GATE 2025 Question Paper Metallurgical Engineering (MT)
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Page 1
GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.
Page 2
General Aptitude
Q.1 – Q.5 Carry ONE mark Each
Q.1 Despite his initial hesitation, Rehman’s _________ to contribute to the success of
the project never wavered.
Select the most appropriate option to complete the above sentence.
(A) ambivalence
(B) satisfaction
(C) resolve
(D) revolve
Organizing Institute: IIT Roorkee Page 1 of 51
Q.1 – Q.5 Carry ONE mark Each
Q.1 Despite his initial hesitation, Rehman’s _________ to contribute to the success of
the project never wavered.
Select the most appropriate option to complete the above sentence.
(A) ambivalence
(B) satisfaction
(C) resolve
(D) revolve
Organizing Institute: IIT Roorkee Page 1 of 51
Page 3
Q.2 Bird : Nest :: Bee : _______
Select the correct option to complete the analogy.
(A) Kennel
(B) Hammock
(C) Hive
(D) Lair
Organizing Institute: IIT Roorkee Page 2 of 51
Select the correct option to complete the analogy.
(A) Kennel
(B) Hammock
(C) Hive
(D) Lair
Organizing Institute: IIT Roorkee Page 2 of 51
Page 4
Q.3 If 𝑃𝑒 𝑥 = 𝑄𝑒 −𝑥 for all real values of 𝑥, which one of the following statements is
true?
(A) 𝑃=𝑄=0
(B) 𝑃=𝑄=1
(C) 𝑃 = 1; 𝑄 = −1
(D) 𝑃
=0
𝑄
Organizing Institute: IIT Roorkee Page 3 of 51
true?
(A) 𝑃=𝑄=0
(B) 𝑃=𝑄=1
(C) 𝑃 = 1; 𝑄 = −1
(D) 𝑃
=0
𝑄
Organizing Institute: IIT Roorkee Page 3 of 51
Page 5
Q.4 The paper as shown in the figure is folded to make a cube where each square
corresponds to a particular face of the cube. Which one of the following options
correctly represents the cube?
Note: The figures shown are representative.
(A)
(B)
(C)
(D)
Organizing Institute: IIT Roorkee Page 4 of 51
corresponds to a particular face of the cube. Which one of the following options
correctly represents the cube?
Note: The figures shown are representative.
(A)
(B)
(C)
(D)
Organizing Institute: IIT Roorkee Page 4 of 51
Page 6
Q.5 Let 𝑝1 and 𝑝2 denote two arbitrary prime numbers. Which one of the following
statements is correct for all values of 𝑝1 and 𝑝2 ?
(A) 𝑝1 + 𝑝2 is not a prime number.
(B) 𝑝1 𝑝2 is not a prime number.
(C) 𝑝1 + 𝑝2 + 1 is a prime number.
(D) 𝑝1 𝑝2 + 1 is a prime number.
Organizing Institute: IIT Roorkee Page 5 of 51
statements is correct for all values of 𝑝1 and 𝑝2 ?
(A) 𝑝1 + 𝑝2 is not a prime number.
(B) 𝑝1 𝑝2 is not a prime number.
(C) 𝑝1 + 𝑝2 + 1 is a prime number.
(D) 𝑝1 𝑝2 + 1 is a prime number.
Organizing Institute: IIT Roorkee Page 5 of 51
Page 7
Q.6 – Q.10 Carry TWO marks Each
Q.6 Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to
see you”, Ramya told Josephine.
(A) Ramya knew that Josephine was in the hospital.
(B) Ramya did not know that Josephine was in the hospital.
(C) Ramya and Josephine were once close friends; but now, they are not.
(D) Josephine was in the hospital due to an injury to her leg.
Organizing Institute: IIT Roorkee Page 6 of 51
Q.6 Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to
see you”, Ramya told Josephine.
(A) Ramya knew that Josephine was in the hospital.
(B) Ramya did not know that Josephine was in the hospital.
(C) Ramya and Josephine were once close friends; but now, they are not.
(D) Josephine was in the hospital due to an injury to her leg.
Organizing Institute: IIT Roorkee Page 6 of 51
Page 8
Q.7 If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which
one among the given options is the most appropriate code for BEACH ?
(A) CEADP
(B) IDBFC
(C) JGIBC
(D) IBCEC
Organizing Institute: IIT Roorkee Page 7 of 51
one among the given options is the most appropriate code for BEACH ?
(A) CEADP
(B) IDBFC
(C) JGIBC
(D) IBCEC
Organizing Institute: IIT Roorkee Page 7 of 51
Page 9
Q.8 Which one of the following options is correct for the given data in the table?
Iteration (i) 0 1 2 3
Input (I) 20 −4 10 15
Output (X) 20 16 26 41
Output (Y) 20 −80 −800 −12000
(A) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0
(B) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1) + 𝐼(𝑖); 𝑖>0
(C) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0
(D) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖 − 1); 𝑖>0
Organizing Institute: IIT Roorkee Page 8 of 51
Iteration (i) 0 1 2 3
Input (I) 20 −4 10 15
Output (X) 20 16 26 41
Output (Y) 20 −80 −800 −12000
(A) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0
(B) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1) + 𝐼(𝑖); 𝑖>0
(C) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0
(D) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖 − 1); 𝑖>0
Organizing Institute: IIT Roorkee Page 8 of 51
Page 10
Q.9 In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The
corner L of the rectangle is on the side QR. Side MN of the rectangle passes through
the corner S of the square.
What is the area (in cm2) of the rectangle PLMN?
Note: The figure shown is representative.
N
P S
M
Q L R
(A) 2√2
(B) 2
(C) 8
(D) 4
Organizing Institute: IIT Roorkee Page 9 of 51
corner L of the rectangle is on the side QR. Side MN of the rectangle passes through
the corner S of the square.
What is the area (in cm2) of the rectangle PLMN?
Note: The figure shown is representative.
N
P S
M
Q L R
(A) 2√2
(B) 2
(C) 8
(D) 4
Organizing Institute: IIT Roorkee Page 9 of 51
Page 11
Q.10 The diagram below shows a river system consisting of 7 segments, marked P, Q, R,
S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We
need to connect these zones using the least number of bridges. Out of the following
options, which one is correct?
Note: The figure shown is representative.
Z2 Z3
R
V
P T
Q Z4
Z1 U
S Z5
(A) Bridges on P, Q, and T
(B) Bridges on P, Q, S, and T
(C) Bridges on Q, R, T, and V
(D) Bridges on P, Q, S, U, and V
Organizing Institute: IIT Roorkee Page 10 of 51
S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We
need to connect these zones using the least number of bridges. Out of the following
options, which one is correct?
Note: The figure shown is representative.
Z2 Z3
R
V
P T
Q Z4
Z1 U
S Z5
(A) Bridges on P, Q, and T
(B) Bridges on P, Q, S, and T
(C) Bridges on Q, R, T, and V
(D) Bridges on P, Q, S, U, and V
Organizing Institute: IIT Roorkee Page 10 of 51
Page 12
Q.11 – Q.35 Carry ONE mark Each
Q.11 Which one of the following matrices has eigenvalues 1 and 6?
(A) 5 −2
[ ]
−2 2
(B) 3 −1
[ ]
−2 2
(C) 3 −1
[ ]
−1 2
(D) 2 −1
[ ]
−1 3
Organizing Institute: IIT Roorkee Page 11 of 51
Q.11 Which one of the following matrices has eigenvalues 1 and 6?
(A) 5 −2
[ ]
−2 2
(B) 3 −1
[ ]
−2 2
(C) 3 −1
[ ]
−1 2
(D) 2 −1
[ ]
−1 3
Organizing Institute: IIT Roorkee Page 11 of 51
Page 13
Q.12 For an isobaric process, the heat transferred is equal to the change in ____________
of the system.
(A) enthalpy
(B) entropy
(C) Helmholtz free energy
(D) Gibbs free energy
Organizing Institute: IIT Roorkee Page 12 of 51
of the system.
(A) enthalpy
(B) entropy
(C) Helmholtz free energy
(D) Gibbs free energy
Organizing Institute: IIT Roorkee Page 12 of 51
Page 14
Q.13 Match each crystal defect in Column I with the corresponding type in Column II
Column I Column II
P. Edge dislocation 1. Zero-dimensional defect
Q. Stacking fault 2. One-dimensional defect
R. Frenkel defect 3. Two-dimensional defect
S. Porosity 4. Three-dimensional defect
(A) P – 3, Q – 4, R – 2, S – 1
(B) P – 3, Q – 4, R – 1, S – 2
(C) P – 2, Q – 3, R – 1, S – 4
(D) P – 2, Q – 4, R – 3, S – 1
Organizing Institute: IIT Roorkee Page 13 of 51
Column I Column II
P. Edge dislocation 1. Zero-dimensional defect
Q. Stacking fault 2. One-dimensional defect
R. Frenkel defect 3. Two-dimensional defect
S. Porosity 4. Three-dimensional defect
(A) P – 3, Q – 4, R – 2, S – 1
(B) P – 3, Q – 4, R – 1, S – 2
(C) P – 2, Q – 3, R – 1, S – 4
(D) P – 2, Q – 4, R – 3, S – 1
Organizing Institute: IIT Roorkee Page 13 of 51
Page 15
Q.14 At high temperatures, which one of the following empirical expressions correctly
describes the variation of dynamic viscosity 𝜇 of a Newtonian liquid with absolute
temperature 𝑇?
Given: 𝐴 and 𝐵 are positive constants.
(A) 𝜇 = 𝐴 + 𝐵𝑇
𝐵
(B) 𝜇 = 𝐴 exp (− )
𝑇
(C) 𝜇 = 𝐴 exp(𝐵𝑇)
𝐵
(D) 𝜇 = 𝐴 exp ( )
𝑇
Organizing Institute: IIT Roorkee Page 14 of 51
describes the variation of dynamic viscosity 𝜇 of a Newtonian liquid with absolute
temperature 𝑇?
Given: 𝐴 and 𝐵 are positive constants.
(A) 𝜇 = 𝐴 + 𝐵𝑇
𝐵
(B) 𝜇 = 𝐴 exp (− )
𝑇
(C) 𝜇 = 𝐴 exp(𝐵𝑇)
𝐵
(D) 𝜇 = 𝐴 exp ( )
𝑇
Organizing Institute: IIT Roorkee Page 14 of 51
Page 16
Q.15 Which one of the following is an intensive property?
(A) Chemical potential
(B) Volume
(C) Mass
(D) Entropy
Organizing Institute: IIT Roorkee Page 15 of 51
(A) Chemical potential
(B) Volume
(C) Mass
(D) Entropy
Organizing Institute: IIT Roorkee Page 15 of 51
Page 17
Q.16 Hot metal from a blast furnace is treated with mill scale prior to oxygen steelmaking
for ______.
(A) dephosphorization
(B) decarburization
(C) desulphurization
(D) desiliconization
Organizing Institute: IIT Roorkee Page 16 of 51
for ______.
(A) dephosphorization
(B) decarburization
(C) desulphurization
(D) desiliconization
Organizing Institute: IIT Roorkee Page 16 of 51
Page 18
Q.17 In optical microscopy, which one of the following combinations of wavelength (λ)
and numerical aperture (NA) provides the best spatial resolution?
(A) λ = 400 nm and NA = 1.0
(B) λ = 600 nm and NA = 1.2
(C) λ = 400 nm and NA = 1.2
(D) λ = 600 nm and NA = 1.0
Organizing Institute: IIT Roorkee Page 17 of 51
and numerical aperture (NA) provides the best spatial resolution?
(A) λ = 400 nm and NA = 1.0
(B) λ = 600 nm and NA = 1.2
(C) λ = 400 nm and NA = 1.2
(D) λ = 600 nm and NA = 1.0
Organizing Institute: IIT Roorkee Page 17 of 51
Page 19
Q.18 The coordination number for an octahedral site in pure copper is ______.
(A) 4
(B) 6
(C) 8
(D) 12
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(A) 4
(B) 6
(C) 8
(D) 12
Organizing Institute: IIT Roorkee Page 18 of 51
Page 20
Q.19 Consider the following gas-phase reaction:
2SO2 + O2 ⇌ 2SO3
If the enthalpy of reaction is negative, which one of the following conditions
promotes a higher equilibrium concentration of SO3?
(A) Higher pressure and higher temperature
(B) Higher pressure and lower temperature
(C) Lower pressure and higher temperature
(D) Lower pressure and lower temperature
Organizing Institute: IIT Roorkee Page 19 of 51
2SO2 + O2 ⇌ 2SO3
If the enthalpy of reaction is negative, which one of the following conditions
promotes a higher equilibrium concentration of SO3?
(A) Higher pressure and higher temperature
(B) Higher pressure and lower temperature
(C) Lower pressure and higher temperature
(D) Lower pressure and lower temperature
Organizing Institute: IIT Roorkee Page 19 of 51
Page 21
Q.20 Which one of the following slag components is responsible for the oxidizing power
of steelmaking slags?
(A) SiO2
(B) CaO
(C) MgO
(D) FeO
Organizing Institute: IIT Roorkee Page 20 of 51
of steelmaking slags?
(A) SiO2
(B) CaO
(C) MgO
(D) FeO
Organizing Institute: IIT Roorkee Page 20 of 51
Page 22
Q.21 Two randomly oriented polycrystalline copper samples with average grain sizes of
10 µm (Sample A) and 100 µm (Sample B) were tested at room temperature.
Given:
EA = Young’s modulus of Sample A
EB = Young’s modulus of Sample B
YSA = Yield strength of Sample A
YSB = Yield strength of Sample B
Which one of the following statements is CORRECT?
(A) EA > EB and YSA > YSB
(B) EA = EB and YSA < YSB
(C) EA > EB and YSA = YSB
(D) EA = EB and YSA > YSB
Organizing Institute: IIT Roorkee Page 21 of 51
10 µm (Sample A) and 100 µm (Sample B) were tested at room temperature.
Given:
EA = Young’s modulus of Sample A
EB = Young’s modulus of Sample B
YSA = Yield strength of Sample A
YSB = Yield strength of Sample B
Which one of the following statements is CORRECT?
(A) EA > EB and YSA > YSB
(B) EA = EB and YSA < YSB
(C) EA > EB and YSA = YSB
(D) EA = EB and YSA > YSB
Organizing Institute: IIT Roorkee Page 21 of 51
Page 23
Q.22 In metal casting, which one of the following gating ratios (sprue-runner-gate area
ratio) represents a non-pressurized gating system?
(A) 1:2:3
(B) 3:2:1
(C) 4:3:1
(D) 5:4:1
Organizing Institute: IIT Roorkee Page 22 of 51
ratio) represents a non-pressurized gating system?
(A) 1:2:3
(B) 3:2:1
(C) 4:3:1
(D) 5:4:1
Organizing Institute: IIT Roorkee Page 22 of 51
Page 24
Q.23 In the Fe-C system, the invariant reaction Liquid + 𝛿 ⇌ 𝛾 takes place at 1493 ℃.
This type of reaction is called ______.
(A) eutectic
(B) eutectoid
(C) peritectic
(D) monotectic
Organizing Institute: IIT Roorkee Page 23 of 51
This type of reaction is called ______.
(A) eutectic
(B) eutectoid
(C) peritectic
(D) monotectic
Organizing Institute: IIT Roorkee Page 23 of 51
Page 25
Q.24 Match the following elements in Column I with their respective ores in Column II.
Column I Column II
P. Al 1. Rutile
Q. Fe 2. Hematite
R. Ti 3. Chalcopyrite
S. Cu 4. Bauxite
(A) P – 4, Q – 2, R – 3, S – 1
(B) P – 2, Q – 4, R – 1, S – 3
(C) P – 3, Q – 1, R – 4, S – 2
(D) P – 4, Q – 2, R – 1, S – 3
Organizing Institute: IIT Roorkee Page 24 of 51
Column I Column II
P. Al 1. Rutile
Q. Fe 2. Hematite
R. Ti 3. Chalcopyrite
S. Cu 4. Bauxite
(A) P – 4, Q – 2, R – 3, S – 1
(B) P – 2, Q – 4, R – 1, S – 3
(C) P – 3, Q – 1, R – 4, S – 2
(D) P – 4, Q – 2, R – 1, S – 3
Organizing Institute: IIT Roorkee Page 24 of 51
Page 26
Q.25 Which of the following functions is/are expandable using Maclaurin series?
(A) ln(1 + 𝑧)
(B) ln 𝑧
(C) 1
𝑧2
(D) exp(𝑧)
Organizing Institute: IIT Roorkee Page 25 of 51
(A) ln(1 + 𝑧)
(B) ln 𝑧
(C) 1
𝑧2
(D) exp(𝑧)
Organizing Institute: IIT Roorkee Page 25 of 51
Page 27
Q.26 With reference to edge and screw dislocations, which of the following statements
is/are CORRECT?
(A) Both edge and screw dislocations can leave the slip plane by climb.
(B) Burgers vector of a screw dislocation is parallel to its line vector.
(C) Both edge and screw dislocations can leave the slip plane by cross-slip.
(D) Strain energy per unit length of an edge dislocation is higher than that of a screw
dislocation.
Organizing Institute: IIT Roorkee Page 26 of 51
is/are CORRECT?
(A) Both edge and screw dislocations can leave the slip plane by climb.
(B) Burgers vector of a screw dislocation is parallel to its line vector.
(C) Both edge and screw dislocations can leave the slip plane by cross-slip.
(D) Strain energy per unit length of an edge dislocation is higher than that of a screw
dislocation.
Organizing Institute: IIT Roorkee Page 26 of 51
Page 28
Q.27 Which of the following conditions is/are favorable for producing low-silicon hot
metal in blast furnace ironmaking?
(A) Reduced raceway adiabatic flame temperature
(B) Oxygen-enriched blast
(C) Lime injection through tuyeres
(D) Increased hearth temperature
Organizing Institute: IIT Roorkee Page 27 of 51
metal in blast furnace ironmaking?
(A) Reduced raceway adiabatic flame temperature
(B) Oxygen-enriched blast
(C) Lime injection through tuyeres
(D) Increased hearth temperature
Organizing Institute: IIT Roorkee Page 27 of 51
Page 29
Q.28 Which of the following statements is/are CORRECT with respect to the initial stage
of GP zone formation in a precipitation hardenable Al - 4.5 wt.% Cu alloy?
(A) GP zones are Cu-rich clusters.
(B) GP zones are CuAl2 precipitates.
(C) GP zones are incoherent with the matrix.
(D) GP zones are coherent with the matrix.
Organizing Institute: IIT Roorkee Page 28 of 51
of GP zone formation in a precipitation hardenable Al - 4.5 wt.% Cu alloy?
(A) GP zones are Cu-rich clusters.
(B) GP zones are CuAl2 precipitates.
(C) GP zones are incoherent with the matrix.
(D) GP zones are coherent with the matrix.
Organizing Institute: IIT Roorkee Page 28 of 51
Page 30
Q.29 Which of the following techniques can be used to detect an internal defect in a
metal casting?
(A) Ultrasonic inspection
(B) Liquid (or dye) penetrant inspection
(C) Gamma-ray radiography
(D) X-ray radiography
Organizing Institute: IIT Roorkee Page 29 of 51
metal casting?
(A) Ultrasonic inspection
(B) Liquid (or dye) penetrant inspection
(C) Gamma-ray radiography
(D) X-ray radiography
Organizing Institute: IIT Roorkee Page 29 of 51
Page 31
Q.30 Standard Gibbs free energies of formation of some solid oxides per mole of O2 at
1000 K are given below.
SiO2: −728 kJ, TiO2: −737 kJ, VO: −712 kJ, MnO: −624 kJ
Regarding thermodynamic feasibility of oxide reduction, which of the following
statements is/are CORRECT under standard conditions at 1000 K?
(A) Si can reduce TiO2.
(B) Mn can reduce VO.
(C) Ti can reduce MnO.
(D) V can reduce SiO2.
Organizing Institute: IIT Roorkee Page 30 of 51
1000 K are given below.
SiO2: −728 kJ, TiO2: −737 kJ, VO: −712 kJ, MnO: −624 kJ
Regarding thermodynamic feasibility of oxide reduction, which of the following
statements is/are CORRECT under standard conditions at 1000 K?
(A) Si can reduce TiO2.
(B) Mn can reduce VO.
(C) Ti can reduce MnO.
(D) V can reduce SiO2.
Organizing Institute: IIT Roorkee Page 30 of 51
Page 32
Q.31 Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian
liquid through a pipe. The maximum velocity in the pipe is proportional to which
of the following quantities?
Given: Δ𝑃 is the difference between the outlet and inlet pressure, 𝜇 is the dynamic
viscosity of the liquid, and 𝑅 and 𝐿 are radius and length of the pipe, respectively.
(A) Δ𝑃
(B) 1/𝑅 2
(C) 1/𝜇
(D) 1/𝐿
Organizing Institute: IIT Roorkee Page 31 of 51
liquid through a pipe. The maximum velocity in the pipe is proportional to which
of the following quantities?
Given: Δ𝑃 is the difference between the outlet and inlet pressure, 𝜇 is the dynamic
viscosity of the liquid, and 𝑅 and 𝐿 are radius and length of the pipe, respectively.
(A) Δ𝑃
(B) 1/𝑅 2
(C) 1/𝜇
(D) 1/𝐿
Organizing Institute: IIT Roorkee Page 31 of 51
Page 33
Q.32 The hydrostatic stress for the stress tensor provided below is ______ MPa
(in integer).
150 0 0
[ 0 −100 100] MPa
0 100 250
Q.33 For an application where the Reynolds number is to be kept constant, a liquid with
a density of 1 g cm−3 and viscosity 0.01 Poise results in a characteristic speed of
1 cm s −1 .
If this liquid is replaced by another with a density of 1.25 g cm−3 and viscosity of
0.015 Poise, the characteristic velocity will be ______ cm s−1 (rounded off to one
decimal place).
Assume the characteristic length of the flow to be the same in both cases.
Q.34 Consider the gas phase reaction:
1
CO + 2 O2 ⇌ CO2
At equilibrium for a particular temperature, the partial pressures of CO, O2, and CO2
are found to be 10−6 atm, 10−6 atm, and 16 atm, respectively. The equilibrium
constant for the reaction is ______ × 1010 (rounded off to one decimal place).
Organizing Institute: IIT Roorkee Page 32 of 51
(in integer).
150 0 0
[ 0 −100 100] MPa
0 100 250
Q.33 For an application where the Reynolds number is to be kept constant, a liquid with
a density of 1 g cm−3 and viscosity 0.01 Poise results in a characteristic speed of
1 cm s −1 .
If this liquid is replaced by another with a density of 1.25 g cm−3 and viscosity of
0.015 Poise, the characteristic velocity will be ______ cm s−1 (rounded off to one
decimal place).
Assume the characteristic length of the flow to be the same in both cases.
Q.34 Consider the gas phase reaction:
1
CO + 2 O2 ⇌ CO2
At equilibrium for a particular temperature, the partial pressures of CO, O2, and CO2
are found to be 10−6 atm, 10−6 atm, and 16 atm, respectively. The equilibrium
constant for the reaction is ______ × 1010 (rounded off to one decimal place).
Organizing Institute: IIT Roorkee Page 32 of 51
Page 34
Q.35 A linear regression model was fitted to a set of (𝑥, 𝑦) data. The total sum of squares
and sum of squares of error are 1200 and 120, respectively.
The coefficient of determination (𝑅 2 ) of the fit is ______ (rounded off to one
decimal place).
Organizing Institute: IIT Roorkee Page 33 of 51
and sum of squares of error are 1200 and 120, respectively.
The coefficient of determination (𝑅 2 ) of the fit is ______ (rounded off to one
decimal place).
Organizing Institute: IIT Roorkee Page 33 of 51
Page 35
Q.36 – Q.65 Carry TWO marks Each
Q.36 For two continuous functions 𝑀(𝑥, 𝑦) and 𝑁(𝑥, 𝑦), the relation 𝑀 𝑑𝑥 + 𝑁 𝑑𝑦 = 0
describes an exact differential equation if
(A) 𝜕𝑀 𝜕𝑁
=
𝜕𝑥 𝜕𝑦
(B) 𝜕𝑀 𝜕𝑁
=−
𝜕𝑥 𝜕𝑦
(C) 𝜕𝑀 𝜕𝑁
=
𝜕𝑦 𝜕𝑥
(D) 𝜕𝑀 𝜕𝑁
=−
𝜕𝑦 𝜕𝑥
Organizing Institute: IIT Roorkee Page 34 of 51
Q.36 For two continuous functions 𝑀(𝑥, 𝑦) and 𝑁(𝑥, 𝑦), the relation 𝑀 𝑑𝑥 + 𝑁 𝑑𝑦 = 0
describes an exact differential equation if
(A) 𝜕𝑀 𝜕𝑁
=
𝜕𝑥 𝜕𝑦
(B) 𝜕𝑀 𝜕𝑁
=−
𝜕𝑥 𝜕𝑦
(C) 𝜕𝑀 𝜕𝑁
=
𝜕𝑦 𝜕𝑥
(D) 𝜕𝑀 𝜕𝑁
=−
𝜕𝑦 𝜕𝑥
Organizing Institute: IIT Roorkee Page 34 of 51
Page 36
Q.37 Consider the phase diagram of a one component system given below. Vα, Vβ, and
VLiquid are the molar volumes of α, β, and liquid phases, respectively.
Which one of the following statements is TRUE?
Given: The change in molar enthalpies, ∆𝐻 𝛼→𝛽 and ∆𝐻𝛽→Liquid , are positive.
(A) Vα < Vβ and Vβ < VLiquid
(B) Vα > Vβ and Vβ < VLiquid
(C) Vα < Vβ and Vβ > VLiquid
(D) Vα > Vβ and Vβ > VLiquid
Organizing Institute: IIT Roorkee Page 35 of 51
VLiquid are the molar volumes of α, β, and liquid phases, respectively.
Which one of the following statements is TRUE?
Given: The change in molar enthalpies, ∆𝐻 𝛼→𝛽 and ∆𝐻𝛽→Liquid , are positive.
(A) Vα < Vβ and Vβ < VLiquid
(B) Vα > Vβ and Vβ < VLiquid
(C) Vα < Vβ and Vβ > VLiquid
(D) Vα > Vβ and Vβ > VLiquid
Organizing Institute: IIT Roorkee Page 35 of 51
Page 37
Q.38 Match the steel plant related processes in Column I with the associated information
in Column II.
Column I Column II
P. Corex 1. Melter-gasifier
Q. Electric Arc Furnace 2. Natural gas reformer
R. Midrex 3. Electromagnetic stirrer
S. Continuous Casting 4. Hot heel
(A) P – 1, Q – 4, R – 2, S – 3
(B) P – 1, Q – 4, R – 3, S – 2
(C) P – 2, Q – 4, R – 1, S – 3
(D) P – 1, Q – 3, R – 2, S – 4
Organizing Institute: IIT Roorkee Page 36 of 51
in Column II.
Column I Column II
P. Corex 1. Melter-gasifier
Q. Electric Arc Furnace 2. Natural gas reformer
R. Midrex 3. Electromagnetic stirrer
S. Continuous Casting 4. Hot heel
(A) P – 1, Q – 4, R – 2, S – 3
(B) P – 1, Q – 4, R – 3, S – 2
(C) P – 2, Q – 4, R – 1, S – 3
(D) P – 1, Q – 3, R – 2, S – 4
Organizing Institute: IIT Roorkee Page 36 of 51
Page 38
Q.39 Radiative heat flux 𝑞̇ at a hot surface at a temperature 𝑇𝑠 can be expressed as
𝑞̇ = 𝐴 𝑓(𝑇𝑠 , 𝑇∞ ) (𝑇𝑠 − 𝑇∞ )
where 𝐴 is a constant and 𝑇∞ is the temperature of the surroundings (temperatures
are expressed in K).
The function 𝑓(𝑇𝑠 , 𝑇∞ ) is given by ______.
(A) (𝑇𝑠 + 𝑇∞ )2(𝑇𝑠 − 𝑇∞ )
(B) (𝑇𝑠2 + 𝑇∞2 )(𝑇𝑠 + 𝑇∞ )
(C) (𝑇𝑠2 − 𝑇∞2 ) (𝑇𝑠 + 𝑇∞ )
(D) (𝑇𝑠 − 𝑇∞ )2(𝑇𝑠 + 𝑇∞ )
Organizing Institute: IIT Roorkee Page 37 of 51
𝑞̇ = 𝐴 𝑓(𝑇𝑠 , 𝑇∞ ) (𝑇𝑠 − 𝑇∞ )
where 𝐴 is a constant and 𝑇∞ is the temperature of the surroundings (temperatures
are expressed in K).
The function 𝑓(𝑇𝑠 , 𝑇∞ ) is given by ______.
(A) (𝑇𝑠 + 𝑇∞ )2(𝑇𝑠 − 𝑇∞ )
(B) (𝑇𝑠2 + 𝑇∞2 )(𝑇𝑠 + 𝑇∞ )
(C) (𝑇𝑠2 − 𝑇∞2 ) (𝑇𝑠 + 𝑇∞ )
(D) (𝑇𝑠 − 𝑇∞ )2(𝑇𝑠 + 𝑇∞ )
Organizing Institute: IIT Roorkee Page 37 of 51
Page 39
Q.40 Match the phenomena in Column I with the typical observations in Column II.
Column I Column II
P. Dynamic strain aging 1. Grain boundary sliding
Q. Recrystallization 2. Decrease in yield stress with a
reversal of loading direction
R. Bauschinger effect 3. Decrease in dislocation density
S. Superplasticity 4. Serrations in stress-strain curve
(A) P – 4, Q – 1, R – 2, S – 3
(B) P – 4, Q – 3, R – 2, S – 1
(C) P – 3, Q – 4, R – 2, S – 1
(D) P – 1, Q – 4, R – 2, S – 3
Organizing Institute: IIT Roorkee Page 38 of 51
Column I Column II
P. Dynamic strain aging 1. Grain boundary sliding
Q. Recrystallization 2. Decrease in yield stress with a
reversal of loading direction
R. Bauschinger effect 3. Decrease in dislocation density
S. Superplasticity 4. Serrations in stress-strain curve
(A) P – 4, Q – 1, R – 2, S – 3
(B) P – 4, Q – 3, R – 2, S – 1
(C) P – 3, Q – 4, R – 2, S – 1
(D) P – 1, Q – 4, R – 2, S – 3
Organizing Institute: IIT Roorkee Page 38 of 51
Page 40
Q.41 Which one of the following matrices is orthogonal?
(A) 1/2 −√3/2
[ ]
−√3/2 1/2
(B) 1/2 −√3/2
[ ]
√3/2 1/2
(C) 1/√2 −√3/2
[ ]
−√3/2 1/2
(D) 1/√2 −√3/2
[ ]
√3/2 −1/√2
Organizing Institute: IIT Roorkee Page 39 of 51
(A) 1/2 −√3/2
[ ]
−√3/2 1/2
(B) 1/2 −√3/2
[ ]
√3/2 1/2
(C) 1/√2 −√3/2
[ ]
−√3/2 1/2
(D) 1/√2 −√3/2
[ ]
√3/2 −1/√2
Organizing Institute: IIT Roorkee Page 39 of 51
Page 41
Q. 42 Match the casting defects in Column I with the characteristic features
in Column II.
Column I Column II
P. Misrun 1. Penetration of liquid metal behind
surface layer of sand moulds
Q. Expansion scab 2. Metal solidifies prematurely in the
mould and some sections of the
casting are not filled
R. Pin holes 3. Cracking because of restraint to
contraction in certain areas of the
casting during solidification and
cooling to room temperature
S. Hot tearing 4. Evolution of gases during
solidification resulting in porosity
(A) P – 2, Q – 4, R – 3, S – 1
(B) P – 1, Q – 3, R – 2, S – 4
(C) P – 1, Q – 2, R – 4, S – 3
(D) P – 2, Q – 1, R – 4, S – 3
Organizing Institute: IIT Roorkee Page 40 of 51
in Column II.
Column I Column II
P. Misrun 1. Penetration of liquid metal behind
surface layer of sand moulds
Q. Expansion scab 2. Metal solidifies prematurely in the
mould and some sections of the
casting are not filled
R. Pin holes 3. Cracking because of restraint to
contraction in certain areas of the
casting during solidification and
cooling to room temperature
S. Hot tearing 4. Evolution of gases during
solidification resulting in porosity
(A) P – 2, Q – 4, R – 3, S – 1
(B) P – 1, Q – 3, R – 2, S – 4
(C) P – 1, Q – 2, R – 4, S – 3
(D) P – 2, Q – 1, R – 4, S – 3
Organizing Institute: IIT Roorkee Page 40 of 51
Page 42
Q.43 The following are the activation energies for diffusion of carbon and iron at 773 K
in polycrystalline BCC iron:
P = Activation energy for diffusion of carbon in BCC iron through the lattice
Q = Activation energy for diffusion of iron in BCC iron through the lattice
R = Activation energy for diffusion of iron in BCC iron along the grain boundary
Which one of the following statements is CORRECT?
(A) R<P<Q
(B) R<Q<P
(C) Q<P<R
(D) P<R<Q
Organizing Institute: IIT Roorkee Page 41 of 51
in polycrystalline BCC iron:
P = Activation energy for diffusion of carbon in BCC iron through the lattice
Q = Activation energy for diffusion of iron in BCC iron through the lattice
R = Activation energy for diffusion of iron in BCC iron along the grain boundary
Which one of the following statements is CORRECT?
(A) R<P<Q
(B) R<Q<P
(C) Q<P<R
(D) P<R<Q
Organizing Institute: IIT Roorkee Page 41 of 51
Page 43
Q.44 Front tension is applied during cold rolling of a thin metal sheet. Which of the
following statements is/are TRUE?
(A) The neutral point shifts towards the roll entrance.
(B) The rolling load is decreased.
(C) The neutral point shifts towards the roll exit.
(D) The rolling load is increased.
Q.45 Which of the following statements is/are CORRECT when Ni is added as an
alloying element to a low alloy steel?
(A) Hardenability is increased AND the Ms temperature is lowered.
(B) Hardenability is decreased AND the Ms temperature is lowered.
(C) Hardenability is increased AND the Ms temperature is raised.
(D) Hardenability is decreased AND the Ms temperature is raised.
Organizing Institute: IIT Roorkee Page 42 of 51
following statements is/are TRUE?
(A) The neutral point shifts towards the roll entrance.
(B) The rolling load is decreased.
(C) The neutral point shifts towards the roll exit.
(D) The rolling load is increased.
Q.45 Which of the following statements is/are CORRECT when Ni is added as an
alloying element to a low alloy steel?
(A) Hardenability is increased AND the Ms temperature is lowered.
(B) Hardenability is decreased AND the Ms temperature is lowered.
(C) Hardenability is increased AND the Ms temperature is raised.
(D) Hardenability is decreased AND the Ms temperature is raised.
Organizing Institute: IIT Roorkee Page 42 of 51
Page 44
Q.46 Which of the following statements is/are CORRECT with respect to fusion welding
and solid-state welding of metals and alloys?
(A) Thermomechanically affected zone is found in the fusion welding of pure metals.
(B) Partially melted zone is NOT found in the fusion welding of pure metal.
(C) Diffusion bonding is one type of solid-state welding process.
(D) Partially melted zone is found in the fusion welding of alloys with a large freezing
range.
Q.47 Which of the following welding processes does NOT / do NOT utilize consumable
electrode?
(A) Plasma arc welding
(B) Gas metal arc welding
(C) Shielded metal arc welding
(D) Electron beam welding
Organizing Institute: IIT Roorkee Page 43 of 51
and solid-state welding of metals and alloys?
(A) Thermomechanically affected zone is found in the fusion welding of pure metals.
(B) Partially melted zone is NOT found in the fusion welding of pure metal.
(C) Diffusion bonding is one type of solid-state welding process.
(D) Partially melted zone is found in the fusion welding of alloys with a large freezing
range.
Q.47 Which of the following welding processes does NOT / do NOT utilize consumable
electrode?
(A) Plasma arc welding
(B) Gas metal arc welding
(C) Shielded metal arc welding
(D) Electron beam welding
Organizing Institute: IIT Roorkee Page 43 of 51
Page 45
Q.48 1
For a two-dimensional field described by 𝑇(𝑥, 𝑦) = 3 𝑥𝑦(𝑥 + 𝑦), the magnitude of
its gradient at the point (1,1) is ______ (rounded off to two decimal places).
Q. 49 X-ray diffraction using a monochromatic radiation of wavelength 0.154 nm is
performed on powder samples of metal A (with FCC crystal structure) and metal B
(with BCC crystal structure).
If the first peak in both the cases occurs at a Bragg angle 𝜃 = 20º, then the value of
lattice parameter of metal A
= ______ (rounded off to two decimal places).
lattice parameter of metal B
Organizing Institute: IIT Roorkee Page 44 of 51
For a two-dimensional field described by 𝑇(𝑥, 𝑦) = 3 𝑥𝑦(𝑥 + 𝑦), the magnitude of
its gradient at the point (1,1) is ______ (rounded off to two decimal places).
Q. 49 X-ray diffraction using a monochromatic radiation of wavelength 0.154 nm is
performed on powder samples of metal A (with FCC crystal structure) and metal B
(with BCC crystal structure).
If the first peak in both the cases occurs at a Bragg angle 𝜃 = 20º, then the value of
lattice parameter of metal A
= ______ (rounded off to two decimal places).
lattice parameter of metal B
Organizing Institute: IIT Roorkee Page 44 of 51
Page 46
Q.50 The excess molar Gibbs free energy of a solution of element A and B at 1000 K is
given by 𝐺 𝑋𝑆 = −3000 𝑋𝐴 𝑋𝐵 J mol−1 , where 𝑋𝐴 and 𝑋𝐵 are mole fractions of A
and B, respectively.
The activity of B in a solution of A and B containing 40 mol% of B at 1000 K is
______ (rounded off to two decimal places).
Given: Ideal gas constant R = 8.314 J mol−1 K −1
Q.51 Molten steel at 1900 K having dissolved hydrogen needs to be vacuum degassed.
The equilibrium partial pressure of hydrogen to be maintained to achieve 1 ppm
(mass basis) of dissolved hydrogen is ______ Torr (rounded off to two decimal
places).
Given: For the hydrogen dissolution reaction in molten steel (½ H2(g) = [H]), the
equilibrium constant (expressed in terms of ppm of dissolved H) is:
1900
log10 𝐾eq = − + 2.4
𝑇
1 atm = 760 Torr
Q.52 6(𝑥−sin 𝑥)
The value of lim is ______(in integer).
𝑥→0 𝑥3
Organizing Institute: IIT Roorkee Page 45 of 51
given by 𝐺 𝑋𝑆 = −3000 𝑋𝐴 𝑋𝐵 J mol−1 , where 𝑋𝐴 and 𝑋𝐵 are mole fractions of A
and B, respectively.
The activity of B in a solution of A and B containing 40 mol% of B at 1000 K is
______ (rounded off to two decimal places).
Given: Ideal gas constant R = 8.314 J mol−1 K −1
Q.51 Molten steel at 1900 K having dissolved hydrogen needs to be vacuum degassed.
The equilibrium partial pressure of hydrogen to be maintained to achieve 1 ppm
(mass basis) of dissolved hydrogen is ______ Torr (rounded off to two decimal
places).
Given: For the hydrogen dissolution reaction in molten steel (½ H2(g) = [H]), the
equilibrium constant (expressed in terms of ppm of dissolved H) is:
1900
log10 𝐾eq = − + 2.4
𝑇
1 atm = 760 Torr
Q.52 6(𝑥−sin 𝑥)
The value of lim is ______(in integer).
𝑥→0 𝑥3
Organizing Institute: IIT Roorkee Page 45 of 51
Page 47
Q.53 Consider the following reactions and their standard Gibbs free energies (in J):
1
Fe(s) + 2 O2(g) ⇌ FeO(s) ∆𝐺 ° = −264900 + 65𝑇
2 H2(g) + O2(g) ⇌ 2 H2O(g) ∆𝐺 ° = −492900 + 109𝑇
Assuming Fe and FeO to be pure and no solubility of gases in the solids, the value
𝑝H O
of 𝑝 2 required to reduce solid FeO to solid Fe at 1000 K is ______ (rounded off to
H2
two decimal places).
Given: Ideal gas constant R = 8.314 J mol−1 K −1
Q.54 The diameter of spherical galena particles that have the same settling velocity as
spherical quartz particles of diameter 25 μm (both settling in water) is ______ μm
(rounded off to one decimal place).
Assume Stokes law of settling to be valid.
Given: Density of galena = 7400 kg m−3 , density of quartz = 2600 kg m−3 , density
of water = 1000 kg m−3 .
Organizing Institute: IIT Roorkee Page 46 of 51
1
Fe(s) + 2 O2(g) ⇌ FeO(s) ∆𝐺 ° = −264900 + 65𝑇
2 H2(g) + O2(g) ⇌ 2 H2O(g) ∆𝐺 ° = −492900 + 109𝑇
Assuming Fe and FeO to be pure and no solubility of gases in the solids, the value
𝑝H O
of 𝑝 2 required to reduce solid FeO to solid Fe at 1000 K is ______ (rounded off to
H2
two decimal places).
Given: Ideal gas constant R = 8.314 J mol−1 K −1
Q.54 The diameter of spherical galena particles that have the same settling velocity as
spherical quartz particles of diameter 25 μm (both settling in water) is ______ μm
(rounded off to one decimal place).
Assume Stokes law of settling to be valid.
Given: Density of galena = 7400 kg m−3 , density of quartz = 2600 kg m−3 , density
of water = 1000 kg m−3 .
Organizing Institute: IIT Roorkee Page 46 of 51
Page 48
Q.55 Consider the following cell reaction:
Mg + Cd2+ ⇌ Mg2+ + Cd
The standard Gibbs free energy change for the reaction is ______ kJ (rounded off
to an integer).
Given: Standard oxidation potentials for the reactions with respect to standard
hydrogen electrode are:
Mg ⇌ Mg2+ + 2e− E = 2.37 V
Cd ⇌ Cd2+ + 2e− E = 0.403 V
Faraday’s constant = 96500 C mol–1
Q.56 Copper is being electrodeposited from a CuSO4 bath onto a stainless steel cathode
of total surface area of 2 m2 in an electrolytic cell operated at a current density of
200 A m−2 with a current efficiency of 90%.
The mass of copper deposited in 24 h is______ kg (rounded off to two decimal
places).
Given: Faraday’s constant = 96500 C mol–1, atomic mass of copper = 63.5 g mol−1
Organizing Institute: IIT Roorkee Page 47 of 51
Mg + Cd2+ ⇌ Mg2+ + Cd
The standard Gibbs free energy change for the reaction is ______ kJ (rounded off
to an integer).
Given: Standard oxidation potentials for the reactions with respect to standard
hydrogen electrode are:
Mg ⇌ Mg2+ + 2e− E = 2.37 V
Cd ⇌ Cd2+ + 2e− E = 0.403 V
Faraday’s constant = 96500 C mol–1
Q.56 Copper is being electrodeposited from a CuSO4 bath onto a stainless steel cathode
of total surface area of 2 m2 in an electrolytic cell operated at a current density of
200 A m−2 with a current efficiency of 90%.
The mass of copper deposited in 24 h is______ kg (rounded off to two decimal
places).
Given: Faraday’s constant = 96500 C mol–1, atomic mass of copper = 63.5 g mol−1
Organizing Institute: IIT Roorkee Page 47 of 51
Page 49
Q.57 An intrinsic semiconductor has conductivity of 100 Ω−1 m−1 at 300 K and
300 Ω−1 m−1 at 500 K.
The band gap of the semiconductor is ______ eV (rounded off to two decimal
places).
Given: Boltzmann constant 𝑘𝐵 = 8.6× 10−5 eV K −1
Q.58 For a component fabricated from an alloy A with plane strain fracture toughness,
KIC = 50 MPa m1/2 , fracture was observed to take place at a crack length of 0.4 mm
at a tensile service stress of 𝜎.
If the same component is instead fabricated from alloy B with KIC = 75 MPa m1/2 ,
the crack length at which a similar crack geometry will result in fracture (under
identical tensile service stress of 𝜎) is ______ mm (rounded off to one decimal
place).
Organizing Institute: IIT Roorkee Page 48 of 51
300 Ω−1 m−1 at 500 K.
The band gap of the semiconductor is ______ eV (rounded off to two decimal
places).
Given: Boltzmann constant 𝑘𝐵 = 8.6× 10−5 eV K −1
Q.58 For a component fabricated from an alloy A with plane strain fracture toughness,
KIC = 50 MPa m1/2 , fracture was observed to take place at a crack length of 0.4 mm
at a tensile service stress of 𝜎.
If the same component is instead fabricated from alloy B with KIC = 75 MPa m1/2 ,
the crack length at which a similar crack geometry will result in fracture (under
identical tensile service stress of 𝜎) is ______ mm (rounded off to one decimal
place).
Organizing Institute: IIT Roorkee Page 48 of 51
Page 50
Q.59 Temperatures at two sides of a 0.4 m thick copper plate are 1000 and 500 ℃.
Assuming steady state, one-dimensional conductive heat transfer through the wall
and ignoring end-effects, the magnitude of the heat flux through the wall is
______ × 105 W m−2 (in integer).
Given: Thermal conductivity of copper is 400 W m−1 K −1
Q.60 In polycrystalline Ni, Nabarro-Herring diffusion creep was found to be the rate
controlling creep mechanism at a certain temperature.
At that temperature, if the steady state strain rate is 10−8 s −1 at a stress of 10 MPa,
the steady state strain rate of 10−9 s−1 will be obtained at a stress value of ______
MPa (in integer).
Assume that the same creep mechanism is rate controlling during the creep
deformation.
Organizing Institute: IIT Roorkee Page 49 of 51
Assuming steady state, one-dimensional conductive heat transfer through the wall
and ignoring end-effects, the magnitude of the heat flux through the wall is
______ × 105 W m−2 (in integer).
Given: Thermal conductivity of copper is 400 W m−1 K −1
Q.60 In polycrystalline Ni, Nabarro-Herring diffusion creep was found to be the rate
controlling creep mechanism at a certain temperature.
At that temperature, if the steady state strain rate is 10−8 s −1 at a stress of 10 MPa,
the steady state strain rate of 10−9 s−1 will be obtained at a stress value of ______
MPa (in integer).
Assume that the same creep mechanism is rate controlling during the creep
deformation.
Organizing Institute: IIT Roorkee Page 49 of 51
Page 51
Q.61 A single crystal BCC metal with a lattice parameter 𝑎 = 0.4 nm is subjected to
deformation at a shear strain rate of 0.001 s −1 .
If the average mobile dislocation density in the single crystal is 1010 m−2 , the
average dislocation velocity is ______ × 10−3 m s −1 (rounded off to two decimal
places).
𝑎
Given: Burgers vector 𝐛 = 2 〈111〉
Q.62 A cylindrical specimen is subjected to plastic deformation in tension up to a uniform
elongation of 10%. The final cross-sectional area of the gage section is found to be
20 mm2.
The initial cross-sectional area of the gage section is ______mm2 (rounded off to an
integer).
Q.63 The reaction represented by 𝐴 → 𝐵 follows first order kinetics. At a given
temperature, 20% of the reaction is completed in 223 s.
The time taken to complete 50% of the reaction at the same temperature is ______ s
(rounded off to the nearest integer).
Organizing Institute: IIT Roorkee Page 50 of 51
deformation at a shear strain rate of 0.001 s −1 .
If the average mobile dislocation density in the single crystal is 1010 m−2 , the
average dislocation velocity is ______ × 10−3 m s −1 (rounded off to two decimal
places).
𝑎
Given: Burgers vector 𝐛 = 2 〈111〉
Q.62 A cylindrical specimen is subjected to plastic deformation in tension up to a uniform
elongation of 10%. The final cross-sectional area of the gage section is found to be
20 mm2.
The initial cross-sectional area of the gage section is ______mm2 (rounded off to an
integer).
Q.63 The reaction represented by 𝐴 → 𝐵 follows first order kinetics. At a given
temperature, 20% of the reaction is completed in 223 s.
The time taken to complete 50% of the reaction at the same temperature is ______ s
(rounded off to the nearest integer).
Organizing Institute: IIT Roorkee Page 50 of 51
Page 52
Q.64 A cylindrical Al alloy billet of 300 mm diameter is hot extruded to produce a
cylindrical rod of 75 mm diameter at a constant true strain rate ( 𝜀̇) of 10 s −1. The
flow stress (𝜎) of the alloy at the extrusion temperature is given by
𝜎 = 10 (𝜀̇)0.3 MPa.
Assume the alloy is perfectly plastic and there is no temperature rise during the
extrusion process.
The ideal plastic work of deformation per unit volume is ______ × 106 J m−3
(rounded off to one decimal place).
Q.65 Two consecutive estimates of the root of a function 𝑓(𝑥) obtained using the
Newton-Raphson method are 𝑥𝑖 = 8.5 and 𝑥𝑖+1 = 13.5, and the value of the
function at 𝑥𝑖 is 15.
The numerical value of first derivative of the function evaluated at 𝑥𝑖 is ______
(in integer).
Organizing Institute: IIT Roorkee Page 51 of 51
cylindrical rod of 75 mm diameter at a constant true strain rate ( 𝜀̇) of 10 s −1. The
flow stress (𝜎) of the alloy at the extrusion temperature is given by
𝜎 = 10 (𝜀̇)0.3 MPa.
Assume the alloy is perfectly plastic and there is no temperature rise during the
extrusion process.
The ideal plastic work of deformation per unit volume is ______ × 106 J m−3
(rounded off to one decimal place).
Q.65 Two consecutive estimates of the root of a function 𝑓(𝑥) obtained using the
Newton-Raphson method are 𝑥𝑖 = 8.5 and 𝑥𝑖+1 = 13.5, and the value of the
function at 𝑥𝑖 is 15.
The numerical value of first derivative of the function evaluated at 𝑥𝑖 is ______
(in integer).
Organizing Institute: IIT Roorkee Page 51 of 51
Page 53
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Document Details
| Board / Org | IIT |
| Exam | Graduate Aptitude Test in Engineering |
| Type | Question Paper |
| Pages | 53 |
| Updated | 30 Apr 2026 |