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Recent questions and answers in Numerical Methods

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Numerical Method Analysis : Help...
Use Secant method to find roots of:$x^3-2x^2+3x-5=0$x+1 = 4sinx$e^x = x + 2$
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Numerical Method Analysis : Help....
Use NR method to find a root of the equation with tolerance x=0.00001.$x^3-2x-5=0$e^x-3x^2=0$
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Numerical Method Analysis : Help...
Use Bisection method to find all roots of $x^3 – 5x + 3 = 0$
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Numerical Method Analysis : Help...
Use Bisection method to find the root of the following equation with tolerance 0.001.$x^4 - 2x^3 - 4x^2 + 4x + 4 = 0$x^3 – e^x + sin(x) = 0$
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NIELIT 2021 Dec Scientist B - Section B: 60
One root of $x^{3} – x – 4 = 0$ lies in $(1, 2).$ In bisection method, after first iteration the root lies in the interval ___________ .$(1, 1.5)$(1.5, 2)$(1.25, 1.75)$(1.75, 2)$
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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.
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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 methodFalse positionNewton-RaphsonBairsto method
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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}$\pi$
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GATE CSE 2008 | Question: 21
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is1000e1000100e100
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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.
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UGC NET CSE | June 2019 | Part 2 | Question: 10
Consider an LPP given as$\text{Max } Z=2x_1-x_2+2x_3$subject to the constraints$2x_1+x_2 \leq 10 \\ x_1+2x_2-2x_3 \leq 20 \\ x_1 + 2x_3 \leq 5 \\ x_1, \: x_2 \: x_3 \geq 0 $ ... x_3=0, \: Z=-\frac{5}{2}$x_1 = 0, x_2=0, \: x_3=10, \: Z=20$
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UGC NET CSE | December 2018 | Part 2 | Question: 8
In PERT/CPM, the merge event represents _____ of two or more events.completionbeginningsplittingjoining
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NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 7
The convergence of the bisection method isCubicQuadraticLinearNone
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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$
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NIELIT 2017 OCT Scientific Assistant A (IT) - Section B: 17
The convergence of the bisection method isCubicQuadraticLinearNone
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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.
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NIELIT 2017 DEC Scientist B - Section B: 20
Let $u$ and $v$ be two vectors in $R^2$ whose Eucledian norms satisfy $\mid u\mid=2\mid v \mid$. What is the value $\alpha$ such that $w=u+\alpha v$ bisects the angle between $u$ and $v$?$2$1$\dfrac{1}{2}$-2$
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Is reading comprehension asked in IIITH
Does in iiith pgeee exam , does Reading comprehension is being asked. Do we need to prepare for it?
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ISRO2009-48
The cubic polynomial $y(x)$ which takes the following values: $y(0)=1, y(1)=0, y(2)=1$ and $y(3)=10$ is$x^3 +2x^2 +1$x^3 +3x^2 -1$x^3 +1$x^3 -2x^2 +1$
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GATE CSE 1994 | Question: 3.4
Match the following items(i) Newton-Raphson(a) Integration(ii) Runge-Kutta(b) Root finding(iii) Gauss-Seidel(c) Ordinary Differential Equations(iv) Simpson's Rule(d) Solution of Systems of Linear Equations
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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$
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Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the ... warder turns the key in just the last cell. Which doors are left unlocked and why?
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ISRO2017-3
Using Newton-Raphson method, a root correct to 3 decimal places of $x^3 - 3x -5 = 0$2.2222.2752.279None of the above
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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.
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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.
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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 ... a root where the second differential coefficient vanishes.None of the above.
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UGC NET CSE | December 2014 | Part 3 | Question: 69
Five men are available to do five different jobs. From past records, the time (in hours) that each man takes to do each job is known and is given in the ... $11$13$15$
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ISRO-2013-48
The Guass-Seidal iterative method can be used to solve which of the following sets?Linear algebraic equationsLinear and non-linear algebraic equationsLinear differential equationsLinear and non-linear differential equations
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ISRO2009-51
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n-1)}{n!} \triangledown ^n y_0$ isNewton's backward formulaGauss forward formulaGauss backward formulaStirling's formula
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ISRO2011-52
GivenX:01016Y:61628The interpolated value X=4 using piecewise linear interpolation is1142210
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ISRO2009-47
The formula ... is calledSimpson ruleTrapezoidal ruleRomberg's ruleGregory's formula
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ISRO2009-46
The shift operator $E$ is defined as $E [f(x_i)] = f (x_i+h)$ and $E'[f(x_i)]=f (x_i -h)$ then $\triangle$ (forward difference) in terms of $E$ is$E-1$E$1-E^{-1}$1-E$
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GATE CSE 2000 | Question: 2.1
X, Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half a unit. The overlap of Y and Z is also half a unit. Let ... true?k must be 1k must be 0k can take any value between 0 and 1None of the above
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GATE CSE 2006 | Question: 1, ISRO2009-57
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is:3469
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GATE CSE 1999 | Question: 1.23
The Newton-Raphson method is to be used to find the root of the equation $f(x)=0$ where $x_o$ is the initial approximation and $f'$ is the derivative ... convergesalwaysonly if $f$ is a polynomialonly if $f(x_o) <0$none of the above
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GATE CSE 1997 | Question: 4.10
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f&rsquo;&rsquo;(x), x \in [a, b]$ where $h$ ... $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is6010060010000
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GATE CSE 1997 | Question: 1.2
The Newton-Raphson method is used to find the root of the equation $X^2-2=0$. If the iterations are started from -1, the iterations willconverge to -1converge to $\sqrt{2}$converge to $\sqrt{-2}$not converge
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GATE CSE 1996 | Question: 2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is$x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$
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GATE CSE 1995 | Question: 2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is$x_{k+1} = 3(x_k+b)/2x_k$x_{k+1} = (x_{k}^2+b)/2x_k$x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$None of the above
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GATE CSE 1993 | Question: 01.3
Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$2$3$4$
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