GATE MA Numerical Analysis PYQs & Answers — Page 4

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Questions 31–40 of 41. Imported answers require independent review unless marked reviewed.

Topic practice 41 questionsPage 4 of 5

Let

(the set of all real numbers) be any function which is twice differentiable in

with only one root

. Let

and

denote the first and second order derivatives of

with respect to

. If

is a simple root and is computed by the Newton-Raphson method, then the method converges if

Your answerChoose one option.

, for all

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If the differential equation

is solved using the Euler’s method with step-size

, then

is equal to ____ (round off to 2 places of decimal).

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The maximum value of the error term of the composite Trapezoidal rule when it is used to evaluate the definite integral

with 12 sub-intervals of equal length, is equal to ______ (round off to 3 places of decimal).

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Let

be a twice continuously differentiable function. The order of convergence of the secant method for finding root of the equation

Your answerChoose one option.

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Let

be such that the quadrature rule

is exact for all polynomials of degree less than or equal to 3. Then

________.

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Consider the following two statements:

P: The matrix

has infinitely many LU factorizations, where

is lower triangular with each diagonal entry 1 and

is upper triangular.

Q: The matrix

has no LU factorization, where

is lower triangular with each diagonal entry 1 and

is upper triangular.

Then which one of the following options is correct?

Your answerChoose one option.

P is TRUE and Q is FALSE

Both P and Q are TRUE

P is FALSE and Q is TRUE

Both P and Q are FALSE

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interpolates the points

in the table

then

_________.

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If the fourth order divided difference of

, at the points 0.1, 0.2, 0.3, 0.4, 0.5 is 5, then

equals ______.

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If the quadrature rule

, where

, is exact for all polynomials of degree

, then

equals ______.

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Let

be the polynomial of degree at most 2 that interpolates the data

and

. If

is a polynomial of degree at most 3 such that

interpolates the data

and

, then

equals ________.

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GATE MA Numerical Analysis PYQs

Question 2

Question 15

Question 51

Question 9

Question 22

Question 32

Question 49

Question 15

Question 16

Question 41