GATE 2021 Question Paper MT Metallurgical Engineering

General Aptitude (GA)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 Five persons P, Q, R, S and T are to be seated in a row, all facing the same
direction, but not necessarily in the same order. P and T cannot be seated at
either end of the row. P should not be seated adjacent to S. R is to be seated
at the second position from the left end of the row. The number of distinct
seating arrangements possible is:

(A) 2

(B) 3

(C) 4

(D) 5

Q.2 Consider the following sentences:
(i) The number of candidates who appear for the GATE
examination is staggering.
(ii) A number of candidates from my class are appearing for the
GATE examination.
(iii) The number of candidates who appear for the GATE
examination are staggering.
(iv) A number of candidates from my class is appearing for the GATE
examination.
Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iii)

(C) (ii) and (iii)

(D) (ii) and (iv)

MT-Copyright © GATE 2021 Page 1 of 27

Q.3 A digital watch X beeps every 30 seconds while watch Y beeps every 32
seconds. They beeped together at 10 AM.
The immediate next time that they will beep together is ________

(A) 10.08 AM

(B) 10.42 AM

(C) 11.00 AM

(D) 10.00 PM

Q.4 If ⊕÷⊙= 2 ; ⊕÷ Δ = 3; ⊙ +Δ = 5; Δ ×⊗ =10,

Then, the value of (  −  ) , is:
2

(A) 0

(B) 1

(C) 4

(D) 16

Q.5 The front door of Mr. X’s house faces East. Mr. X leaves the house, walking
50 m straight from the back door that is situated directly opposite to the front
door. He then turns to his right, walks for another 50 m and stops. The
direction of the point Mr. X is now located at with respect to the starting point
is ______

(A) South-East

(B) North-East

(C) West

(D) North-West

MT-Copyright © GATE 2021 Page 2 of 27

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q.6 Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.
Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.
Based on the above statements and conclusions, which one of the following
options is CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(C) Neither conclusion I nor II is correct

(D) Both conclusions I and II are correct

Q.7 A box contains 15 blue balls and 45 black balls. If 2 balls are selected
randomly, without replacement, the probability of an outcome in which the
first selected is a blue ball and the second selected is a black ball, is _____

(A) 3
16
(B) 45
236
(C) 1
4
(D) 3
4

MT-Copyright © GATE 2021 Page 3 of 27

Q.8

The ratio of the area of the inscribed circle to the area of the circumscribed
circle of an equilateral triangle is____

(A) 1
8
(B) 1
6
(C) 1
4
(D) 1
2

Q.9 Consider a square sheet of side 1 unit. The sheet is first folded along the main
diagonal. This is followed by a fold along its line of symmetry. The resulting
folded shape is again folded along its line of symmetry. The area of each face
of the final folded shape, in square units, equal to _______

(A) 1
4
(B) 1
8
(C) 1
16
(D) 1
32

MT-Copyright © GATE 2021 Page 4 of 27

Q.10 The world is going through the worst pandemic in the past hundred years.
The air travel industry is facing a crisis, as the resulting quarantine
requirement for travelers led to weak demand.
In relation to the first sentence above, what does the second sentence do?

(A) Restates an idea from the first sentence.

(B) Second sentence entirely contradicts the first sentence.

(C) The two statements are unrelated.

(D) States an effect of the first sentence.

MT-Copyright © GATE 2021 Page 5 of 27

Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 For the matrix given below, the eigenvalues are:
𝟏 𝟎 −𝟏
(𝟎 𝟏 𝟎)
−𝟏 𝟎 𝟏
(A) 0, 2, 2

(B) 1, 1, 2

(C) 0, 1, 2

(D) 0, 1, 3

Q.2 Which one of the following is a homogeneous function of degree three?

(A) 𝑥 3 + 2𝑥 2 𝑦 2

(B) 𝑦 2 𝑥 + 2𝑦𝑥 2

(C) 𝑦 3 + 2𝑥 2

(D) 𝑥𝑦 2 + 3𝑥𝑦

MT-Copyright © GATE 2021 Page 6 of 27

Q.3 The divergence of a vector field 𝑽 ⃗ (𝒙, 𝒚, 𝒛), where its three components (𝑽𝒙 ,
𝑽𝒚 , 𝑽𝒛 ) are functions of x,y,z, is:

(A) 𝜕𝑉𝑥 𝜕𝑉𝑦 𝜕𝑉𝑧
+ +
𝜕𝑥 𝜕𝑦 𝜕𝑧

(B) 𝜕𝑉𝑧 𝜕𝑉𝑦 𝜕𝑉𝑥 𝜕𝑉𝑧 𝜕𝑉𝑦 𝜕𝑉𝑥
( − )𝒊 + ( − )𝒋 + ( − )𝒌
𝜕𝑦 𝜕𝑧 𝜕𝑧 𝜕𝑥 𝜕𝑥 𝜕𝑦

(C) 𝜕𝑉𝑥 𝜕𝑉𝑦 𝜕𝑉𝑧
𝒊+ 𝒋+ 𝒌
𝜕𝑥 𝜕𝑦 𝜕𝑧

(D) 𝜕 2 𝑉𝑥 𝜕 2 𝑉𝑦 𝜕 2 𝑉𝑧
+ + 2
𝜕𝑥 2 𝜕𝑦 2 𝜕𝑧

MT-Copyright © GATE 2021 Page 7 of 27

Q.4 Which one of the following is ‘center split’ defect in rolling operation?

(A)

(B)

(C)

(D)

Q.5 Single crystal turbine blades of nickel-based superalloys for aero-engines
are manufactured using:

(A) Investment casting

(B) Die casting

(C) Squeeze casting

(D) Directional solidification

MT-Copyright © GATE 2021 Page 8 of 27

Q.6 Elements A and B have the same crystal structure. For a dilute solution of
B in A, which one of the following is true?
(Given: 𝑯𝒎𝒊𝒙 – Mixing enthalpy, aB – Activity of B and X B – Mole
fraction of B)

(A) 𝐼𝑓 𝐻𝑚𝑖𝑥 = 0, then 𝑎𝐵 < 𝑋𝐵

(B) 𝐼𝑓 𝐻𝑚𝑖𝑥 = 0, then 𝑎𝐵 > 𝑋𝐵

(C) 𝐼𝑓 𝐻𝑚𝑖𝑥 > 0, then 𝑎𝐵 < 𝑋𝐵

(D) 𝐼𝑓 𝐻𝑚𝑖𝑥 < 0, then 𝑎𝐵 < 𝑋𝐵

Q.7 For uniaxial tensile stress-strain behaviour of polycrystalline aluminium,
which one of the following statements is FALSE?

(A) True stress is always higher than the engineering stress.

(B) At the ultimate tensile stress point on the true stress - strain curve, 𝑑 = 0
𝑑

(C) Resilience is the area under the elastic region of the engineering stress - strain
curve.

(D) Maximum true stress does not correspond to the maximum load.

Q.8 Which one of the following is FALSE for creep deformation?

(A) The minimum creep rate is obtained in the primary stage (stage I).

(B) Creep resistance decreases with decrease in grain size.

(C) Coble creep occurs via grain boundary diffusion.

(D) Nabarro-Herring creep occurs via lattice diffusion.

MT-Copyright © GATE 2021 Page 9 of 27

Q.9 Which one of the following elements alloyed with iron is a ferrite
stabilizer?

(A) Nickel

(B) Manganese

(C) Carbon

(D) Silicon

Q.10 Which one of the following is the correct decreasing sequence of Quenching
Power for quenchants used in heat treatment of steels?

(A) Oil > Water > Brine > Air

(B) Brine > Oil > Water > Air

(C) Brine > Water > Oil > Air

(D) Water > Brine > Oil > Air

Q.11 For a zeroth order chemical reaction, which one of the following is
FALSE?

(A) Concentration versus time plot is a straight line.

(B) Increase in concentration of reacting species increases the rate of reaction.

(C) Half-life depends on the initial concentration and zero-order rate constant.

(D) Rate of reaction depends on temperature.

MT-Copyright © GATE 2021 Page 10 of 27

Q.12 Which one of the following elements oxidizes first in basic oxygen steel
making process?

(A) Silicon

(B) Carbon

(C) Manganese

(D) Phosphorus

Q.13 Which one of the following is a hydrometallurgical operation?

(A) Roasting

(B) Leaching

(C) Zone refining

(D) Smelting

MT-Copyright © GATE 2021 Page 11 of 27

Q.14 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.14 𝒔𝒊𝒏𝟐 𝟓𝒙
The value of 𝐥𝐢𝐦 𝒔𝒊𝒏𝟐 𝒙 is: ____________ (round off to nearest integer).
𝒙→𝟎

Q.15 The grain size (X) of annealed specimens follows a symmetric distribution
with a mean (µ) of 5 µm and a standard deviation () of 0.5 µm. The
percentage of specimens with grain size in the range 5 to 6 µm is expected
to be: __________ (round off to nearest integer).
Given: For the symmetric distribution: Probability 𝐏(𝐗  µ + 𝟐) = 𝟎. 𝟗𝟖

Q.16 If 𝑬𝒐𝑵𝒊𝟐+/𝑵𝒊 = − 0.25 V, the value of µ𝒐𝑵𝒊𝟐+ (in J mol-1) at 298 K is: ________
(round off to nearest integer).
Given: F = 96500 C mol-1

Q.17 Melting point of Cu is 1358 K and its enthalpy of melting is 13400 J mol-1.
The value of free energy change (in J mol-1) for liquid to solid
transformation at 1058 K is: _____________ (round off to nearest integer).
𝒍𝒊𝒒𝒖𝒊𝒅
Assume: 𝑪𝑷 = 𝑪𝒔𝒐𝒍𝒊𝒅
𝑷

Q.18 A body is subjected to a state of stress given by the following stress tensor:
𝟓𝟎 𝟎 𝟎
( 𝟎 𝟐𝟎𝟎 𝟎 ) MPa.
𝟎 𝟎 𝟏𝟎𝟎
If yielding is predicted by the Tresca Criterion, the uniaxial tensile yield
stress (in MPa) of the body should be less than or equal to: ___________
(round off to nearest integer).

Q.19 Consider homogeneous nucleation of a spherical solid in liquid. For a given
undercooling, if surface energy of a nucleus increases by 20 %, the
corresponding increase (in percent) in the critical radius of the nucleus is:
__________ (round off to nearest integer).

MT-Copyright © GATE 2021 Page 12 of 27

Q.20 If saturation magnetization of iron at room temperature is 1700 kA m-1, the
magnetic moment (in A m2) per iron atom in the crystal is: _______  10-23
(round off to 1 decimal place).
(Given: Lattice parameter of iron at room temperature = 0.287 nm)

Q.21 In the X-ray diffraction pattern of a FCC crystal, the first reflection occurs
at a Bragg angle () of 30. The Bragg angle (in degree) for the second
reflection will be: _______________ (round off to 1 decimal place).

Q.22 A 0.6 wt.% C steel sample is slowly cooled from 900 C to room
temperature. The fraction of proeutectoid ferrite in the microstructure is:
___________ (round off to 2 decimal places).
Given: Eutectoid composition: 0.8 wt.% C
Maximum solubility of carbon in α-Fe: 0.025 wt.% C

Q.23 If the degree of polymerization of polyethylene is 30000, the average
molecular weight (in g mol-1) is: _____________ (round off to nearest
integer).
(Given: Atomic weights of carbon and hydrogen are 12 and 1, respectively)

MT-Copyright © GATE 2021 Page 13 of 27

Q.24 Water flows over a plate of finite length. At 𝒙 = 𝒙𝟏 from the leading edge,
the velocity of the flow is 𝑽𝒙 = 𝟎. 𝟓𝒚 – 𝟎. 𝟓𝒚𝟑 . The thickness,  (in meter)
of the boundary layer at 𝒙 = 𝒙𝟏 is: _________ (round off to 2 decimal
places).
Given: V is the free stream velocity.

Q.25 The vacancy concentration in a crystal doubles upon increasing the
temperature from 27 C to 127 C. The enthalpy (in kJ mol-1) of vacancy
formation is: ________ (round off to 2 decimal places).
Given: R = 8.314 J mol-1 K-1

MT-Copyright © GATE 2021 Page 14 of 27

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong
answer: – 2/3).

Q.26 The minimum value of y for the equation 𝒚 = 𝒙𝟐 − 𝟐𝒙 + 𝟒 is ______.

(A) 3

(B) 1

(C) 4

(D) 6

MT-Copyright © GATE 2021 Page 15 of 27

Q.27 Match the forming process (in Column I) with its name (in Column II):

Column I Column II

1. Extrusion
(P)

(Q) 2. Rolling

(R) 3. Deep Drawing

(S) 4. Open Die Forging

(A) P−1, Q−2, R−3, S−4

(B) P−3, Q−1, R−4, S−2

(C) P−3, Q−4, R−1, S−2

(D) P−1, Q−4, R−3, S−2

MT-Copyright © GATE 2021 Page 16 of 27

Q.28 Match the nondestructive technique (in Column I) with its underlying
phenomenon (in Column II):

Column I Column II

(P) Dye penetrant test 1. X-ray absorption

(Q) Radiography 2. Capillary action

(R) Eddy current test 3. Elastic waves reflection

(S) Ultrasonic inspection 4. Electromagnetic induction

(A) P−4, Q−3, R−2, S−1

(B) P−2, Q−1, R−3, S−4

(C) P−2, Q−1, R−4, S−3

(D) P−3, Q−2, R−1, S−4

Q.29 Number of degrees of freedom for the following reacting system is:
M (s) + CO2 (g) = MO (s) + CO (g)

(A) 0

(B) 1

(C) 2

(D) 3

MT-Copyright © GATE 2021 Page 17 of 27

Q.30 The condition for getting the binary phase diagram of A-B (shown below)
is:

Given: 𝑯𝒔𝒐𝒍𝒊𝒅
𝒎𝒊𝒙 – Enthalpy of mixing of solid

𝑯𝒍𝒊𝒒𝒖𝒊𝒅
𝒎𝒊𝒙 – Enthalpy of mixing of liquid

(A) 𝐻𝑚𝑖𝑥
𝑠𝑜𝑙𝑖𝑑
= 0 and 𝐻𝑚𝑖𝑥
𝑙𝑖𝑞𝑢𝑖𝑑
=0

(B) 𝐻𝑚𝑖𝑥
𝑠𝑜𝑙𝑖𝑑
≪ 0 and 𝐻𝑚𝑖𝑥
𝑙𝑖𝑞𝑢𝑖𝑑
=0

(C) 𝐻𝑚𝑖𝑥
𝑠𝑜𝑙𝑖𝑑
> 0 and 𝐻𝑚𝑖𝑥
𝑙𝑖𝑞𝑢𝑖𝑑
=0

(D) 𝐻𝑚𝑖𝑥
𝑠𝑜𝑙𝑖𝑑
= 0 and 𝐻𝑚𝑖𝑥
𝑙𝑖𝑞𝑢𝑖𝑑
≪0

Q.31 In the absence of any external stress, which one of the following statements
related to the interaction of point defect and a dislocation is FALSE:

(A) An oversized solute atom would preferentially migrate below the slip plane of
an edge dislocation.

(B) A spherically symmetric point defect can interact with both the hydrostatic and
shear stress fields of a dislocation.

(C) A point defect can locally modify the elastic modulus and thereby can change
the interaction energy.

(D) Vacancies are attracted towards the compressive region of dislocation.

MT-Copyright © GATE 2021 Page 18 of 27

Q.32 A single crystal aluminium sample is subjected to uniaxial tension along
[112] direction. If the applied tensile stress is 100 MPa and the critical
resolved shear stress (CRSS) is 25 MPa, which one of the following slip
systems will be activated?

(A) [1̅01](111)

(B) [1̅10](111)

(C) [101](111̅)

(D) [011](111̅)

Q.33 One-dimensional steady-state temperature distribution in two adjacent
refractory blocks (with thermal conductivities, k1 and k2) of unit cross-
sectional area are shown below. The temperature T1 and thermal contact
resistance of the interface, respectively, are:

(A) 200 K, 0.5 K W-1

(B) 400 K, 1.0 K W-1

(C) 200 K, 0.25 K W-1

(D) 500 K, 0.5 K W-1

MT-Copyright © GATE 2021 Page 19 of 27

Q.34 For a fully developed 1-D flow of a Newtonian fluid through a horizontal
pipe of radius R (see figure), the axial velocity (𝒗𝒛 ) is given by:
𝑷 𝑹𝟐 −𝒓𝟐
𝒗𝒛 = [ ] ( ),
𝑳 𝟒𝛍
where, 𝑷 is the pressure difference (𝑷𝟏 – 𝑷𝟐), μ is the viscosity, 𝒓 is the
radial distance from the axis and L is the length of the tube. The shear
stress exerted by the fluid on the tube wall is:

∆𝑃𝑅
(A)
2𝐿
∆𝑃𝑅
(B)
𝐿
3∆𝑃𝑅
(C)
2𝐿
2∆𝑃𝑅
(D)
𝐿

MT-Copyright © GATE 2021 Page 20 of 27

Q.35 Match the terms (in Column I) with the unit process (in Column II)

Column I Column II

(P) Submerged Entry Nozzle 1. Ladle Furnace
(Q) Electric Heating 2. Continuous Casting
(R) Raceway Zone 3. LD Converter
(S) Oxygen Lancing 4. Blast Furnace

(A) P−2, Q−1, R−4, S−3

(B) P−4, Q−1, R−2, S−3

(C) P−4, Q−3, R−1, S−2

(D) P−2, Q−3, R−4, S−1

Q.36 A blast furnace uses hematite ore with 80% Fe2O3 and 20% gangue
materials. It uses 600 kg coke per ton of hot metal. The coke contains 85%
C and 15% ash. The composition of hot metal is 95.5% Fe and 4.5% C.
The weight of iron ore used and slag produced per ton of hot metal
respectively, are:
Given: Atomic weight: O = 16, C = 12, N = 14, Fe = 56
All the compositions are in wt.%.
1 ton = 1000 kg
Assume that the gangue materials of the ore and ash content of coke form
slag while Fe2O3 in the ore is consumed in making hot metal.

(A) 1705 kg, 431 kg

(B) 2131 kg, 546 kg

(C) 1705 kg, 331 kg

(D) 1500 kg, 431 kg

MT-Copyright © GATE 2021 Page 21 of 27

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

Q.37 Consider the function 𝒇(𝒙) = 𝒙 − 𝐜𝐨𝐬 𝒙. Using Newton-Raphson method,
the estimated root of 𝒇(𝒙) after the first iteration is: ______ (round off to 3
decimal places).
Assume: Initial guess of the root = 0.5 radians.

Q.38 The work done by a force ⃗𝑭 = 𝟐𝒙𝒊 + 𝟑𝒚𝒋 along a straight line from point
(0, 0) to (1, 2) is: ____________ (round off to nearest integer).

Q.39 A coin is tossed three times. Given that there are more heads than tails, the
probability of getting exactly one tail is: ___________ (round off to 2
decimal places).

Q.40 A continuous fillet weld is made using a 3000 W welding machine. At a
travel speed of 6 mm s-1, the cross-sectional area (in mm2) of the weld is:
___________ (round off to nearest integer).
Given: The unit energy required to melt the metal is 6 J mm-3.
Heat transfer factor = 0.6
Melting factor = 0.5

Q.41 Liquid iron is cast into a spherical sand mold (6 cm radius) and a cubical
sand mold (12 cm edge length). If solidification time is 60 minutes in the
spherical casting, the time (in minutes) required to solidify in the cubical
casting is: ____________ (round off to nearest integer).

Q. 42 True strain for 60% height reduction of a sample subjected to hot forging
is: ___________ (round off to 2 decimal places).

MT-Copyright © GATE 2021 Page 22 of 27

Q.43 For the equilibrium reaction: 𝟐𝑪𝒖 (𝒔) + 𝑺𝑶𝟐 (𝒈) = 𝑪𝒖𝟐 𝑺 (𝒔) + 𝑶𝟐 (𝒈), the
𝑷𝑶
value of 𝒍𝒏 (𝑷 𝟐 ) at 973 K is: ________ (round off to 2 decimal places).
𝑺𝑶𝟐

Given: 𝟐𝑪𝒖 (𝒔) + 𝟎. 𝟓𝑺𝟐 (𝒈) = 𝑪𝒖𝟐 𝑺 (𝒔) ΔGo at 973 K = -100 kJ
𝑺𝑶𝟐 (𝒈) = 𝟎. 𝟓𝑺𝟐 (𝒈) + 𝑶𝟐 (𝒈) ΔGo at 973 K = 292 kJ
R = 8.314 J mol-1 K-1
Assume: Cu and Cu2S are pure solids.

Q.44 One mole of an ideal gas at 10 atm. and 300 K undergoes reversible
adiabatic expansion to a pressure of one atm. The work done (in Joule) by
the gas is: __________ (round off to nearest integer).
Given: R = 8.314 J mol-1 K-1; 1 atm. = 101325 Pa; Cp = 2.5R

Q.45 The figure shows the entropy versus temperature (S-T) plot of a reversible
cycle of an engine. If T1 = 200 K and T2 = 600 K, the efficiency of the engine
(in percent) is: ___________ (round off to 2 decimal places).

MT-Copyright © GATE 2021 Page 23 of 27

Q. 46 Two dislocation lines parallel to z-axis lying in the x-z plane are shown in
the figure. The glide force (in Newton) exerted by the edge dislocation on
the screw dislocation is: ______________ (round off to nearest integer).

For the edge, the shear stress component is given by:
𝐆𝐛 𝐱(𝐱 𝟐 −𝐲 𝟐 )
𝛕𝐱𝐲 =
𝟐(𝟏−) (𝐱 𝟐 +𝐲 𝟐 )𝟐

Given: Shear modulus, G = 28 GPa
Poisson’s ratio,  = 0.3
Burgers vector, b = 0.29 nm
Distance between the two dislocations = 0.5 nm

Q.47 In a material, a shear stress of 100 MPa is required to bow a dislocation
line between precipitates with a spacing of 0.2 µm. If the spacing between
the precipitates is increased to 0.5 µm, the shear stress (in MPa) to bow the
dislocation would be: _________ (round off to nearest integer).

Q.48 A metal plate is in a state of plane strain (𝒛𝒛 = 𝟎) with 𝒙𝒙 = 𝒚𝒚  𝟎 and
𝒙𝒚 = 𝒙𝒛 = 𝒚𝒛 = 𝟎. If the Poisson’s ratio is 0.3, the ratio, 𝒛𝒛 /𝒙𝒙 is
___________ (round off to 1 decimal place).

MT-Copyright © GATE 2021 Page 24 of 27

Q.49 𝟖𝟎
An infinite metal plate has a central through-thickness crack of length
𝝅
mm. The maximum applied stress (in MPa) that the plate can sustain in
mode I is: _________ (round off to nearest integer).
Assume: Linear elastic fracture mechanics is valid
Given: Fracture toughness, 𝑲𝑰𝑪 = 20 MPa m1/2

Q.50 A hypothetical binary eutectic phase diagram of A – B is shown below. An
alloy with 5 wt.% B solidifies with no convection. Assuming steady state,
the critical temperature gradient (in K mm-1) required to maintain planar
solidification front is: ___________ (round off to nearest integer).

Given: Diffusivity of B in liquid = 10-9 m2 s-1
Velocity of solidification front = 4 µm s-1

Q.51 A thick steel plate containing 0.1 wt.% C is carburized at 950 C. The
plate’s surface carbon concentration is maintained at 1.1 wt.% C. After 9
hours, the depth (in mm) below the surface at which the carbon
concentration is 0.6 wt.% C will be: _____________ (round off to 2 decimal
places).
Given: Diffusivity of carbon in γ-Fe at 950 C = 1.6 x 10-11 m2 s-1
Error function table:

z 0.35 0.40 0.45 0.50 0.55 0.60

erf(z) 0.3794 0.4284 0.4755 0.5205 0.5633 0.6039

MT-Copyright © GATE 2021 Page 25 of 27

Q.52 At 25 C, iron corrodes in a deaerated acid of pH 3 with a corrosion
current density of 4 µA cm-2. The corrosion potential (V) is: ________
(round off to 2 decimal places).
Given: βc = 0.1 V per decade of current density
Exchange current density of hydrogen on iron surface = 10-9 A cm-2
R = 8.314 J mol-1 K-1, F = 96500 C mol-1
All potentials are with reference to standard hydrogen electrode.

Q.53 The radius of an interstitial atom which just fits (without distorting the
structure) inside an octahedral void of a bcc-iron crystal (in nm) is:
___________ (round off to 3 decimal places).
Assume the radius of Fe atom to be 0.124 nm.

Q.54 Nickel undergoes isothermal oxidation at 800 K for a duration of 400 s
resulting in a weight gain of 2 mg cm-2. The weight gain (mg cm-2) after a
duration of 1600 s is: __________ (round off to nearest integer).
Assume: Weight gain is proportional to square root of time.

MT-Copyright © GATE 2021 Page 26 of 27

Q.55 A solid sphere (0.5 m radius) is enclosed within a larger hollow sphere (1 m
radius), as shown in figure. The radiation exchange takes place between the
outer surface (surface 1) of the small sphere and the inner surface (surface
2) of the bigger sphere. The value of the view factor, F22 is: _________
(round off to 2 decimal places).
Given: View factor (Fij) is the fraction of the radiation leaving surface i
that is intercepted by surface j.

END OF THE QUESTION PAPER

MT-Copyright © GATE 2021 Page 27 of 27