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gate question from engineering mathematics in ordinary differential equation
for the differential equation ,d^2y/dx^2+3dy/dx+4y=3cos2x,then value of particular integral is
for the differential equation ,d^2y/dx^2+3dy/dx+4y=3cos2x,then value of particular integral is
saswati mahapatra
240
points
saswati mahapatra
asked
Aug 28, 2023
0
votes
0
answers
2
GATE Civil 2021 Set 2 | Question: 1
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is $0$ $1.0$ $0.5$ $\infty$
The value of $\lim \limits_{x\rightarrow \infty } \dfrac{x \:\text{ln}\left ( x \right )}{1+x^{2}}$ is$0$$1.0$$0.5$$\infty$
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
calculus
limits
+
–
0
votes
0
answers
3
GATE Civil 2021 Set 2 | Question: 2
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is $1$ $2$ $3$ $4$
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is$1$$2$$3$$4$
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Linear Algebra
gatecivil-2021-set2
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
4
GATE Civil 2021 Set 2 | Question: 3
The unit normal vector to the surface $X^{2} + Y^{2} + Z^{2} – 48 = 0$ at the point $(4, 4, 4)$ is $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ $\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}}$ $\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}}$
The unit normal vector to the surface $X^{2} + Y^{2} + Z^{2} – 48 = 0$ at the point $(4, 4, 4)$ is $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$$\frac{1}{\...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
calculus
vector-calculus
vector-identities
unit-normal-vector
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–
0
votes
0
answers
5
GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$
If $\text{A}$ is a square matrix then orthogonality property mandates$AA^{T}=I$$AA^{T}=0$$AA^{T}=A^{-1}$$AA^{T}=A^{2}$
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Linear Algebra
gatecivil-2021-set2
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
6
GATE Civil 2021 Set 2 | Question: 18
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
The value ($\textit{round off to one decimal place}$) of $\int_{-1}^{1}x\:e^{\left | x \right |}dx$ is ______________
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
numerical-answers
calculus
definite-integral
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–
0
votes
0
answers
7
GATE Civil 2021 Set 2 | Question: 26
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$
If $\text{k}$ is a constant, the general solution of $\dfrac{dy}{dx}-\dfrac{y}{x}=1$ will be in the form of$y=x\text{ ln}(kx)$$y=k\text{ ln}(kx)$$y=x\text{ ln}(x)$$y=xk\t...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Ordinary Differential Equation (ODE)
gatecivil-2021-set2
ordinary-differential-equation
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–
0
votes
0
answers
8
GATE Civil 2021 Set 2 | Question: 27
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are $1.55$ and $\begin{Bmatrix} 2.00\\ 0.45 \end{Bmatrix}$ $2.00$ ... and $\begin{Bmatrix} -2.55\\ -0.45 \end{Bmatrix}$ $1.55$ and $\begin{Bmatrix} 2.00\\ -0.45 \end{Bmatrix}$
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are$1.55$ and $\begin{Bmatrix} 2.0...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Linear Algebra
gatecivil-2021-set2
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
9
GATE Civil 2021 Set 2 | Question: 36
A function is defined in Cartesian coordinate system as $f(x,y)=xe^{y}$. The value of the directional derivative of the function ($\textit{in integer}$) at the point $(2,0)$ along the direction of the straight line segment from point $(2, 0)$ to point $\left ( \dfrac{1}{2} ,2\right )$ is _________
A function is defined in Cartesian coordinate system as $f(x,y)=xe^{y}$. The value of the directional derivative of the function ($\textit{in integer}$) at the point $(2,...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
numerical-answers
calculus
directional-derivatives
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–
0
votes
0
answers
10
GATE Civil 2021 Set 2 | Question: 46
Numerically integrate, $f(x)=10x-20x^2$ from lower limit $a=0$ to upper limit $b=0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in $\text{units}, \textit{round off to two decimal places}$) obtained is ________________
Numerically integrate, $f(x)=10x-20x^2$ from lower limit $a=0$ to upper limit $b=0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in $\text{units}, \te...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Numerical Methods
gatecivil-2021-set2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
11
GATE Civil 2021 Set 1 | Question: 1
The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3\\ 3 & 4 & 2 & 5\\ 5 & 6 & 2 & 7\\ 7 & 8 & 2 & 9 \end{bmatrix}$ is $1$ $2$ $3$ $4$
The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3\\ 3 & 4 & 2 & 5\\ 5 & 6 & 2 & 7\\ 7 & 8 & 2 & 9 \end{bmatrix}$ is$1$$2$$3$$4$
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gatecivil-2021-set1
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
12
GATE Civil 2021 Set 1 | Question: 2
If $P=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^{T}\:P^{T}$ is $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ $\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}$ $\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$ $\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$
If $P=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^{T}\:P^{T}$ is$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatri...
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Linear Algebra
gatecivil-2021-set1
linear-algebra
matrices
matrix-algebra
+
–
0
votes
0
answers
13
GATE Civil 2021 Set 1 | Question: 3
The shape of the cumulative distribution function of Gaussian distribution is Horizontal line Straight line at $45$ degree angle Bell-shaped $S$-shaped
The shape of the cumulative distribution function of Gaussian distribution isHorizontal lineStraight line at $45$ degree angleBell-shaped$S$-shaped
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Probability and Statistics
gatecivil-2021-set1
probability-and-statistics
statistics
gaussian-distributions
+
–
0
votes
0
answers
14
GATE Civil 2021 Set 1 | Question: 18
Consider the limit: $\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x} - \frac{1}{x-1}\right )$ The limit (correct up to one decimal place) is _____________
Consider the limit:$$\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x} - \frac{1}{x-1}\right )$$The limit (correct up to one decimal place) is _____________
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Calculus
gatecivil-2021-set1
numerical-answers
calculus
limits
+
–
0
votes
0
answers
15
GATE Civil 2021 Set 1 | Question: 19
The volume determined from $\int \int \int _{V}\:8\:xyz\:dV$ for $V=\left [ 2,3 \right ]\times \left [ 1,2 \right ]\times \left [ 0,1 \right ]$ will be ($\textit{in integer}$) _____________
The volume determined from $\int \int \int _{V}\:8\:xyz\:dV$ for $V=\left [ 2,3 \right ]\times \left [ 1,2 \right ]\times \left [ 0,1 \right ]$ will be ($\textit{in integ...
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Calculus
gatecivil-2021-set1
numerical-answers
calculus
tripple-integrals
volume
+
–
0
votes
0
answers
16
GATE Civil 2021 Set 1 | Question: 26
The solution of the second-order differential equation $\dfrac{d^{2}y}{dx^{2}}+2\dfrac{dy}{dx}+y=0$ with boundary conditions $y\left ( 0 \right )=1$ and $y\left ( 1 \right )=3$ is $e^{-x}+\left ( 3e-1 \right )xe^{-x}$ ... $e^{-x}-\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) -1\right ]xe^{-x}$
The solution of the second-order differential equation $\dfrac{d^{2}y}{dx^{2}}+2\dfrac{dy}{dx}+y=0$ with boundary conditions $y\left ( 0 \right )=1$ and $y\left ( 1 \righ...
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Ordinary Differential Equation (ODE)
gatecivil-2021-set1
ordinary-differential-equation
second-order-differential-equation
+
–
0
votes
0
answers
17
GATE Civil 2021 Set 1 | Question: 27
The value of $\int_{0}^{1}\:e^{x}\:dx$ using the trapezoidal rule with four equal subintervals is $1.718$ $1.727$ $2.192$ $2.718$
The value of $\int_{0}^{1}\:e^{x}\:dx$ using the trapezoidal rule with four equal subintervals is$1.718$$1.727$$2.192$$2.718$
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Numerical Methods
gatecivil-2021-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
18
GATE Civil 2021 Set 1 | Question: 36
The value of abscissa $(x)$ and ordinate $(y)$ ... $1/3^\text{rd}$ rule, the area under the curve $\textit{(round off to two decimal places)}$ is __________________
The value of abscissa $(x)$ and ordinate $(y)$ of a curve are as follows:$$\begin{array}{|cl|cI|}\hline&x & y\\ \hline & \text{$2.0$} & \text{$5.00$} \\ \hline & \text{$2...
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Numerical Methods
gatecivil-2021-set1
numerical-answers
numerical-methods
simpsons-rule
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
19
GATE2020-CE-1-1
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ ... The above equation is a second order linear equation a second degree linear equation a second order non-linear equation a second degree non-linear equation
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$$$D(\theta)\frac{\partial^2\theta}{\partia...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Partial Differential Equation (PDE)
gate2020-ce-1
partial-differential-equation
+
–
0
votes
1
answer
20
GATE2020-CE-1-2
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is$0 \\$$\dfrac{1}{4} \\$$\dfrac{1}{2} \\$$1$
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
limits
+
–
0
votes
0
answers
21
GATE2020-CE-1-3
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round ...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Numerical Methods
gate2020-ce-1
numerical-methods
linear-interpolation
+
–
0
votes
0
answers
22
GATE2020-CE-1-4
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is$\dfrac{\pi ab}{4} \\$$\dfrac{\pi ab}{2} \\$$\pi ab \\$$\dfrac{4\pi ab}{3}$
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
curves
area-under-curve
+
–
0
votes
1
answer
23
GATE2020-CE-1-18
The probability that a $50$ year flood may $\textbf{NOT}$ occur at all during $25$ years life of a project (round off to two decimal places), is _______.
The probability that a $50$ year flood may $\textbf{NOT}$ occur at all during $25$ years life of a project (round off to two decimal places), is _______.
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Probability and Statistics
gate2020-ce-1
probability-and-statistics
probability
numerical-answers
+
–
0
votes
0
answers
24
GATE2020-CE-1-26
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $-5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $-10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the s...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Ordinary Differential Equation (ODE)
gate2020-ce-1
ordinary-differential-equation
+
–
0
votes
0
answers
25
GATE2020-CE-1-27
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step length $=h$ ...
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step ...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
derivatives
continuous-function
+
–
0
votes
0
answers
26
GATE2020-CE-1-39
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral $\int_C [(y+z)dx+(x+z)dy+(x+y)dz] $ is ______
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral$$\int_C [(y+z)dx+(x...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
line-integral
+
–
0
votes
0
answers
27
GATE2020-CE-1-40
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.
Consider the system of equations$$\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 ...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Linear Algebra
gate2020-ce-1
linear-algebra
matrices
system-of-equations
numerical-answers
+
–
0
votes
0
answers
28
GATE2020 CE-2-1
The ordinary differential equation $\dfrac{d^2u}{dx^2}$- 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous
The ordinary differential equation $\dfrac{d^2u}{dx^2}$$- 2x^2u +\sin x = 0$ islinear and homogeneouslinear and nonhomogeneousnonlinear and homogeneousnonlinear and nonho...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Ordinary Differential Equation (ODE)
gate2020-ce-2
ordinary-differential-equation
+
–
0
votes
0
answers
29
GATE2020 CE-2-2
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
The value of $$\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$$$\dfrac{7}{9}$$1$$3$indeterminable
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Calculus
gate2020-ce-2
calculus
limits
+
–
0
votes
0
answers
30
GATE2020 CE-2-3
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NON-zero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson’s r...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Numerical Methods
gate2020-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
31
GATE2020 CE-2-4
The following partial differential equation is defined for $u:u (x,y)$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$ The set of auxiliary ... the equation uniquely, is three initial conditions three boundary conditions two initial conditions and one boundary condition one initial condition and two boundary conditions
The following partial differential equation is defined for $u:u (x,y)$$$\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Partial Differential Equation (PDE)
gate2020-ce-2
partial-differential-equation
+
–
0
votes
0
answers
32
GATE2020 CE-2-18
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Probability and Statistics
gate2020-ce-2
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
33
GATE2020 CE-2-24
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vertical coordinate $y,\: U_\infty$ is the free stream velocity and $\delta$ is the boundary layer ... $\ s^{-1}$, round off to two decimal places) at $y = 0$, is ________.
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vert...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Calculus
gate2020-ce-2
numerical-answers
calculus
gradient
+
–
0
votes
0
answers
34
GATE2020 CE-2-26
An ordinary differential equation is given below $6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}-y=0$ The general solution of the above equation (with constants $C_1$ and $C_2$), is $y(x) = C_1e^\frac{-x}{3} + C_2e^\frac{x}{2}$ $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{-x}{2}$ $ y(x) = C_1xe^\frac{-x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1e^\frac{-x}{3} + C_2xe^\frac{x}{2}$
An ordinary differential equation is given below$$6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}-y=0$$The general solution of the above equation (with constants $C_1$ and $C_2$), is$y...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Ordinary Differential Equation (ODE)
gate2020-ce-2
ordinary-differential-equation
+
–
0
votes
0
answers
35
GATE2020 CE-2-27
A $4 \times 4$ matrix $[P]$ is given below $[P] = \begin{bmatrix}0 &1 &3 &0 \\-2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$ The eigen values of $[P]$ are $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
A $4 \times 4$ matrix $[P]$ is given below$$[P] = \begin{bmatrix}0 &1 &3 &0 \\-2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$$The eigen values of $[P]$ are $0, 3, 6,...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Linear Algebra
gate2020-ce-2
linear-algebra
matrices
eigen-values
+
–
0
votes
0
answers
36
GATE2020 CE-2-39
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by $ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by$$ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \si...
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5.3k
points
go_editor
asked
Feb 13, 2020
Partial Differential Equation (PDE)
gate2020-ce-2
numerical-answers
partial-differential-equation
fourier-series
+
–
0
votes
0
answers
37
GATE2020 CE-2-40
The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The absolute error in the computed volume ( in $cm^3$ ,round off to three decimal places), is ________
The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The abso...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Numerical Methods
gate2020-ce-2
numerical-answers
numerical-methods
+
–
0
votes
0
answers
38
GATE2017 CE-2-1
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants):$3x_1+2x_2=c_1$$4x_1+x_2=c_2$The characteristic equation for these simultaneous equat...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Linear Algebra
gate2017-ce-2
linear-algebra
system-of-equations
+
–
0
votes
0
answers
39
GATE2017 CE-2-2
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to$\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \df...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Calculus
gate2017-ce-2
calculus
partial-derivatives
+
–
0
votes
0
answers
40
GATE2017 CE-2-19
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Calculus
gate2017-ce-2
calculus
vector-calculus
divergence
numerical-answers
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–
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