GATE PH format:mcq PYQs & Answers — Page 3

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Questions 21–30 of 380. Imported answers require independent review unless marked reviewed.

Topic practice 380 questionsPage 3 of 38

Given

and

, the tensor product

Your answerChoose one option.

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Sketch of a two-dimensional vector field

is shown below. Here, length and arrow head of the arrows denote magnitude and direction of the vector field, respectively. Which of the following statements is correct for

Your answerChoose one option.

It is zero everywhere in the two-dimensional space.

Its magnitude is non-zero and its direction is out of the two-dimensional plane.

Its magnitude is non-zero and its direction is into the two-dimensional plane.

It points in opposite directions above and below the x-axis.

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Which one of the following is an allowed process?

Your answerChoose one option.

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The function

of complex variable

given below,

has singular points at

Your answerChoose one option.

1 and

and

1 and

only

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Consider the Pauli matrices

. The value of

Your answerChoose one option.

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Which one of the following statements is true?

Your answerChoose one option.

In the decay

, CPT is violated.

The decay

is allowed and strangeness is violated.

The decay

is allowed.

The decay

is allowed.

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The Hamiltonian for a quantum particle of mass

is given below, where

. The Schrödinger equation for this system can be solved exactly using the orthogonal transformations:

and

The ground state energy of this system is

Your answerChoose one option.

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Consider two particles with angular momenta

and

. If the expression

gives an eigenstate of the total angular momentum of the two particles, using standard notation. Which of the following is true?

(Hint:

)

Your answerChoose one option.

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The energy

and degeneracy

of the second excited state of a three-dimensional, isotropic quantum harmonic oscillator with angular frequency

are

Your answerChoose one option.

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Two identical particles with a fixed total energy

are in thermal equilibrium in a one-dimensional harmonic oscillator potential

. Let the entropy of the particles be denoted by

if they are fermions with spin

and

if they are bosons with spin 0. Then, which of the following options is correct? (

is the Boltzmann constant)

Your answerChoose one option.

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GATE PH format:mcq PYQs

Question 21

Question 22

Question 23

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42