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Previous GATE
0
votes
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1
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 $(\infty ,0)$ $(0,1)$ $(1,\infty )$ $(0,\infty )$
asked
Feb 12, 2017
in
Numerical Methods
by
piyag476
(
1.5k
points)
gate2013ee
roots
equations
0
votes
0
answers
2
GATE201351
The state variable formulation of a system is given as $\begin{vmatrix} x^\cdot_1 \\ x^\cdot_2 \end{vmatrix}=\begin{vmatrix} 2 & 0\\ 0 & 1 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}+\begin{vmatrix} 1\\ 1 \end{vmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1\frac{1}{2}e^{2t}\frac{1}{2}e^{t}$ $e^{2t}e^{t}$ $1e^{t}$
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
stateequations
systemoflinearequations
0
votes
0
answers
3
GATE201350
The state variable formulation of a system is given as $\begin{vmatrix} x^\cdot_1 \\ x^\cdot_2 \end{vmatrix}=\begin{vmatrix} 2 & 0\\ 0 & 1 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}+\begin{vmatrix} 1\\ 1 \end{vmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ and $y=\begin{vmatrix} 1 & 0 \end{vmatrix}\begin{vmatrix} x_1\\ x_2 \end{vmatrix}$ The system is
asked
Feb 12, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2013ee
matrix
adjoint
0
votes
0
answers
4
GATE201346
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\frac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
asked
Feb 12, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2013ee
directionalderivatives
gausss
theorem
0
votes
0
answers
5
GATE201336
$\oint \frac{z^24}{z^2+4} dz$ evaluated anticlockwise around the circle $zi=2$ , where $i=\sqrt{1}$, is $4\pi$ 0 $2+\pi$ $2+2i$
asked
Feb 12, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2013ee
integral
equations
0
votes
0
answers
6
GATE201323
Square roots of $i$,where $i=\sqrt{1}$, are $i,i$ $cos(\frac{\pi }{4} )+isin(\frac{\pi }{4})+cos(\frac{3\pi }{4})+isin(\frac{3\pi }{4})$ $cos(\frac{\pi }{4} )+isin(\frac{3\pi }{4})+cos(\frac{3\pi }{4})+isin(\frac{\pi }{4})$ $cos(\frac{3\pi }{4} )+isin(\frac{3\pi }{4})+cos(\frac{3\pi }{4})+isin(\frac{3\pi }{4})$
asked
Feb 12, 2017
in
Complex Variables
by
piyag476
(
1.5k
points)
gate2013ee
taylorsseries
complex
0
votes
0
answers
7
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
points)
gate2013ee
randomvariable
probabilitydensityfunction
0
votes
0
answers
8
GATE2014326
Integration of the complex function $f(z)=\frac{z^2}{z^21}$ , in the counterclockwise direction, around $z1$ = $1$, is $\pi i$ 0 $\pi i$ 2$\pi i$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
complexfunctions
integration
0
votes
0
answers
9
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$$1$ $N$ $2N$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
matrix
rank
0
votes
0
answers
10
GATE201434
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of k is ________.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
randomvariable
probabilitydensityfunction
0
votes
0
answers
11
GATE20143GA9
The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students in $2011$ and $2012$ is equal, what is the ratio of male students in $2012$ to male students in $2011$? $1:1$ $2:1$ $1.5:1$ $2.5:1$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
graph
stats
0
votes
0
answers
12
GATE20143GA8
The Gross Domestic Product $(GDP)$ in Rupees grew at $7$% during $2012$$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
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
grossdomesticproduct
marketexchangerate
0
votes
0
answers
13
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. What is the average of the marks obtained by the class in the examination? $1.34$ $1.74$ $3.02$ $3.91$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee3
mean
stats
0
votes
0
answers
14
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
(
9.2k
points)
gate2014ee2
linearfunctions
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
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 $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
integral
upperlimit
lowerlimit
0
votes
0
answers
17
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
(
9.2k
points)
gate2014ee2
state
transition
matrix
0
votes
0
answers
18
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
19
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
20
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
+1
vote
1
answer
21
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
1
answer
22
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
0
votes
0
answers
23
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 $2009?$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
linegraph
stats
0
votes
0
answers
24
GATE20142GA8
If x is real and $x^2 − 2x + 3$ = $11$, then possible values of $ x^3 + x^2 − x$ include $2,4$ $2,14$ $4,52$ $14,52$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014ee2
algebra
matrix
0
votes
1
answer
25
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
0
answers
26
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
27
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
28
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
29
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
30
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
31
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
32
GATE201412
Let $f(x)=xe^{x}$ . The maximum value of the function in the interval ($0,\infty$) is $e^{1}$ $e$ $1$$e^{1}$ $1$+$e^{1}$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
interval
functions
0
votes
0
answers
33
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
(
9.2k
points)
gate2014ee1
linearequation
algebra
0
votes
0
answers
34
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
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
roota
realvalued
0
votes
0
answers
35
GATE20141GA4
If $(z+1/z)^2$ = $98$, compute $(z^2+1/z^2)$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
nonlinearequations
algebra
0
votes
0
answers
36
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?
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014ee1
stats
logical
0
votes
0
answers
37
GATE2015228
A differential equation $\frac{di}{dt}0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2015ee2
nonlinearequation
eulersequation
0
votes
0
answers
38
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
39
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
(
9.2k
points)
gate2015ee2
lineequations
3dsystem
0
votes
0
answers
40
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
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