GATE MA 2024 Paper 1 — page 15

Questions 43–45 of 65. Imported answers require review unless explicitly marked reviewed.

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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Consider the initial value problem (IVP)

I. IVP has a unique solution on

II. Every solution of IVP is bounded on its maximal interval of existence.

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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Let

be a

non-diagonalizable real matrix with a real eigenvalue

and

be an eigenvector of

corresponding to

. Which one of the following is the general solution of the system

of first-order linear differential equations?

Your answerChoose one option.

, where

and

is a

real column vector such that

, where

and

is a

real column vector such that

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2024 · Paper 1