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Previous GATE
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Hot questions in Engineering Mathematics
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0
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41
GATE2015-37
The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}$ is __________ .
The probability density function of a random variable $X$ is $P_X(x)=e^{-x}$ for $x\underline{>} 0$ and $0$ otherwise. The expected value of the function $g_X(x)=e^{3x/4}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2015-in
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
42
GATE2016-2
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
$\underset{n\rightarrow \infty }{\lim}\:\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is __________.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
limits
+
–
0
votes
0
answers
43
GATE2015-13
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to $\int_0^x\int_0^y f(x,y) dx\;dy$ $\int_0^a \int_x^y f(x,y) dx\;dy$ $\int_0^a \int_x^a f(x,y) dy\;dx$ $\int_0^a \int_0^a f(x,y) dx\;dy$
The double integral $\int_0^a \int_0^y f(x,y) dx\;dy$ is equivalent to$\int_0^x\int_0^y f(x,y) dx\;dy$$\int_0^a \int_x^y f(x,y) dx\;dy$$\int_0^a \int_x^a f(x,y) dy\;dx$$\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
definite-integrals
double-integrals
+
–
0
votes
0
answers
44
GATE2016-5
In the neighborhood of $z=1$, the function $f(z)$ has a power series expansion of the form $f(z)$ = $1$ + $(1-z)$ + $(1-z)^2+ \ldots$ Then $f(z)$ is $\frac{1}{z}$ $\frac{-1}{z-2}$ $\frac{z-1}{z+}$ $\frac{1}{2z-1}$
In the neighborhood of $z=1$, the function $f(z)$ has a power series expansion of the form $f(z)$ = $1$ + $(1-z)$ + $(1-z)^2+ \ldots$Then $f(z)$ is$\frac{1}{z}$$\frac{-1}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Analysis of complex variables
gate2016-in
analysis-of-complex-variables
taylor-series
+
–
0
votes
0
answers
45
GATE2015-36
The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ are defective is 0.001 0.057 0.107 0.3
The probability that a thermistor randomly picked up from a production unit is defective is $0.1$. The probability that out of $10$ thermistors randomly picked up, $3$ ar...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2015-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
46
GATE2015-14
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is $4\sqrt{2}$ $5\sqrt{2}$ $7\sqrt{2}$ $9\sqrt{2}$
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is$4\sqrt{2}$$5\sqrt{...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
directional-derivatives
+
–
0
votes
0
answers
47
GATE2016-30
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in the complex plane is $\_\_\_\_\_\_\_\_.$
The value of the integral $\displaystyle{}\frac{1}{2\pi j}\int_c \frac{Z^2+1}{Z^2-1}dz$ where $z$ is a complex number and $C$ is a unit circle with center at $1+0j$ in th...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Analysis of complex variables
gate2016-in
numerical-answers
analysis-of-complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
48
GATE2016-28
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_\_.$
Consider the matrix $A= \begin{pmatrix} 2 & 1 & 1\\ 2& 3& 4\\ -1& -1 & -2 \end{pmatrix} $ whose eigenvalues are $1, -1$ and $3$. Then Trace of $(A^3-3A^2)$ is $\_\_\_\_\_...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2016-in
numerical-answers
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
49
GATE2016-4
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______. $(i-2j+k)$ $(-i+2j-k)$ $(0i+0j+0k)$ $(4i+3j+5k)$
The vector that is $NOT$ perpendicular to the vectors $(i+j+k)$ and $(i+2j+3k)$ is ______.$(i-2j+k)$ $(-i+2j-k)$$(0i+0j+0k)$$(4i+3j+5k)$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
calculus
vector-calculus
vector-identities
+
–
0
votes
0
answers
50
GATE2015-57
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
The fundamental period of the signal $x(t)=2\cos(\frac{2\pi t}{3})+\cos(\pi t)$, in seconds, is ________________ s.
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
numerical-answers
calculus
trigonometry
+
–
0
votes
0
answers
51
GATE2015-11
Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is $r$ $n$ $n-r$ $n+r$
Let $A$ be an $n\times n$ matrix with rank $r(0<r<n).$ Then $\text{Ax=0}$ has $p$ independent solutions, where $p$ is$r$$n$$n-r$$n+r$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2015-in
linear-algebra
matrices
system-of-equations
+
–
0
votes
0
answers
52
GATE2014-4
A vector is defined as $f=y\hat{i}+x\hat{j}+z\hat{k}$ where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system. The surface integral $f.ds$ over the closed surface S of a cube with vertices having the following coordinates: $(0,0,0), (1,0,0),(1,1,0),(0,1,0),(0,0,1),(1,0,1),(1,1,1),(0,1,1)$ is __________.
A vector is defined as $$f=y\hat{i}+x\hat{j}+z\hat{k}$$where $\hat{i},\hat{j},\hat{k}$ are unit vectors in Cartesian $(x,y,z)$ coordinate system.The surface integral $f....
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2014-in
numerical-answers
calculus
vector-calculus
surface-integral
+
–
0
votes
0
answers
53
GATE2014-44
$X(k)$ is the Discrete Fourier Transform of a 6-point real sequence $x(n).$ If $X(0)=9+j0, X(2)=2+j2, X(3)=3-j0, X(5)=1-j1, x(0)$ is $3$ $9$ $15$ $18$
$X(k)$ is the Discrete Fourier Transform of a 6-point real sequence $x(n).$If $X(0)=9+j0, X(2)=2+j2, X(3)=3-j0, X(5)=1-j1, x(0)$ is$3$$9$$15$$18$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014-in
differential-equations
fourier-transform
+
–
0
votes
0
answers
54
GATE2014-26
A scalar valued function is defined as $f(X)=X^TAX+b^TX+c,$ where A is a symmetric positive definite matrix with dimension $n\times n$; b and X are vectors of dimension $n\times 1$. The minimum value of f(x) will occur when X equals $(A^TA)^{-1}b$ $-(A^TA)^{-1}b$ $-(\frac{A^{-1}b}{2})$ $\frac{A^{-1}b}{2}$
A scalar valued function is defined as $f(X)=X^TAX+b^TX+c,$ where A is a symmetric positive definite matrix with dimension $n\times n$; b and X are vectors of dimension $...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
55
GATE2012-27
Given that $A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is $15A+12I$ $19A+30I$ $17A+15I$ $17A+21I$
Given that$A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is$15A+12I$$19A+30I$$17A+15I$$17A+21I$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
56
GATE2013-27
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ is $\begin{bmatrix}1\\-j\end{bmatrix}$,$\begin{bmatrix}j\\-1\end{bmatrix}$ $\begin{bmatrix}0\\1\end{bmatrix}$,$\begin{bmatrix}-1\\0\end{bmatrix}$ $\begin{bmatrix}1\\j\end{bmatrix}$,$\begin{bmatrix}0\\1\end{bmatrix}$ $\begin{bmatrix}1\\j\end{bmatrix}$,$\begin{bmatrix}j\\1\end{bmatrix}$
One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\begin{bmatrix}0&-1\\1&0\end{bmatrix}$ is$\begin{bmatrix}1\\-j\end{bmatrix}$,$\begin{bmatrix}...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-in
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
57
GATE2014-3
The figure shows the plot of $y$ as a function of $x$ The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is : $\frac{d^2y}{dx^2}=1$ $\frac{dy}{dx}=x$ $\frac{dy}{dx}=-x$ $\frac{dy}{dx}=|x|$
The figure shows the plot of $y$ as a function of $x$The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is :$\fr...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014-in
differential-equations
+
–
0
votes
0
answers
58
GATE2014-2
Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________.
Given that $x$ is a random variable in the range $[0,\infty]$ with a probability density function $\frac{e \frac{-x}{2}}{K}$, the value of the constant $K$ is __________....
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-in
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
59
GATE2014-27
The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson’s method is $x_{k+1}=x_k+\frac{1}{3}(N-x^3_k)$ $x_{k+1}=\frac{1}{3}(2x_k+\frac{N}{x^2_k})$ $x_{k+1}=x_k-\frac{1}{3}(N-x^3_k)$ $x_{k+1}=\frac{1}{3}(2x_k-\frac{N}{x^2_k})$
The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson’s method is $x_{k+1}=x_k+\frac{1}{3}(N-x^3_k)$$x_{k+1}=\frac{1}{3}(...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2014-in
numerical-methods
newton-raphson-method
+
–
0
votes
0
answers
60
GATE2013-38
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$ $\frac{1}{s^2}[1-2e^{-s}+e^{-2s}]$
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$$\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
laplace-transform
+
–
0
votes
0
answers
61
GATE2014-28
For the matrix $A$ satisfying the equation given below, the eigenvalues are $[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$ $(1,-j,j)$ $(1,1,0)$ $(1,1,-1)$ $(1,0,0)$
For the matrix $A$ satisfying the equation given below, the eigenvalues are$$[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\en...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-in
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
62
GATE2013-5
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$? If $\Delta.E=0,\;E$ is called solenoidal If $\Delta \times E=0,\;E$ is called conservative If $\Delta\times E=0,\;E$ is called irrotational If $\Delta.E=0,\;E$ is called irrotational
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$?If $\Delta.E=0,\;E$ is called solenoidalIf $\Delta \times E=0,\;E$ is called conservativeIf $...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-in
calculus
vector-calculus
+
–
0
votes
0
answers
63
GATE2013-26
While numerically solving the differential equation $\frac{dy}{dx}+2xy^2=0,\; y(0)=1$ using Euler’s predictor-corrector (improved Euler-Cauchy) method with a step size of 0.2, the value of $y$ after the first step is $1.00$ $1.03$ $0.97$ $0.96$
While numerically solving the differential equation $\frac{dy}{dx}+2xy^2=0,\; y(0)=1$ using Euler’s predictor-corrector (improved Euler-Cauchy) method with a step size ...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2013-in
numerical-methods
improved-euler-cauchy-method
+
–
0
votes
0
answers
64
GATE2013-13
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ is Parabolic Elliptic Hyperbolic Nonlinear
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ isParabolicEllipticHyperbolicNonlinear
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
65
GATE2013-16
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is $0.368$ $0.5$ $0.632$ $1.0$
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0<x<\propto$. Then $\text{P{X>1}}$ is $0.368$$0.5$$0.632$$1.0$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-in
probability-and-statistics
probability
probability-density-function
random-variable
+
–
0
votes
0
answers
66
GATE2013-1
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is $0$ $1$ $2$ $3$
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is$0$$1$$2$$3$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2013-in
linear-algebra
matrices
null-space
+
–
0
votes
0
answers
67
GATE2013-37
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$ $2$ $\pi$ $\sqrt{2}$
The maximum value of the solution y(t) of the differential equation $y(t)+\ddot{y}(t)=0$ with initial conditions $\dot{y}(0)=1$ and $y(0)=1,$ for $t\underline{>}0$ is $1$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
+
–
0
votes
0
answers
68
GATE2012-36
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$$1/2$$1$$2$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
fourier-transform
+
–
0
votes
0
answers
69
GATE2012-30
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$.The numerical value of $\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
+
–
0
votes
0
answers
70
GATE2012-1
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$ $e^{\pi/2}$ $x$ $1$
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$$e^{\pi/2}$$x$$1$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
functions
complex-number
+
–
0
votes
0
answers
71
GATE2012-2
With initial condition $x(1)=0.5$, the solution of the differential equation, $t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$ $x=t^2-\frac{1}{2}$ $x=\frac{t^2}{2}$ $x=\frac{t}{2}$
With initial condition $x(1)=0.5$, the solution of the differential equation,$t\frac{dx}{dt}+x=t$ is $x=t-\frac{1}{2}$$x=t^2-\frac{1}{2}$$x=\frac{t^2}{2}$$x=\frac{t}{2}$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
+
–
0
votes
0
answers
72
GATE2012-4
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}.$ The unilateral Laplace transform of $tf(t)$ is $-\frac{s}{(s^2+s+1)^2}$ $-\frac{2s+1}{(s^2+s+1)^2}$ $\frac{s}{(s^2+s+1)^2}$ $\frac{2s+1}{(s^2+s+1)^2}$
The unilateral Laplace transform of $f(t)$ is $\frac{1}{s^2+s+1}.$ The unilateral Laplace transform of $tf(t)$ is$-\frac{s}{(s^2+s+1)^2}$$-\frac{2s+1}{(s^2+s+1)^2}$$\frac...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
laplace-transform
+
–
0
votes
0
answers
73
GATE2012-29
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$$25$$41$$46$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
maxima-minima
+
–
0
votes
0
answers
74
GATE2012-5
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is $-2$ $-1$ $1$ $2$
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2$$-1$$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2012-in
numerical-methods
cauchys-integral-theorem
+
–
0
votes
0
answers
75
GATE2012-3
Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$
Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-in
probability-and-statistics
probability
random-variable
uniform-distribution
+
–
0
votes
0
answers
76
GATE2012-28
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla.$ $\text{A=0}$ is $-2$ $2$ $1$ $0$
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla....
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
curl
divergence
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–
0
votes
0
answers
77
GATE2012-26
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
78
GATE2018IN: 37
Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for this system is $x(t) = \begin{bmatrix}e^{-t} & te^{-2t} \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1 \\1\end{bmatrix}$ ... $\begin{bmatrix}1 \\1\end{bmatrix}$ $x(t) = \begin{bmatrix}e^{-t} & 0 \\0 & e^{-2t}\end{bmatrix}$ $\begin{bmatrix}1 \\1\end{bmatrix}$
Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Numerical Methods
gate2018-in
numerical-methods
linear-system
+
–
0
votes
0
answers
79
GATE2018IN: 27
Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red? 20% 25% 30% 40%
Two bags A and B have equal number of balls. Bag A has 20% red balls and 80% green balls. Bag B has 30% red balls,60% green balls and 10% yellow balls. Contents of Bags A...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Probability and Statistics
gate2018-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
80
GATE2018IN: 26
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$\overrightarrow{k}$, the value of the linear integral $\int_c$\overrightarrow{F}$ . d$\overrightarrow{l}$ along the straight line c from (0,0,0) to (1,1,1) is 3/16 0 -5/12 -1
Given $\overrightarrow{F}$ = (x$^2$ – 2y) $\overrightarrow{i}$ – 4xz$\overrightarrow{j}$ + 4xz$^2$$\overrightarrow{k}$, the value of the linear integral $\int_c$$\ove...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Calculus
gate2018-in
calculus
vector-calculus
line-integral
+
–
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