GATE 2019 Paper with Answer Keys for Material Science (XE-C)

XE (C): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Q.1- On decreasing the objective aperture size in an optical microscope

(A) the spherical aberration increases

(B) the depth of field increases

Ans: (B) the depth of field increases

Q.2- Pilling-Bedworth ratios for oxides of some metals are given in the table.

Metal	Pilling-Bedworth Ratio
Li	0.57
Ce	1.16
Ta	2.33
W	3.40

Based on the criterion of Pilling-Bedworth ratio alone, which one of the following metals will be most protected from high temperature oxidation?

(A) Li

(B) Ce

(D) W

Ans: (B) Ce

Q.3- In NaCl, the substitution of a Na⁺ ion by a Ca²⁺ ion would most probably lead to

(A) the formation of a Na+ vacancy

(B) the creation of a Cl‾ interstitial

(C) the formation of a Cl‾ vacancy

(D) the formation of a Na+ and Cl‾ vacancy pair

Ans: (A) the formation of a Na+ vacancy

Q.4- Which one of the following is time-independent?

(A) Elastic deformation

(B) Anelastic deformation

Ans: (A) Elastic deformation

Q.5- Copper is diffused into aluminium at 400 °C for 100 hours to obtain a certain concentration at a given depth. In another experiment conducted at 500 °C, to achieve the same concentration of copper at the same depth, the time required in hours is

(Given: Diffusion coefficients of copper in aluminium at 400 °C and 500 °C are 5 × 10‾¹⁴ m² s‾¹ and 6 × 10‾¹³ m2 s‾¹, respectively)

(A) 7.33

(B) 8.33

(D) 10.33

Ans: (B) 8.33

Q.6- If carbon (C) in iron (Fe) is 6 percent by weight, then its atomic percent is approximately

(Given: atomic weight C = 12, Fe = 56)

(A) 13

(B) 23

(D) 50

Ans: (B) 23

Q.7- GaAs has advantage over silicon when used in intergrated circuits at low power because it has

(A) larger band up

(B) more than one element

(D) higher hole mobility

Ans: (C) higher electron mobility

Q.8- Glass transition temperature of a polymer can be determined by

(A) Thermo-gravimetric analysis

(B) Raman spectroscopy

(D) Differential scanning calorimetry

Ans: (D) Differential scanning calorimetry

Q.9- The maximum wavelength of radiation to which Germanium (Ge) is opaque will be

(Given: energy gap of Ge = 0.67 eV, Planck’s constant h = 6.63 × 10‾34 J s, velocity of light c = 3×108 m s‾1 and 1 eV = 1.6×10‾19 J )

(A) 0.8 µm

(B) 1.8 µm

(D) 4.8 µm

Ans: (B) 1.8 µm

Q.10- An alternating copolymer has number-averaged molecular weight of 105 g mol‾¹ and degree of polymerization of 2210. If one of the repeat units is ethylene, the other one is

(Given: atomic weight of H = 1, C = 12, F = 19 and Cl = 35.5)

(A) −CH2−CH(CH3)−

(B) −CH2−CHCl−

Ans: (B) −CH2−CHCl−

Q.11- Match the sintering processes in column I with the most suitable products in column II.

Column I	Column II
(P) Solid state sintering	(1) Carbon nanotube products
(Q) Liquid phase sintering	(2) Mixture of Cu and Zn powder products
(R) Spark plasma sintering	(3) Iron powder products
(S) Laser sintering	(4) 3D printed products

(A) P-4; Q-1; R-2; S-3

(B) P-3; Q-2; R-1; S-4

(D) P-2; Q-3; R-1; S-4

Ans: (B) P-3; Q-2; R-1; S-4

Q.12- Which one of the following conditions will NOT favour the separation of impurities in zone refining process?

(A) Increase in the gap between solidus and liquidus lines

(B) Increase in the solubility of impurities in solid as compared to that in liquid phase

(C) Agitation of melt

(D) Low cooling rate of melt

Ans: (B) Increase in the solubility of impurities in solid as compared to that in liquid phase

Q.13- A monochromatic X-ray beam of wavelength 0.154 nm is incident on a cubic crystal having lattice parameter a = 0.245 nm. The diffraction angle (2θ) for the first order reflection from a set of planes represented by the schematic plane below is ______degrees. (round off to 1 decimal place)

Ans: 100.0 to 102.0

Q.14- Nickel corrodes at 298 K in a solution of 0.06 M nickel chloride having pH 4. Assuming complete dissociation of nickel chloride, the partial pressure of hydrogen required to stop the corrosion of nickel is _ atm. (round off to the nearest integer)

(Given: Standard reduction potential of nickel = ̶ 0.25 V, Faraday’s constant = 96500 C mol⁻¹, Universal gas constant = 8.314 J K⁻¹mol⁻¹)

Ans: 45 to 52

Q.15- The potential energy, U(r), of a pair of atoms spaced at a distance r in a solid is given by

U\;\left(r\right)=\frac A{r^3}+\frac B{r^7}

The equilibrium distance between the atom pair is __ nm.
(round off to 2 decimal places)

(Given: Constants A = 6×10‾²⁰J nm3, B = 2.1×10‾²² J nm7)

Ans: 0.28 to 0.32

Q.16 Tensile true stress – true strain curve for plastic region of an alloy is given by ???? (MPa) = 600 ???? ^???? . When true strain is 0.05, the true stress is 350 MPa. For the same alloy, when engineering strain is 0.12 then the engineering stress is ______MPa. (round off to the nearest integer)

Ans: 360 to 364

Q.17- Box-S has 2 white and 4 black balls and box-T has 5 white and 3 black balls. A ball is drawn at random, from the box-S and put in box-T. Subsequently, the probability of drawing a white ball from box-T is __. (round off to 2 decimal places)

Ans: 0.58 to 0.61

Q.18- The zero point energy of an electron in a box of 0.2 nm width is __ eV. (round off to 1 decimal place)

(Given: Planck’s constant = 6.63×10‾³⁴ J s, electron mass = 9.11×10‾³¹ kg and 1 eV = 1.6×10‾¹⁹ J )

Ans: 9.2 to 9.6

Q.19- The de Broglie wavelength of an electron accelerated across a 300 kV potential in an electron microscope is __ ×10‾¹² m. Ignore relativistic effects. (round off to 2 decimal places)

(Given: Planck’s constant = 6.63×10‾³⁴ J s, electron rest mass = 9.11×10‾³¹ kg, electron charge = 1.6×10‾¹⁹ C)

Ans: 2.10 to 2.35

Q.20- A stress of 17 MPa is applied to a polymer serving as a fastener in a complex assembly. At constant strain the stress drops to 16.6 MPa after 100 hours. The stress on the polymer must remain above 14.5 MPa in order for the assembly to function properly. The expected life of the assembly is __ hours. (round off to the nearest integer)

Ans: 666 to 670

Q.21- A piezoelectric material has a Young’s modulus of 72 GPa. The stress required to change the polarization from 640 to 645 C m m‾³ is __ MPa. (round off to the nearest integer)

Ans: 560 to 565

Q.22- An iron bar magnet having coercivity of 7000 A m‾¹ is to be demagnetized. The bar is introduced fully inside a 0.25 m long solenoid having 150 turns of wire. The electric current required to generate the necessary magnetic field is __ A. (round off to 1 decimal place)

Ans: 11.0 to 12.5

END OF THE QUESTION PAPER