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Recent questions and answers in Numerical Methods
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1
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 ________________
go_editor
asked
in
Numerical Methods
Mar 1, 2021
by
go_editor
5.3k
points
gatecivil-2021-set2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
2
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 $1.718$ $1.727$ $2.192$ $2.718$
Arjun
asked
in
Numerical Methods
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
3
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 __________________
Arjun
asked
in
Numerical Methods
Feb 20, 2021
by
Arjun
11.6k
points
gatecivil-2021-set1
numerical-answers
numerical-methods
simpsons-rule
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
4
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 $35$ $48$ $69$ $84$
go_editor
asked
in
Numerical Methods
Feb 28, 2020
by
go_editor
5.3k
points
gate2020-ce-1
numerical-methods
linear-interpolation
0
votes
0
answers
5
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.
go_editor
asked
in
Numerical Methods
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
6
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 ________
go_editor
asked
in
Numerical Methods
Feb 13, 2020
by
go_editor
5.3k
points
gate2020-ce-2
numerical-answers
numerical-methods
0
votes
2
answers
7
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 ________
moinkhan
answered
in
Numerical Methods
Feb 20, 2019
by
moinkhan
140
points
gate2019-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
0
votes
0
answers
8
GATE2019 CE-2: 18
The value of the function $f(x)$ is given at $n$ distinct values of $x$ and its value is to be interpolated at the point $x^*$, using all the $n$ points. The estimate is obtained first by the Lagrange polynomial, denoted by $I_L$, and then by the ... than $I_N$ $I_L$ and $I_N$ are always equal $I_L$ is always less than $I_N$ Not definite relation exists between $I_L$ and $I_N$
Arjun
asked
in
Numerical Methods
Feb 12, 2019
by
Arjun
11.6k
points
gate2019-ce-2
numerical-methods
newtons-polynomial
0
votes
0
answers
9
GATE2016-2-30
The quadratic approximation of $f(x)=x^3 – 3x^2 -5$ at the point $x=0$ is $3x^2 -6x-5$ $-3x^2-5$ $-3x^2+6x-5$ $3x^2-5$
Milicevic3306
asked
in
Numerical Methods
Mar 28, 2018
by
Milicevic3306
11.9k
points
gate2016-ce-2
numerical-methods
quadratic-approximation
0
votes
0
answers
10
GATE2016-1-1
Newton-Raphson method is to be used to find root of equation $3x-e^x+ \sin x=0$.If the initial trial value for the root is taken as $0.333$, the next approximation for the root would be _______ (note: answer up to three decimal)
Milicevic3306
asked
in
Numerical Methods
Mar 28, 2018
by
Milicevic3306
11.9k
points
gate2016-ce-1
numerical-answers
numerical-methods
newton-raphson-method
0
votes
0
answers
11
GATE2015-2-2
In newton-Raphson iterative method, the initial guess value $(x_{\text{ini}})$ is considered as zero while finding the roots of the equation: $f(x) = -2+6x-4x^2+0.5x^3$. The correction, $\Delta x$, to be added to $x_{\text{ini}}$ in the first iteration is _________
Milicevic3306
asked
in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-2
numerical-answers
numerical-methods
newton-raphson-method
0
votes
0
answers
12
GATE2015-2-29
For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______. $\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) dx$
Milicevic3306
asked
in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
13
GATE2015-1-2
The integral $\int_{x_{1}}^{x_{2}}x^{2}\:dx$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and ... , which of the following statement is correct about their relationship? $J>I$ $J<I$ $J=I$ Insufficient data to determine the relationship
Milicevic3306
asked
in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
14
GATE2015-1-27
The quadratic equation $x^2 – 4x +4 =0$ is to be solved numerically, starting with the initial guess $x_0=3$. The Newton-Raphson method is applied once to get a new estimate and then the Secant method is applied once using the initial guess and this new estimate. The estimated value of the root after the application of the Secant method is _________.
Milicevic3306
asked
in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2015-ce-1
numerical-answers
numerical-methods
newton-raphson-method
0
votes
0
answers
15
GATE2014-1-5
With reference to the conventional Cartesian $(x,y)$ coordinate system, the vertices of a triangle have the following coordinates: $(x_1, y_1) = (1,0)$; $(x_2,y_2) = (2,2)$; and $(x_3,y_3)=(4,3)$. The area of the triangle is equal to $\dfrac{3}{2} \\$ $\dfrac{3}{4} \\$ $\dfrac{4}{5} \\$ $\dfrac{5}{2}$
Milicevic3306
asked
in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2014-ce-1
numerical-answers
numerical-ability
triangle
cartesian-coordinate-system
0
votes
0
answers
16
GATE Civil 2013 | Question: 27
Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$ _________ $\int_0^4 (x^4+10) dx$
Milicevic3306
asked
in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2013-ce
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
0
answers
17
GATE Civil 2013 | Question: 1
There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of $x$ that minimizes the sum of squares of the errors in the two equations. _____ $2x=3$ $4x=1$
Milicevic3306
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in
Numerical Methods
Mar 26, 2018
by
Milicevic3306
11.9k
points
gate2013-ce
numerical-answers
numerical-methods
0
votes
0
answers
18
GATE Civil 2012 | Question: 26
The error in $\dfrac{d}{dx} f(x) \mid_{x=x_0}$ for a continuous function estimated with $h=0.03$ using the central difference formula $\dfrac{d}{dx} f(x) \mid_{x=x_0} \approx \dfrac{f(x_0+h)-f(x_0-h)}{2h}$, is $2 \times 10^{-3}$. The values of $x_0$ ... $1.3 \times 10^{-4}$ $3.0 \times 10^{-4}$ $4.5 \times 10^{-4}$ $9.0 \times 10^{-4}$
Milicevic3306
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Numerical Methods
Mar 25, 2018
by
Milicevic3306
11.9k
points
gate2012-ce
numerical-methods
0
votes
0
answers
19
GATE Civil 2012 | Question: 1
The estimate of $\int_{0.5}^{1.5} \dfrac{dx}{x}$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by $0.235$ $0.068$ $0.024$ $0.012$
Milicevic3306
asked
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Numerical Methods
Mar 25, 2018
by
Milicevic3306
11.9k
points
gate2012-ce
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
0
votes
1
answer
20
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 _________
Pushpendra Tiwari
answered
in
Numerical Methods
Feb 17, 2018
by
Pushpendra Tiwari
gate2018-ce-2
numerical-methods
newton-raphson-method
numerical-answers
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