GATE PH format:msq PYQs & Answers

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Questions 1–10 of 88. Imported answers require independent review unless marked reviewed.

Topic practice 88 questionsPage 1 of 9

Given

is the electromagnetic charge and

is the strangeness quantum number, identify the particle(s) for which

is satisfied.

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Schematic variation of the specific heat

of an ideal gas of diatomic molecules with temperature

is shown in the figure below. For rotational energy

and vibrational energy

of the molecule, which of the following options is/are correct? Here

is the Boltzmann constant.

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If the perturbation

is added to the Hamiltonian of a one-dimensional harmonic oscillator, the matrix element

is/are non-zero for which of the following states? Here, the eigenstates of the harmonic oscillator are denoted by

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For which of the following functions does the Laplacian vanish?

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Which of the following operators is/are self-adjoint?

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Consider two operators

and

which are related as

. If

is a non-zero real number, which of the following statements is/are true?

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is Hermitian, then

is unitary.

is anti-Hermitian, then

is unitary.

is Hermitian, then

is anti-Hermitian, then

is Hermitian.

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Consider operators

, and

for three observables of a quantum system satisfying

, and

, with uncertainties

, respectively. From the options given below, which is/are implied by the commutation relations among

, and

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can be simultaneously diagonalized.

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Consider the distribution of outcomes generated by

(

) independent throws of (i) a coin or (ii) a six-sided dice. A coin (dice) is unbiased if (all) its sides have equal probability to show up in a throw; it is biased otherwise. For the cases (i) and (ii) above, which of the following statements is/are true?

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The entropy of an unbiased coin is smaller than that of an unbiased dice.

The entropy of an unbiased coin is greater than that of an unbiased dice.

The entropy of a biased dice is smaller than that of an unbiased dice.

The entropy of a biased coin is greater than that of an unbiased coin.

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The dispersion (

) of the conduction band (CB) and valence band (VB) for a semiconductor are shown schematically in the figure. Considering the possibility of an electron making a transition from the bottom of the CB to the top of the VB, which of the following options is/are correct?

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The transition is forbidden.

A photon can be emitted with an energy exactly equal to

A photon can be emitted with an energy less than

A phonon can be created with crystal momentum

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A symmetric rigid body has moment of inertia

about its principal axes 1, 2, and 3, respectively, with

and

. It is rotating in space with no torque on it so that its angular momentum

is constant. Let

be the components of its angular velocity along the principal axes 1, 2, and 3, respectively. Which of the following quantities is/are constant during the motion of this rigid body?

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Angle between axis 2 and

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GATE PH format:msq PYQs

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