GATE PH purpose:exam-prep PYQs & Answers — Page 6

Questions 51–60 of 650. Imported answers require independent review unless marked reviewed.

Consider two operators

and

which are related as

. If

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

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

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

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

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?

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

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?

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

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?

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

Angle between axis 2 and

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particle moves towards a fixed nucleus carrying charge

, with initial speed

and impact parameter

. Starting from a large distance from the nucleus, its distance of closest approach is

and its speed there is

. Then which of the following options is/are correct? (

and

)

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

For

ignoring higher order corrections in

For

ignoring higher order corrections in

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Consider a particle of mass

kg and charge

C in a uniform electromagnetic field

. The particle is released from the coordinates

at time

. Starting from initial speed zero, it comes back to the

-axis for the first time at time

. The value of

in seconds (rounded off to two decimal places) is ____

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An atom has two energy levels with energy difference 2.2 eV between them. A gas of these atoms is with

atoms in the upper state and

atoms in the lower state. Ignoring spontaneous emission, the maximum possible energy released by gas of atoms by stimulated emission is

Joules. The value of

(rounded off to one decimal place) is ____ (

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The Hamiltonian of two interacting spin-1/2 particles is

, where

and

are the spin angular momenta of particles 1 and 2, respectively. Here,

eV. The energy in eV required to induce an excitation from the ground state to the excited state (rounded off to two decimal places) is ____

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The output signal (current

) of a reverse biased (with a voltage

) photodiode, on which light is incident, is fed to an amplifier (see figure). The output voltage is digitized by a 10 bit Analog to Digital converter (ADC) which has a reference voltage of 5 V. The smallest current

which can be measured by the circuit in nano-Amperes (rounded off to one decimal place) is _____.

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GATE PH purpose:exam-prep PYQs

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60