GATE MA Numerical Analysis PYQs & Answers

Questions 1–10 of 41. Imported answers require independent review unless marked reviewed.

Consider the differential equation

with the initial condition

. Use the modified Euler’s method, the second approximation to

, where

(step size), is equal to ________. (rounded off to TWO decimal places)

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If Jacobi method is used to solve the following system of linear equations

with the initial guess

and

, denotes the

iterate, then the value of

is equal to ________. (answer in integer)

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To find a real root of the equation

in the interval

by using the fixed-point iteration scheme, consider the following two statements:

S1: The iteration scheme

, converges for any initial guess

S2: The iteration scheme

, diverges for some initial guess

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

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Let

be such that the quadrature formula

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

is equal to _____ (in integer)

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Let

be the solution of the initial value problem

. Using Euler’s method, with the step-size

, the approximate value of

is equal to _____ (in integer)

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Let

and

be a

real column vector. Consider the statements.

I. The Jacobi iteration method for the system

converges for any initial approximation and

II. The Gauss–Seidel iteration method for the system

converges for any initial approximation and

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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For the initial value problem

generate approximations

, for a fixed

and

, using the recursion formula

Which one of the following choices of

for the above recursion formula gives the Runge–Kutta method of order 2?

Your answerChoose one option.

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Let

and

be a positive real number. For any twice-differentiable function

, let

be the interpolating polynomial of degree at most two that interpolates

at the points

. Define

to be the largest integer such that any polynomial

of degree

satisfies

The value of

is equal to ______ (answer in integer)

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Let

be the interpolating polynomial of degree at most two that interpolates the function

at the points

. Then

(round off to TWO decimal places)

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Let

. Which one of the following numerical integration rules gives the exact value of the integral

Your answerChoose one option.

The Simpson’s rule

The trapezoid rule

The composite Simpson’s rule by dividing

into 4 equal subintervals

The composite trapezoid rule by dividing

into 3 equal subintervals

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GATE MA Numerical Analysis PYQs

How to practice Numerical Analysis

Question 30

Question 65

Question 13

Question 34

Question 35

Question 21

Question 22

Question 32

Question 33

Question 43