GATE XE year:2020 PYQs & Answers — Page 6

Questions 51–60 of 175. Imported answers require independent review unless marked reviewed.

A ceramic material is periodically heated and cooled between 25°C and a higher temperature, Tf. During thermal cycling, the material remains dimensionally constrained. The material can withstand a maximum compressive stress of 200 MPa without failure. Material’s coefficient of thermal expansion is 7.5×10⁻⁶ °C⁻¹ and modulus of elasticity (E) is 200 GPa. The lowest value of Tf (in °C) at which material will fail is ______ °C (round-off to the nearest integer). Assume that there is no plastic deformation during the thermal cycling.

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During homogeneous solidification of a liquid metal, the radius of critical nucleus (in nanometer, nm) at a temperature Ts which is below the melting point (Tm), is ______ nm (round-off to one decimal place). Given that γsl (solid liquid interfacial energy) is 0.18 J.m⁻² and ΔGv (change in volume free energy upon transformation from liquid to solid) at Ts is 0.18 × 10⁹ J.m⁻³.

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Read the two statements related to sintering and select the correct option.

Statement-1: Sintering in vacuum leads to improved densification as compared to sintering under ambient (at atmospheric pressure) condition.

Statement-2: Closed pores formed during sintering inhibit full densification.

Your answerChoose one option.

Both Statement-1 and Statement-2 are FALSE

Both Statement-1 and Statement-2 are TRUE

Statement-1 is TRUE but Statement-2 is FALSE

Statement-1 is FALSE but Statement-2 is TRUE

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Select the correct option that appropriately matches the process to the material/product that can be fabricated using them.

Process (I) Powder processing (II) Spin coating (III) Czochralski process (IV) Chemical vapor deposition

Material/Product (P) Organic semiconductor thin films (Q) Single crystal silicon (R) Poly-silicon (S) Porous bronze bearings

Your answerChoose one option.

I-S, II-P, III-R, IV-Q

I-S, II-R, III-Q, IV-P

I-S, II-P, III-Q, IV-R

I-P, II-R, III-Q, IV-S

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Consider a FCC structured metal with lattice parameter a = 3.5 Å. If the material is irradiated using X-rays of wavelength λ = 1.5405 Å, the Bragg angle (2θ) corresponding to the fourth reflection will be:

Your answerChoose one option.

88.21°

76.99°

99.35°

93.80°

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The number of Schottky defects per mole of KCl at 300 °C under equilibrium condition will be:

Given: Activation energy for the formation of Schottky defect = 250 kJ.mol⁻¹ Avogadro number = 6.023 × 10²³ mol⁻¹ Universal Gas Constant = 8.314 J.K⁻¹.mol⁻¹

Your answerChoose one option.

1.21 × 10¹⁸

1.52 × 10¹⁶

9.75

2.42 × 10¹²

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In an industry, the probability of an accident occurring in a given month is 1/100. Let P(n) denote the probability that there will be no accident over a period of ‘n’ months. Assume that the events of individual months are independent of each other. The smallest integer value of ‘n’ such that P(n) ≤ 1/2 is ______ (round off to the nearest integer).

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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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GATE XE year:2020 PYQs

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Question 17