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Recent activity in Engineering Mathematics
0
votes
0
answers
1
Gate2006EE
...
asked
Sep 29
in
Linear Algebra
by
Kushagra गुप्ता
(
120
points)
gate2006ee
linearalgebra
0
votes
1
answer
2
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
in
Probability & Statistics
by
srestha
(
870
points)
gate2014ee2
stats
infer
0
votes
0
answers
3
GATE201363
The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p1)=0$ are of opposite sign is $(\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$
edited
May 27
in
Numerical Methods
by
Lakshman Patel RJIT
(
110
points)
gate2013ee
roots
equations
+1
vote
1
answer
4
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 ________.
commented
Feb 15
in
Probability & Statistics
by
hina firdaus
(
100
points)
gate2014ee2
event
randomvariable
0
votes
1
answer
5
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
6
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
0
votes
0
answers
7
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: $0, 1$ $1, 0$ $0, 1$ $1, 2$
recategorized
Feb 28, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2015ee2
maxima
minima
0
votes
0
answers
8
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
recategorized
Feb 28, 2017
in
Complex Variables
by
piyag476
(
1.5k
points)
gate2015ee2
complexvaluedfunctions
complexvariable
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? $f(a) . f(b)=0$ $f(a) . f(b) < 0$ $f(a) . f(b) > 0$ $f(a) / f(b) \leq 0$
recategorized
Feb 28, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2015ee1
continuousfunction
roots
interval
0
votes
0
answers
10
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 $x(t)$ ... $e^{\lambda_{2}t}\beta$ $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
recategorized
Feb 28, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2016ee2
lineartimeinvariantsystem
eigenvalues
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 ________
recategorized
Feb 28, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2015ee1
diagonalelements
determinant
matrix
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?
recategorized
Feb 28, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2015ee1
charts
stats
0
votes
0
answers
13
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 $16$? $0.20$ $0.25$ $0.30$ $0.33$
recategorized
Feb 28, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2015ee1
samplespace
events
0
votes
0
answers
14
GATE201511
A random variable $X$ has probability density function $f(x)$ as given below: $ f(x)= \begin{cases} a+bx & \\ 0 & \end{cases}$ for $0 < x < 1$ otherwise If the expected value $E[x] = 2/3$, then $Pr[x < 0..5]$ is __________.
recategorized
Feb 28, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2015ee1
randomvariable
probabilitydensityfunction
0
votes
0
answers
15
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.
recategorized
Feb 28, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2015ee1
events
samplespace
0
votes
0
answers
16
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 $\frac{2}{3\sqrt{3}}$ $\frac{1}{3\sqrt{3}}$ $\frac{1+2\sqrt{3}}{3\sqrt{3}}$ $\frac{1+\sqrt{3}}{3\sqrt{3}}$
recategorized
Feb 28, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2015ee1
eigenvalues
eigenmatrix
0
votes
0
answers
17
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 _______.
recategorized
Feb 28, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2015ee1
ordinarydifferentialequation
0
votes
0
answers
18
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 $5/11$ $1/2$ $7/13$ $6/11$
recategorized
Feb 28, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2015ee1
events
population
0
votes
0
answers
19
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 $fg (h (2, 5, 7, 3), 4, 6, 8)$ ?
recategorized
Feb 28, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2015ee2
remainder
operator
0
votes
0
answers
20
GATE201522
We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equivalent statements. P: There is a unique solution. Q: The equations are linearly independent. R: All ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
recategorized
Feb 28, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2015ee2
linearequations
eigenvalues
0
votes
0
answers
21
GATE201523
Match the following. P. Stokes’s Theorem 1. $∯ D.ds = Q$ Q. Gauss’s Theorem 2. $\oint f(z) dz =0$ R. Divergence Theorem 3. $\int \int \int (\triangledown. A) dv = ∯ A. ds$ S. Cauchy’s Integral Theorem 4. $\int \int (\triangledown \times A).ds = \oint A. dl$ (A) P2 Q1 R4 S3 (B) P4 Q1 R3 S2 (C) P4 Q3 R1 S2 (D) P3 Q4 R2 S1
recategorized
Feb 28, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2015ee2
gausselimination
integraltheorem
0
votes
0
answers
22
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 ________.
recategorized
Feb 28, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2015ee2
lineequations
3dsystem
0
votes
0
answers
23
GATE2015227
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the following is TRUE? The coin tosses are independent. R is fair, S is not. S is fair, R is not. The coin tosses are dependent.
recategorized
Feb 28, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2015ee2
events
samplespace
0
votes
0
answers
24
GATE2015228
A differential equation $\frac{di}{dt}0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
recategorized
Feb 28, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2015ee2
nonlinearequation
eulersequation
0
votes
0
answers
25
GATE2014128
The line integral of function $F$ = $yzi$, in the counterclockwise direction, along the circle $x^2$+$y^2$ = $1$ at $z$ = $1$ is $2\pi$ $\pi$ $\pi$ $2\pi$
retagged
Feb 16, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2014ee1
lineintegral
circleequation
quadraticfunction
0
votes
0
answers
26
GATE201413
The solution for the differential equation $\frac{d^2x}{dt^2}=9x$ with initial conditions $x(0)=1$ and $\frac{dx}{dt}_{t=0}=1$ , is $t^2+t+1$ $sin3t+\frac{1}{3}cos3t+\frac{2}{3}$ $\frac{1}{3}sin3t+cos3t$ $cos3t$+$t$
retagged
Feb 16, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2014ee1
boundarylimits
differential
equation
0
votes
0
answers
27
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 $b_2$
retagged
Feb 16, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2014ee1
linearequation
algebra
0
votes
0
answers
28
GATE20141GA9
In a survey, $300$ respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?
retagged
Feb 16, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2014ee1
stats
logical
0
votes
0
answers
29
GATE20141GA4
If $(z+1/z)^2$ = $98$, compute $(z^2+1/z^2)$
retagged
Feb 16, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2014ee1
nonlinearequations
algebra
0
votes
0
answers
30
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 _______
recategorized
Feb 16, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2014ee1
eigenvalues
eigenmatrix
0
votes
0
answers
31
GATE2014127
A fair coin is tossed n times. The probability that the difference between the number of heads and tails is $(n3)$ is $2^{n}$ $0$ $n_{C_{n3}}2^{n}$ $2^{n+3}$
recategorized
Feb 16, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2014ee1
event
population
0
votes
0
answers
32
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
recategorized
Feb 16, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2014ee1
routhhurwitz
array
polynomial
0
votes
0
answers
33
GATE201415
Let $S$ be the set of points in the complex plane corresponding to the unit circle. (That is, $S$={$z$ : $z$=$1$}). Consider the function $f(z)=zz^*$ where $z^*$ denotes the complex conjugate of $z$. The $f(z)$ maps $s$ to which one 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
recategorized
Feb 16, 2017
in
Complex Variables
by
piyag476
(
1.5k
points)
gate2014ee1
complexconjugate
complexvariables
0
votes
0
answers
34
GATE201412
Let $f(x)=xe^{x}$ . The maximum value of the function in the interval ($0,\infty$) is $e^{1}$ $e$ $1$$e^{1}$ $1$+$e^{1}$
recategorized
Feb 16, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2014ee1
interval
functions
0
votes
0
answers
35
GATE20141GA5
The roots of $ax^2+bx+c=0$ are real and positive. $a$, $b$ and $c$ are real. Then $ax^2+bx+c=0$ has no roots $2$ real roots $3$ real roots $4$ real roots
recategorized
Feb 16, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2014ee1
roota
realvalued
0
votes
0
answers
36
GATE2014228
The minimum value of the function $f(x)=x^33x^224x+100$ in the interval $[3,3]$ is $20$ $28$ $16$ $32$
recategorized
Feb 15, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2014ee2
linearfunctions
0
votes
0
answers
37
GATE2014227
Let $X$ be a random variable with probability density function $f(x)=\left\{\begin{matrix} 0.2,& forx\leq 1\\ 0.1,& for 1< x\leq 4\\ 0 & otherwise \end{matrix}\right.$ The probability $P(0.5<X<5)$ is ______.
recategorized
Feb 15, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2014ee2
randomvariable
probabilitydensityfunction
0
votes
0
answers
38
GATE2014226
To evaluate the double integral $\int_{0}^{8}(\int_{(y/2)}^{y/2+1}(\frac{2xy}{2})dx)dy$ , we make the substitution $u=(\frac{2xy}{2})$ and $v=\frac{y}{2}$ The integral will reduce $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$
recategorized
Feb 15, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2014ee2
integral
upperlimit
lowerlimit
0
votes
0
answers
39
GATE2014218
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
recategorized
Feb 15, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2014ee2
state
transition
matrix
0
votes
0
answers
40
GATE201425
Consider the differential equation $x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}y=0$ . Which of the following is a solution to this differential equation for$x>0$? $e^x$ $x^2$ $1/x$ $lnx$
recategorized
Feb 15, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2014ee2
derivatives
equations
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