GATE PH topic:mathematical-physics PYQs & Answers — Page 3

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topic:mathematical-physics

Questions 21–30 of 46. Imported answers require independent review unless marked reviewed.

Topic practice 46 questionsPage 3 of 5

and

are two Hermitian matrices and there exists a matrix

, which diagonalizes both of them, such that

and

, where

and

are diagonal matrices. The correct statement(s) is(are)

Your answerSelect all correct options. You can choose more than one.

All the elements of both matrices

and

are real.

The matrix

can have complex eigenvalues.

The matrix

can have complex eigenvalues.

The matrices

and

commute.

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A contour integral is defined as

where

is a positive integer and

is the closed contour, as shown in the figure, consisting of the line from −100 to 100 and the semicircle traversed in the counter-clockwise sense.

The value of

(in integer) is _____.

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Which one of the following is a solution of

, for

real?

Your answerChoose one option.

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A real, invertible

matrix

has eigenvalues

and the corresponding eigenvectors are

respectively. Which one of the following is correct?

Your answerChoose one option.

, for

The eigenvalues of

and

are not related.

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For a complex variable

and the contour

taken in the counter clockwise direction,

_____.

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The product of eigenvalues of

Your answerChoose one option.

-1

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Let

and

. Let

denote the three-dimensional real vector space. Which one of the following is correct?

Your answerChoose one option.

is an orthonormal set

is a linearly dependent set

is a basis for

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Let

denote the 4-velocity of a relativistic particle whose square

. If

is the Levi-Civita tensor then the value of

is _____.

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, for

, the value of

is _____.

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Let

The value of

is _____.

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GATE PH topic:mathematical-physics PYQs

Question 43

Question 50

Question 1

Question 2

Question 22

Question 26

Question 27

Question 43

Question 48

Question 49