GATE PH format:nat PYQs & Answers — Page 4

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Questions 31–40 of 182. Imported answers require independent review unless marked reviewed.

Topic practice 182 questionsPage 4 of 19

The minimum number of basic logic gates required to realize the Boolean expression

is ____ (in integer).

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The vapor pressure (P) of solid ammonia is given by

, while that of liquid ammonia is given by

, where

is the temperature in K. The temperature of the triple point of ammonia is ____ K (rounded off to two decimal places).

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The electric field in a region depends on the

and

coordinates as

where

is a constant. The flux of

through the surface of a sphere of radius

with its center at the origin is

, where the value of

is ____ (in integer).

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The Hamiltonian of a system of

particles in volume

at temperature

where

and

are positive constants. The ensemble average of the Hamiltonian is

, where

is the Boltzmann constant. The value of

is ____ (in integer).

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A typical biasing of a silicon transistor is shown in figure.

The value of common-emitter current gain

for the transistor is 100. Ignore reverse saturation current. The output voltage

(in V) is ______ (in integer).

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The canonical partition function of an ideal gas is

where

and

denote temperature, volume, number of particles, and thermal de Broglie wavelength, respectively. Let

be the Boltzmann constant and

be the chemical potential. Take

. If the number density

at a temperature

, then

is ______

(rounded off to one decimal place).

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Lagrangian of a particle of mass

, where

is a positive constant. If the particle oscillates with total energy

, then the time period of oscillations is

The value of

is _____ (in integer).

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A particle of mass

in an infinite potential well of width

is subjected to a perturbation,

as shown in figure, where

is Planck’s constant.

The first order energy shift of the fourth energy eigenstate due to this perturbation is

The value of

is _____ (in integer).

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Consider a three-dimensional system of non-interacting bosons with zero chemical potential. The energy of the system

, where

is the wavevector. The low temperature specific heat of the system at constant volume depends on the temperature as

. The value of

is _____ (in integer).

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Consider the operational amplifier circuit shown in figure.

The output voltage

is ______ V (in integer).

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GATE PH format:nat PYQs

Question 32

Question 33

Question 34

Question 35

Question 58

Question 59

Question 60

Question 61

Question 62

Question 63