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Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test)


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Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 1

“When she fell down the _______, she received many _______ but little help.” The words that best fill the blanks in the above sentence are

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 2

“In spite of being warned repeatedly, he failed to correct his _________ behaviour.” The word that best fills the blank in the above sentence is

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 3

For 0 ≤ �� ≤ 2��, sin �� and cos �� are both decreasing functions in the interval ________.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 4

The area of an equilateral triangle is √3. What is the perimeter of the triangle? 

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 5

Arrange the following three-dimensional objects in the descending order of their volumes: (i) A cuboid with dimensions 10 cm, 8 cm and 6 cm (ii) A cube of side 8 cm (iii) A cylinder with base radius 7 cm and height 7 cm (iv) A sphere of radius 7 cm

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 6

An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 7

A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 8

To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 9

 If �� 2 + �� − 1 = 0 what is the value of ?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 10

 In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another unrelated study, it was found that the revenue from cracker sales in India which remained fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. The solid line in the graph below refers to annual sale of crackers and the dashed line refers to the annual crow births in India. Choose the most appropriate inference from the above data.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 11

For a laminar flow of a liquid metal over a flat plate, the thicknesses of the velocity and thermal boundary layers are δv and δt respectively. Kinematic viscosity (viscosity/density) of liquid metal is significantly lower than its thermal diffusivity [thermal conductivity / (density × specific heat)]. Based on this information, pick the correct option.

(Note: The temperature of the liquid metal is different from that of the plate).

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 12

What is the most-abundant anion in a 2CaO.SiO2 melt?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 13

Analysis of a flow phenomenon in a system requires the following variables:

i. Pressure [M L-1 T -2]

ii. Velocity of the fluid [L T -1]

iii. Size of the system [L]

iv. Density of the fluid [M L-3]

v. Viscosity of the fluid [M L-1 T -1]

According to Buckingham Pi theorem (dimensional analysis) what is the number of independent DIMENSIONLESS variables needed to describe this system?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 14

In froth flotation, the primary purpose of adding collectors is to:

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 15

Arrange the following in the correct sequence of operations in an integrated steel plant:

i. Basic Oxygen Furnace (BOF)

ii. Blast Furnace (BF)

iii. Ruhrstahl Heraeus Degassing Process (RH)

iv. Ladle Furnace Process (LF)

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 16

During decarburization in a steel bath at 1550 oC, the compositions of dissolved C (wt.%C) and dissolved O (wt.%O) follow the relation: (wt.%C)(wt.%O) = K

When the partial pressure of CO (��co ) is 1 atm, K =  0.002.

If ��co = 0.1 atm, what is the value of K, at the same temperature?

Note: Assume Henry’s law is applicable.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 17

During upset forging, and considering friction, which of the following profiles represents the axial compressive stress?Note: In these profiles, the absolute value of the axial compressive stress is plotted on the y-axis.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 18

Consider the following engineering components:

P. Gas turbine blades

Q. Tungsten-based heavy alloy penetrators

R. Self-lubricating bearings

S. Engine block of an automobile

Which of the following two components are produced by powder metallurgy?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 19

Which of the following materials are protected by passivation (i.e., formation of a thin adherent film on the surface) from corrosion?

P. Aluminium alloys

Q. Mild steel

R. Stainless steel

S. Silver

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 20

The c/a ratio of Zn (hcp) is 1.856. Slip at room temperature occurs most easily on which of the following slip systems in Zn: Note: In hcp metals, the ideal c/a ratio is 1.633.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 21

At equilibrium, the maximum number of phases in a three-component system at CONSTANT PRESSURE is:

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 22

For a single phase system with K components, the exact differential of Gibbs free energy is given as : 

Which one of the following can be derived from the above expression as a Maxwell’s relation?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 23

For intrinsic Si at room temperature, the electron concentration = the hole concentration = 1 × 1016 m−3 , and the electron and hole mobilities are 0.1 and 0.2 m2 . V −1 . s−1 respectively.

What is the room temperature electrical conductivity?The charge of an electron is 1.6 × 10−19 C.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 24

To minimize refractory loss during BOF steel-making, slag is supersaturated with which of the following:

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 25

Which of the following welding processes is NOT suitable for joining thin metal sheets?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 26

Which of the following categories of materials is suitable as a filler for brazing of steel sheets?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 27

Arrange the following processes in INCREASING magnitude of surface roughness of the casting.

P. Investment casting

Q. Permanent mould casting

R. Pressure die casting

S. Sand casting

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 28

In a Jominy end-quench test of the eutectoid plain-carbon steel, which of the following represents the sequence of microstructures observed from the quenched end of the specimen?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 29

A long oil pipeline made of steel is suspected to have developed a scale on the inner surface due to corrosion. Which of the following non-destructive techniques is the most suitable for detecting and quantifying such a defect?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 30

A steel is plastically worked in the temperature range below the nose of the TTT curve and above Ms, followed by quenching to produce fine martensite. What is this process called?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 31

What is the requirement for equilibrium at a triple junction as shown in the schematic, with γ12 , γ23 and γ13 as grain boundary tensions and δ1  , δ2  and δ3 as dihedral angles?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 32

In the A-rich end of the A-B binary eutectic phase diagram (shown below), the solidus and liquidus are straight lines. 


The freezing range of the alloy with 16% B is _________ (in oC to one decimal place)


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 33

A vector field is given as follows:
The divergence of this field evaluated at (x, y) = (2, 2) is _______________ .


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 34

A plate of thickness h = 120 mm is cold rolled in a mill with a roll diameter of 200 mm. If the coefficient of friction µ is 0.1, the maximum possible reduction Δh in a single pass is ________ (in mm to one decimal place)


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 35

A copper-aluminium diffusion couple develops a certain concentration profile after an isothermal treatment at 600°C for 10 hours. The time required to achieve the same concentration profile at 500°C is _________ (in hours to 1 decimal place) Given: The interdiffusion coefficient for copper in aluminium at 500°C and 600°C are 4×10-14 m2s-1 and 8×10-13 m2s-1.


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 36

The molar free energy (J mol-1) of a liquid solution of a binary A-B alloy as a function of temperature ( T ) and composition (x, the mole fraction of B) is given by:

where are the molar free energies of pure liquid A and pure liquid B.What is the excess molar free energy,  for an alloy with x = 0.5 at T = 1000 K?Given:

Gas constant R = 8.314 J K-1 mol-1

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 37

Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Assertion [A]: For a material exhibiting Coble creep, a reduction in grain size results in a significant increase in creep rate

Reason [R]: Grain boundaries act as a barrier to motion of dislocations

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 38

 Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Assertion [A]: Refractory BCC metals like W and Mo are less ductile than FCC metals like Ni and Pt at room temperature

Reason [R]: BCC metals have fewer independent slip systems than FCC metals

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 39

A glass fibre of 5 micron diameter is subjected to a tensile stress of 20 MPa. The surface energy and elastic modulus of this material are 0.3 Jm-2 and 70 GPa, respectively. Pick the correct answer based on the information provided above:

Note: The glass fibre contains a population of flaws of different lengths.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 40

Two equal and opposite point charges + Q and  - Q are located as shown in the figure above. A surface integral, Fi is defined on surface Si of a sphere of radius ���� as follows:

where is the electric field, and ��̂ is the unit normal to the surface of integration.
If ��1: ��2: ��3 are in the ratio 1: 2: 5, use the Gauss divergence theorem to determine the ratio F1: F2 : F3 .

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 41

Match the four tensile stress-strain curves (P,Q, R, S) with the materials listed in the box:


 

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 42

Match the metal in Group 1 with the appropriate extractive process in Group 2

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 43

Fe is produced in a reactor using pure Fe2O3, C and O2. For every mole of Fe produced, 2.38 moles of C is used.  The exit gas from the reactor contains CO and CO2 in the molar ratio of 1:1.  How many moles of O2 is consumed for every mole of Fe produced?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 44

What is the voltage required to electrolytically refine impure copper of activity ��cu = 0.9 (Raoultian standard state) to pure copper at 300 K

Given: Gas constant R = 8.314 J mol- 1 K- 1, and Faraday’s constant F = 96500 C mol - 1.

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 45

Consider the following Ordinary Differential Equation:


In a domain 0 ≤ x ≤ t, with boundary conditions c(0) = 0.5 and c(t) = 1.0, pick the appropriate choice for  c(x) from the following options:

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 46

Match the manufacturing processes in Group 1, with the types of cracks in Group 2:

Detailed Solution for Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 46

C (or) D

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 47

Consider a dilute substitutional solid solution of X in a metal A. The powder diffraction pattern of this alloy reveals that all the peaks have shifted to the left when compared to those for pure A (with no splitting of peaks). If such a solute interacts and segregates to an edge dislocation, which of the following positions around the dislocation will it preferentially occupy?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 48

A classroom of 20 students can be categorized on the basis of blood-types: 5 students each with “A”, “B”, “AB”, and “O” blood-types. If four students are selected at random from this class, what is the probability that each student has a different blood-type?

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 49

If the solid-liquid interfacial energy increases by 10%, the energy barrier for homogeneous nucleation of a spherical solid from the liquid, will change by:

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 50

Consider the following stress state imposed on a material:.If the material responds elastically with a volumetric strain Δ = 3.5 × 10−4 , what is its bulk modulus?

Detailed Solution for Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 50

0.96 to 0.98

Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 51

A continuous and aligned carbon-fiber composite consists of 25 vol. % of fibers in an epoxy matrix. The Young’s modulus of fiber and matrix, respectively are Ef = 250 GPa and Em = 2.5 GPa. 

If the composite is subjected to longitudinal loading (iso-strain condition and assuming elastic response), the fraction of load borne by the reinforcement is ________ (to two decimal places)


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 52

Pure iron transforms from body centered cubic (BCC) to face centered cubic (FCC) crystal structure at 912 °C. If the lattice parameter of the BCC phase is 0.293 nm and that of the FCC phase is 0.363 nm, the associated volume change is  _______ (in % to one decimal place)


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 53

As shown in schematic below, an alloy is cast as a rectangular slab between two thick mould walls that differ in their thermal conductivities. Shrinkage defects are found at a distance L1 from Mould-1 with thermal conductivity ��1 and distance L2 from Mould-2 with thermal conductivity ��2. If the ratio L1:L2 = 3:2, and assuming 1-D heat transfer, the ratio  (��1⁄��2 ) is ________ (to two decimal places)


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 54

The temperature profile (T in Kelvin) of an arc weld across its width is given as T = 2000 exp(−0.3x 2) where x (in mm) is the distance from the weld centre. The melting point of the base material is 1500 K. The width of the fusion zone is _______ (in mm to two decimal places).


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 55

The terminal velocity (��) of a spherical inclusion of diameter D = 50 micrometers rising in liquid steel is __________ (in mm s-1 to two decimal places)

Assume Stokes law; i.e., drag force Fd = 35 5πμDv, where μ is the viscosity of steel.
Given: Density of liquid steel = 7900 kg m-3; Viscosity of liquid steel = 0.0079 Pa s; Density of the inclusion = 2500 kg m-3; Acceleration due to gravity = 9.8 m s-2


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 56

A single crystal of aluminium is subjected to 10 MPa tensile stress along the [321] crystallographic direction. The resolved shear stress on the (111̅ ) [101] slip system is ______ (in MPa to two decimal places)


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 57

If the net magnetic moment of an Fe atom in BCC structure is 2 ��B , then the saturation magnetization of Fe is ___________ (kA m-1 to one decimal place)

Given: ��B = 9.273 × 10- 24 A m2; Lattice parameter of BCC iron is 0.287 nm Note: kA is kiloAmperes


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 58

If 2 moles of Au and 3 moles of Ag are mixed to form a single-phase ideal solid solution, the total entropy of mixing is __________ (on J K-1 to one decimal place )

Given: Gas constant R = 8.314 J K-1 mol-1


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 59

A spherical liquid metal droplet of diameter 1 mm is solidified in a stream of gas at 300 K. Assuming that the metal droplet remains at its melting point of 900 K and neglecting radiative losses, the time to complete the solidification is __________ (in seconds to one decimal place).
Given: The enthalpy of fusion for the metal is 4000 kJ kg-1; The gas-droplet convective heat transfer coefficient is 200 W m-2 K-1; Density of liquid metal is 2700 kg m-3.


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 60

At a temperature of 710 K, the vapour pressure of pure liquid Zn is given by: ����n (����n = 1.0) = 3.6 × 10−4atm.
The Raoultian activity coefficient (γ��n ) of Zn in Zn-Cd alloy liquid  at 710 K is approximated by: 
ln(γ��n ) = 0.875(1 − ����n )2
The ratio for a liquid alloy with ����n = 0.7 is __________ (to two decimal places).


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 61

For the reaction: 4Ag(s, pure) + O2 (g) ⟶ 2Ag2 O(s, pure), the standard enthalpy change, ∆S0 = − 61080 J, and the standard entropy change, ∆H0 = − 132.22 J K−1, in the temperature range from 298 K to 500 K. The temperature above which Ag2 O decomposes in an atmosphere containing oxygen at a partial pressure ��o2 = 0.3 atm is __________ (in K to one decimal place).
Given: Gas constant R = 8.314 J K-1 mol-1


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 62

In a powder diffraction experiment on BCC iron, the first peak occurs at 2�� = 68.7°. The wavelength of X-rays is  _________ (in nm to three decimal places).

Given: The lattice parameter of iron  = 0.287 nm


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 63

A 1 mol piece of copper at 400 K is brought in contact with another 1 mol piece of copper at 300 K, and allowed to reach thermal equilibrium. The entropy change for this process is __________  (in J K-1 to three decimal places)

Given: Specific heat capacity of copper (between 250 K and 500 K) is 22.6 J K-1mol-1.
Assume that the system containing the two pieces of copper remains isolated during this process.


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 64

Using the trapezoidal rule with two equal intervals (n = 2, Δx = 1), the definite integral 
______________ (to two decimal places).


Metallurgical Engineering - (MT) 2018 GATE Paper (Practice Test) - Question 65

The ideal plastic work involved in extruding a cylindrical billet of length 100 mm, from an initial diameter of 20 mm to a final diameter of 16 mm is __________ (in J to one decimal place). 
The flow stress in compression is 40 MPa, and remains constant throughout the process.


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