1

GATE ME 2024

MCQ (Single Correct Answer)

+1

-0.33

In order to numerically solve the ordinary differential equation *dy/dt = -y* for *t > 0*, with an initial condition *y(0) = 1*, the following scheme is employed:

$\frac{y_{n+1} - y_{n}}{\Delta t} = -\frac{1}{2}(y_{n+1} + y_{n}).$

Here, $\Delta t$ is the time step and $y_n = y(n\Delta t)$ for $n = 0, 1, 2, \ldots.$ This numerical scheme will yield a solution with non-physical oscillations for $\Delta t > h.$ The value of *h* is

2

GATE ME 2016 Set 3

MCQ (Single Correct Answer)

+1

-0.3

The root of the function $$f\left( x \right) = {x^3} + x - 1$$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $${x_0} = 1$$ is

3

GATE ME 2016 Set 2

MCQ (Single Correct Answer)

+1

-0.3

Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

4

GATE ME 2014 Set 3

Numerical

+1

-0

The real root of the equation $$5x-2cosx=0$$ (up to two decimal accuracy) is

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Questions Asked from Numerical Methods (Marks 1)

Number in Brackets after Paper Indicates No. of Questions

GATE ME Subjects

Engineering Mechanics

Machine Design

Strength of Materials

Heat Transfer

Production Engineering

Industrial Engineering

Turbo Machinery

Theory of Machines

Engineering Mathematics

Fluid Mechanics

Thermodynamics

General Aptitude