TS PGECET 2024 Metallurgical Engineering Question Paper with Answer Key PDF

Question 1:

If \( X_1 = \begin{bmatrix} 1
i \end{bmatrix} \), \( X_2 = \begin{bmatrix} i
1 \end{bmatrix} \) are given vectors and \( A = \begin{bmatrix} \cos \theta & \sin \theta
-\sin \theta & \cos \theta \end{bmatrix} \).

If \( P = [X_1, X_2] \), then \( P^{-1} A P \) is:

• (A) \( \begin{bmatrix} e^{i\theta} & 0
  0 & e^{-i\theta} \end{bmatrix} \)
• (B) \( \begin{bmatrix} e^{\theta} & 0
  0 & e^{\theta} \end{bmatrix} \)
• (C) \( \begin{bmatrix} 1 & 1
  0 & 0 \end{bmatrix} \)
• (D) \( \begin{bmatrix} 1 & 0
  0 & 1 \end{bmatrix} \)

The rank of the matrix \( A = \begin{bmatrix} 1 & 2 & 3 & 0
0 & -4 & -8 & 3
2 & 4 & 3 & 2
0 & -4 & -11 & 5 \end{bmatrix} \)
is:

• (A) 4
• (B) 2
• (C) 1
• (D) 3

If \( x > 0 \), the series \( x + 2x^2 + 3x^3 + \ldots \) is:

• (A) convergent if \( x > 1 \) and divergent \( x \geq 1 \)
• (B) convergent if \( x < 1 \) and divergent \( x \geq 1 \)
• (C) divergent if \( x > 1 \) and convergent \( x > 1 \)
• (D) convergent if \( x \leq 1 \) and convergent \( x \geq 1 \)

If \( u = \sin^{-1}\left(\frac{x}{y}\right) + \tan^{-1}\left(\frac{y}{x}\right) \), then the value of \( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \) is:

• (A) \( \frac{1}{\sqrt{y^2 - x^2}} \)
• (B) \( \frac{-1}{y^2 - x^2} \)
• (C) \( 0 \)
• (D) \( 1 \)

If \( \vec{r} = x \hat{i} + y \hat{j} + z \hat{k} \) is the position vector of a point, then \( curl(\vec{r}) \) is:

• (A) null vector
• (B) \( 0 \)
• (C) \( \hat{i} + \hat{j} + \hat{k} \)
• (D) \( \hat{i} - \hat{j} \)

Laplace transform of \( \frac{e^{-at} - e^{-bt}}{t} \) is:

• (A) \( \log\left( \frac{s+a}{s+b} \right) \)
• (B) \( \log\left( \frac{s+b}{s+a} \right) \)
• (C) \( \frac{\pi}{2} - \tan^{-1}(s) \)
• (D) \( \frac{\pi}{2} - \cot^{-1}(s) \)

The particular integral of \( (D^2 + 4)y = \cos 3x + \sin 2x \) is:

• (A) \( \frac{1}{20}(\cos 3x + 5x \cos 2x) \)
• (B) \( \frac{1}{20}(4 \cos 3x + 5x \cos 2x) \)
• (C) \( \frac{-1}{20}(4 \cos 3x + 5x \cos 2x) \)
• (D) \( \frac{1}{20}(4 \cos 3x + x \cos 2x) \)

The table below gives the values of \( f(x) \) at five equidistant points of \( x \):
x        0   0.5   1.0   1.5   2.0
f(x)    0   0.25   1    2.25   4
Then the approximate value of \( \int_0^2 f(x) \, dx \) by Trapezoidal Rule is:

• (A) \(1.75\)
• (B) \(2\)
• (C) \(2.5\)
• (D) \(2.75\)

If \(2Y - X - 50 = 0\), \(3Y - 2X - 10 = 0\) are the two regression equations, then the mean values of the variables \(X\) and \(Y\) respectively are:

• (A) \(80 and 90\)
• (B) \(130 and 90\)
• (C) \(96 and 130\)
• (D) \(90 and 80\)

Which of the following cannot be the probability mass function of any discrete random variable \(X\)?

• (A) \(P(X = x) = \frac{1}{6} for x = 1,2,3,4,5,6\)
• (B) \(P(X = x) = \frac{1}{3} for x = 1,2,3\)
• (C) \(P(X = x) = \frac{1}{2} for x = 1,2\)
• (D) \(P(X = x) = \frac{1}{4} for x = 1,2\)

“It is impossible for a heat engine to be 100% efficient.” This statement is related to:

• (A) First law of thermodynamics
• (B) Second law of thermodynamics
• (C) Enthalpy
• (D) Diffusion

If a system is completely ordered and the atoms are at rest at zero Kelvin, then the entropy of the system is:

• (A) Zero
• (B) Positive
• (C) Negative
• (D) Cannot be defined

Electrodes used in anodizing process are:

• (A) Iron as cathode and work piece as anode
• (B) Lead as cathode and work piece as anode
• (C) Work piece as cathode and copper as anode
• (D) Work piece as cathode and zinc as anode

Units for quantity of electricity are:

• (A) Volt
• (B) Ampere
• (C) Joule
• (D) Coulomb

Identify the wrong statement:

• (A) Alkali halides are highly conductive
• (B) Mercury chloride is very good conductor of electricity
• (C) Fused salts are good conductor of electricity
• (D) Easily polarizable ions in the fused salt mixtures reduces the ionic mobility

Identify the noble metal:

• (A) Silver
• (B) Lead
• (C) Zinc
• (D) Platinum

Hydrogen overvoltage is observed in:

• (A) Oxidation processes
• (B) Cathodic processes
• (C) Anodic processes
• (D) Smelting processes

Tafel equation defines the relation between:

• (A) Oxygen overvoltage and current density
• (B) Hydrogen overvoltage and current density
• (C) Decomposition voltage and current density
• (D) Cell voltage and current density

Second law of thermodynamics can be stated as:

• (A) Work done by the system is zero
• (B) \( \Delta H = 0 \)
• (C) \( \Delta U_{cycle} = 0 \)
• (D) \( dS = \frac{\delta q_{rev}}{T} \)

An expression for Gibbs free energy is:

• (A) \( H - TS \)
• (B) \( U - TS \)
• (C) \( dS_{system} + dS_{surroundings} \)
• (D) \( dU = T dS - P dV \)

Identify the incorrect statement:

• (A) \( dH = V dP - T dS \)
• (B) \( \displaystyle \frac{d\left(\frac{G}{T}\right)}{d\left(\frac{1}{T}\right)} = H \)
• (C) \( \displaystyle \frac{d\left(\frac{\Delta G}{T}\right)}{d\left(\frac{1}{T}\right)} = \Delta H \)
• (D) \( T dG - G dT = -H dT \)

“The heat capacity of a solid compound is equal to the sum of the heat capacities of its constituent elements”. This statement is known as:

• (A) Trouton’s rule
• (B) Dulong and Petit’s law
• (C) Kirchhoff’s law
• (D) Neumann–Kopps rule

The difference of \( C_P \) and \( C_V \) of a substance is:

• (A) Positive, finite and variable quantity
• (B) Negative, finite and constant quantity
• (C) Positive, finite and constant quantity
• (D) Negative, finite and variable quantity

Ellingham diagram for metal–oxide system doesn’t give idea about:

• (A) Kinetics of the oxidation reaction
• (B) Oxidation of metals
• (C) Value of partial pressure of oxygen for the reactions shown in a diagram
• (D) Reduction of metal oxides

In a reversible cycle, the sum of change in \( \frac{q}{T} \) is

(where \( q \) is heat absorbed and \( T \) is absolute temperature):

• (A) Zero
• (B) One
• (C) Two
• (D) Three

With increase in pressure, the bulk diffusion in catalyst pore:

• (A) Decreases
• (B) Increases
• (C) Increases exponentially
• (D) Remains unchanged

Equilibrium of a chemical reaction as viewed by kinetics is in a:

• (A) Static steady state
• (B) Dynamic steady state
• (C) Dynamic unsteady state
• (D) Static unsteady state

The rate of homogeneous reaction is a function of:

• (A) Pressure and composition only
• (B) Temperature and pressure only
• (C) Composition and temperature only
• (D) Temperature, pressure and composition

The reactions with low activation energy are:

• (A) Slow
• (B) Fast
• (C) Non-spontaneous
• (D) Always spontaneous

Arrhenius equation represents graphically the variation between the:

• (A) Rate constant and temperature
• (B) Rate of reaction and temperature
• (C) Activation energy and temperature
• (D) Frequency factor and temperature

Xanthates are used as:

• (A) Collectors
• (B) pH reagents
• (C) Moderators
• (D) Frothers

Primary step of ore processing is:

• (A) Grinding
• (B) Crushing
• (C) Magnetic separation
• (D) Jigging

Liberation is done for:

• (A) Separation of particles
• (B) Sizing of the ore
• (C) Concentration of the ore
• (D) Oxidising the ores

Direct coal is charged as fuel in:

• (A) SR process
• (B) COREX process
• (C) ELRED process
• (D) MIDREX process

TISCO located at:

• (A) Hazira
• (B) Vijayanagaram
• (C) Raigarh
• (D) Jamshedpur

In Indian blast furnaces for iron production, the oxygen enrichment is done up to:

• (A) 12% of oxygen
• (B) 20% of oxygen
• (C) 25% of oxygen
• (D) 40% of oxygen

Bleeder valves in the blast furnace is provided at:

• (A) Below mantle region
• (B) Below stack region
• (C) Top of stack region
• (D) Top of uptakes

The important reactions that occur in tuyeres region in blast furnace is:

• (A) Slag melting
• (B) Combustion of coke
• (C) Reduction of iron oxides
• (D) Solution loss reaction

JFN number in LD converter process is defined as:

• (A) \( JFN = Gas pressure \times \left(\frac{Lance height}{Nozzle diameter}\right) \)
• (B) \( JFN = Nozzle diameter \times \left(\frac{Lance height}{Gas pressure}\right) \)
• (C) \( JFN = Gas pressure \times \left(\frac{Nozzle diameter}{Lance height}\right) \)
• (D) \( JFN = (Gas pressure + Lance height) \times Nozzle diameter \)

First element to be removed during steel making by BOF method is:

• (A) Cadmium
• (B) Carbon
• (C) Silicon
• (D) Manganese

Calamine is an ore of:

• (A) Lead
• (B) Iron
• (C) Copper
• (D) Zinc

VAD process is a:

• (A) Iron extraction process
• (B) Reduction process
• (C) Secondary refining process
• (D) Concentration process

Sulphide shape control in steel making is done by adding:

• (A) Copper
• (B) Argon
• (C) Zinc
• (D) Nickel

Hoopes’ process used for:

• (A) Extraction of copper
• (B) Concentration of lead ore
• (C) Refining of aluminium
• (D) Refining of titanium

Metallurgical coke is charged to:

• (A) LD convertor
• (B) Secondary steel making
• (C) Iron blast furnace
• (D) Bayer process

Ladle metallurgy does not include the following operation:

• (A) Deoxidation
• (B) Decarburisation
• (C) Desulphurisation
• (D) Sulphide shape control

Titanium is produced by:

• (A) Magnesium reduction of TiCl\(_4\)
• (B) Electrolytic reduction of TiCl\(_4\)
• (C) Thermal dissociation of TiCl\(_4\)
• (D) Calcium reduction of TiCl\(_4\)

Which of the following is a suitable method to remove hydrogen from molten aluminium?

• (A) Cover melt surface with a flux
• (B) Increase melt temperature
• (C) Expose flowing melt to vacuum
• (D) Bubble humidified argon gas through the melt

Aluminium is not commercially produced by carbo-thermic reduction because:

• (A) It melts at a low temperature
• (B) It does not vaporise at reasonable temperature
• (C) Al–Al\(_2\)O\(_3\) line is too low in the Ellingham diagram and need excessively high temperature
• (D) Aluminium metal will have excessive dissolved oxygen

The process of cementation involves:

• (A) Elimination of a more reactive metal from molten metal by preferential oxidation
• (B) Refining by preferential dissolution of the desired metal in an organic solvent
• (C) Extraction by selective dissolution of the desired metal in an inorganic solvent
• (D) Separation of the desired metal by adding a more reactive metal

Ratio of packing factor of an FCC crystal to the packing factor of a simple cubic crystal is:

• (A) 1.0
• (B) 0.702
• (C) 1.423
• (D) 2.502

Interplanar spacing between parallel planes can be determined by:

• (A) Scanning Electron Microscope
• (B) Transmission Electron Microscope
• (C) Spectrophotometer
• (D) Thermogravimetric Analyser

Thin sheets of ceramic material is produced by:

• (A) Tape casting
• (B) Rolling
• (C) Forging
• (D) Injection molding

Which one of the following is used as solder in an electronic industry?

• (A) Pb–Cu
• (B) Cu–Sn
• (C) Sn–Sb
• (D) Pb–Sn

Reinforcing material which possesses highest tensile strength from the following is:

• (A) Si\(_3\)N\(_4\) fiber
• (B) S-glass fiber
• (C) SiC fiber
• (D) Graphite fiber

Composite products such as pressure vessels, liquid storage tanks and rocket motor castings are made by:

• (A) Pultrusion
• (B) Resin transfer molding
• (C) Vacuum bagging
• (D) Filament winding

Which of the following is not the characteristics of a gray cast iron?

• (A) Brittle
• (B) Breaks preferentially along the graphite flakes
• (C) Produce a white fracture surface
• (D) Good damping property

Identify the element which increases the Ms temperature of a steel containing 1.0% C:

• (A) Chromium
• (B) Copper
• (C) Manganese
• (D) Aluminium

Bain distortion model explains:

• (A) The atomic movement involved in martensitic transformation
• (B) Formation of bainite by isothermal transformation
• (C) Formation of pearlite by eutectoid transformation
• (D) Formation of ledeburite by eutectic transformation

Stepped quenching process is also called as:

• (A) Austempering
• (B) Self tempering
• (C) Martempering
• (D) Spray quenching

Grossman’s critical diameter method is adopted to determine:

• (A) Case depth in carburising methods
• (B) Percentage of ductility
• (C) Percentage of carbon in steel
• (D) Hardenability of steel

Permanent magnets are made of:

• (A) High energy hard magnetic material
• (B) Ti–Al–V alloy
• (C) Commercial iron
• (D) Copper–Zinc alloy

Nitriding of the steel is done at low temperatures because:

• (A) To favour nitrogen diffusion
• (B) To favour carbon diffusion
• (C) To minimize thermal cracks
• (D) To soften the ferrite phase

Minimum percent of nickel needed in stainless steel to stabilize the austenitic FCC phase is:

• (A) 2
• (B) 4
• (C) 9
• (D) 16

Cu–Be alloys are strengthened by:

• (A) Solid solution strengthening
• (B) Dispersion strengthening
• (C) Grain refinement
• (D) Precipitation strengthening

Polystyrene belongs to:

• (A) Ceramic material
• (B) Composite material
• (C) Thermoplastic material
• (D) Structural material

Which of the following are the low molecular weight substances added to polymers to increase plasticity and flexibility?

• (A) Fillers
• (B) Plasticizers
• (C) Inoculants
• (D) Stabilisers

Hard magnetic material is characterised by:

• (A) Only low coercive force
• (B) High coercive force and low residual magnetic induction
• (C) High coercive force and high residual magnetic induction
• (D) Low coercive force and high residual magnetic induction

In a single component system, the maximum number of phases that can co-exist in equilibrium is:

• (A) 0
• (B) 2
• (C) 3
• (D) 4

Magnetic permeability of iron is increased by:

• (A) Purification
• (B) Decarburising
• (C) Alternating heating and cooling
• (D) Alloying with cobalt

Plastics as a material of construction suffer from the drawback of low:

• (A) Strength
• (B) Density
• (C) Machinability
• (D) Plastic deformation

Machinability of hard alloys and tool steels is improved by:

• (A) Annealing
• (B) Normalising
• (C) Spheroidising
• (D) Tempering

Copper is not present as an alloying constituent in:

• (A) Nichrome
• (B) Delta metal
• (C) Silicone bronze
• (D) Constantan

In precipitation hardenable alloy, like duralumin, intermediate precipitates can form due to:

• (A) Coherency strains
• (B) Ease of diffusion
• (C) Difficulty of the growth of the final precipitate
• (D) Difficulty of nucleation of the final precipitate

Vanadium in high speed steels:

• (A) Provides high hot hardness
• (B) Promotes retention of austenite
• (C) Increases toughness
• (D) Forms very hard carbides and thus increases wear resistance

Which of the following is not a point defect?

• (A) Dislocation
• (B) Interstitials
• (C) Vacancies
• (D) Frenkel defect

True strain (\( \varepsilon \)) and engineering strain (\( e \)) are related by

• (A) \( \varepsilon = 1 + e \)
• (B) \( \varepsilon = \ln(1 + e) \)
• (C) \( e = \ln(1 + \varepsilon) \)
• (D) \( \varepsilon = \dfrac{1}{1 + e} \)

Perfect plastic material is

• (A) Rigid
• (B) Exhibits elastic property
• (C) Very hard
• (D) Very brittle

The value of Poisson’s ratio of most of the metals is

• (A) \( 0.20 \)
• (B) \( 0.28 \)
• (C) \( 0.33 \)
• (D) \( 1.5 \)

Levy–Mises equations are valid for

• (A) Soft material
• (B) Ideal plastic material with elastic region
• (C) Hardened material
• (D) Ideal plastic material

Extensive plastic deformation occurs during

• (A) Cold work
• (B) Injection molding
• (C) Casting
• (D) Heat treatment

Metals with high monotonic strain-hardening exponents (\(n > 0.15\)) and those with a low strain-hardening exponent (\(n < 0.15\)) respectively would undergo

• (A) Ideal plastic, Ideal elastic
• (B) Ideal elastic, Ideal plastic
• (C) Cyclic hardening, cyclic softening
• (D) Cyclic softening, cyclic hardening

Deformation by slip occurs in

• (A) Ceramics
• (B) Composites
• (C) Metals
• (D) Nonmetals

The Vicker’s diamond pyramid method of hardness determination does not give accurate result, when employed for the

• (A) Hard metals
• (B) Forged parts with rough surface
• (C) Soft metals
• (D) Polished and hardened steel surface

The yield point in fatigue loading compared to that in static loading is less. The ratio of ultimate tensile strength to endurance limit of a material subjected to fatigue loading is

• (A) 0.5
• (B) 1
• (C) 1.5
• (D) 2

Which of the following mechanical properties of a material is most structure insensitive?

• (A) Toughness
• (B) Tensile strength
• (C) Young’s modulus
• (D) Percentage reduction of area

Decrease in stress at constant deformation under creep conditions is termed as the

• (A) Stress relaxation
• (B) Residual stress
• (C) Stress relief
• (D) Proof stress

Creep resistance can be improved by allowing the

• (A) Fine grains to grow
• (B) Soft particles to precipitate along grain boundaries
• (C) Directional solidification of alloys
• (D) Uniformly dispersed coarse particles precipitation in the metal matrix

The elastic strain energy of a unit length of an edge dislocation as compared to that of a screw dislocation is

• (A) Less
• (B) More
• (C) Equal
• (D) Double

The yield point phenomenon observed in annealed low carbon steel is due to the presence of the following element

• (A) Silicon
• (B) Chromium
• (C) Carbon
• (D) Phosphorous

Stretcher strains found in a low carbon sheet are associated with

• (A) Thickness of the sheet
• (B) Texture
• (C) Dislocation density
• (D) Yield point phenomenon

Movement of jogs can produce

• (A) Interstitials
• (B) Vacancies
• (C) Grain boundary segregation
• (D) Grain boundary sliding

Von Mises criterion for plastic yielding of a ductile material predicts that the yield stress in uniaxial tension is related to that in pure torsion as

• (A) Equal to each other
• (B) 2 times
• (C) One half
• (D) \( \sqrt{3} \) times

Stress intensity factor, \( K_{IC} \), not depends on

• (A) Geometry of the solid containing the crack
• (B) The size and location of the crack
• (C) Magnitude and distribution of the loads imposed on the solid
• (D) Tensile strength of the material

The primary strengthening mechanism in 70:30 brass is

• (A) Precipitation hardening
• (B) Dispersion strengthening
• (C) Fiber strengthening
• (D) Solid solution strengthening

Frank–Read source

• (A) Generates dislocation
• (B) Hinders the movement of dislocation
• (C) Is responsible for polygonization in edge dislocation
• (D) Is responsible for dislocation climb

The tensile load-elongation curve of a metal does not describe

• (A) Yield stress
• (B) Necking strain
• (C) Anisotropy index
• (D) Work hardening

Strain ageing is common in

• (A) High carbon steels
• (B) Low carbon steels
• (C) High manganese steels
• (D) High chromium steels

Which of the following has the lowest tensile strength?

• (A) Cementite
• (B) Bainite
• (C) Martensite
• (D) Ferrite

The most serious manufacturing defect from fracture toughness point of view is

• (A) Crack
• (B) Pore
• (C) Surface roughness
• (D) Spherical inclusion

Which of the following occupy maximum percentage of powder metallurgy parts distribution in the engineering industry?

• (A) Hardware
• (B) Household appliances
• (C) Automotive
• (D) Industrial motors

Which of the following assumptions is not related to continuous casting?

• (A) Solidification begins only when the metal reaches the secondary cooling zone
• (B) The radial temperature gradient in the billet is linear
• (C) The longitudinal heat flow in the billet is significant
• (D) The metal is poured with zero superheat

The objection with the use of ------------- is a tendency for producing a fountain effect in the casting.

• (A) Ring gate
• (B) Horn gate
• (C) Pencil gate
• (D) Top gate

The microsegregation observed in casting is called

• (A) Impurities
• (B) Diffusion
• (C) Dissolution
• (D) Coring

Forging is accomplished in drop forging by dropping the

• (A) Work piece at high velocity
• (B) Hammer at high velocity
• (C) Die with hammer at high velocity
• (D) Weight on hammer to produce the required impact

Hot extrusion of aluminium is done in the temperature range of

• (A) \(250^\circ C - 300^\circ C\)
• (B) \(350^\circ C - 500^\circ C\)
• (C) \(600^\circ C - 800^\circ C\)
• (D) \(850^\circ C - 950^\circ C\)

Which of the following is \textbf{not} a non-destructive test?

• (A) Magnaflux method
• (B) Radiography
• (C) Ultrasonic testing
• (D) Fatigue testing

Which of the following is an exclusively cold working process?

• (A) Spinning
• (B) Deep drawing
• (C) Rolling
• (D) Extrusion

In cold working of steel

• (A) Grain structure does not change
• (B) Internal stresses disappear
• (C) Strength and hardness increases
• (D) It is heated above recrystallisation temperature

In two high reversing mill, the rolls used are

• (A) Two vertical
• (B) Two horizontal
• (C) Four vertical
• (D) Four horizontal

Die casting of aluminium is not done because of the reason that, it is

• (A) Prone to high expansion on solidification
• (B) Having high tendency to react chemically with the die surface
• (C) Strong and light weight
• (D) Having high melting point and cooling time

A tooth paste tube can be produced by

• (A) Hollow backward extrusion
• (B) Solid backward extrusion
• (C) Hollow forward extrusion
• (D) Solid forward extrusion

In casting, to promote / provide unidirectional solidification which of the following are used?

• (A) Cores
• (B) Patterns
• (C) Chills
• (D) Chaplets

A casting defect, which occurs near the ingates as rough lumps on the surface of a casting is known as

• (A) Swell
• (B) Scab
• (C) Blow hole
• (D) Sand wash

Skim bob is attached to

• (A) Along the runner
• (B) Ingates
• (C) Risers
• (D) Pouring cup

Which of the following welding uses consumable electrode?

• (A) Thermit
• (B) MIG
• (C) TIG
• (D) Laser

Stainless steel is welded using

• (A) Arc welding
• (B) Oxy-acetylene flame
• (C) Inert gas welding
• (D) Oxy-hydrogen flame

Melting rates of electrodes in manual metal arc welding process is mainly governed by the

• (A) Length of the electrode
• (B) Type of coating
• (C) Welding current
• (D) Arc voltage

Welds made with high heat input will show reduction in

• (A) Yield strength
• (B) Toughness
• (C) Fatigue strength
• (D) Mechanical strength

Which of the following is not a solid state metal joining technique?

• (A) Friction welding
• (B) Diffusion welding
• (C) Electroslag welding
• (D) Ultrasonic welding