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1
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 $0$ $1.0$ $0.5$ $\infty$
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Mar 1
in
Calculus
by
jothee
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gatecivil2021set2
calculus
limits
0
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2
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 $1$ $2$ $3$ $4$
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Mar 1
in
Linear Algebra
by
jothee
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5.2k
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gatecivil2021set2
linearalgebra
matrices
rankofmatrix
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3
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 $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}$ $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ $\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}},\frac{2}{\sqrt{2}}$ $\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}}$
asked
Mar 1
in
Calculus
by
jothee
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5.2k
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gatecivil2021set2
calculus
vectorcalculus
vectoridentities
unitnormalvector
0
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0
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4
GATE Civil 2021 Set 2  Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates $AA^{T}=I$ $AA^{T}=0$ $AA^{T}=A^{1}$ $AA^{T}=A^{2}$
asked
Mar 1
in
Linear Algebra
by
jothee
(
5.2k
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gatecivil2021set2
linearalgebra
matrices
matrixalgebra
0
votes
0
answers
5
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 ______________
asked
Mar 1
in
Calculus
by
jothee
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5.2k
points)
gatecivil2021set2
numericalanswers
calculus
definiteintegral
0
votes
0
answers
6
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 $y=x\text{ ln}(kx)$ $y=k\text{ ln}(kx)$ $y=x\text{ ln}(x)$ $y=xk\text{ ln}(k)$
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Mar 1
in
Ordinary Differential Equation (ODE)
by
jothee
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5.2k
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gatecivil2021set2
ordinarydifferentialequation
0
votes
0
answers
7
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 $\begin{Bmatrix} 2.00\\ 0.45 \end{Bmatrix}$
asked
Mar 1
in
Linear Algebra
by
jothee
(
5.2k
points)
gatecivil2021set2
linearalgebra
matrices
eigenvalues
eigenvectors
0
votes
0
answers
8
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 _________
asked
Mar 1
in
Calculus
by
jothee
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5.2k
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gatecivil2021set2
numericalanswers
calculus
directionalderivatives
0
votes
0
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9
GATE Civil 2021 Set 2  Question: 46
Numerically integrate, $f(x)=10x20x^2$ 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 ________________
asked
Mar 1
in
Numerical Methods
by
jothee
(
5.2k
points)
gatecivil2021set2
numericalanswers
numericalmethods
integrationbytrapezoidalandsimpsonsrule
0
votes
0
answers
10
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 $1$ $2$ $3$ $4$
asked
Feb 20
in
Linear Algebra
by
Arjun
(
8.7k
points)
gatecivil2021set1
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
11
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 $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ $\begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}$ $\begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix}$ $\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$
asked
Feb 20
in
Linear Algebra
by
Arjun
(
8.7k
points)
gatecivil2021set1
linearalgebra
matrices
matrixalgebra
0
votes
0
answers
12
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 Bellshaped $S$shaped
asked
Feb 20
in
Probability and Statistics
by
Arjun
(
8.7k
points)
gatecivil2021set1
probabilityandstatistics
statistics
gaussiandistributions
0
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0
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13
GATE Civil 2021 Set 1  Question: 18
Consider the limit: $\lim_{x\rightarrow 1}\left ( \frac{1}{\text{ln}\:x}  \frac{1}{x1}\right )$ The limit (correct up to one decimal place) is _____________
asked
Feb 20
in
Calculus
by
Arjun
(
8.7k
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gatecivil2021set1
numericalanswers
calculus
limits
0
votes
0
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14
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 ($\textit{in integer}$) _____________
asked
Feb 20
in
Calculus
by
Arjun
(
8.7k
points)
gatecivil2021set1
numericalanswers
calculus
trippleintegrals
volume
0
votes
0
answers
15
GATE Civil 2021 Set 1  Question: 26
The solution of the secondorder 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 $e^{x}+\left ( 3e1 \right )xe^{x}$ ... $e^{x}\left [ 3e\sin\left ( \frac{\pi x}{2} \right ) 1\right ]xe^{x}$
asked
Feb 20
in
Ordinary Differential Equation (ODE)
by
Arjun
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8.7k
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gatecivil2021set1
ordinarydifferentialequation
secondorderdifferentialequation
0
votes
0
answers
16
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 $1.718$ $1.727$ $2.192$ $2.718$
asked
Feb 20
in
Numerical Methods
by
Arjun
(
8.7k
points)
gatecivil2021set1
numericalmethods
integrationbytrapezoidalandsimpsonsrule
0
votes
0
answers
17
GATE Civil 2021 Set 1  Question: 36
The value of abscissa $(x)$ and ordinate $(y)$ of a curve are as follows: $\begin{array}{clcI}\hline &x & y\\ \hline & \text{$2.0$} & \text{$5.00$} \\ \hline & \text{$2.5$} & \text{$ ... $1/3^\text{rd}$ rule, the area under the curve $\textit{(round off to two decimal places)}$ is __________________
asked
Feb 20
in
Numerical Methods
by
Arjun
(
8.7k
points)
gatecivil2021set1
numericalanswers
numericalmethods
simpsonsrule
0
votes
0
answers
18
GATE2020CE11
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 nonlinear equation a second degree nonlinear equation
asked
Feb 28, 2020
in
Partial Differential Equation (PDE)
by
jothee
(
5.2k
points)
gate2020ce1
partialdifferentialequation
0
votes
1
answer
19
GATE2020CE12
The value of $\displaystyle{} \lim_{x\to\infty}\dfrac{x^25x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
asked
Feb 28, 2020
in
Calculus
by
jothee
(
5.2k
points)
gate2020ce1
calculus
limits
0
votes
0
answers
20
GATE2020CE13
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 $35$ $48$ $69$ $84$
asked
Feb 28, 2020
in
Numerical Methods
by
jothee
(
5.2k
points)
gate2020ce1
numericalmethods
linearinterpolation
0
votes
0
answers
21
GATE2020CE14
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
asked
Feb 28, 2020
in
Calculus
by
jothee
(
5.2k
points)
gate2020ce1
calculus
curves
areaundercurve
0
votes
0
answers
22
GATE2020CE118
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 _______.
asked
Feb 28, 2020
in
Probability and Statistics
by
jothee
(
5.2k
points)
gate2020ce1
probabilityandstatistics
probability
numericalanswers
0
votes
0
answers
23
GATE2020CE126
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 $5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
asked
Feb 28, 2020
in
Ordinary Differential Equation (ODE)
by
jothee
(
5.2k
points)
gate2020ce1
ordinarydifferentialequation
0
votes
0
answers
24
GATE2020CE127
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finitedivideddifference scheme (with step length $=h$ ...
asked
Feb 28, 2020
in
Calculus
by
jothee
(
5.2k
points)
gate2020ce1
calculus
derivatives
continuousfunction
0
votes
0
answers
25
GATE2020CE139
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 ______
asked
Feb 28, 2020
in
Calculus
by
jothee
(
5.2k
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gate2020ce1
calculus
lineintegral
0
votes
0
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26
GATE2020CE140
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 ___________.
asked
Feb 28, 2020
in
Linear Algebra
by
jothee
(
5.2k
points)
gate2020ce1
linearalgebra
matrices
systemofequations
numericalanswers
0
votes
0
answers
27
GATE2020 CE21
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
asked
Feb 13, 2020
in
Ordinary Differential Equation (ODE)
by
jothee
(
5.2k
points)
gate2020ce2
ordinarydifferentialequation
0
votes
0
answers
28
GATE2020 CE22
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
asked
Feb 13, 2020
in
Calculus
by
jothee
(
5.2k
points)
gate2020ce2
calculus
limits
0
votes
0
answers
29
GATE2020 CE23
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 ... NONzero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
asked
Feb 13, 2020
in
Numerical Methods
by
jothee
(
5.2k
points)
gate2020ce2
numericalmethods
integrationbytrapezoidalandsimpsonsrule
0
votes
0
answers
30
GATE2020 CE24
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
asked
Feb 13, 2020
in
Partial Differential Equation (PDE)
by
jothee
(
5.2k
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gate2020ce2
partialdifferentialequation
0
votes
0
answers
31
GATE2020 CE218
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
asked
Feb 13, 2020
in
Probability and Statistics
by
jothee
(
5.2k
points)
gate2020ce2
numericalanswers
probabilityandstatistics
probability
0
votes
0
answers
32
GATE2020 CE224
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 ________.
asked
Feb 13, 2020
in
Calculus
by
jothee
(
5.2k
points)
gate2020ce2
numericalanswers
calculus
gradient
0
votes
0
answers
33
GATE2020 CE226
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}$
asked
Feb 13, 2020
in
Ordinary Differential Equation (ODE)
by
jothee
(
5.2k
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gate2020ce2
ordinarydifferentialequation
0
votes
0
answers
34
GATE2020 CE227
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 $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
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Feb 13, 2020
in
Linear Algebra
by
jothee
(
5.2k
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gate2020ce2
linearalgebra
matrices
eigenvalues
0
votes
0
answers
35
GATE2020 CE239
The Fourier series to represent $x x^2$ for $\pi\leq x\leq \pi$ is given by $ xx^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 ________.
asked
Feb 13, 2020
in
Partial Differential Equation (PDE)
by
jothee
(
5.2k
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gate2020ce2
numericalanswers
partialdifferentialequation
fourierseries
0
votes
0
answers
36
GATE2020 CE240
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 ________
asked
Feb 13, 2020
in
Numerical Methods
by
jothee
(
5.2k
points)
gate2020ce2
numericalanswers
numericalmethods
0
votes
0
answers
37
GATE2017 CE21
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 $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
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Aug 7, 2019
in
Linear Algebra
by
gatecse
(
4k
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gate2017ce2
linearalgebra
systemofequations
0
votes
0
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38
GATE2017 CE22
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 $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
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Aug 7, 2019
in
Calculus
by
gatecse
(
4k
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gate2017ce2
calculus
partialderivatives
0
votes
0
answers
39
GATE2017 CE219
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
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Aug 7, 2019
in
Calculus
by
gatecse
(
4k
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gate2017ce2
calculus
vectorcalculus
divergence
numericalanswers
0
votes
0
answers
40
GATE2017 CE220
A twofaced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be ________
asked
Aug 7, 2019
in
Probability and Statistics
by
gatecse
(
4k
points)
gate2017ce2
numericalanswers
probabilityandstatistics
probability
conditionalprobability
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