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Most answered questions in Engineering Mathematics
0
votes
2
answers
1
GATE2019 CE-2: 43
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \: 1.87$, and $1.15 \:m$. The area (in $m^2$, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \:...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Numerical Methods
gate2019-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
+
–
0
votes
1
answer
2
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
1
answer
3
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
1
answer
4
GATE2017 CE-2-28
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to$\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{b...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Linear Algebra
gate2017-ce-2
linear-algebra
matrices
matrix-algebra
+
–
2
votes
1
answer
5
GATE2019 CE-1: 1
Which one of the following is correct? $\displaystyle{} \lim_{x\rightarrow 0} \left( \dfrac{\sin4x}{\sin2x}\right)=2\;\text{and}\: \lim_{x\rightarrow 0} \left( \dfrac{\tan x}{x}\right)=1$ ...
Which one of the following is correct?$\displaystyle{} \lim_{x\rightarrow 0} \left( \dfrac{\sin4x}{\sin2x}\right)=2\;\text{and}\: \lim_{x\rightarrow 0} \left( \dfrac{\tan...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Calculus
gate2019-ce-1
calculus
limits
+
–
0
votes
1
answer
6
GATE2014-2-2
The determinant of matrix $\begin{bmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 0 \\ 2 & 3 & 0 & 1 \\ 3 & 0 & 1 & 2 \end{bmatrix}$ is ________
The determinant of matrix $\begin{bmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 0 \\ 2 & 3 & 0 & 1 \\ 3 & 0 & 1 & 2 \end{bmatrix}$ is ________
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Linear Algebra
gate2014-ce-2
numerical-answers
linear-algebra
matrices
determinant
+
–
0
votes
1
answer
7
GATE2018 CE-2: 20
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using Newton-Raphson method is _________
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using New...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Numerical Methods
gate2018-ce-2
numerical-methods
newton-raphson-method
numerical-answers
+
–
0
votes
1
answer
8
GATE2018 CE-2: 26
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ has real eigenvalues and eigenvectors real eigenvalues but complex eigenvectors complex eigenvalues but real eigenvectors complex eigenvalues and eigenvectors
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ hasreal eigenvalues and eigenvectorsreal eigenvalues but complex eigenvectorscomplex eigenvalues but real eige...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-2
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
1
answer
9
GATE2018 CE-1: 37
The solution at $x=1$, $t=1$ of the partial differential equation $\dfrac{\partial ^2 u}{\partial x^2} = 25 \dfrac{\partial ^2 u}{\partial t^2}$ subject to initial conditions of $u(0) = 3x$ and $\dfrac{\partial u}{\partial t}(0) =3$ is _______ $1$ $2$ $4$ $6$
The solution at $x=1$, $t=1$ of the partial differential equation $\dfrac{\partial ^2 u}{\partial x^2} = 25 \dfrac{\partial ^2 u}{\partial t^2}$ subject to initial condit...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Partial Differential Equation (PDE)
gate2018-ce-1
partial-differential-equation
+
–
0
votes
1
answer
10
GATE2018 CE-1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ and $\dfrac{dy}{dx}(0) = -1$ is _____
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ a...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-1
ordinary-differential-equation
numerical-answers
+
–
0
votes
1
answer
11
GATE2018 CE-1: 1
Which one of the following matrices is singular? $\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 2 & 4\\ 3 & 6 \end{bmatrix} \\$ $\begin{bmatrix} 4 & 3\\ 6 & 2 \end{bmatrix}$
Which one of the following matrices is singular?$\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$$\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$$\begin{bmatrix} 2 & 4\\...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-1
linear-algebra
matrices
determinant
+
–
0
votes
0
answers
12
GATE Civil 2024 Set 1 | Question: 1
The smallest positive root of the equation \[ x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0 \] lies in the range $0 < x \leq 2$ $2 < x \leq 4$ $6 \leq x \leq 8$ $10 \leq x \leq 100$
The smallest positive root of the equation\[x^{5}-5 x^{4}-10 x^{3}+50 x^{2}+9 x-45=0\]lies in the range$0 < x \leq 2$$2 < x \leq 4$$6 \leq x \leq 8$$10 \le...
admin
4.2k
points
admin
asked
Feb 16
Linear Algebra
gatecivil-2024-set1
algebra
+
–
0
votes
0
answers
13
GATE Civil 2024 Set 1 | Question: 2
The second-order differential equation in an unknown function $u: u(x, y)$ is defined as \[ \frac{\partial^{2} u}{\partial x^{2}}=2 \] Assuming $g: g(x), f: f(y)$, and $h: h(y)$, the general solution of the above differential equation is $u=x^{2}+f(y)+g(x)$ $u=x^{2}+x f(y)+h(y)$ $u=x^{2}+x f(y)+g(x)$ $u=x^{2}+f(y)+y g(x)$
The second-order differential equation in an unknown function $u: u(x, y)$ is defined as\[\frac{\partial^{2} u}{\partial x^{2}}=2\]Assuming $g: g(x), f: f(...
admin
4.2k
points
admin
asked
Feb 16
Linear Algebra
gatecivil-2024-set1
second-order-differential-equation
+
–
0
votes
0
answers
14
GATE Civil 2024 Set 1 | Question: 3
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the ... one of these two subjects is $\frac{17}{18}$ $\frac{11}{18}$ $\frac{14}{18}$ $\frac{1}{18}$
The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. Th...
admin
4.2k
points
admin
asked
Feb 16
Linear Algebra
gatecivil-2024-set1
probability
fractions
+
–
0
votes
0
answers
15
GATE Civil 2024 Set 1 | Question: 18
For the following partial differential equation, \[ x \frac{\partial^{2} f}{\partial x^{2}}+y \frac{\partial^{2} f}{\partial y^{2}}=\frac{x^{2}+y^{2}}{2} \] which of the following option(s) is/are CORRECT? elliptic for $x>0$ and $y>0$ parabolic for $x>0$ and $y>0$ elliptic for $x=0$ and $y>0$ hyperbolic for $x<0$ and $y>0$
For the following partial differential equation,\[x \frac{\partial^{2} f}{\partial x^{2}}+y \frac{\partial^{2} f}{\partial y^{2}}=\frac{x^{2}+y^{2}}{2}\...
admin
4.2k
points
admin
asked
Feb 16
Partial Differential Equation (PDE)
gatecivil-2024-set1
engineering-mathematics
partial-differential-equation
+
–
0
votes
0
answers
16
GATE Civil 2024 Set 1 | Question: 26
What are the eigenvalues of the matrix $\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2\end{array}\right]$ ? $1,2,5$ $1,3,4$ $-5,1,2$ $-5,-1,2$
What are the eigenvalues of the matrix $\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2\end{array}\right]$ ?$1,2,5$$1,3,4$$-5,1,2$$-5,-1,2$
admin
4.2k
points
admin
asked
Feb 16
Linear Algebra
gatecivil-2024-set1
linear-algebra
eigen-values
+
–
0
votes
0
answers
17
GATE Civil 2024 Set 1 | Question: 27
A vector field $\vec{p}$ and a scalar field $r$ are given by \[ \begin{aligned} \vec{p} & =\left(2 x^{2}-3 x y+z^{2}\right) \hat{\imath}+\left(2 y^{2}-3 y z+x^{2}\right) \hat{\jmath}+\left(2 z^{2}-3 x z+x^{2}\right) \ ... $\text{P}$ is TRUE and $\text{Q}$ is FALSE $\mathrm{P}$ is FALSE and $\mathrm{Q}$ is TRUE Both $\mathrm{P}$ and $\mathrm{Q}$ are TRUE
A vector field $\vec{p}$ and a scalar field $r$ are given by\[\begin{aligned}\vec{p} & =\left(2 x^{2}-3 x y+z^{2}\right) \hat{\imath}+\left(2 y^{2}-3 y z+x...
admin
4.2k
points
admin
asked
Feb 16
Calculus
gatecivil-2024-set1
vector-calculus
gradient
divergence
+
–
0
votes
0
answers
18
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
19
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$$\infty$
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
calculus
limits
+
–
0
votes
0
answers
20
GATE Civil 2021 Set 2 | Question: 2
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is $1$ $2$ $3$ $4$
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is$1$$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
21
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}}$$\frac{1}{\...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
calculus
vector-calculus
vector-identities
unit-normal-vector
+
–
0
votes
0
answers
22
GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$
If $\text{A}$ is a square matrix then orthogonality property mandates$AA^{T}=I$$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
23
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
+
–
0
votes
0
answers
24
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
+
–
0
votes
0
answers
25
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
26
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
+
–
0
votes
0
answers
27
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
28
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
29
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
30
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
31
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
32
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
33
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
34
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$$2.718$
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Numerical Methods
gatecivil-2021-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
35
GATE Civil 2021 Set 1 | Question: 36
The value of abscissa $(x)$ and ordinate $(y)$ ... $1/3^\text{rd}$ rule, the area under the curve $\textit{(round off to two decimal places)}$ is __________________
The value of abscissa $(x)$ and ordinate $(y)$ of a curve are as follows:$$\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
36
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$$$D(\theta)\frac{\partial^2\theta}{\partia...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Partial Differential Equation (PDE)
gate2020-ce-1
partial-differential-equation
+
–
0
votes
0
answers
37
GATE2020-CE-1-3
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round ...
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5.3k
points
go_editor
asked
Feb 27, 2020
Numerical Methods
gate2020-ce-1
numerical-methods
linear-interpolation
+
–
0
votes
0
answers
38
GATE2020-CE-1-4
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is$\dfrac{\pi ab}{4} \\$$\dfrac{\pi ab}{2} \\$$\pi ab \\$$\dfrac{4\pi ab}{3}$
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5.3k
points
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asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
curves
area-under-curve
+
–
0
votes
0
answers
39
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...
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5.3k
points
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asked
Feb 27, 2020
Ordinary Differential Equation (ODE)
gate2020-ce-1
ordinary-differential-equation
+
–
0
votes
0
answers
40
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 ...
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5.3k
points
go_editor
asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
derivatives
continuous-function
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