Recent questions in Numerical Methods

#1
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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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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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Use Bisection method to find all roots of $x^3 – 5x + 3 = 0$
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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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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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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$
#7
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The convergence of the bisection method isCubicQuadraticLinearNone
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The convergence of the bisection method isCubicQuadraticLinearNone
#9
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In which of the following methods proper choice of initial value is very important?Bisection methodFalse positionNewton-RaphsonBairsto method
#10
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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.
#11
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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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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}$x_1 = 0, x_2=0, \: x_3=10, \: Z=20$
#13
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Does in iiith pgeee exam , does Reading comprehension is being asked. Do we need to prepare for it?
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In PERT/CPM, the merge event represents _____ of two or more events.completionbeginningsplittingjoining
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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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Using Newton-Raphson method, a root correct to 3 decimal places of $x^3 - 3x -5 = 0$2.2222.2752.279None of the above
#17
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Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
#18
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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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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.
#20
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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.