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NIELIT 2016 MAR Scientist C - Section B: 1
Choose the most appropriate option. The Newton-Raphson iteration $x_{n+1}=\dfrac{x_{n}}{2}+\dfrac{3}{2x_{n}}$ can be used to solve the equation $x^{2}=3$ $x^{3}=3$ $x^{2}=2$ $x^{3}=2$

Lakshman Patel RJIT asked in Numerical Methods Apr 2, 2020

by Lakshman Patel RJIT

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NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 7
The convergence of the bisection method is Cubic Quadratic Linear None

Lakshman Patel RJIT asked in Numerical Methods Apr 1, 2020

by Lakshman Patel RJIT

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NIELIT 2016 MAR Scientist B - Section B: 7
In which of the following methods proper choice of initial value is very important? Bisection method False position Newton-Raphson Bairsto method

Lakshman Patel RJIT asked in Numerical Methods Mar 31, 2020

by Lakshman Patel RJIT

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NIELIT 2017 DEC Scientist B - Section B: 3
Using bisection method, one root of $x^4-x-1$ lies between $1$ and $2$. After second iteration the root may lie in interval: $(1.25,1.5)$ $(1,1.25)$ $(1,1.5)$ None of the options.

Lakshman Patel RJIT asked in Numerical Methods Mar 30, 2020

by Lakshman Patel RJIT

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5

Which books are good to practice linear algebra and calculas?

aditi19 asked in GATE Oct 1, 2018

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6

Syllabus:Numerical methods like newton method or bisection method part of syllabus of Gate?
Numerical methods like newton method or bisection method part of syllabus of Gate?

bts1jimin asked in Mathematical Logic Sep 15, 2018

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7

#Numerical methods-syllabus
What is the syllabus for Engineering Mathematics - Numerical methods?

Swati Rauniyar asked in Mathematical Logic Oct 13, 2017

by Swati Rauniyar

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Virtual Gate Test Series: Numerical Ability - Percentage
A country’s GDP grew by $7.8%$ within a period. During the same period, the country’s per-capita-GDP (= ratio of GDP to the total population) increased by $10%.$ During this period, the total population of the country$?$ increased by $4\%$ decreased by $4\%$ increased by $2\%$ decreased by $2\%$

Purple asked in Quantitative Aptitude Jan 19, 2017

by Purple

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2 votes

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9

GATE CSE 1988 | Question: 1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.

go_editor asked in Numerical Methods Dec 10, 2016

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GATE CSE 1987 | Question: 11b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.

makhdoom ghaya asked in Numerical Methods Nov 15, 2016

by makhdoom ghaya

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11

GATE CSE 1987 | Question: 11a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula.

makhdoom ghaya asked in Numerical Methods Nov 15, 2016

by makhdoom ghaya

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12

GATE CSE 1987 | Question: 1-xxv
Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.

makhdoom ghaya asked in Numerical Methods Nov 9, 2016

by makhdoom ghaya

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GATE CSE 1987 | Question: 1-xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.

makhdoom ghaya asked in Numerical Methods Nov 9, 2016

by makhdoom ghaya

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3 votes

2 answers

14

ISRO2009-51
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n-1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula

go_editor asked in Numerical Methods Jun 15, 2016

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ISRO2009-47
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n-1} + y_n) - h/12 (\triangledown y_n - \triangle y_0)$ $- h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) -19h/720 (\triangledown ^3 y_n - \triangle ^3 y_0) \dots $ is called Simpson rule Trapezoidal rule Romberg's rule Gregory's formula

go_editor asked in Numerical Methods Jun 15, 2016

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8 votes

1 answer

16

ISRO2009-44
A root $\alpha$ of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_0$ is chosen for which $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$

Desert_Warrior asked in Numerical Methods Jun 3, 2016

by Desert_Warrior

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3 votes

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17

ISRO-2013-48
The Guass-Seidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and non-linear algebraic equations Linear differential equations Linear and non-linear differential equations

makhdoom ghaya asked in Numerical Methods Apr 29, 2016

by makhdoom ghaya

3.2k views

5 votes

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18

GATE2015 EC-1: GA-5
If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is $343/125$ $25/343$ $-25/49$ $-49/25$

Akash Kanase asked in Quantitative Aptitude Feb 12, 2016

by Akash Kanase

4.1k views

12 votes

3 answers

19

GATE CSE 2015 Set 3 | Question: 50
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.

go_editor asked in Numerical Methods Feb 16, 2015

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7 votes

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20

GATE CSE 2015 Set 2 | Question: 39
The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is ... $x_b - (x_b-x_a) f_b / (f_b-f(x_a)) $ $x_a - (x_b-x_a) f_a / (f_b-f(x_a)) $

go_editor asked in Numerical Methods Feb 13, 2015

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21

calculus
The estimate of $\int_{0.5}^{1.5}\frac{dx}{x}$ obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by (A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012

Nisha kumari asked in Numerical Methods Jan 30, 2015

by Nisha kumari

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2012 numerical methed

Nisha kumari asked in Numerical Methods Jan 29, 2015

by Nisha kumari

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1 vote

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23

GATE IT 2005 | Question: 2
If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained is always > (1/3) is always < (1/3) is always = (1/3) may be greater or lesser than (1/3)

Ishrat Jahan asked in Numerical Methods Nov 3, 2014

by Ishrat Jahan

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2 votes

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GATE IT 2004 | Question: 39
Consider the following iterative root finding methods and convergence properties: Iterative root finding methods Convergence properties Q. False Position I. Order of convergence = 1.62 R. Newton Raphson II. Order of convergence = 2 S. Secant III. Order of convergence = 1 with guarantee of convergence T. ... R-II, S-I, T-IV Q-II, R-I, S-IV, T-III Q-I, R-IV, S-II, T-III

Ishrat Jahan asked in Numerical Methods Nov 2, 2014

by Ishrat Jahan

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3 votes

1 answer

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GATE IT 2004 | Question: 38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9

Ishrat Jahan asked in Numerical Methods Nov 2, 2014

by Ishrat Jahan

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1 vote

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GATE IT 2006 | Question: 77
$x + y/2 = 9$ $3x + y = 10$ What can be said about the Gauss-Siedel iterative method for solving the above set of linear equations? it will converge It will diverse It will neither converge nor diverse It is not applicable

Ishrat Jahan asked in Linear Algebra Nov 1, 2014

by Ishrat Jahan

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27

GATE IT 2006 | Question: 76
x + y/2 = 9 3x + y = 10 The value of the Frobenius norm for the above system of equations is $0.5$ $0.75$ $1.5$ $2.0$

Ishrat Jahan asked in Linear Algebra Nov 1, 2014

by Ishrat Jahan

1.1k views

7 votes

3 answers

28

GATE IT 2006 | Question: 28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$

Ishrat Jahan asked in Numerical Methods Oct 31, 2014

by Ishrat Jahan

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GATE IT 2006 | Question: 27
Match the following iterative methods for solving algebraic equations and their orders of convergence. Method Order of Convergence 1. Bisection P. 2 or more 2. Newton-Raphson Q. 1.62 3. Secant R. 1 4. Regula falsi S. 1 bit per iteration I-R, II-S, III-P, IV-Q I-S, II-R, III-Q, IV-P I-S, II-Q, III-R, IV-P I-S, II-P, III-Q, IV-R

Ishrat Jahan asked in Numerical Methods Oct 31, 2014

by Ishrat Jahan

1.2k views

4 votes

1 answer

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GATE IT 2007 | Question: 77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$. For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv

Ishrat Jahan asked in Numerical Methods Oct 31, 2014

by Ishrat Jahan

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