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Recent questions in Engineering Mathematics
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1
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
2
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
3
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
4
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
5
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
6
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
7
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
8
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$$\infty$
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
calculus
limits
+
–
0
votes
0
answers
9
GATE Civil 2021 Set 2 | Question: 2
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is $1$ $2$ $3$ $4$
The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0\\ 0 & 2 & 0 & 1\\ -5 & 0 & 5 & 0\\ 0 & 1 & 0 & 2 \end{bmatrix}$ is$1$$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
10
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}}$$\frac{1}{\...
go_editor
5.3k
points
go_editor
asked
Mar 1, 2021
Calculus
gatecivil-2021-set2
calculus
vector-calculus
vector-identities
unit-normal-vector
+
–
0
votes
0
answers
11
GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{-1}$ $AA^{T}=A^{2}$
If $\text{A}$ is a square matrix then orthogonality property mandates$AA^{T}=I$$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
12
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
13
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
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
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
22
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
23
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$$2.718$
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Numerical Methods
gatecivil-2021-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
24
GATE Civil 2021 Set 1 | Question: 36
The value of abscissa $(x)$ and ordinate $(y)$ ... $1/3^\text{rd}$ rule, the area under the curve $\textit{(round off to two decimal places)}$ is __________________
The value of abscissa $(x)$ and ordinate $(y)$ of a curve are as follows:$$\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
25
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$$$D(\theta)\frac{\partial^2\theta}{\partia...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Partial Differential Equation (PDE)
gate2020-ce-1
partial-differential-equation
+
–
0
votes
1
answer
26
GATE2020-CE-1-2
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is$0 \\$$\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
27
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
28
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
29
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
30
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
31
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
32
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$$\int_C [(y+z)dx+(x...
go_editor
5.3k
points
go_editor
asked
Feb 27, 2020
Calculus
gate2020-ce-1
calculus
line-integral
+
–
0
votes
0
answers
33
GATE2020-CE-1-40
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.
Consider the system of equations$$\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
34
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}$$- 2x^2u +\sin x = 0$ islinear and homogeneouslinear and nonhomogeneousnonlinear and homogeneousnonlinear and nonho...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Ordinary Differential Equation (ODE)
gate2020-ce-2
ordinary-differential-equation
+
–
0
votes
0
answers
35
GATE2020 CE-2-2
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
The value of $$\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$$$\dfrac{7}{9}$$1$$3$indeterminable
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Calculus
gate2020-ce-2
calculus
limits
+
–
0
votes
0
answers
36
GATE2020 CE-2-3
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NON-zero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson’s r...
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Numerical Methods
gate2020-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
37
GATE2020 CE-2-4
The following partial differential equation is defined for $u:u (x,y)$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$ The set of auxiliary ... the equation uniquely, is three initial conditions three boundary conditions two initial conditions and one boundary condition one initial condition and two boundary conditions
The following partial differential equation is defined for $u:u (x,y)$$$\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x...
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Partial Differential Equation (PDE)
gate2020-ce-2
partial-differential-equation
+
–
0
votes
0
answers
38
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 _______.
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Feb 13, 2020
Probability and Statistics
gate2020-ce-2
numerical-answers
probability-and-statistics
probability
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–
0
votes
0
answers
39
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...
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Feb 13, 2020
Calculus
gate2020-ce-2
numerical-answers
calculus
gradient
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0
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0
answers
40
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...
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Feb 13, 2020
Ordinary Differential Equation (ODE)
gate2020-ce-2
ordinary-differential-equation
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