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Hot questions in Engineering Mathematics
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1
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
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
stats
infer
0
votes
1
answer
2
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.
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
eigenvalues
eigenmatrix
+1
vote
1
answer
3
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 ________.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
event
randomvariable
0
votes
0
answers
4
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
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
routhhurwitz
array
polynomial
0
votes
0
answers
5
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 $5/11$ $1/2$ $7/13$ $6/11$
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Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2015ee1
events
population
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
(
9.2k
points)
gate2015ee1
eigenvalues
eigenmatrix
0
votes
0
answers
7
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 ________.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
randomvariable
probabilitydensityfunction
0
votes
0
answers
8
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 _______
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
eigenvalues
eigenmatrix
0
votes
0
answers
9
GATE2014127
A fair coin is tossed n times. The probability that the difference between the number of heads and tails is $(n3)$ is $2^{n}$ $0$ $n_{C_{n3}}2^{n}$ $2^{n+3}$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
event
population
0
votes
0
answers
10
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
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
complexconjugate
complexvariables
0
votes
0
answers
11
GATE201423
Minimum of the real valued function $f(x)=(x1)^{2/3}$ occurs at x equal to $\infty$ 0 1 $\infty$
asked
Feb 12, 2017
in
Numerical Methods
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
complexfunctions
minima
maxima
0
votes
0
answers
12
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$x>0$? $e^x$ $x^2$ $1/x$ $lnx$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
derivatives
equations
0
votes
0
answers
13
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.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2015ee2
events
samplespace
0
votes
0
answers
14
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
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2015ee2
gausselimination
integraltheorem
0
votes
0
answers
15
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 ______.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
randomvariable
probabilitydensityfunction
0
votes
0
answers
16
GATE201424
All the values of the multivalued complex function $1^i$,where $i=\sqrt{1}$ are purely imaginary. real and nonnegative on the unit circle. equal in real and imaginary parts.
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
imaginary
complexfunctions
0
votes
0
answers
17
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 $t^2+t+1$ $sin3t+\frac{1}{3}cos3t+\frac{2}{3}$ $\frac{1}{3}sin3t+cos3t$ $cos3t$+$t$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
boundarylimits
differential
equation
0
votes
0
answers
18
GATE201431
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$ ; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N$$1$ $N$ $2N$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
matrix
rank
0
votes
0
answers
19
GATE2014128
The line integral of function $F$ = $yzi$, in the counterclockwise direction, along the circle $x^2$+$y^2$ = $1$ at $z$ = $1$ is $2\pi$ $\pi$ $\pi$ $2\pi$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
lineintegral
circleequation
quadraticfunction
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 ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2015ee2
linearequations
eigenvalues
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