GATE XE format:nat PYQs & Answers — Page 41

Questions 401–410 of 668. Imported answers require independent review unless marked reviewed.

Topic practice 668 questionsPage 41 of 67

For a FCC metal, the ratio of surface energy of surface to surface is ______ (round-off to two decimal places). Assume that only the nearest neighbor broken bonds contribute to the surface energy.

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Pure silicon (Si) has a band gap (Eg) of 1.1 eV. This Si is doped with 1 ppm (parts per million) of phosphor atoms. Si contains 5 × 10²⁸ atoms per m³ in pure form. At temperature T = 300 K, the shift in Fermi energy upon doping with respect to intrinsic Fermi level of pure Si will be ______ eV (with appropriate sign and round-off to two decimal places).

Intrinsic carrier concentration of Si, ni, is given as:

Given: Mass of an electron, m = 9.1 × 10⁻³¹ kg Charge of an electron, e = 1.6 × 10⁻¹⁹ C Boltzmann constant, kB = 1.38 × 10⁻²³ J.K⁻¹ Planck’s constant, h = 6.6 × 10⁻³⁴ J.s⁻¹

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The schematic diagram shows the light of intensity

incident on a material (shaded grey) of thickness,

, which has an absorption coefficient,

and reflectance,

. The intensity of transmitted light is

. The reflection of light (of a particular wavelength) occurs at both the surfaces (surfaces indicated in the diagram). The transmittance is estimated to be ______ (round-off to three decimal places).

Given that for the wavelength used,

and

Diagram for Engineering Sciences question 17

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Fe₃O₄ (also represented as FeO·Fe₂O₃) is a FCC structured inverse spinel (AB₂O₄) material where 1/8 of tetrahedral sites are occupied by half of B cations and 1/2 of the octahedral sites are occupied by remaining B and A cations. The magnetic moments of cations on octahedral sites are antiparallel with respect to those on tetrahedral sites. Atomic number of Fe is 26 and that of O is 8. The saturation magnetic moment of Fe₃O₄ per formula unit in terms of Bohr magnets (μB) will be ______ μB. Ignore contribution from orbital magnetic moments.

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A piezoelectric ceramic with piezoelectric coefficient (

) value of

is subjected to a force,

, of 10 N, applied normal to its x-y face, as shown in the figure. If relative dielectric constant (

) of the material is 100, the voltage developed along the z-direction of the sample will be ______ Volts (round-off to two decimal places). Ignore any nonlinear effects.

Given: Permitivity of free space (

) is

Diagram for Engineering Sciences question 19

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Silicon carbide (SiC) particles are added to Aluminum (Al) matrix to fabricate particle reinforced Al-SiC composite. The resulting composite is required to possess specific modulus (E/ρ; E: elastic modulus, ρ: density) three times that of pure Al. Assuming iso-strain condition, the volume fraction of SiC particles in the composite will be ______ (round-off to two decimal places).

Material	E (GPa)	ρ (g.cm⁻³)
Al	69	2.70
SiC	379	2.36

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Isothermal weight gain per unit area (ΔW/A, where ΔW is the weight gain (in mg) and A is the area (in cm²)) during oxidation of a metal at 600 °C follows parabolic rate law, where ΔW/A = 1.0 mg.cm⁻² after 100 min of oxidation. The ΔW/A after 500 min at 600 °C will be ______ mg.cm⁻² (round-off to two decimal places).

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A plain carbon steel sample containing 0.1 wt% carbon is undergoing carburization at 1100 °C in a carbon rich surroundings with fixed carbon content of 1.0 wt% all the time. The carburization time necessary to achieve a carbon concentration of 0.46 wt% at a depth of 5 mm at 1100 °C is ______ hour (round-off to the nearest integer).

Given: Diffusivity of carbon in iron at 1100 °C is 6.0 × 10⁻¹¹ m².s⁻¹.

erf(z)	z
0.56	0.55
0.60	0.60
0.64	0.65
0.68	0.70

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A particle of mass 0.1 kg, which is released from rest, falls vertically downward under gravity in a fluid. The fluid offers a resistive force, which is linearly proportional to the particle velocity with 0.1 N.s/m as the constant of proportionality. The uniform gravitational acceleration is 10 m/s

throughout the trajectory of the particle. The magnitude of the particle velocity (in m/s) at time 1 s after release (rounded off to two decimal places) is _____.

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The state of two-dimensional plane stress at a point in a body is shown on the triangular element ABC, where

and

. The normal stress (in MPa) on the plane AC is _____.

Diagram for Engineering Sciences question 8

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GATE XE format:nat PYQs

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 7

Question 8