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Hot questions in Engineering Mathematics
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1
GATE201612
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only nonzero eigenvalue is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
characteristicequation
diagonalizingmatrices
invertiblematrix
numericalanswers
0
votes
0
answers
2
GATE201629
The value of the line integral $\int_{c}^{} (2xy^{2}dx+2x^{2}y dy+dz)$ along a path joining the origin $(0, 0, 0)$ and the point $(1, 1, 1)$ is $0$ $2$ $4$ $6$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
compositefunctions
additivity
space
riemannsum
0
votes
0
answers
3
GATE2016249
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ corresponding to distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$ respectively. Then the response $x(t)$ ... $e^{\lambda_{2}t}\beta$ $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
lineartimeinvariantsystem
eigenvalues
0
votes
0
answers
4
GATE201614
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{1}$, is a solution of the differential equation $\frac{d^{2}y}{dt^{2}}+2\frac{dy}{dt}+y=0$. Then $y(2)$ is $5e^{1}$ $5e^{2}$ $7e^{1}$ $7e^{2}$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
quadraticequation
repeatedroots
linearordinarydifferentialequation
0
votes
0
answers
5
GATE20162GA9
Shaquille 'O' Neal is a $60$% career free throw shooter, meaning that he successfully makes $60$ free throws out of $100$ attempts on average. What is the probability that he will successfully make exactly $6$ free throws in $10$ attempts? $0.2508$ $0.2816$ $0.2934$ $0.6000$
asked
Jan 30, 2017
in
Probability & Statistics
by
makhdoom ghaya
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9.3k
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gate2016ee2
probabilityspace
conditionalprobability
randomvariable
0
votes
0
answers
6
GATE2016128
Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, 2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}3A+4I$ would, respectively, be $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1}  x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1}  x_{2}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
eigenmatrix
eigenvalues
0
votes
0
answers
7
GATE20161GA5
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\frac{\alpha^{n}+\beta^{n}}{\alpha^{n}+\beta^{n}}$ $n^{4}$ $4^{n}$ $2^{2n1}$ $4^{n1}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
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gate2016ee1
functions
roots
sequence
0
votes
0
answers
8
GATE201627
A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
eigenspace
nontrivialsolution
determinant
0
votes
0
answers
9
GATE2016230
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then the value of $y(1)$ is _________.
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
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9.3k
points)
gate2016ee2
quadraticequation
boundarylimits
numericalanswers
0
votes
0
answers
10
GATE201615
The value of the integral $\oint _{c}\frac{2z+5}{\left ( z\frac{1}{2} \right ) \left (z^{2} 4z+5 \right )}dz$ over the contour $z=1$, taken in the anticlockwise direction, would be $\frac{24 \pi i}{13}$ $\frac{48 \pi i}{13}$ $\frac{24}{13}$ $\frac{12}{13}$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
partialderivative
upperlimit
lowerlimit
0
votes
0
answers
11
GATE20162GA5
If $9y−6 =3$, then $y^{2}4y/3$ is . $0$ $+1/3$ $1/3$ undefined
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
linearequation
quadraticequation
mode
0
votes
0
answers
12
GATE201619
The value of $\int_{\infty}^{+\infty} e^{t} \delta (2t2){d}t$, where $\delta (t)$ is the Dirac delta function, is $\frac{1}{2e}$ $\frac{2}{e}$ $\frac{1}{e^{2}}$ $\frac{1}{2e^{2}}$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
pauldirac
operationalcalculus
weaklimit
0
votes
0
answers
13
GATE201628
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), $te^{t}u(t)$ $(e^{t}te^{t})u(t)$ $(e^{t}+te^{t})u(t)$ $e^{t}u(t)$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
higherorderdifferentialequations
euler'sequation
initialboundaryconditions
0
votes
0
answers
14
GATE2016229
The value of the integral $2\int_{\infty}^{\infty} (\frac{\sin2\pi t}{\pi t}) \text{d}t$ is equal to $0$ $0.5$ $1$ $2$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
theoremofintegral
definiteintegral
0
votes
0
answers
15
GATE2016233
Let the probability density function of a random variable, $X$, be given as: $f_{x}(x)=\frac{3}{2}e^{3x}u(x)+ae^{4x}u(x)$ where u(x) is the unit step function. Then the value of 'a' and prob $\left\{X \leq 0\right\}$, respectively are $2, \frac{1}{2}$ $4, \frac{1}{2}$ $2, \frac{1}{4}$ $4, \frac{1}{4}$
asked
Jan 30, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
randomvariable
probabilitydensity
unitstepfunction
0
votes
0
answers
16
GATE2016129
Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE? Rank of $A^{T} A$ is less than $2$. Rank of $A^{T} A$ is equal to $2$. Rank of $A^{T} A$ is greater than $2$. Rank of $A^{T} A$ can be any number between $1$ and $3$.
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
numberofnonzerorows
gaussreduction
gausselimination
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