LinkedIn Insight GATE 2015 Question Paper with Answer Keys for Metallurgical Engineering (MT) - Grad Plus

GATE 2015 Question Paper with Answer Keys for Metallurgical Engineering (MT)

Q. 1 – Q. 25 carry ONE mark each

Q.1 Consider the following five readings from an experiment: 19, 17, 15, 13, 11. The standard deviation of the readings is________.

ANS:-3.1 to 3.33

Q.2  $latex \frac{y\left(x+h\right)-y(x)}h$ is a numerical approximation for

(A) dy/dx

(B) dy/dh

(C) ∫y dx

(D) ∫x dy

ANS:-(A) dy/dx

Q.3  If A and B are matrices, (AB)T =

(A) ATB

(B) B TA

(C) ATBT

(D)BTAT   

ANS:-(D)BTA

Q.4 Which of the following properties is intensive?

(A) Volume

(B) Gibbs free energy

(C) Chemical potential

(D) Entropy

ANS:-(C) Chemical potential

Q.5 In an Ellingham diagram, the standard free energy change \triangle G^o for the oxidation reaction of a metal M given by: xM(s) + O2(g)→ MxO2(s) , is plotted as a function of temperature. The slope of this line is positive because

(A) \triangle S^o is positive

(B) \triangle S^o is negative

(C) \triangle H^o is positive

(D) \triangle H^o is negative

ANS:- (B) \triangle S^o is negative

Q.6 In froth flotation, hydrophobic mineral particles ascend with air bubbles preferentially over hydrophilic mineral particles. The figure below shows a schematic of a water droplet placed on the surfaces of two mineral P and Q.

Given this information, pick the CORRECT statement from the following:

(A) Mineral P ascends with air bubbles preferentially over mineral Q.

(B) Mineral Q ascends with air bubbles preferentially over mineral P.

(C) Both minerals P and Q ascend with the air bubbles without preference.

(D) Both minerals P and Q sink to the bottom.

ANS:- (A) Mineral P ascends with air bubbles preferentially over mineral Q.

Q.7 Which of the following oxide addition results in polymerization (i.e., network formation) in a silicate slag?

(A) CaO

(B) MgO

(C) P2O5

(D) Na2O

ANS:- (C) P2O5

Q.8 Zn is commercially extracted from which of the following minerals?

(A) Sphalerite

(B) Magnetite

(C) Chalcopyrite

(D) Galena

ANS:-(A) Sphalerite

Q.9 Self supporting arches for furnace roofs can be fabricated using silica bricks but not using magnesia bricks. Why?

(A) Silica has a significantly lower thermal expansion coefficient than magnesia at high temperatures.

(B) Silica has a significantly higher thermal conductivity than magnesia at high temperatures.

(C) Silica has a significantly lower melting point than magnesia.

(D) Silica is significantly more acidic than magnesia.

ANS:-(A) Silica has a significantly lower thermal expansion coefficient than magnesia at high temperatures.

Q.10 A species can diffuse through the lattice (diffusion coefficient, DL ), along grain boundaries (diffusion coefficient, DGB ), and along free surfaces (diffusion coefficient, DS ). Which of the following relations is CORRECT?

(A) DL > DGB > DS

(B) DS > DL > DGB

(C) DGB > DS > DL

(D) DS > DGB > DL

ANS:- (D) DS > DGB > DL

Q.11 Select the CORRECT plot of Gibbs free energy (G) vs. temperature (T) for a single component system from the following:

(A) P

(B) Q

(C) R

(D) S

ANS:-(B) Q

Q.12 If Δx represents adherent oxide layer thickness and t is time, which of the following curves represents diffusion-controlled oxidation kinetics?

(A) P

(B) Q

(C) R

(D) S

ANS:-(B) Q

Q.13 Based on the standard galvanic series, select the CORRECT sequence of metals in the increasing order of anodic behaviour:

(A) Zn, Fe, Pt, Cu

(B) Pt, Zn, Cu, Fe

(C) Fe, Pt, Cu, Zn

(D) Pt, Cu, Fe, Zn

ANS:-(D) Pt, Cu, Fe, Zn

Q.14 In a conventional unit cell of a crystal, a = b ≠ c and α= β = γ=90^o This crystal belongs to which of the following systems?

(A) Cubic

(B) Tetragonal

(C) Orthorhombic

(D) Triclinic

ANS:-(B) Tetragonal

Q.15In an X-Ray powder pattern of a simple cubic crystal, the 2nd peak corresponds to

(A) (111)

(B) (100)

(C) (200)

(D) (110)

ANS:-(D) (110)

Q.16 When boron (trivalent) is doped to silicon, the resulting material is

(A) a p-type semiconductor.

(B) an n-type semiconductor.

(C) a superconductor.

(D) an insulator.

ANS:-(A) a p-type semiconductor.

Q.17  Which of the following metal working operations can be categorized as an indirect compression process?

(A) Forging

(B) Wire drawing

(C) Extrusion

(D) Stretch forming

ANS:-(C) Extrusion
Q.18 Which of the following is a typical rolling defect?

(A) Buckling

(B) Edge cracking

(C) Cold shut

(D) Porosity

ANS:-(B) Edge cracking

Q.19 Which of the following manufacturing processes is NOT used for producing fine grained metals?

(A) Electrodeposition

(B) Czochralski method

(C) Equi-Channel Angular Pressing (ECAP)

(D) Sintering of milled powders

ANS:-(B) Czochralski method

Q.20 Which of the following metal forming techniques is used to produce soft drink cans from aluminium sheets?

(A) Rolling

(B) Forging

(C) Deep drawing

(D) Extrusion

ANS:-(C) Deep drawing

Q.21 Which of the following is NOT a solid state metal joining technique?

(A) Ultrasonic welding

(B) Friction welding

(C) Diffusion bonding

(D) Electroslag welding

ANS:-(D) Electroslag welding

Q.22  The stress required for Orowan dislocation bypass is 200 MPa in an alloy when the inter-precipitate spacing is 500 nm. In the same alloy, if the inter-precipitate spacing is reduced to 200 nm, the stress required (in MPa) is _ .

ANS:-490 to 510

Q.23 Which of the following Mohr’s circles of a plane-stress condition corresponds to equi-biaxial tension?

(A) P

(B) Q

(C) R

(D) S

ANS:-(D) S

Q.24 Select the INCORRECT statement related to the effect of a small amount of carbon addition on mechanical properties of iron.

(A) Ductile-Brittle-Transition-Temperature (DBTT) increases.

(B) Hardenability increases.

(C) Toughness increases.

(D) Yield point phenomenon occurs.

ANS:-(C) Toughness increases.

Q.25 In polymers such as epoxies, creep resistance can be enhanced by

(A) increasing the bulkiness of side groups.

(B) increasing the cross-link density.

(C) addition of plasticizers.

(D) annealing.

ANS:-(B) increasing the cross-link density.

Q. 26 – Q. 55 carry TWO marks each

Q.26 One of the eigenvalues of the matrix $latex \begin{bmatrix}-2&1\1&-2\end{bmatrix}$ is −3. The other eigenvalue is __.

ANS:- -1

Q.27 Consider the scalar function f=xyz . The magnitude of the gradient, i.e. \left|\nabla f\right| at the point (0,2,2) is _.

ANS:-4

Q.28 The determinant of the matrix $latex \begin{bmatrix}\cos\theta&\sin\theta&0\-\sin\theta&\cos\theta&0\0&0&1\end{bmatrix}$ is _

ANS:-1

Q.29 The solution of the ordinary differential equation \frac{dy}{dx}=5x for y|x=0=0

(A) 5

(B) \frac{5x^2}2

(C) 5x2

(D) e5x

ANS:- (B) \frac{5x^2}2

Q.30 The maximum value of the function f\left(x\right)=-x^2+2x is _.

ANS:-1

Q.31 C (s) + CO2 (g) ⇋ 2CO (g) is an important reaction in iron making.
Given ΔH0298= 172000 joules per mole of CO2, which of the following conditions will favour the forward reaction?

(A) Increasing both temperature and pressure.

(B) Decreasing temperature and increasing pressure.

(C) Decreasing both temperature and pressure.

(D) Increasing temperature and decreasing pressure.

ANS:-(D) Increasing temperature and decreasing pressure.

Q.32 Consider the reaction: Fe3O4 (solid, pure) + CO (gas, 1 atm) →3FeO (solid, pure) + CO2 (gas, 1 atm)
For this reaction, ΔG01200=−8000 joules per mole of CO and R = 8.314 J mol-1K-1.
The equilibrium ratio, pcO2 /pc0 for the reaction at 1200 K and 1 atm is __

ANS:-2.1 to 2.3

Q.33 An iron blast furnace produces hot metal containing 95% Fe. The iron ore charged into the furnace contains 95% Fe2O3 and the rest is gangue. Assume that all the iron in the ore goes to hot metal. The amount of iron ore (in kg) required for producing 1000 kg of hot metal is _ . (Atomic weight of Fe = 56 g mol-1 and that of Fe2O3 = 160 g mol-1)

ANS:-1400 to 1450

Q.34 The figure below shows water flowing through a pipe. The pressure difference between points P and Q measured using a water-over-mercury manometer is

(A) ρ2gH

(B) ρ1gℎ

(C) \left(\rho_2-\rho_1\right)g\;H

(D) \left(\rho_2-\rho_1\right)g\;h

ANS:-(C) \left(\rho_2-\rho_1\right)g\;H

Q.35 Match the metals listed in Group I with the most appropriate extraction routes listed in Group II.

Group IGroup II
P. Al1. Blast Furnace
Q. Ti2. Matte Smelting S. Fe
R. Cu3. Electrolysis of Fused Salts
S. Fe4. Halide Metallurgy

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

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

(C) P-2, Q-4, R-3, S-1

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

ANS:- (B) P-3, Q-4, R-2, S-1

Q.36 The figure below shows the cumulative size distribution of particles of a crushed mineral. 10 kg of this material is first passed through a sieve of size 400 micron and then through a sieve of size 300 micron. The weight of mineral (in kg) that is retained on the 300 micron sieve is __ .

ANS:-2.9 to 3.1

Q.37  In electrolytic refining of Ni, the anode is Cu-10 atom % Ni and the cathode is pure Ni. Assuming the Cu-Ni solution to be ideal, the ABSOLUTE value of the minimum voltage (in mV) required for refining is __ .

Given: Faraday constant = 96490 C mol-1, Temperature = 300 K, R = 8.314 J mol-1 K-1.

ANS:-29.5 to 30.0

Q.38 Configurational entropy due to ideal mixing in a binary A-B system is expressed as:
\triangle S_{mix}=-R\left(X_A\ln X_A+X_B\ln X_B\right), whereXAand XB are mole fractions of A and B respectively.
ΔSmix is maximum at XA =_

ANS:-0.5

Q.39 Melting point of a metal is 1356 K. When the liquid metal is undercooled to 1256 K, the free energy change for solidification, ΔGL→S = −1000 J mol-1. On the other hand, if the liquid metal is undercooled to 1200 K, the free energy change (in J mol-1) for solidification is _.

ANS:- -1600 to -1500

Q.40 Match the names listed in Group I with the reactions listed in Group II

Group IGroup II
P. Eutectic1. ????+????→????
Q. Peritectic2. ????→????+????
R. Peritectoid3. ????1→????2+????
S. Monotectic4. ????+????→????

(A) P-2, Q-3, R-1, S-4
(B) P-3, Q-4, R-1, S-2
(C) P-2, Q-4, R-1, S-3
(D) P-4, Q-1, R-2, S-3

ANS:-(C) P-2, Q-4, R-1, S-3

Q.41 It takes 10 hours to homogenize an alloy at 1273 K. The time required (in hours) to achieve the same extent of homogenization at 1373 K is _ .
Given: Diffusivity, D1373 K = 10−18m2s-1 and D1273 K = 10−19m2 s-1

ANS:-1

Q.42  Match the materials listed in Group I with the most appropriate applications listed in Group II

Group IGroup II
P. Iron-Silicon alloy1. Heating element
Q. GaAs2. Ultrasonic generator
R. Nichrome3. Transformer core
S. Quartz crystals4. Light emitting diode

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

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

(C) P-1, Q-3, R-4, S-2

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

ANS:-(A) P-3, Q-4, R-1, S-2

Q.43 Match the heat treatments for an eutectoid steel shown in the TTT diagram below (as P, Q, R and S) with the resulting microstructures listed below:

  1. Fine pearlite
  2. Martensite
  3. Bainite
  4. Coarse pearlite

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

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

(C) P-2, Q-1, R-3, S-4

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

ANS:-(B) P-4, Q-1, R-3, S-2

Q.44 An alloy of overall composition XB=0.7 was equilibrated at temperature T1. Microstructural analysis showed two phases, α and β, and that the phase fraction of β was 0.75. Given that the equilibrium composition of β at T1 is 0.9 as shown in the phase diagram below, the maximum solubility of B in α (in mole fraction) at this temperature is _.

ANS:- 0.09 to 0.11

Q.45  If a cylindrical billet of height 1.0 m and diameter 0.5 m is upset forged to form a cylindrical pancake of height 0.25 m, the diameter of the pancake (in m) is __ .

ANS:-0.9 to 1.1

Q.46 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r] Assertion: In a pure metal weld, elastic modulus in the heat affected zone (HAZ) is the same as that in the base metal. Reason: Coarse grained microstructure in the HAZ results in lower hardness.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true and [r] is not the correct reason for [a]

(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

ANS:-(B) Both [a] and [r] are true and [r] is not the correct reason for [a]

Q.47 At the mould exit of a continuous caster, the metal consisting of a solidified shell with a liquid metal core exits at the rate of 35 kg s-1. Given that the latent heat of fusion is 3 × 105 J kg-1 and the total rate of heat removal by the mould is 4.2 × 106 W, the mass fraction of solid at the mould exit is _. Assume that both solid and liquid remain at the melting point while they are in the mould.

ANS:-0.39 to 0.41

Q.48 Match the features observed in castings listed in Group I with the most appropriate reasons listed in Group II

Group IGroup II
P. Macrosegregation1. Inoculation
Q. Fine grained structure2. Gas evolution and shrinkage
R. Porosity3. Temperature gradients and supercooling
S. Dendrites4. Density difference and convection currents

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

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

(C) P-2, Q-4, R-1, S-3

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

ANS:-(B) P-4, Q-1, R-2, S-3

Q.49 The driving force for sintering a compact consisting of spherical particles of radius R1 is ΔG1. If the particle size is reduced to R2 = 0.1 R1, the corresponding driving force ΔG2 = α ΔG1 , where α is _ .

ANS:-10

Q.50 Which of the following techniques are NOT applicable for detecting internal flaws in a ceramic material?

  1. Liquid penetration test
  2. Radiography
  3. Ultrasonic testing
  4. Eddy current method

(A) 1 and 3

(B) 3 and 4

(C) 2 and 4

(D) 1 and 4

ANS:-(D) 1 and 4

Q.51 Match the following fracture surface features listed in Group I with the fracture mechanisms listed in Group II

Group IGroup II
P. Striations1. Intergranular fracture
Q. Dimples and microvoids2. Cleavage fracture
R. Flat facets and “river markings”3. Ductile fracture
S. Jagged surface with grain-like features4. Fatigue fracture

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

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

(C) P-4, Q-3, R-2, S-1

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

ANS:-(C) P-4, Q-3, R-2, S-1

Q.52 Match the scientist pairs listed in Group I with phenomena listed in Group II

Group IGroup II
P. Hall-Petch1. Dislocation reaction product
Q. Nabarro-Herring2. Diffusional creep
R. Lomer-Cottrell3. Dislocation source
S. Frank-Read4. Grain boundary strengthening

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

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

(C) P-4, Q-2, R-1, S-3

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

ANS:-(C) P-4, Q-2, R-1, S-3

Q.53 In an FCC crystal, the strain energy per unit length of a dislocation with Burgers vector \frac a2<110> is _ times that of a a\frac a6<112> dislocation.

ANS:-3

Q.54 Match the desired mechanical properties listed in Group I with the microstructural features listed in Group II

Group IGroup II
P. Creep resistance1. Fine grained two-phase microstructure
Q. Elastic modulus enhancement2. Single crystal
R. Super plasticity3. Coherent precipitates
S. Increased strength4. Glass fibres in epoxy

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

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

(C) P-2, Q-4, R-1, S-3

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

ANS:-(C) P-2, Q-4, R-1, S-3

Q.55 A brittle material is mechanically tested in medium P in which it has surface energy γg= 0.9 J m-2. This material has a fracture strength of 300 MPa for a given flaw size. The same solid containing the same flaws is then tested in medium Q in which γs= 0.1 J m -2. The fracture strength (in MPa) in medium Q based on Griffith’s theory is _ .

ANS:-100

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