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Recent questions in Engineering Mathematics
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0
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41
GATE2016-26
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
Let $f: [-1,1]\rightarrow \mathbb{R}$, where $f(x)=2x^3-x^4-10$. The minimum value of $f(x)$ is $\_\_\_\_\_\_\_.$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2016-in
numerical-answers
calculus
maxima-minima
+
–
0
votes
0
answers
42
GATE2016-27
An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same color. The probability of getting a red ball in the next draw is $\frac{65}{156}$ $\frac{67}{156}$ $\frac{79}{156}$ $\frac{89}{156}$
An urn contains $5$ red and $7$ green balls. A ball is drawn at random and its color is noted. The ball is placed back into the urn along with another ball of the same co...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2016-in
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
43
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
44
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
45
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$$n+r$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2015-in
linear-algebra
matrices
system-of-equations
+
–
0
votes
0
answers
46
GATE2015-12
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is $-2\pi i$ $0$ $2\pi i$ $4\pi i$
The value of $\oint \frac{1}{Z^2} dZ,$ where the contour is the unit circle traversed clockwise, is$-2\pi i$$0$$2\pi i$$4\pi i$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Analysis of complex variables
gate2015-in
analysis-of-complex-variables
cauchys-integral-theorem
+
–
0
votes
0
answers
47
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$$\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
definite-integrals
double-integrals
+
–
0
votes
0
answers
48
GATE2015-14
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is $4\sqrt{2}$ $5\sqrt{2}$ $7\sqrt{2}$ $9\sqrt{2}$
The magnitude of the directional derivative of the function $f(x,y)=x^2+3y^2$ in a direction normal to the circle $x^2+y^2=2,$ at the point $(1,1),$ is$4\sqrt{2}$$5\sqrt{...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 26, 2018
Calculus
gate2015-in
calculus
directional-derivatives
+
–
0
votes
0
answers
49
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
50
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
51
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
52
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
53
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
54
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
55
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
56
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)$$x_{k+1}=\frac{1}{3}(...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2014-in
numerical-methods
newton-raphson-method
+
–
0
votes
0
answers
57
GATE2014-28
For the matrix $A$ satisfying the equation given below, the eigenvalues are $[A] \begin {bmatrix} 1&2&3\\7&8&9\\4&5&6\end{bmatrix}=\begin {bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$ $(1,-j,j)$ $(1,1,0)$ $(1,1,-1)$ $(1,0,0)$
For the matrix $A$ satisfying the equation given below, the eigenvalues are$$[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
58
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$$18$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2014-in
differential-equations
fourier-transform
+
–
0
votes
0
answers
59
GATE2013-38
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+e^{-2s}]$ $\frac{1}{s^2}[1-e^{-s}+2e^{-2s}]$ $\frac{1}{s^2}[1-2e^{-s}+e^{-2s}]$
The Laplace Transform representation of the triangular pulse shown below is $\frac{1}{s^2}[1+e^{-2s}]$$\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
60
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
61
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
62
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
63
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$$1.0$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-in
probability-and-statistics
probability
probability-density-function
random-variable
+
–
0
votes
0
answers
64
GATE2013-13
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ is Parabolic Elliptic Hyperbolic Nonlinear
The type of the partial differential equation $\frac{\partial f}{\partial t}=\frac{\partial^2 f}{\partial x^2}$ isParabolicEllipticHyperbolicNonlinear
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2013-in
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
65
GATE2013-5
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$? If $\Delta.E=0,\;E$ is called solenoidal If $\Delta \times E=0,\;E$ is called conservative If $\Delta\times E=0,\;E$ is called irrotational If $\Delta.E=0,\;E$ is called irrotational
For a vector $E$, which one of the following statements is $\text{NOT TRUE}$?If $\Delta.E=0,\;E$ is called solenoidalIf $\Delta \times E=0,\;E$ is called conservativeIf $...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-in
calculus
vector-calculus
+
–
0
votes
0
answers
66
GATE2013-1
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is $0$ $1$ $2$ $3$
The dimension of the null space of the matrix $\begin{bmatrix} 0&1&1\\1&-1&0\\-1&0&-1 \end{bmatrix}$ is$0$$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
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$$2$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
fourier-transform
+
–
0
votes
0
answers
68
GATE2012-30
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$.The numerical value of $\...
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Differential equations
gate2012-in
differential-equations
+
–
0
votes
0
answers
69
GATE2012-29
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$$25$$41$$46$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
maxima-minima
+
–
0
votes
0
answers
70
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$$17A+21I$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2012-in
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
71
GATE2012-26
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$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
72
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
+
–
0
votes
0
answers
73
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
74
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
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
GATE2012-2
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}$$x=\frac{t}{2}$
Milicevic3306
7.9k
points
Milicevic3306
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Mar 25, 2018
Differential equations
gate2012-in
differential-equations
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–
0
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0
answers
77
GATE2012-1
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$ $e^{\pi/2}$ $x$ $1$
If $x=\sqrt{-1},$ then the value of $x^x$ is $e^{-\pi/2}$$e^{\pi/2}$$x$$1$
Milicevic3306
7.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2012-in
calculus
functions
complex-number
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–
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: 29
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy $\frac {\partial {V(x,y)}}{\partial y}$ = x$^2$ + qy$^2$ + 2xy where p and q are constant ,V(x,y) that satisfies the above equations is p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 2xy + 6 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + 5 p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$ + xy p$\frac{x^3}{3}$ + q$\frac{y^3}{3}$ + x$^2$y + xy$^2$
Consider the following equations $\frac {\partial {V(x,y)}}{\partial x}$ = px$^2$ + y$^2$ + 2xy ...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Differential equations
gate2018-in
differential-equations
partial-differential-equations
+
–
0
votes
0
answers
80
GATE2018IN: 28
Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2 Here x and y are the unknows and k is real constant. The value of k for which there are infinite number of solutions is 3 1 -3 -6
Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y =2Here x and y are the unknows and k is real c...
gatecse
1.4k
points
gatecse
asked
Feb 20, 2018
Linear Algebra
gate2018-in
linear-algebra
system-of-equations
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