GATE PH format:nat PYQs & Answers — Page 3

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Questions 21–30 of 182. Imported answers require independent review unless marked reviewed.

Topic practice 182 questionsPage 3 of 19

Powder X-ray diffraction pattern of a cubic solid with lattice constant

has the (111) diffraction peak at

. If the lattice expands such that the lattice constant becomes

, the angle (in degrees) corresponding to the (111) peak changes to

. The value of

(rounded off to one decimal place) is _____

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Consider a monatomic chain of length 30 cm. The phonon density of states is

s. Assuming the Debye model, the velocity of sound in m/s (rounded off to one decimal place) is _____

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The

baryon with spin

, at rest, decays to a proton and a pion (

). The

has positive intrinsic parity and

has negative intrinsic parity. The orbital angular momentum of the proton-pion system (in integer) is _____

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Cyclotrons are used to accelerate ions like deuterons (

) and

particles. Keeping the magnetic field same for both,

and

are extracted with energies 10 MeV and 20 MeV with extraction radii

and

, respectively. Taking the masses

and

, the value of

(in integer) is ______

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In the transistor circuit shown in the figure,

and

. The value of the base current in

(rounded off to one decimal place) is ________

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Consider the set

. An orthonormal basis in

is formed from these three terms, where the normalization of a function

is defined via

. If the orthonormal basis set is

, then the value of

(in integer) is ______

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The Hamiltonian for a one dimensional system with mass

, position

and momentum

, where

is a real function of

. If

, then

. The value of

(in integer) is _____.

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A system of five identical, non-interacting particles with mass

and spin

is confined to a one-dimensional potential well of length

. If the lowest energy of the system is

, the value of

(in integer) is _____.

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A wheel of mass

and radius

is made of a thin uniform distribution of mass

at the rim and a point mass

at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal mass rod of length

, with one end fixed to O, as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed

. If

is the total angular momentum of the wheel about O, then the magnitude

. The value of

(in integer) is _____.

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The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from

V supplies. If a +1 V signal is applied at the input, the output voltage (rounded off to one decimal place) is _____.

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GATE PH format:nat PYQs

Question 33

Question 34

Question 35

Question 59

Question 60

Question 61

Question 62

Question 63

Question 64

Question 65