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Recent activity in Engineering Mathematics
0
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0
answers
1
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 _________.
retagged
Dec 6, 2019
in
Differential Equations
by
jothee
(
100
points)
gate2016ee2
quadraticequation
boundarylimits
numericalanswers
0
votes
0
answers
2
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 ____.
retagged
Dec 6, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2016ee2
collection
interpretation
standardizedtesting
numericalanswers
0
votes
0
answers
3
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 ________.
retagged
Dec 4, 2019
in
Linear Algebra
by
jothee
(
100
points)
gate2016ee1
multiplicity
degreeofpolynomial
numericalanswers
0
votes
0
answers
4
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 _________.
retagged
Dec 4, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2016ee1
randomvariable
event
mean
numericalanswers
0
votes
0
answers
5
GATE201612
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only nonzero eigenvalue is ________.
retagged
Dec 4, 2019
in
Linear Algebra
by
jothee
(
100
points)
gate2016ee1
characteristicequation
diagonalizingmatrices
invertiblematrix
numericalanswers
0
votes
0
answers
6
GATE201611
The maximum value attained by the function. $f(x) = x(x1) (x2)$ in the interval $[1, 2]$ is ___________.
retagged
Dec 4, 2019
in
Differential Equations
by
jothee
(
100
points)
gate2016ee1
maxima
minima
criticalpoint
closedinterval
numericalanswers
0
votes
0
answers
7
GATE2015228
A differential equation $\frac{di}{dt}0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
retagged
Dec 4, 2019
in
Differential Equations
by
jothee
(
100
points)
gate2015ee2
nonlinearequation
eulersequation
numericalanswers
0
votes
0
answers
8
GATE2015226
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
retagged
Dec 4, 2019
in
Calculus
by
jothee
(
100
points)
gate2015ee2
lineequations
3dsystem
numericalanswers
0
votes
0
answers
9
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 $fg (h (2, 5, 7, 3), 4, 6, 8)$ ?
retagged
Dec 4, 2019
in
Linear Algebra
by
jothee
(
100
points)
gate2015ee2
remainder
operator
num
numericalanswers
0
votes
0
answers
10
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 _______.
retagged
Dec 4, 2019
in
Differential Equations
by
jothee
(
100
points)
gate2015ee1
ordinarydifferentialequation
numericalanswers
0
votes
0
answers
11
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 ________
retagged
Dec 4, 2019
in
Calculus
by
jothee
(
100
points)
gate2015ee1
diagonalelements
determinant
matrix
numericalanswers
0
votes
0
answers
12
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?
retagged
Dec 4, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2015ee1
charts
stats
numericalanswers
0
votes
0
answers
13
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 __________.
retagged
Dec 4, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2015ee1
randomvariable
probabilitydensityfunction
numericalanswers
0
votes
0
answers
14
GATE201434
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of k is ________.
retagged
Dec 3, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2014ee3
randomvariable
probabilitydensityfunction
numericalanswers
0
votes
0
answers
15
GATE2014227
Let $X$ be a random variable with probability density function $f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \text{otherwise } \end{cases} \\$ The probability $P(0.5 < X < 5)$ is ______.
edited
Dec 3, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2014ee2
randomvariable
probabilitydensityfunction
numericalanswers
0
votes
0
answers
16
GATE20142GA9
The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in $2009$, by what percent did the number of male students increase in $2009?$
edited
Dec 2, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2014ee2
linegraph
stats
numericalanswers
+1
vote
1
answer
17
GATE201422
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 ________.
retagged
Dec 2, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2014ee2
event
randomvariable
numericalanswers
0
votes
0
answers
18
GATE2014146
A system matrix is given as follows. $A=\begin{bmatrix} 0 & 1 & 1\\ 6 & 11 &6 \\ 6& 11& 5 \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
retagged
Dec 2, 2019
in
Linear Algebra
by
jothee
(
100
points)
gate2014ee1
linearalgebra
eigenvalues
eigenmatrix
numericalanswers
0
votes
0
answers
19
GATE20141GA4
If $(z+1/z)^2 = 98,$ compute $(z^2+1/z^2).$
retagged
Dec 2, 2019
in
Linear Algebra
by
jothee
(
100
points)
gate2014ee1
complexnumber
numericalanswers
0
votes
0
answers
20
GATE201412
Let $f(x)=xe^{x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{1}$ $e$ $1e^{1}$ $1+e^{1}$
edited
Nov 21, 2019
in
Differential Equations
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
interval
functions
0
votes
0
answers
21
GATE201415
Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\ast}$ where $z^{\ast}$ denotes the complex conjugate of $z$. The ... of the following in the complex plane unit circle horizontal axis line segment from origin to $(1, 0)$ the point $(1, 0)$ the entire horizontal axis
edited
Nov 21, 2019
in
Complex Variables
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
complexconjugate
complexvariables
0
votes
0
answers
22
GATE201411
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its solutions The system has a unique solution for any given $b_1$ and $b_2$ The system will have infinitely many solutions for any given $b_1$ and $b_2$ Whether ... a solution exists depends on the given $b_1$ and $b_2$ The system would have no solution for any values of $b_1$ and $b_2$
edited
Nov 21, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
linearequation
matrix
systemoflinearequations
0
votes
0
answers
23
GATE201413
The solution for the differential equation $\dfrac{d^2x}{dt^2}=9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\mid_{t=0}=1$ , is $t^2+t+1$ $\sin3t+\frac{1}{3}\cos3t+\frac{2}{3}$ $\frac{1}{3}\sin3t+\cos3t$ $\cos3t+t$
edited
Nov 21, 2019
in
Differential Equations
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
boundarylimits
differential
equation
0
votes
0
answers
24
GATE2014117
In the formation of RouthHurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots
edited
Nov 21, 2019
in
Differential Equations
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
routhhurwitz
array
polynomial
+1
vote
0
answers
25
GATE2014127
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n3)$ is $2^{n}$ $0$ $^{n}C_{n3}2^{n}$ $2^{n+3}$
edited
Nov 21, 2019
in
Probability & Statistics
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
probability
coins
0
votes
0
answers
26
GATE2014128
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is $2\pi$ $\pi$ $\pi$ $2\pi$
edited
Nov 21, 2019
in
Calculus
by
Lakshman Patel RJIT
(
120
points)
gate2014ee1
lineintegral
circleequation
quadraticfunction
0
votes
0
answers
27
GATE2014326
Integration of the complex function $f(z)=\frac{z^2}{z^21}$ , in the counterclockwise direction, around $\mid z1 \mid$ = $1$, is $\pi i$ $0$ $\pi i$ $2 \pi i$
edited
Nov 21, 2019
in
Calculus
by
jothee
(
100
points)
gate2014ee3
complexfunctions
integration
0
votes
0
answers
28
GATE20143GA8
The Gross Domestic Product $(GDP)$ in Rupees grew at $7$% during $2012$$2013$.For international comparison, the $GDP$ is compared in $US$ Dollars $(USD)$ after conversion based on the market exchange rate. During the period $2012$$2013$ ... $USD$ during the period $2012$$2013$ increased by $5 $% decreased by $13$% decreased by $20$% decreased by $11$%
recategorized
Nov 21, 2019
in
Engineering Mathematics
by
jothee
(
100
points)
gate2014ee3
grossdomesticproduct
marketexchangerate
0
votes
0
answers
29
GATE20143GA5
The table below has questionwise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. ... $1.34$ $1.74$ $3.02$ $3.91$
edited
Nov 21, 2019
in
Probability & Statistics
by
jothee
(
100
points)
gate2014ee3
mean
stats
+1
vote
0
answers
30
GATE201350
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
edited
Nov 21, 2019
in
Linear Algebra
by
jothee
(
100
points)
gate2013ee
linearalgebra
stateequations
systemoflinearequations
0
votes
0
answers
31
GATE201311
A continuous random variable $X$ has a probability density function $f(x)=e^{x}, 0< x< \infty$. then $P\{X> 1\}$ $0.368$ $0.5$ $0.632$ $1.0$
edited
Nov 20, 2019
in
Probability & Statistics
by
Lakshman Patel RJIT
(
120
points)
gate2013ee
randomvariable
probabilitydensityfunction
0
votes
0
answers
32
GATE201323
Square roots of $i$,where $i=\sqrt{1}$, are $i,i$ $\cos(\frac{\pi }{4} )+i\sin(\frac{\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$ $\cos(\frac{\pi }{4} )+i\sin(\frac{3\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{\pi }{4})$ $\cos(\frac{3\pi }{4} )+i\sin(\frac{3\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$
retagged
Nov 20, 2019
in
Complex Variables
by
Lakshman Patel RJIT
(
120
points)
gate2013ee
complexnumber
trigonometry
0
votes
0
answers
33
GATE201325
The equation$\begin{bmatrix} 2&2 \\ 1& 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ has no solution only one solution $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ nonzero unique solution multiple solutions
edited
Nov 20, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
(
120
points)
gate2013ee
linearalgebra
matrix
systemoflinearequations
0
votes
0
answers
34
GATE201336
$\displaystyle{}\oint \frac{z^24}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid zi \mid=2$ , where $i=\sqrt{1}$, is $4\pi$ $0$ $2+\pi$ $2+2i$
edited
Nov 20, 2019
in
Differential Equations
by
Lakshman Patel RJIT
(
120
points)
gate2013ee
integral
equations
0
votes
0
answers
35
GATE201351
The state variable formulation of a system is given as $\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} 2 & 0\\ 0 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1\frac{1}{2}e^{2t}\frac{1}{2}e^{t}$ $e^{2t}e^{t}$ $1e^{t}$
edited
Nov 20, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
(
120
points)
gate2013ee
linearalgebra
stateequations
systemoflinearequations
0
votes
0
answers
36
GATE201346
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
retagged
Nov 20, 2019
in
Calculus
by
Lakshman Patel RJIT
(
120
points)
gate2013ee
calculus
directionalderivatives
gaussstheorem
0
votes
0
answers
37
Gate2006EE
...
asked
Sep 29, 2019
in
Linear Algebra
by
Kushagra गुप्ता
(
120
points)
gate2006ee
linearalgebra
0
votes
1
answer
38
GATE20142GA6
The old city of Koenigsberg, which had a German majority population before World War $2$, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the ... Kaliningrad, as that was its original Russian name Poland and Lithuania are on the route from Kaliningrad to the rest of Russia
answered
Sep 13, 2019
in
Probability & Statistics
by
srestha
(
870
points)
gate2014ee2
stats
infer
0
votes
1
answer
39
GATE201421
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.
answered
Oct 26, 2018
in
Linear Algebra
by
Abhisek Tiwari 4
(
140
points)
gate2014ee2
eigenvalues
eigenmatrix
0
votes
0
answers
40
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 $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
recategorized
Feb 28, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2016ee2
circleequations
vectors
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