GATE PH exam:gate PYQs & Answers — Page 52

Questions 511–520 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 52 of 65

Let

be a variable in the range

. Now consider a function

If its Fourier-series is written as

, then the value of

(rounded off to three decimal places) is

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Two spaceships A and B, each of the same rest length

, are moving in the same direction with speeds

and

, respectively, where

is the speed of light. As measured by B, the time taken by A to completely overtake B [see figure below]

in units of

(to the nearest integer) is

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A radioactive element X has a half-life of 30 hours. It decays via alpha, beta and gamma emissions with the branching ratio for beta decay being 0.75. The partial half-life for beta decay in unit of hours is

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In a thermally insulated container, 0.01 kg of ice at 273 K is mixed with 0.1 kg of water at 300 K. Neglecting the specific heat of the container, the change in the entropy of the system in J/K on attaining thermal equilibrium (rounded off to two decimal places) is (Specific heat of water is 4.2 kJ/kg-K and the latent heat of ice is 335 kJ/kg).

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Consider a system of three charges as shown in the figure below:

For

;

degrees;

Coulomb, and

, the electric dipole potential in volts (rounded off to three decimal places) at a point

is ______

[Use:

]

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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 exam:gate PYQs

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