GATE XE 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 11. Imported answers require independent review unless marked reviewed.

Topic practice 11 questionsPage 1 of 2

The initial value problem

with

, is solved by using the explicit Euler method with step size

. Then, the value of

(rounded off up to two decimal places) is ________.

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Suppose the polynomial

interpolates the data

and

. Then which one of the following statements is correct?

Your answerChoose one option.

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The approximate value (rounded off to two decimal places) of the integral

using the Trapezoid rule with step-size

, is _____

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If the quadrature formula

is exact for all polynomials of degree less than or equal to 2, then

Your answerChoose one option.

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If the polynomial

interpolates the points

, and

, then the value of

is __________ (round off to 2 decimal places).

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If the quadrature rule

where

and

are real constants, is exact for all polynomials of degree

, then

is equal to ______.

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If the numerical approximation of the value of the integral

using the Trapezoidal rule with two subintervals is 9, then the value of the real constant

is ______ (round off to one decimal place).

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Let

be the sequence generated by the Newton-Raphson method applied to the function

with

. Then the sequence

Your answerChoose one option.

converges to 0.

becomes unbounded.

converges to a root of

does not converge.

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is the polynomial obtained by Lagrange interpolation satisfying

and

, then the value of

Your answerChoose one option.

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For real numbers

and

, if the formula

is exact for all polynomials of degree

then

equals ______________

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GATE XE Numerical Methods PYQs

How to practice Numerical Methods

Question 21

Question 14

Question 17

Question 13

Question 16

Question 21

Question 5

Question 2

Question 9

Question 4