$ denotes the unit-step function)?$e^{j\omega_0t...
Milicevic3306
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points
116
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Mar 27, 2018
Complex Analysis
gate2016-ec-1
complex-analysis
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