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Hot questions in Engineering Mathematics
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41
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
42
GATE Electrical 2018 | Question: 42
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$ is ________ (up to $2$ decimal places).
As shown in the figure, $C$ is the arc from the point $(3,0)$ to the point $(0,3)$ on the circle $x^2+y^2=9$. The value of the integral $\int_C (y^2+2yx) dx +(2xy+x^2)dy$...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Calculus
gate2018-ee
numerical-answers
calculus
definite-integral
+
–
0
votes
0
answers
43
GATE Electrical 2018 | Question: 17
Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textbf{A}$ is _________ (up to $1$ decimal place).
Consider a non-singular $2 \times 2$ square matrix $\textbf{A}$. If $\text{trace}(\textbf{A})=4$ and $\text{trace}(\textbf{A}^2)=5$, the determinant of the matrix $\textb...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Linear Algebra
gate2018-ee
numerical-answers
linear-algebra
matrices
determinant
+
–
0
votes
0
answers
44
GATE Electrical 2018 | Question: 18
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(x) dx$ is _______ (up to $2$ decimal places).
Let $f$ be a real-valued function of a real variable defined as $f(x)=x – [x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Calculus
gate2018-ee
numerical-answers
calculus
definite-integral
+
–
0
votes
0
answers
45
GATE Electrical 2018 | Question: 43
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Calculus
gate2018-ee
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
46
GATE Electrical 2018 | Question: 44
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$ is _______ (up to $1$ decimal place).
Let $A= \begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B=A^3-A^2-4A+5I$, where $I$ is the $3 \times 3$ identify matrix. The determinant of $B$...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Linear Algebra
gate2018-ee
numerical-answers
linear-algebra
matrices
determinant
+
–
0
votes
0
answers
47
GATE Electrical 2018 | Question: 34
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is $3$ $4$ $5$ $6$
The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is$3$$4$$5$$6$
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
complex-valued-functions
+
–
0
votes
0
answers
48
GATE Electrical 2018 | Question: 12
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2 \textbf{j} + 2 \textbf{k}$ is $1$ $0.95$ $0.93$ $0.9$
The value of the directional derivative of the function $\Phi (x,y,z) = xy^2 +yz^2+zx^2$ at the point $(2,-1,1)$ in the direction of the vector $\textbf{p}= \textbf{i} +2...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Calculus
gate2018-ee
calculus
directional-derivatives
+
–
0
votes
0
answers
49
GATE Electrical 2018 | Question: 40
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\omega$ denoes frequency. Then the value of $\mid \text{ln } x(t) \mid$ at $t=1$ is _________ (up to $1$ decimal place). ($\text{ln}$ denotes the logarithm base $e$)
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\om...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Transform Theory
gate2018-ee
numerical-answers
transform-theory
fourier-transform
+
–
0
votes
0
answers
50
GATE Electrical 2018 | Question: 13
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is $\frac{\pi i}{2} \\ $ $2 \pi i\\$ $ – \frac{\pi i}{2}\\$ $-2 \pi i$
The value of the integral $\oint _c \frac{z+1}{z^2-4} dz$ in counter clockwise direction around a circle $C$ of radius $1$ with center at the point $z=-2$ is$\frac{\pi i}...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
51
GATE Electrical 2018 | Question: 33
Consider a system governed by the following equations $ \frac{dx_1(t)}{dt} = x_2(t)-x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)-x_2(t)$ The initial conditions are such that $x_1(0)<x_2(0)< \infty$. Let $x_{1f}= \underset{t \to \infty}{\lim} x_1(t)$ ... $x_{1f}<x_{2f}<\infty$ $x_{2f}<x_{1f}<\infty$ $x_{1f}<=_{2f}<\infty$ $x_{1f}=x_{2f}=\infty$
Consider a system governed by the following equations $$ \frac{dx_1(t)}{dt} = x_2(t)-x_1(t) \\ \frac{dx_2(t)}{dt} = x_1(t)-x_2(t)$$ The initial conditions are such that $...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Differential Equations
gate2018-ee
differential-equations
+
–
0
votes
0
answers
52
GATE Electrical 2018 | Question: 11
Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true? $f(x)$ is discontinuous at $x=0$ $f(x)$ ... is differentiable but its first derivative is not continuous at $x=0$ $f(x)$ is differentiable but its first derivative is not differentiable at $x=0$
Let $f$ be a real-valued function of a real variable defined as $f(x)=x^2$ for $x \geq 0$, and $f(x)=-x^2$ for $x<0$. Which one of the following statements is true?$f(x)$...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Calculus
gate2018-ee
calculus
continuity-and-differentiability
+
–
0
votes
0
answers
53
GATE Electrical 2018 | Question: 35
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is $1$ $0$ $-1$ $-2$
If $C$ is a circle $\mid z \mid=4$ and $f(z)=\frac{z^2}{(z^2-3z+2)^2}$, then $\underset{C}{\oint} f(z) dz$ is$1$$0$$-1$$-2$
Arjun
15.9k
points
Arjun
asked
Feb 19, 2018
Complex Variables
gate2018-ee
complex-variables
cauchys-integral-theorem
+
–
1
votes
1
answer
54
GATE Electrical 2014 Set 2 | Question: 1
Which one of the following statements is true for all real symmetric matrices? All the eigenvalues are real. All the eigenvalues are positive. All the eigenvalues are distinct. Sum of all the eigenvalues is zero.
Which one of the following statements is true for all real symmetric matrices?All the eigenvalues are real.All the eigenvalues are positive.All the eigenvalues are distin...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Linear Algebra
gate2014-ee-2
linear-algebra
eigen-values
+
–
2
votes
1
answer
55
GATE Electrical 2014 Set 2 | Question: 2
Consider a dice with the property that the probability of a face with $n$ dots showing up is proportional to $n$. The probability of the face with three dots showing up is ________.
Consider a dice with the property that the probability of a face with $n$ dots showing up is proportional to $n$. The probability of the face with three dots showing up i...
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2014-ee-2
probability-and-statistics
probability
+
–
0
votes
0
answers
56
GATE Electrical 2017 Set 2 | Question: 25
In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $100 \times 100$. If there are $20$PV buses in addition to $PQ$ buses and a slack bus, the total number of buses in the system is ______.
In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $100 \times 100$. If there are $20$PV buses in addition to $PQ$...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Numerical Methods
gate2017-ee-2
numerical-answers
numerical-methods
newton-raphson-method
+
–
0
votes
0
answers
57
GATE Electrical 2017 Set 2 | Question: 26
Let $ g(x)= \begin{cases} -x & \ x \leq 1 \\ x+1 & \ x \geq 1 \end{cases}$ and $ f(x)= \begin{cases} 1-x & \ x \leq 0 \\ x^{2} & \ x > 0 \end{cases}$. Consider the composition of $f$ and $g$ ... $(f {\circ} g) (x)$ present in the interval $(-\infty, 0)$ is: $0$ $1$ $2$ $4$
Let $ g(x)= \begin{cases} -x & \ x \leq 1 \\ x+1 & \ x \geq 1 \end{cases}$ and $ f(x)= \begin{cases} 1-x & \ x \leq 0 \\ x^{2} & \ x 0 \end{cases}$.Consider the co...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
calculus
continuity
+
–
0
votes
0
answers
58
GATE Electrical 2017 Set 1 | Question: 42
Only one of the real roots of $f(x)=x^{6}-x-1$ lies in the interval $1 \leq x \leq 2$ and bisection method is used to find its value. For achieving an accuracy of $0.001$, the required minimum number of iterations is _________.
Only one of the real roots of $f(x)=x^{6}-x-1$ lies in the interval $1 \leq x \leq 2$ and bisection method is used to find its value. For achieving an accuracy of $0.001$...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Numerical Methods
gate2017-ee-1
numerical-answers
numerical-methods
bisection-method
+
–
0
votes
0
answers
59
GATE Electrical 2017 Set 2 | Question: 19
Let $x$ and $y$ be integers satisfying the following equations $2x^{2}+y^{2}=34$ $x+2y=11$ The value of $(x+y)$ is _______.
Let $x$ and $y$ be integers satisfying the following equations$2x^{2}+y^{2}=34$$x+2y=11$The value of $(x+y)$ is _______.
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-2
numerical-answers
calculus
curves
+
–
0
votes
0
answers
60
GATE Electrical 2017 Set 1 | Question: 26
A function $f(x)$ is defined as $f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$ Which one of the following statement is TRUE? $f(x)$ is NOT differentiable at $x=1$ ... for all values of $a$ and $b$ such that $a+b=e$. $f(x)$ is differentiable at $x=1$ for all values of $a$ and $b$.
A function $f(x)$ is defined as$f(x)= \begin{cases} e^{x}, & x < 1 \\ \text{In } x+ax^{2}+bx, & x\geq 1 \end{cases}$, where $x \in \mathbb{R}$Which one of the followin...
Arjun
15.9k
points
Arjun
asked
Feb 26, 2017
Calculus
gate2017-ee-1
calculus
continuity-and-differentiability
+
–
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