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Most viewed questions in Engineering Mathematics
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121
GATE Electrical 2016 Set 2 | Question: 29
The value of the integral $2\int_{-\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to $0$ $0.5$ $1$ $2$
The value of the integral $2\int_{-\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to$0$$0.5$ $1$$2$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-2
calculus
definite-integral
+
–
0
votes
0
answers
122
GATE Electrical 2016 Set 1 | Question: 5
The value of the integral $\oint _{c}\dfrac{2z+5}{\left ( z-\dfrac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$ over the contour $\mid z \mid=1$, taken in the anti-clockwise direction, would be $\dfrac{24 \pi i}{13} \\$ $\dfrac{48 \pi i}{13} \\$ $\dfrac{24}{13} \\$ $\dfrac{12}{13}$
The value of the integral$$\oint _{c}\dfrac{2z+5}{\left ( z-\dfrac{1}{2} \right ) \left (z^{2} -4z+5 \right )}dz$$over the contour $\mid z \mid=1$, taken in the anti-cloc...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Calculus
gate2016-ee-1
calculus
definite-integral
+
–
0
votes
0
answers
123
GATE Electrical 2017 Set 2 | Question: 20
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
numerical-answers
calculus
curves
+
–
0
votes
0
answers
124
GATE Electrical 2014 Set 2 | Question: 5
Consider the differential equation $x^2\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-y=0$. Which of the following is a solution to this differential equation for $x>0$? $e^x$ $x^2$ $1/x$ $\ln x$
Consider the differential equation $x^2\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-y=0$. Which of the following is a solution to this differential equation for $x>0$?$e^x$$x^2$$1/...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Differential Equations
gate2014-ee-2
derivatives
equations
+
–
0
votes
0
answers
125
GATE Electrical 2016 Set 2 | Question: 8
The solution of the differential equation, for $t > 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function), $te^{-t}u(t)$ $(e^{-t}-te^{-t})u(t)$ $(-e^{-t}+te^{-t})u(t)$ $e^{-t}u(t)$
The solution of the differential equation, for $t 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function),$te^...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Jan 29, 2017
Differential Equations
gate2016-ee-2
differential-equations
+
–
0
votes
0
answers
126
GATE Electrical 2017 Set 2 | Question: 27
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is $-18 \pi i$ $0$ $14 \pi i$ $48 \pi i$
The value of the contour integral in the complex plane $\oint \frac{z^{3}-2z+3}{z-2} dz$ along the contour $\mid z \mid =3$, taken counter- clockwise is$-18 \pi i$$0$$14...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
calculus
contour-integral
+
–
0
votes
0
answers
127
GATE Electrical 2012 | Question: 15
The unilateral Laplace transform of $f(t)$ is $\dfrac{1}{s^2+s+1}$. The unilateral Laplace transform of $t f(t)$ is $ – \dfrac{s}{(s^2+s+1)^2} \\ $ $ – \dfrac{2s+1}{(s^2+s+1)^2} \\$ $ \dfrac{s}{(s^2+s+1)^2} \\$ $ \dfrac{2s+1}{(s^2+s+1)^2}$
The unilateral Laplace transform of $f(t)$ is $\dfrac{1}{s^2+s+1}$. The unilateral Laplace transform of $t f(t)$ is$ – \dfrac{s}{(s^2+s+1)^2} \\ $$ – \dfrac{2s+1}{(s^...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Transform Theory
gate2012-ee
transform-theory
laplace-transform
+
–
0
votes
0
answers
128
GATE Electrical 2012 | Question: 26
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is$15 \: \text...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Linear Algebra
gate2012-ee
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
129
GATE Electrical 2012 | Question: 27
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Calculus
gate2012-ee
calculus
maxima-minima
+
–
0
votes
0
answers
130
GATE Electrical 2017 Set 2 | Question: 3
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ ... $\bigtriangledown . \vec{X}=0,\bigtriangledown \times \vec{Y} = 0, \bigtriangledown \times \vec{Z}=0$
The figures show diagramatic representations of vector fields $\vec{X}, \vec{Y}, \text{and} \vec{Z}$ respectively. Which one of the following choices is true?$\bigtriangl...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
calculus
field-vectors
+
–
0
votes
0
answers
131
GATE Electrical 2017 Set 1 | Question: 28
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below. The value of $I$ is $\frac{1}{2}i \\ $ $\frac{2}{3}i \\ $ $\frac{3}{4}i \\ $ $\frac{4}{5}i$
Consider the line integral $I=\int_{c} (x^{2}+iy^{2})dz$, where $z=x+iy$. The line $c$ is shown in the figure below.The value of $I$ is$\frac{1}{2}i \\ $$\frac{2}{3}i \\ ...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
calculus
line-integral
+
–
0
votes
0
answers
132
GATE Electrical 2017 Set 1 | Question: 27
Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belongs to the interval $(-2, 2)$ $(-10, 10)$ $(-10, 2)$ $(0, 10)$
Consider the differential equation $(t^{2}-81)\frac{dy}{dt}+5t y=\sin(t)$ with $y(1)=2 \pi$. There exists a unique solution for this differential equation when $t$ belong...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Differential Equations
gate2017-ee-1
differential-equations
+
–
0
votes
0
answers
133
GATE Electrical 2017 Set 1 | Question: 30
Let a causal LTI system be characterised by the following differential equation, with initial rest condition $\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(t)}{dt}$ where, $x(t)$ and $y(t)$ are the input and output respectively. The impulse response of the system ... $7e^{-2t}u(t)-2e^{-5t}u(t)$ $-7e^{-2t}u(t)+2e^{-5t}u(t)$
Let a causal LTI system be characterised by the following differential equation, with initial rest condition$\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Differential Equations
gate2017-ee-1
differential-equations
+
–
0
votes
0
answers
134
GATE Electrical 2017 Set 1 | Question: 2
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is $-2i$ $-i$ $i$ $2i$
For a complex number $z,\displaystyle{} \lim_{z \rightarrow i} \frac{z^{2}+1}{z^{3}+2z-i (z^{2}+2)}$ is$-2i$$-i$$i$$2i$
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
calculus
limits
complex-number
+
–
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