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1
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
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9.3k
points)
gate2014ee2
event
randomvariable
numericalanswers
0
votes
0
answers
2
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
(
9.3k
points)
gate2014ee1
routhhurwitz
array
polynomial
0
votes
0
answers
3
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
1
answer
4
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
(
9.3k
points)
gate2014ee2
eigenvalues
eigenmatrix
0
votes
0
answers
5
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
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9.3k
points)
gate2016ee1
randomvariable
event
mean
numericalanswers
0
votes
0
answers
6
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
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gate2015ee1
events
population
0
votes
0
answers
7
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
(
9.3k
points)
gate2014ee1
linearalgebra
eigenvalues
eigenmatrix
numericalanswers
0
votes
0
answers
8
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
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9.3k
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gate2014ee3
randomvariable
probabilitydensityfunction
numericalanswers
0
votes
0
answers
9
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
+1
vote
0
answers
10
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
(
9.3k
points)
gate2014ee1
probability
coins
0
votes
0
answers
11
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
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gate2016ee2
function
derivative
numerical methods
0
votes
0
answers
12
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
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gate2016ee2
circleequations
vectors
0
votes
0
answers
13
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
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gate2016ee1
multiplicity
degreeofpolynomial
numericalanswers
0
votes
1
answer
14
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
(
9.3k
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gate2014ee2
stats
infer
0
votes
0
answers
15
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
(
9.3k
points)
gate2014ee2
complexfunctions
minima
maxima
0
votes
0
answers
16
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 ______.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.3k
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gate2014ee2
randomvariable
probabilitydensityfunction
numericalanswers
0
votes
0
answers
17
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
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.3k
points)
gate2014ee1
complexconjugate
complexvariables
0
votes
0
answers
18
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
19
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
(
9.3k
points)
gate2015ee2
events
samplespace
0
votes
0
answers
20
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
(
9.3k
points)
gate2014ee2
imaginary
complexfunctions
0
votes
0
answers
21
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
(
9.3k
points)
gate2014ee2
derivatives
equations
0
votes
0
answers
22
GATE2014218
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
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gate2014ee2
state
transition
matrix
0
votes
0
answers
23
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 ________.
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
lineequations
3dsystem
numericalanswers
0
votes
0
answers
24
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
25
GATE201311
A continuous random variable $X$ has a probability density function $f(x)=e^{x}, 0< x< \infty$. then $P\{X> 1\}$ $0.368$ $0.5$ $0.632$ $1.0$
asked
Feb 12, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
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gate2013ee
randomvariable
probabilitydensityfunction
0
votes
0
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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 $2\pi$ $\pi$ $\pi$ $2\pi$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
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gate2014ee1
lineintegral
circleequation
quadraticfunction
0
votes
0
answers
27
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
(
9.3k
points)
gate2014ee3
matrix
rank
0
votes
0
answers
28
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$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.3k
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gate2014ee1
boundarylimits
differential
equation
+1
vote
0
answers
29
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
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
stateequations
systemoflinearequations
0
votes
0
answers
30
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})$
asked
Feb 12, 2017
in
Complex Variables
by
piyag476
(
1.5k
points)
gate2013ee
complexnumber
trigonometry
0
votes
0
answers
31
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$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee1
linearequation
matrix
systemoflinearequations
0
votes
0
answers
32
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
(
9.3k
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gate2015ee2
gausselimination
integraltheorem
0
votes
0
answers
33
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
(
9.3k
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gate2015ee2
linearequations
eigenvalues
0
votes
0
answers
34
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 ________
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Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
diagonalelements
determinant
matrix
numericalanswers
0
votes
0
answers
35
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
36
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
37
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
0
votes
0
answers
38
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 $11$%
asked
Feb 12, 2017
in
Engineering Mathematics
by
makhdoom ghaya
(
9.3k
points)
gate2014ee3
grossdomesticproduct
marketexchangerate
0
votes
0
answers
39
GATE2014228
The minimum value of the function $f(x)=x^33x^224x+100$ in the interval $[3,3]$ is $20$ $28$ $16$ $32$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
linearfunctions
0
votes
0
answers
40
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
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