Numerical Methods MCQs Question and Answer in Engineering Maths

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2.
Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson's rule is
Angle (degree) 0   60 120 180 240 300 360
Torque (Nm) 0 1066 -323   0 323 -355   0

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4.
In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 ... is obtained for the function 0.75x3 - 2x2 - 2x + 4 = 0
Consider the statements
I. x3 = 0.
II. The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?

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5.
While numerically solving the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{x}}{{\text{y}}^2} = 0,\,{\text{y}}\left( 0 \right) = 1$$     using Euler's predictor-corrector (improved Euler-Cauchy) with a step size of 0.2, the value of y after the first step is

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6.
The Newton-Raphson iteration $${{\text{x}}_{{\text{n}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{n}}} + \frac{{\text{R}}}{{{{\text{x}}_{\text{n}}}}}} \right)$$    can be used to compute the

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7.
When the Newton-Raphson method is applied to solve the equation f(x) = x3 + 2x - 1 = 0, the solution at the end of the first iteration with the initial guess value as x0 = 1.2 is

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8.
The matrix \[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}} 2&1 \\ 4&{ - 1} \end{array}} \right]\]   is decomposed into a product of a lower triangular matrix x[L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

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9.
Consider a differential equation $$\frac{{{\text{dy}}\left( {\text{x}} \right)}}{{{\text{dx}}}} - {\text{y}}\left( {\text{x}} \right) = {\text{x}}$$    with the initial condition y(0) = 0. Using Euler's first order method with a step size of 0.1, the value of y(0.3) is

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10.
Consider an ordinary differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} = 4{\text{t}} + 4.$$   If x = x0 at t = 0, the increment in x calculated using Runge-Kutta fourth order multistep method with a step size of Δt = 0.2 is

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