GATE ME Numerical Methods PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 15. Imported answers require independent review unless marked reviewed.

Topic practice 15 questionsPage 1 of 2

Newton-Raphson method for solving algebraic equations is based on

Your answerChoose one option.

Taylor series

Fourier series

Laurent series

Power series

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The exact solution of

is represented as

. If

represents numerically evaluated value of the above integral using Trapezoidal rule by considering four equal subintervals in the range of

, then

Your answerChoose one option.

0.074

− 0.074

− 0.003

0.003

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The values of a function

obtained for different values of x are shown in the table below.

x	0	0.25	0.5	0.75	1.0
	0.9	2.0	1.5	1.8	0.4

Using Simpson’s one-third rule,

(rounded off to 2 decimal places).

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In order to numerically solve the ordinary differential equation

for

, with an initial condition

, the following scheme is employed

Here,

is the time step and

for

This numerical scheme will yield a solution with non-physical oscillations for

. The value of

Your answerChoose one option.

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The initial value problem

is solved numerically using the forward Euler’s method with a constant and positive time step of

Let

represent the numerical solution obtained after

steps. The condition

is satisfied if and only if

does not exceed ____________.

(Answer in integer)

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Consider the definite integral

Let

be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is

. The percentage error is defined as

. The value of

Your answerChoose one option.

2.5

3.5

1.2

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The ordinary differential equation

subject to an initial condition

is solved numerically using the following scheme:

where

is the time step,

, and

. This numerical scheme is stable for all values of

in the interval ________.

Your answerChoose one option.

for all

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Value of

using Simpson’s one-third rule with interval size 0.3 is

Your answerChoose one option.

1.83

1.60

1.51

1.06

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Find the positive real root of

using Newton-Raphson method. If the starting guess (

) is 2, the numerical value of the root after two iterations (

) is ______ (round off to two decimal places).

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The evaluation of the definite integral

by using Simpson’s 1/3rd (one-third) rule with step size

yields

Your answerChoose one option.

0.914

1.248

0.581

0.592

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GATE ME Numerical Methods PYQs

How to practice Numerical Methods

Question 14

Question 15

Question 31

Question 11

Question 50

Question 13

Question 4

Question 18

Question 35

Question 26