GATE PH year:2019 PYQs & Answers — Page 7

Questions 61–65 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 7 of 7

Consider two systems A and B each having two distinguishable particles. In both the systems, each particle can exist in states with energies 0, 1, 2 and 3 units with equal probability. The total energy of the combined system is 5 units. Assuming that the system A has energy 3 units and the system B has energy 2 units, the entropy of the combined system is

. The value of

is ______

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Electrons with spin in the

-direction (

) are passed through a Stern-Gerlach (SG) set up with the magnetic field at

from

. The fraction of electrons that will emerge with their spin parallel to the magnetic field in the SG set up (rounded off to two decimal places) is ______

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The Hamiltonian of a system is

with

. The fourth order contribution to the ground state energy of

. The value of

(rounded off to three decimal places) is ______

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Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth’s frame. The time difference between the two events as seen by an observer in a spaceship moving with velocity

in the earth’s frame along the line joining the earth to the Sun is

, where

is the speed of light. Given that light travels from the Sun to the earth in 8.3 minutes in the earth’s frame, the value of

in minutes (rounded off to two decimal places) is ______

(Take the earth’s frame to be inertial and neglect the relative motion between the earth and the sun)

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In a certain two-dimensional lattice, the energy dispersion of the electrons is

where

denotes the wave vector,

is the lattice constant and

is a constant in units of eV. In this lattice the effective mass tensor

of electrons calculated at the center of the Brillouin zone has the form

. The value of

(rounded off to three decimal places) is ______

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GATE PH year:2019 PYQs

Question 51

Question 52

Question 53

Question 54

Question 55