Engineering Sciences
GATE XE exam:gate PYQs
Build your understanding with focused practice from past exam papers.
Questions 781–790 of 1772. Imported answers require independent review unless marked reviewed.
Question 59
Open questionXE-CMSQ2 marksNeeds review
For a diffusional transformation (i.e., growth of β precipitates in an α matrix), which of the following is/are true with increasing degree of undercooling?
Your answerSelect all correct options. You can choose more than one.
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Open questionXE-CNAT2 marksNeeds review
A two-phase (α + β) mixture in an A-B binary system has the following properties:
(i) Phase α has equal weight percentages of A and B.
(ii) Phase β has twice the mole fraction of A compared to B.
(iii) The two-phase mixture has equal amounts of α and β.
(iv) Atomic mass of A is twice that of B.
The mole fraction of A in the resultant two-phase mixture is _________. (Round off to one decimal)
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Open questionXE-CNAT2 marksNeeds review
It is known that component A diffuses into a solid to a depth of 10 μm in 1 hour at 300 K. Treat diffusion in one dimension. The time taken for A to diffuse to the same depth at 600 K is ________ seconds. (Round off to 1 decimal).
Diffusivity of A in the solid is given by
: Diffusivity coefficient
: Activation energy = 0.3 eV
: Boltzmann’s constant = 8.62×10⁻⁵ eV/K
: Absolute temperatureLog in to check the answer
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Open questionXE-CNAT2 marksNeeds review
A spherical β particle nucleates from the α matrix on a non-deformable substrate δ, forming a contact angle of θ as shown in the schematic.
The value of
is ________. (Round off to three decimal places)
= Gibbs free energy change at the critical radius for homogeneous nucleation
= Gibbs free energy change at the critical radius for heterogeneous nucleationα-β interfacial energy = 0.4 J/m²
α-δ interfacial energy = 0.3 J/m²
β-δ interfacial energy = 0.02 J/m²
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Open questionXE-CNAT2 marksNeeds review
The resistivity of a pure semiconductor at 298 K is 300 Ωm. Assume that the number of electrons excited (
) across the band gap is given by the relation
: Avogadro’s number = 6.02×10²³ mole⁻¹
: Boltzmann’s constant = 8.62×10⁻⁵ eV/K
: Absolute temperatureMobility of electrons in the semiconductor = 0.14 m²/(V s)
Mobility of holes in the semiconductor = 0.06 m²/(V s)
Absolute charge of an electron = 1.60×10⁻¹⁹ C
The band gap (
) of the semiconductor is ________ eV. (Round off to two decimals)Log in to check the answer
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Open questionXE-CNAT2 marksNeeds review
A new glass material is developed to minimize the transmission of the light through the window with glass panel of thickness 5 mm. The refractive index of the glass material is 1.5 and the absorption coefficient can be changed from 0.3 cm⁻¹ to 1 cm⁻¹. In the given range of absorption coefficients, the ratio of the maximum to the minimum fraction of the light coming out of the other side of the glass panel is ________. (Round off to two decimal places)
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Open questionXE-CNAT2 marksNeeds review
The third peak in the X-ray diffraction pattern of a face-centered cubic crystal is at 2θ value of 45°, where 2θ is the angle between the incident and reflected rays. The wavelength of the monochromatic X-ray beam is 1.54 Å. Considering first-order reflection, the lattice parameter of the crystal is ________ Å. (Round off to two decimal places)
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Open questionXE-DMCQ1 markNeeds review
A force
is applied at an angle θ = 30° on an elastic column as shown in the figure.
and
are respectively the Young’s modulus and area moment of inertia. The smallest magnitude of
needed to cause buckling is 
Your answerChoose one option.
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Open questionXE-DMCQ1 markNeeds review
The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section
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Open questionXE-DMCQ1 markNeeds review
A massless semicircular rod held fixed at end
in the
-plane, as shown in the figure. A force
along the negative
direction is acting at point
on the rod. The unit vectors along
,
and
directions are denoted respectively as
,
and
. Due to the applied force
, the cross-section of the rod at point
will be subjected to 
Your answerChoose one option.
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