GATE PH purpose:exam-prep PYQs & Answers — Page 50

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Questions 491–500 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 50 of 65

Consider the following Boolean expression:

It can be represented by a single three-input logic gate. Identify the gate.

Your answerChoose one option.

AND

XOR

NAND

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The value of the integral

, where

and

, is

Your answerChoose one option.

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The wave function

of a particle is as shown below

Here

is a constant, and

. The position uncertainty

of the particle is

Your answerChoose one option.

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A solid cylinder of radius

has total charge

distributed uniformly over its volume. It is rotating about its axis with angular speed

. The magnitude of the total magnetic moment of the cylinder is

Your answerChoose one option.

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Consider the motion of a particle along the

-axis in a potential

. Its ground state energy

is estimated using the uncertainty principle. Then

is proportional to

Your answerChoose one option.

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A 3-bit analog-to-digital converter is designed to digitize analog signals ranging from 0 V to 10 V. For this converter, the binary output corresponding to an input of 6 V is

Your answerChoose one option.

011

101

100

010

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The Hamiltonian operator for a two-level quantum system is

. If the state of the system at

is given by

then

at a later time

Your answerChoose one option.

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A particle of mass

moves in a lattice along the

-axis in a periodic potential

with periodicity

. The corresponding Brillouin zone extends from

with the two

-points being equivalent. If a weak force

in the

-direction is applied to the particle, it starts a periodic motion with time period

. Using the equation of motion

for a particle moving in a band, where

is the crystal momentum of the particle, the period

is found to be (

is Planck constant)

Your answerChoose one option.

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Consider a potential barrier

of the form:

where

is a constant. For particles of energy

incident on this barrier from the left, which of the following schematic diagrams best represents the probability density

as a function of

Your answerChoose one option.

Diagram for Physics question 34 (figure 2)

Diagram for Physics question 34 (figure 3)

Diagram for Physics question 34 (figure 4)

Diagram for Physics question 34 (figure 5)

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The spin-orbit interaction term of an electron moving in a central field is written as

, where

is the radial distance of the electron from the origin. If an electron moves inside a uniformly charged sphere, then

Your answerChoose one option.

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GATE PH purpose:exam-prep PYQs

Question 26

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Question 28

Question 29

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Question 31

Question 32

Question 33

Question 34

Question 35