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Recent questions and answers in Engineering Mathematics
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votes
2
answers
1
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 ___________________.
Sonu123x
answered
in
Linear Algebra
Jan 5
by
Sonu123x
140
points
gateee-2021
numerical-answers
linear-algebra
matrices
determinant
0
votes
1
answer
2
GATE Electrical 2020 | Question: 42
The number of purely real elements in a lower triangular representation of the given $3\times 3$ ... $5$ $6$ $8$ $9$
samarpita
answered
in
Linear Algebra
May 7, 2022
by
samarpita
140
points
gate2020-ee
linear-algebra
matrices
0
votes
1
answer
3
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.
Adarsh Joshi
answered
in
Calculus
Mar 17, 2021
by
Adarsh Joshi
150
points
gate2020-ee
calculus
polynomials
0
votes
1
answer
4
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 $-pq$
shreekant98
answered
in
Linear Algebra
Mar 17, 2021
by
shreekant98
280
points
gateee-2021
linear-algebra
matrices
eigen-values
0
votes
0
answers
5
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
Arjun
asked
in
Complex Variables
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
complex-variables
complex-number
0
votes
0
answers
6
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 $x \in \left ( 0,1 \right )$ ... $(0,1)$ one local maximum in $(0,1)$ exactly one local minimum in $(0,1)$ two distinct local minima in $(0,1)$
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
calculus
maxima-minima
0
votes
0
answers
7
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)}$ $10x\hat{X}+20y\hat{Y}-30z\hat{Z}$ $10y\hat{X}+20x\hat{Y}-10z\hat{Z}$ $10z\hat{X}+20y\hat{Y}-30x\hat{Z}$ $10x\hat{X}-30z\hat{Y}+20y\hat{Z}$
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
calculus
field-vectors
0
votes
0
answers
8
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 $u+v=$ _______________.
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
numerical-answers
calculus
curves
0
votes
0
answers
9
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
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
calculus
polynomials
0
votes
0
answers
10
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 $j\pi /2$ $0$ $-j\pi /8$ $j\pi /16$
Arjun
asked
in
Calculus
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
calculus
contour-plots
0
votes
0
answers
11
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 $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty }\:f\left ( t \right )e^{-j\omega t}dt$ ... $f\left ( 0 \right )< 1$ $f\left ( 0 \right )> 1$ $f\left ( 0 \right )= 1$ $f\left ( 0 \right )= 0$
Arjun
asked
in
Transform Theory
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
transform-theory
fourier-transform
0
votes
0
answers
12
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 ___________.
Arjun
asked
in
Transform Theory
Feb 20, 2021
by
Arjun
15.9k
points
gateee-2021
numerical-answers
transform-theory
fourier-transform
0
votes
1
answer
13
GATE Electrical 2015 Set 1 | Question: 29
Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is $5/11$ $1/2$ $7/13$ $6/11$
dheeraj2310
answered
in
Probability & Statistics
Aug 12, 2020
by
dheeraj2310
140
points
gate2015-ee-1
probability-and-statistics
probability
conditional-probability
0
votes
0
answers
14
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 $p,q;p\neq q,$ ...
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
calculus
definite-integral
0
votes
0
answers
15
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: $\int _{C}\frac{z^{2}+1}{z^{2}-2z}\:dz$ $8\pi i$ $-8\pi i$ $-\pi i$ $\pi i$
go_editor
asked
in
Complex Variables
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
complex-variables
cauchys-integral-theorem
0
votes
0
answers
16
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 ______________. $\frac{\mathrm{d} y}{\mathrm{d} x}=2x-y,\:\:y\left ( 0 \right )=1$
go_editor
asked
in
Differential Equations
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
numerical-answers
differential-equations
initial-and-boundary-value-problems
0
votes
0
answers
17
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 $1/4$
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
calculus
maxima-minima
0
votes
0
answers
18
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 ... $k_{1}=3, k_{2}=8,k_{3}=5$ $k_{1}=4, k_{2}=5,k_{3}=3$ $k_{1}=0, k_{2}=0,k_{3}=0$
go_editor
asked
in
Calculus
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
calculus
field-vectors
0
votes
0
answers
19
Gate2006-EE
...
KUSHAGRA गुप्ता
asked
in
Linear Algebra
Sep 29, 2019
by
KUSHAGRA गुप्ता
120
points
gate2006-ee
linear-algebra
0
votes
1
answer
20
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 ______________.
Shalini26
answered
in
Linear Algebra
May 29, 2019
by
Shalini26
520
points
gate2019-ee
numerical-answers
linear-algebra
matrices
rank-of-matrix
0
votes
1
answer
21
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 $81$
Shalini26
answered
in
Linear Algebra
May 29, 2019
by
Shalini26
520
points
gate2019-ee
linear-algebra
matrices
eigen-values
0
votes
0
answers
22
GATE Electrical 2019 | Question: 1
The inverse Laplace transform of $H(s)=\frac{s+3}{s^{2}+2s+1}$ for $t \geq0$ $3te^{-t}+e^{-t}$ $3e^{-t}$ $2te^{-t}+e^{-t}$ $4te^{-t}+e^{-t}$
Arjun
asked
in
Transform Theory
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
transform-theory
laplace-transform
inverse-laplace-transform
0
votes
0
answers
23
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
Arjun
asked
in
Differential Equations
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
differential-equations
partial-differential-equation
0
votes
0
answers
24
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} $
Arjun
asked
in
Complex Variables
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
complex-variables
analytic-functions
0
votes
0
answers
25
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}} \\ $ $100 \sqrt{2}$
Arjun
asked
in
Transform Theory
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
transform-theory
laplace-transform
0
votes
0
answers
26
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___________.
Arjun
asked
in
Calculus
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
numerical-answers
calculus
line-integral
0
votes
0
answers
27
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
Arjun
asked
in
Linear Algebra
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
linear-algebra
matrices
eigen-values
eigen-vectors
0
votes
0
answers
28
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 $+8 j \pi$ $-8 j \pi$ $-4 j \pi$ $+4 j \pi$
Arjun
asked
in
Complex Variables
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
complex-variables
cauchys-integral-theorem
line-integral
0
votes
0
answers
29
GATE Electrical 2019 | Question: 28
A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin nt.$ ... $a_1 = \frac{A}{2}; \: b_1 = 0$ $a_1 = 0; \: b_1 = \frac{A}{\pi}$ $a_1 = 0;b_1 = \frac{A}{2}$
Arjun
asked
in
Calculus
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
calculus
fourier-series
0
votes
0
answers
30
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 _______
Arjun
asked
in
Calculus
Feb 12, 2019
by
Arjun
15.9k
points
gate2019-ee
numerical-answers
calculus
divergence
1
vote
1
answer
31
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.
Abhisek Tiwari 4
answered
in
Linear Algebra
Oct 26, 2018
by
Abhisek Tiwari 4
140
points
gate2014-ee-2
linear-algebra
eigen-values
0
votes
0
answers
32
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 $1/4$ $1/2$ $1$ $2$
Andrijana3306
asked
in
Transform Theory
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
transform-theory
fourier-transform
0
votes
0
answers
33
GATE Electrical 2012 | Question: 41
The state variable description of an LTI system is given by ... $a_1 = 0, \: a_2 \neq 0, \: a_3 = 0$ $a_1 \neq 0, \: a_2 \neq 0, \: a_3 = 0$
Andrijana3306
asked
in
Linear Algebra
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
linear-algebra
matrices
system-of-linear-equations
0
votes
0
answers
34
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 $-2$ $2$ $1$ $0$
Andrijana3306
asked
in
Calculus
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
differential-equations
0
votes
0
answers
35
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 $1/3$ $1/2$ $2/3$ $3/4$
Andrijana3306
asked
in
Probability & Statistics
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
probability-and-statistics
probability
0
votes
0
answers
36
GATE Electrical 2012 | Question: 27
The maximum value of $f(x) = x^3-9x^2+24x+5$ in the interval $[1,6]$ is $21$ $25$ $41$ $46$
Andrijana3306
asked
in
Calculus
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
calculus
maxima-minima
0
votes
0
answers
37
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 $15 \: \textbf{A} + 12 \: \textbf{I}$ $19 \: \textbf{A} + 30 \: \textbf{I}$ $17 \: \textbf{A} + 15 \: \textbf{I}$ $17 \: \textbf{A} + 21 \: \textbf{I}$
Andrijana3306
asked
in
Linear Algebra
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
linear-algebra
matrices
eigen-values
0
votes
0
answers
38
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}$
Andrijana3306
asked
in
Transform Theory
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
transform-theory
laplace-transform
0
votes
0
answers
39
GATE Electrical 2012 | Question: 14
With initial condition $x(1)=0.5$, the solution of the differential equation $t\dfrac{dx}{dt}+x=t$ is $x=t-\dfrac{1}{2} \\ $ $x=t^2-\dfrac{1}{2} \\ $ $x=\dfrac{t^2}{2} \\$ $x=\dfrac{t}{2}$
Andrijana3306
asked
in
Differential Equations
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
differential-equations
0
votes
0
answers
40
GATE Electrical 2012 | Question: 2
If $x=\sqrt{-1}$, then the value of $x^x$ is $e^{- \pi/2}$ $e^{\pi/2}$ $x$ $1$
Andrijana3306
asked
in
Complex Variables
Mar 24, 2018
by
Andrijana3306
1.4k
points
gate2012-ee
complex-variables
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