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Highest voted questions in Engineering Mathematics
2
votes
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1
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
+
–
1
votes
0
answers
2
GATE Electrical 2013 | Question: 50
The state variable formulation of a system is given as ... The system is controllable but not observable not controllable but observable both controllable and observable both not controllable and not observable
The state variable formulation of a system is given as$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x...
piyag476
1.6k
points
piyag476
asked
Feb 11, 2017
Linear Algebra
gate2013-ee
linear-algebra
matrices
state-equations
system-of-linear-equations
+
–
1
votes
1
answer
3
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
+
–
1
votes
0
answers
4
GATE Electrical 2014 Set 1 | Question: 27
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is $2^{-n}$ $0$ $^{n}C_{n-3}2^{-n}$ $2^{-n+3}$
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is$2^{-n}$$0$$^{n}C_{n-3}2^{-n}$$2^{-n+3}$
makhdoom ghaya
9.4k
points
makhdoom ghaya
asked
Feb 11, 2017
Probability & Statistics
gate2014-ee-1
probability-and-statistics
probability
coins
+
–
0
votes
1
answer
5
GATE Electrical 2021 | Question: 1
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are $1$ and $1$ $1$ and $-1$ $j$ and $-j$ $pq$ and $-pq$
Let $p$ and $q$ be real numbers such that $p^{2}+q^{2}=1$ . The eigenvalues of the matrix $\begin{bmatrix} p & q\\ q& -p \end{bmatrix}$are$1$ and $1$$1$ and $-1$$j$ and $...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gateee-2021
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
6
GATE Electrical 2021 | Question: 2
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ ... $p\left ( z \right )=0$ come in conjugate pairs All the roots cannot be real
Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ is a complex number.Which one of the following is true?$\text{conjugate}\:\lef...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Complex Variables
gateee-2021
complex-variables
complex-number
+
–
0
votes
0
answers
7
GATE Electrical 2021 | Question: 3
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right )> 0$ for all $x \in \left ( 0,1 \right )$. ... has no local minimum in $(0,1)$ one local maximum in $(0,1)$ exactly one local minimum in $(0,1)$ two distinct local minima in $(0,1)$
Let $f\left ( x \right )$ be a real-valued function such that ${f}'\left ( x_{0} \right )=0$ for some $x _{0} \in\left ( 0,1 \right ),$ and ${f}''\left ( x \right ) 0$ fo...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gateee-2021
calculus
maxima-minima
+
–
0
votes
0
answers
8
GATE Electrical 2021 | Question: 5
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$? $\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively)}$ $10x\hat{X}+20y\hat{Y}-30z\hat{Z}$ $10y\hat{X}+20x\hat{Y}-10z\hat{Z}$ $10z\hat{X}+20y\hat{Y}-30x\hat{Z}$ $10x\hat{X}-30z\hat{Y}+20y\hat{Z}$
Which one of the following vector functions represents a magnetic field $\overrightarrow{B}$?$\text{($\hat{X}, \hat{Y}$ and $\hat{Z}$ are unit vectors along x-axis, y-axi...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gateee-2021
calculus
field-vectors
+
–
0
votes
0
answers
9
GATE Electrical 2021 | Question: 13
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Then $u+v=$ _______________.
Suppose the circles $x^{2}+y^{2}=1$ and $\left ( x-1\right )^{2}+\left ( y-1 \right )^{2}=r^{2}$ intersect each other orthogonally at the point $\left ( u,v \right )$. Th...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gateee-2021
numerical-answers
calculus
curves
+
–
0
votes
0
answers
10
GATE Electrical 2021 | Question: 26
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ has two real roots one real root three real roots no real roots
In the open interval $\left ( 0,1 \right )$, the polynomial $p\left ( x \right) =x^{4}-4x^{3}+2$ hastwo real rootsone real rootthree real rootsno real roots
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gateee-2021
calculus
polynomials
+
–
0
votes
0
answers
11
GATE Electrical 2021 | Question: 28
Let $\left ( -1 -j \right ), \left ( 3 -j \right ), \left ( 3 + j \right )$ and $\left ( -1+ j \right )$ be the vertices of a rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of the contour integral $\oint _{C}\dfrac{dz}{z^{2}\left ( z-4 \right )}$ is $j\pi /2$ $0$ $-j\pi /8$ $j\pi /16$
Let $\left ( -1 -j \right ), \left ( 3 -j \right ), \left ( 3 + j \right )$ and $\left ( -1+ j \right )$ be the vertices of a rectangle $C$ in the complex plane. Assuming...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Calculus
gateee-2021
calculus
contour-plots
+
–
0
votes
0
answers
12
GATE Electrical 2021 | Question: 32
Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty }\:f\left ( t \right )e^{-j\omega t}dt$ ... $f\left ( 0 \right )< 1$ $f\left ( 0 \right )> 1$ $f\left ( 0 \right )= 1$ $f\left ( 0 \right )= 0$
Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty ...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Transform Theory
gateee-2021
transform-theory
fourier-transform
+
–
0
votes
2
answers
13
GATE Electrical 2021 | Question: 38
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is ___________________.
Let $A$ be a $10\times10$ matrix such that $A^{5}$ is a null matrix, and let $I$ be the $10\times10$ identity matrix. The determinant of $\text{A+I}$ is _________________...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gateee-2021
numerical-answers
linear-algebra
matrices
determinant
+
–
0
votes
0
answers
14
GATE Electrical 2021 | Question: 43
Consider a continuous-time signal $x(t)$ defined by $x(t)=0$ for $\left | t \right |> 1$, and $x\left ( t \right )=1-\left | t \right |$ for $\left | t \right |\leq 1$. Let the Fourier transform of $x(t)$ ... $X\left ( \omega \right )$ is ___________.
Consider a continuous-time signal $x(t)$ defined by $x(t)=0$ for $\left | t \right | 1$, and $x\left ( t \right )=1-\left | t \right |$ for $\left | t \right |\leq 1$. Le...
Arjun
15.9k
points
Arjun
asked
Feb 19, 2021
Transform Theory
gateee-2021
numerical-answers
transform-theory
fourier-transform
+
–
0
votes
1
answer
15
GATE Electrical 2020 | Question: 1
$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true? $\text{d}$ can be chosen to ensure that $\text{x = 0}$ is a root for any ... $\text{a, b, c, d}$ can be chosen to ensure that all roots are complex. $\text{c}$ alone cannot ensure that all roots are real.
$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true?$\text{d}$...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Calculus
gate2020-ee
calculus
polynomials
+
–
0
votes
0
answers
16
GATE Electrical 2020 | Question: 2
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ ...
Which of the following is true for all possible non-zero choices of integers $m,n;m\neq n,$ or all possible non-zero choices of real numbers $p,q;p\neq q,$ as applicable?...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Calculus
gate2020-ee
calculus
definite-integral
+
–
0
votes
0
answers
17
GATE Electrical 2020 | Question: 5
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is: $\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$
The value of the following complex integral, with $\text{C}$ representing the unit circle centered at origin in the counterclockwise sense, is:$$\int _{C}\frac{z^{2}+1}{z...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Complex Variables
gate2020-ee
complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
18
GATE Electrical 2020 | Question: 16
Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is ______________. $\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\:y\left ( 0 \right )=1$
Consider the initial value problem below. The value of y at $x=\ln{2}$, (rounded off to $3$ decimal places) is ______________.$$\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Differential Equations
gate2020-ee
numerical-answers
differential-equations
initial-and-boundary-value-problems
+
–
0
votes
0
answers
19
GATE Electrical 2020 | Question: 26
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively, ______. $7$ and $1/4$ $7$ and $1$ $-2$ and $-1/2$ $1$ and $1/4$
For real numbers, $\text{x}$ and $\text{y}$, with $y=3x^{2}+3x+1$, the maximum and minimum value of $\text{y}$ for $\text{x}$ $\in \left [ -2,0 \right ]$ are respectively...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Calculus
gate2020-ee
calculus
maxima-minima
+
–
0
votes
0
answers
20
GATE Electrical 2020 | Question: 27
The vector function expressed by $F=a_{x}\left ( 5y-k_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y-4x\right )$ represents a conservative field, where $a_{x}, a_{y},a_{z}$ are unit vectors along $x, y$ and $z$ directions, respectively. The values of constants ... $k_{1}=3, k_{2}=8,k_{3}=5$ $k_{1}=4, k_{2}=5,k_{3}=3$ $k_{1}=0, k_{2}=0,k_{3}=0$
The vector function expressed by$$F=a_{x}\left ( 5y-k_{1} z\right )+a_{y}\left ( 3z+k_{2}x \right )+a_{z}\left ( k_{3} y-4x\right )$$represents a conservative field, wher...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Calculus
gate2020-ee
calculus
field-vectors
+
–
0
votes
1
answer
21
GATE Electrical 2020 | Question: 42
The number of purely real elements in a lower triangular representation of the given $3\times 3$ ... $5$ $6$ $8$ $9$
The number of purely real elements in a lower triangular representation of the given $3\times 3$ matrix, obtained through the given decomposition is ______________.$$\beg...
go_editor
1.9k
points
go_editor
asked
Feb 28, 2020
Linear Algebra
gate2020-ee
linear-algebra
matrices
+
–
0
votes
0
answers
22
Gate2006-EE
...
$\\ P=\begin{pmatrix} -10\\ -1\\ 3 \end{pmatrix}^{T} Q=\begin{pmatrix} -2\\ -5\\ 9 \end{pmatrix}^{T} R=\begin{pmatrix} 2\\ -7\\ 12 \end{pmatrix}^{T} are\ three\ vectors.\...
KUSHAGRA गुप्ता
120
points
KUSHAGRA गुप्ता
asked
Sep 29, 2019
Linear Algebra
gate2006-ee
linear-algebra
+
–
0
votes
0
answers
23
GATE Electrical 2019 | Question: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$ $3te^{-t}+e^{-t}$ $3e^{-t}$ $2te^{-t}+e^{-t}$ $4te^{-t}+e^{-t}$
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$$3te^{-t}+e^{-t}$$3e^{-t}$$2te^{-t}+e^{-t}$$4te^{-t}+e^{-t}$
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Transform Theory
gate2019-ee
transform-theory
laplace-transform
inverse-laplace-transform
+
–
0
votes
1
answer
24
GATE Electrical 2019 | Question: 2
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are $4$ and $9$ $2$ and $3$ $-2$ and $-3$ $16$ and $81$
$M$ is $2 \times 2$ matrix with eigenvalues $4$ and $9.$ The eigenvalues of $M^{2}$ are$4$ and $9$$2$ and $3$$-2$ and $-3$$16$ and $81$
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ee
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
25
GATE Electrical 2019 | Question: 3
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}}- C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;$ where $c \neq 0$ is known as heat equation wave equation Poisson’s equation Laplace equation
The partial differential equation $\frac{\partial^{2}u}{\partial t^{2}}- C^{2} \bigg( \frac{\partial^{2}u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}} \bigg )=0;...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Differential Equations
gate2019-ee
differential-equations
partial-differential-equation
+
–
0
votes
0
answers
26
GATE Electrical 2019 | Question: 4
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ? $\frac{z^{2}-1}{z} \\ $ $\frac{z^{2}-1}{z+2} \\ $ $\frac{z^{2}-1}{z-0.5} \\ $ $\frac{z^{2}-1}{z+j0.5} $
Which one of the following functions is analytic in the region $\mid z \mid \leq 1$ ?$\frac{z^{2}-1}{z} \\ $$\frac{z^{2}-1}{z+2} \\ $$\frac{z^{2}-1}{z-0.5} \\ $$\frac{z^...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Complex Variables
gate2019-ee
complex-variables
analytic-functions
+
–
0
votes
0
answers
27
GATE Electrical 2019 | Question: 13
The output response of a system is denoted as $y(t)$, and its Laplace transform is given by $Y(s)=\frac{10}{s(s^{2}+s+100 \sqrt{2})}$ The steady state value of $y(t)$ is $\frac{1}{10 \sqrt{2}} \\ $ $10 \sqrt{2} \\ $ $\frac{1}{100 \sqrt{2}} \\ $ $100 \sqrt{2}$
The output response of a system is denoted as $y(t)$, and its Laplace transform is given by $$Y(s)=\frac{10}{s(s^{2}+s+100 \sqrt{2})}$$ The steady state value of $y(t)$ i...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Transform Theory
gate2019-ee
transform-theory
laplace-transform
+
–
0
votes
0
answers
28
GATE Electrical 2019 | Question: 18
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-3,2)\rightarrow(2,6,2) \rightarrow(2,6,-1) $ is___________.
If $f=2x^{3}+3y^{2}+4z$, the value of line integral $\int_{c} \text{grad}f \cdot d \textbf{r}$ evaluated over contour $C$ formed by the segments $(-3,-3,2)\rightarrow(2,-...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ee
numerical-answers
calculus
line-integral
+
–
0
votes
1
answer
29
GATE Electrical 2019 | Question: 24
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
The rank of the matrix, $M = \begin{bmatrix} 0 &1 &1 \\ 1& 0 &1 \\ 1& 1 & 0 \end{bmatrix}$, is ______________.
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ee
numerical-answers
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
30
GATE Electrical 2019 | Question: 26
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \end{bmatrix}$, where $u_1^T$ and $u_2^T$ are ... True and Statement $2$ is false Statement $2$ is true and Statement $1$ is false Both the Statements are true Both the statements are false
Consider a $2\times 2$ matrix $M=\begin{bmatrix} v_1 & v_2 \end{bmatrix}$, where $v_1$ and $v_2$ are the column vectors. Suppose $M^{-1}=\begin{bmatrix} u_1^T \\ u_2^T \e...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ee
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
31
GATE Electrical 2019 | Question: 27
The closed-loop line integral $\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$ evaluated Counter-clockwise, is $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$
The closed-loop line integral $$\underset{\mid z \mid = 5}{\oint} \frac{z^3 + z^2 + 8}{z+2}dz$$evaluated Counter-clockwise, is $+8 j \pi$$-8 j \pi$$-4 j \pi$$+4 j \pi$
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Complex Variables
gate2019-ee
complex-variables
cauchys-integral-theorem
line-integral
+
–
0
votes
0
answers
32
GATE Electrical 2019 | Question: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $$f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin ...
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ee
calculus
fourier-series
+
–
0
votes
0
answers
33
GATE Electrical 2019 | Question: 39
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
If $\textbf{A}= 2x \textbf{i} + 3y \textbf{j} +4z \textbf{k}$ and $u=x^2+y^2+z^2$, then $\text{div} \big(u \textbf{A} \big)$ at $(1,1,1)$ is _______
Arjun
15.9k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ee
numerical-answers
calculus
divergence
+
–
0
votes
0
answers
34
GATE Electrical 2012 | Question: 42
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is$1/4$$1/2$$1$$2$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Transform Theory
gate2012-ee
transform-theory
fourier-transform
+
–
0
votes
0
answers
35
GATE Electrical 2012 | Question: 41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
The state variable description of an LTI system is given by$$\begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 & a_1 & 0 \\ 0 & 0 & a_2 \\ a_3 & 0 & 0 \...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Linear Algebra
gate2012-ee
linear-algebra
matrices
system-of-linear-equations
+
–
0
votes
0
answers
36
GATE Electrical 2012 | Question: 38
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla \cdot \textbf{A} = 0$ is $-2$ $2$ $1$ $0$
The direction of vector $\textbf{A}$ is radically outward from the origin, with $\mid \textbf{A} \mid k r ^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of ...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Calculus
gate2012-ee
differential-equations
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–
0
votes
0
answers
37
GATE Electrical 2012 | Question: 37
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first ime. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Probability & Statistics
gate2012-ee
probability-and-statistics
probability
+
–
0
votes
0
answers
38
GATE Electrical 2012 | Question: 26
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
Given that $\textbf{A}= \begin{bmatrix} -5 & -3 \\ 2 & 0 \end{bmatrix}$ and $\textbf{I} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, the value of $A^3$ is$15 \: \text...
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Linear Algebra
gate2012-ee
linear-algebra
matrices
eigen-values
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–
0
votes
0
answers
39
GATE Electrical 2012 | Question: 27
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is$21$$25$$41$$46$
Andrijana3306
1.4k
points
Andrijana3306
asked
Mar 23, 2018
Calculus
gate2012-ee
calculus
maxima-minima
+
–
0
votes
0
answers
40
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
+
–
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