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Recent questions tagged engineeringmathematics
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GATE2020ME21
$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $x$ over real coefficients $a,b,c,d$ wherein $a\neq 0$. Which of the following statements is true? $d$ can be chosen to ensure that $x= 0$ is a root for any given set $a,b,c$ No choice of coefficients can make all roots identical $a,b,c,d$ can be chosen to ensure that all roots are complex $c$ alone cannot ensure that all roots are real
asked
Mar 1
in
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by
jothee
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2.7k
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gate2020me2
engineeringmathematics
0
votes
0
answers
GATE2020ME22
Which of the following is true for all possible nonzero choices of integers $m,n;m\neq n$, or all possible nonzero choices of real numbers $p,q;p\neq q$, as applicable? $\frac{1}{\pi}\int_{0}^{\pi}\sin m\theta \sin n\theta d\theta = 0$ ... $\displaystyle \lim_{\alpha\rightarrow \infty }\frac{1}{2\alpha }\int_{\alpha }^{\alpha }\sin p\theta \sin q\theta d\theta = 0$
asked
Mar 1
in
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by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
0
votes
0
answers
GATE2020ME23
Which of the following statements is true about the two sided Laplace transform? It exists for every signal that may or may not have a Fourier transform It has no poles for any bounded signal that is nonzero only inside a finite time interval The ... If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles
asked
Mar 1
in
Others
by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2020ME24
Consider a signal $x[n]=\left(\frac{1}{2}\right)^{n} 1[n]$, where $1[n]= 0$ if $n< 0$, and $1[n]= 1$ if $n\geq0$. The ztransform of $x[nk],k> 0$ is $\dfrac{z^{k}}{1\frac{1}{2}z^{1}}$ with region of convergence being $\mid z \mid < 2$ $\mid z \mid > 2$ $\mid z \mid < \frac{1}{2}$ $\mid z \mid > \frac{1}{2}$
asked
Mar 1
in
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by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE2020ME25
The value of the following complex integral, with $C$ representing the unit circle centered at origin in the counterclockwise sense, is: $\displaystyle{}\int_{C}\frac{z^{2}+1}{z^{2}2z}dz$ $8\pi i$ $8\pi i$ $\pi i$ $\pi i$
asked
Mar 1
in
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by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
0
votes
0
answers
GATE2020ME26
$x_{R}$ and $x_{A}$ are, respectively, the rms and average values of $x(t)= x(tT)$, and similarly, $y_{R}$ and $y_{A}$ are, respectively,the rms and average values of $y(t)= kx(t). k,\:T$ are independent of $t$. Which of the following is true? $y_{A}= kx_{A};y_{R}= kx_{R}$ $y_{A}= kx_{A};y_{R}\neq kx_{R}$ $y_{A}\neq kx_{A};y_{R}= kx_{R}$ $y_{A}\neq kx_{A};y_{R}\neq kx_{R}$
asked
Mar 1
in
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by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
0
votes
0
answers
GATE2020ME210
Consider a linear timeinvariant system whose input $r(t)$ and output $y(t)$ are related by the following differential equation: $\frac{d^{2}y(t)}{dt^{2}}+4y(t)=6r(t)$ The poles of this system are at $+2j, 2j$ $+2,2$ $+4,4$ $+4j,4j$
asked
Mar 1
in
Others
by
jothee
(
2.7k
points)
gate2020me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE2020ME1: 1
Multiplication of real valued square matrices of same dimension is associative commutative always positive definite not always possible to compute
asked
Feb 19
in
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by
jothee
(
2.7k
points)
gate2020me1
engineeringmathematics
linearalgebra
matrixalgebra
0
votes
0
answers
GATE2020ME1: 3
The Laplace transform of a function $f(t)$ is $L( f )=\frac{1}{(s^{2}+\omega ^{2})}.$ Then, $f(t)$ is $f\left ( t \right )=\frac{1}{\omega ^{2}}\left ( 1\cos\:\omega t \right )$ $f\left ( t \right )=\frac{1}{\omega}\cos\:\omega t$ $f\left ( t \right )=\frac{1}{\omega}\sin\:\omega t$ $f\left ( t \right )=\frac{1}{\omega^{2}}\left ( 1\sin\:\omega t \right )$
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2020ME1: 4
Which of the following function $f(z)$, of the complex variable $z,$ is NOT analytic at all the points of the complex plane? $f\left ( z \right )=z^{2}$ $f\left ( z \right )=e^{z}$ $f\left ( z \right )=\sin z$ $f\left ( z \right )=\log z$
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
engineeringmathematics
0
votes
0
answers
GATE2020ME1: 5
The members carrying zero force (i.e. zeroforce members) in the truss shown in the figure, for any load $P > 0$ with no appreciable deformation of the truss (i.e.with no appreciable change in angles between the members), are $BF$ and $DH$ only $BF, DH,$ and $GC$ only $BF, DH, GC, CD$ and $DE$ only $BF, DH, GC, FG$ and $GH$ only
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
appliedmechanicsanddesign
engineeringmathematics
trusses
0
votes
0
answers
GATE2020ME1: 19
For three vectors $\overrightarrow{A}=2\widehat{j}3\widehat{k},\:\overrightarrow{B}=2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}\widehat{j},\:\text{where}\:\widehat{i},\:\widehat{j}\:\text{and}\:\widehat{k}$ are ... system, the value of $\left ( \overrightarrow{A}.\left ( \overrightarrow{B}\times \overrightarrow{C} \right )+6 \right )$ is __________.
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
numericalanswers
engineeringmathematics
0
votes
0
answers
GATE2020ME1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one  third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
engineeringmathematics
0
votes
0
answers
GATE2020ME1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
numericalanswers
engineeringmathematics
differentialequation
randomvariables
0
votes
0
answers
GATE2020ME1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{1} \right )$ is defined as $f\left ( z \right )=x^{2}y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).
asked
Feb 19
in
Others
by
jothee
(
2.7k
points)
gate2020me1
numericalanswers
engineeringmathematics
0
votes
0
answers
GATE2019 ME2: 18
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \\$ $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \\$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \\$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
engineeringmathematics
linearalgebra
matrixalgebra
0
votes
1
answer
GATE2019 ME2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
numericalanswers
engineeringmathematics
0
votes
0
answers
GATE2019 ME2: 26
Given a vector $\overrightarrow{u} = \frac{1}{3} \big(y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $ \frac{\pi}{2} \\$ $\frac{\pi}{3} \\$ $\frac{\pi}{2} \\$ $\pi$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
engineeringmathematics
0
votes
0
answers
GATE2019 ME2: 27
A diffferential equation is given as $x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$ The solution of the differential equation in terms of arbitrary constants $C_1$ and $C_2$ is $y=C_1x^2 +C_2 x+2$ $y=\frac{C_1}{x^2} +C_2x+2$ $y=C_1x^2+C_2x+4$ $y=\frac{C_1}{x^2}+C_2x+4$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
engineeringmathematics
differentialequation
0
votes
0
answers
GATE2019 ME2: 28
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f'(x)=\frac{f(x+h)f(xh)}{2h}$. The percentage error is calculated as $\bigg( \frac{\text{Exact value  Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ ... $> 0.1 \% \text{ and } <1 \%$ $> 1 \% \text{ and } <5 \%$ $>5 \%$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
engineeringmathematics
0
votes
0
answers
GATE2019 ME2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me2
numericalanswers
engineeringmathematics
probabilityandstatistics
0
votes
0
answers
GATE2019 ME1: 2
A parabola $x=y^2$ with $0 \leq x \leq 1$ is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by $360^{\circ}$ around xaxis is $\frac{\pi}{4} \\$ $\frac{\pi}{2} \\$ ${\pi} \\$ $2 \pi$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
engineeringmathematics
calculus
0
votes
1
answer
GATE2019 ME1: 3
For the equation $\frac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is $\frac{7}{3}e^{7/3} \\$ $\frac{7}{3}e^{3/7} \\$ $\frac{3}{7}e^{7/3} \\$ $\frac{3}{7}e^{3/7}$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
engineeringmathematics
calculus
0
votes
0
answers
GATE2019 ME1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$equalsegment trapezoidal rule gives a value of _______
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
numericalanswers
engineeringmathematics
0
votes
0
answers
GATE2019 ME1: 26
The set of equations $x+y+z=1$ $axay+3z=5$ $5x3y+az=6$ has infinite solutions, if $a=$ $3$ $3$ $4$ $4$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
engineeringmathematics
calculus
0
votes
0
answers
GATE2019 ME1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^22y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy2x^2+2y^2+ \text{constant}$ $4y^24xy + \text{constant}$ $2x^22y^2+ xy + \text{constant}$ $4xy+2y^22x^2+ \text{constant}$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
engineeringmathematics
differentialequation
laplacetransforms
0
votes
0
answers
GATE2019 ME1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
engineeringmathematics
probabilityandstatistics
0
votes
1
answer
GATE2019 ME1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
asked
Feb 9, 2019
in
Others
by
Arjun
(
21.2k
points)
gate2019me1
numericalanswers
engineeringmathematics
0
votes
0
answers
GATE201255
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... complete the project remain the same critical path changes but the total duration to complete the project changes to $17$ days
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
+1
vote
0
answers
GATE201254
For a particular project, eight activities are to be carried out. Their relationships with other activities and expected durations are mentioned in the table below. ... $abegh$ $acgh$ $adfh$ $abcfh$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
0
votes
0
answers
GATE201245
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is $1/20$ $1/12$ $3/10$ $1/2$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
probabilityandstatistics
probability
0
votes
0
answers
GATE201247
$x+2y+z=4$ $2x+y+2z=5$ $xy+z=1$ The system of algebraic equations given above has a unique solution of $x=1$, $y=1$ and $z=1$ only the two solutions of $(x=1, y=1, z=1)$ and $(x=2, y=1, z=0)$ infinite number of solutions no feasible solution
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
algebraicequations
numericalmethods
0
votes
0
answers
GATE201246
Consider the differential equation $x^2 \frac{d^2y}{dx^2}+x\frac{dy}{dx}4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the differential equation is $x^2 \\$ $\sin (\frac{\pi x}{2}) \\$ $e^x \sin(\frac{\pi x}{2}) \\$ $e^{x} \sin(\frac{\pi x}{2}) \\$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
differentialequation
boundaryvalueproblems
0
votes
0
answers
GATE201236
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as $\begin{pmatrix} \frac{1}{2} \\ \frac{\sqrt{3}}{2} \end{pmatrix} \\$ ... $\begin{pmatrix} \frac{1}{\sqrt{5}} \\ \frac{2}{\sqrt{5}} \end{pmatrix}$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
linearalgebra
eigenvaluesandeigenvectors
0
votes
0
answers
GATE201235
The inverse Laplace transform of the function $F(s) = \frac{1}{s(s+1)}$ is given by $f(t) = \sin t$ $f(t) = e^{t} \sin t$ $f(t) = e^{t}$ $f(t) = 1e^{t}$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012m
engineeringmathematics
differntialequations
0
votes
0
answers
GATE201224
At $x=0$, the function $f(x)=x^3+1$ has a maximum value a minimum value a singularity a point of inflection
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
calculus
functionsofsinglevariable
0
votes
0
answers
GATE201225
For the spherical surface $x^2+y^2+z^2=1$, the unit outward normal vector at th point $( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0)$ is given by $\frac{1}{\sqrt{2}} \hat{i} +\frac{1}{\sqrt{2}} \hat{j}$ $\frac{1}{\sqrt{2}} \hat{i} \frac{1}{\sqrt{2}} \hat{j}$ $\hat{k}$ $\frac{1}{\sqrt{3}} \hat{i} +\frac{1}{\sqrt{3}} \hat{j} +\frac{1}{\sqrt{3}} \hat{k}$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
calculus
vectoridentities
0
votes
0
answers
GATE201212
$\underset{x \rightarrow 0}{\lim} \bigg( \frac{1 \cos x}{x^2} \bigg)$ is $1/4$ $1/2$ $1$ $2$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
calculus
limits
0
votes
0
answers
GATE201211
The area enclosed between the straight line $y=x$ and the parabola $y=x^2$ in the $xy$ plane is $1/6$ $1/4$ $1/3$ $1/2$
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
0
votes
0
answers
GATE201212
Consider the function $f(x) = \mid x \mid $ in the interval $1 \leq x \leq 1$. At the point $x=0, \: f(x)$ is continuous and differentiable noncontinuous and differentiable continuous and nondifferentiable neither continuous nor differentiable
asked
Mar 20, 2018
in
Others
by
Andrijana3306
(
1.5k
points)
gate2012me
engineeringmathematics
calculus
continuityanddifferentiability
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