GO Electrical
Ask us anything
Toggle navigation
GO Electrical
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Hot!
Unanswered
Tags
Subjects
Users
Ask
New Blog
Blogs
Exams
Recent questions in Engineering Mathematics
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
Recent
Hot!
Most votes
Most answers
Most views
Featured
Previous GATE
0
votes
0
answers
1
GATE201521
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE? If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable at $z_{0}$ ... at $z_{0}$, then it is differentiable at $z_{0}$. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
complexvaluedfunctions
complexvariable
0
votes
0
answers
2
GATE20152GA8
If $p, q, r, s$ are distinct integers such that: $f(p, q, r, s) = \max (p, q, r, s)$ $g(p, q, r, s) = \min (p, q, r, s)$ $h(p, q, r, s)$ = remainder of $(p \times q) / (r \times s)$ if $(p \times q) > (r \times s)$ or remainder of ... $f(p, q)$. What is the value of $fg (h (2, 5, 7, 3), 4, 6, 8)$ ?
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
remainder
operator
num
numericalanswers
0
votes
0
answers
3
GATE20152GA5
Consider a function $f(x) = 1  x$ on $1 \leq x \leq 1$. The value of $x$ at which the function attains a maximum, and the minimum value of the function are: $0, 1$ $1, 0$ $0, 1$ $1, 2$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
maxima
minima
0
votes
0
answers
4
GATE2015129
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 $5/11$ $1/2$ $7/13$ $6/11$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
events
population
0
votes
0
answers
5
GATE2015127
A solution of the ordinary differential equation $\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=0$ is such that $y(0) = 2$ and $y(1)= \frac{13e}{e^{3}}$. The value of $\frac{dy}{dt}(0)$ is _______.
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
ordinarydifferentialequation
numericalanswers
0
votes
0
answers
6
GATE2015126
The maximum value of "a" such that the matrix $\begin{pmatrix} 3&0&2 \\ 1&1&0 \\ 0&a&2 \end{pmatrix}$ has three linearly independent real eigenvectors is $\frac{2}{3\sqrt{3}}$ $\frac{1}{3\sqrt{3}}$ $\frac{1+2\sqrt{3}}{3\sqrt{3}}$ $\frac{1+\sqrt{3}}{3\sqrt{3}}$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
eigenvalues
eigenmatrix
0
votes
0
answers
7
GATE201513
If the sum of the diagonal elements of a $2 \times 2$ matrix is $6$, then the maximum possible value of determinant of the matrix is ________
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
diagonalelements
determinant
matrix
numericalanswers
0
votes
0
answers
8
GATE201511
A random variable $X$ has probability density function $f(x)$ as given below: $ f(x)= \begin{cases} a+bx & \text{ for } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$ If the expected value $E[x] = 2/3$, then $Pr[x < 0.5]$ is __________.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
randomvariable
probabilitydensityfunction
numericalanswers
0
votes
0
answers
9
GATE201512
If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
continuousfunction
roots
interval
0
votes
0
answers
10
GATE20151GA9
The probabilities that a student passes in Mathematics, Physics, and Chemistry are $m, p,$ and $c$ respectively. Of these subjects, the student has $75$% chance of passing in at least one, a $50$% chance of passing in at least two and a $40$% chance of passing in ... $I$ is true. Only relation $II$ is true. Relations $II$ and $III$ are true. Relations $I$ and $III$ are true.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
events
samplespace
0
votes
0
answers
11
GATE20151GA8
The piechart below has the breakup of the number of students from different departments in an engineering college for the year $2012$. The proportion of male to female students in each department is $5:4$. There are $40$ males in ... What is the difference between the numbers of female students in the Civil department and the female students in the Mechanical department?
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
charts
stats
numericalanswers
0
votes
0
answers
12
GATE20151GA5
Given set $A=\left\{ 2, 3, 4, 5\right\}$ and set $B=\left\{ 11, 12, 13, 14, 15\right\}$, two numbers are randomly selected, one from each set. What is the probability that the sum of two numbers equal $16$? $0.20$ $0.25$ $0.30$ $0.33$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
samplespace
events
0
votes
0
answers
13
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
14
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
15
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
16
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
(
9.3k
points)
gate2016ee2
quadraticequation
boundarylimits
numericalanswers
0
votes
0
answers
17
GATE2016232
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... An ellipse with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
circleequations
vectors
0
votes
0
answers
18
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
19
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
20
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
21
GATE201626
Consider the function $f(z)=z+z^{*}$ where $z$ is a complex variable and $z^{*}$ denotes its complex conjugate. Which one of the following is TRUE? $f(z)$ is both continuous and analytic $f(z)$ is continuous but not analytic $f(z)$ is not continuous but is analytic $f(z)$ is neither continuous nor analytic
asked
Jan 30, 2017
in
Numerical Methods
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
complexplane
demoivre'sformula
0
votes
0
answers
22
GATE201624
Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{\frac{t}{3}}u(t)$, where $u(t)$ denotes the unit step function, is $9e^{\frac{t}{3}}u(t)$ $9e^{\frac{t}{6}}u(t)$ $9e^{\frac{t}{3}}u(t)6e^{\frac{t}{6}}u(t)$ $54e^{\frac{t}{6}}u(t)54e^{\frac{t}{3}}u(t)$
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
function
derivative
numerical methods
0
votes
0
answers
23
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
(
9.3k
points)
gate2016ee2
probabilityspace
conditionalprobability
randomvariable
0
votes
0
answers
24
GATE20162GA6
The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to ... is called a small plant. The difference between total production of large plants and small plants, in tonnes is ____.
asked
Jan 30, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
collection
interpretation
standardizedtesting
numericalanswers
0
votes
0
answers
25
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
26
GATE20161GA10
Choose the correct expression for $f(x)$ given in the graph. $f(x) = 1  x  1$ $f(x) = 1 + x  1$ $f(x) = 2  x  1$ $f(x) = 2 + x  1$
asked
Jan 30, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
compositefunctions
arrowdiagram
shifting
0
votes
0
answers
27
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
points)
gate2016ee1
functions
roots
sequence
0
votes
0
answers
28
GATE2016133
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
multiplicity
degreeofpolynomial
numericalanswers
0
votes
0
answers
29
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
0
votes
0
answers
30
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
31
GATE2016126
Candidates were asked to come to an interview with $3$ pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all $3$ pens having the same colour is _________.
asked
Jan 30, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
randomvariable
event
mean
numericalanswers
0
votes
0
answers
32
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
33
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
34
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
35
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
36
GATE201611
The maximum value attained by the function. $f(x) = x(x1) (x2)$ in the interval $[1, 2]$ is ___________.
asked
Jan 30, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
maxima
minima
criticalpoint
closedinterval
numericalanswers
Page:
« prev
1
2
Welcome to GATE Overflow, Electrical, where you can ask questions and receive answers from other members of the community.
Follow @csegate
Gatecse
Recent questions in Engineering Mathematics
912
questions
38
answers
10
comments
27,600
users