GATE PH branch:ph PYQs & Answers — Page 26

Questions 251–260 of 650. Imported answers require independent review unless marked reviewed.

Consider the complex function

, which of the following options is(are) CORRECT?

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

The order of the pole is 4

The order of the pole is 3

The residue at the pole is

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Consider the vector field

consisting of the velocities of points on a thin horizontal disc of radius

, moving anticlockwise with uniform angular speed

about an axis passing through its center. If

, then which of the following options is(are) CORRECT? (In the options,

and

are unit vectors corresponding to the plane polar coordinates

and

You may use the fact that in cylindrical coordinates

(

is the distance from the

-axis), the gradient, divergence, curl and Laplacian operators are:

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

, where

is a unit vector perpendicular to the

plane

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A slow moving

particle is captured by a deuteron

and this reaction produces two neutrons

in the final state, i.e.,

. Neutron and deuteron have even intrinsic parities, whereas

has odd intrinsic parity.

and

are the orbital and spin angular momenta, respectively, of the system of two neutrons. Which of the following statements regarding the final two-neutron state is(are) CORRECT?

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

It has odd parity

is odd

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Two independent electrostatic configurations are shown in the figure. Configuration

consists of an isolated point charge

, and configuration

consists of another identical charge surrounded by a thick conducting shell of inner radius

and outer radius

, with the charge at the center of the shell.

and

, where

and

are the magnitudes of the electric fields for configurations

and

respectively,

is the permittivity of vacuum, and the volume integrations are carried out over all space. If

, what is the value of the integer

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In pion nucleon scattering, the pion and nucleon can combine to form a short lived bound state called the

particle

. The masses of the pion, nucleon and the

particle are 140 MeV/

, 938 MeV/

and 1230 MeV/

, respectively. In the lab frame, where the nucleon is at rest, what is the minimum energy (in MeV/

, rounded off to one decimal place) of the pion to produce the

particle?

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Consider an electromagnetic wave propagating in the

-direction in vacuum, with the magnetic field given by

. If

, the average power passing through a circle of radius 1.0 m placed in the

plane is

(in Watts). Using

, what is the value of

(rounded off to one decimal place)?

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-particle is emitted from the decay of Americium (Am) at rest, i.e.,

. The rest masses of

and

are 224.544 GeV/

, 220.811 GeV/

and 3.728 GeV/

respectively. What is the kinetic energy (in MeV/

, rounded off to two decimal places) of the

-particle?

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Consider 6 identical, non-interacting, spin

atoms arranged on a crystal lattice at absolute temperature

. The

-component of the magnetic moment of each of these atoms can be

. If

and

are the probabilities of the net magnetic moment of the solid being

and

respectively, what is the value of

(in integer)?

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Two identical, non-interacting

atoms are distributed among 4 different non-degenerate energy levels. The probability that they occupy different energy levels is

. Similarly, two

atoms are distributed among 4 different non-degenerate energy levels, and the probability that they occupy different levels is

. What is the value of

(rounded off to one decimal place)?

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Two identical bodies kept at temperatures 800 K and 200 K act as the hot and the cold reservoirs of an ideal heat engine, respectively. Assume that their heat capacity (

) in Joules/K is independent of temperature and that they do not undergo any phase change. Then, the maximum work that can be obtained from the heat engine is

Joules. What is the value of

(in integer)?

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GATE PH branch:ph PYQs

Question 56

Question 57

Question 58

Question 59

Question 60

Question 61

Question 62

Question 63

Question 64

Question 65