TS PGECET 2026 Nanotechnology (NT) Question Paper: Download Answer Key with Solutions PDF

The Hall–Petch relation correlates yield stress with

• (A) Temperature
• (B) Strain rate
• (C) Grain size
• (D) Dislocation density

Cast iron typically shows

• (A) High ductility
• (B) Yield point
• (C) Brittle fracture
• (D) Large plastic deformation

The Clausius–Mossotti equation relates

• (A) Polarization and temperature
• (B) Dielectric constant and polarizability
• (C) Conductivity and permittivity
• (D) Stress and strain

Stacking faults are commonly observed in

• (A) BCC metals
• (B) FCC metals
• (C) Ionic crystals
• (D) Polymers

Burgers vector represents

• (A) Slip plane
• (B) Magnitude and direction of lattice distortion
• (C) Dislocation density
• (D) Atomic spacing

The smallest repeating unit of a crystal lattice is called

• (A) Unit cell
• (B) Primitive cell
• (C) Wigner–Seitz cell
• (D) Crystal system

Type-II superconductors are characterized by

• (A) Single critical field
• (B) No mixed state
• (C) Two critical magnetic fields
• (D) Complete flux expulsion

A semiconductor laser operates mainly on the principle of

• (A) Spontaneous emission
• (B) Stimulated emission
• (C) Black body radiation
• (D) Photoelectric effect

Which of the following is a Bravais lattice?

• (A) Cubic
• (B) Tetragonal
• (C) Face-centered cubic
• (D) Hexagonal

The crystal structure of aluminum at room temperature is

• (A) BCC
• (B) FCC
• (C) HCP
• (D) Diamond cubic

A vacancy is classified as a

• (A) Point defect
• (B) Surface defect
• (C) Line defect
• (D) Volume defect

The number of crystal systems in three dimensions is

• (A) 5
• (B) 7
• (C) 10
• (D) 14

Dislocation climb occurs due to

• (A) Shear stress
• (B) Vacancy diffusion
• (C) Applied magnetic field
• (D) Grain boundary motion

The number of atoms per unit cell in FCC structure is

• (A) 8
• (B) 6
• (C) 4
• (D) 2

Cross-slip is possible only for

• (A) Edge dislocations
• (B) Grain boundaries
• (C) Mixed dislocations
• (D) Screw dislocations

Hot working differs from cold working because it

• (A) Increases strain hardening
• (B) Promotes recrystallization
• (C) Reduces ductility
• (D) Increases dislocation density

Proof stress is used when

• (A) Clear yield point exists
• (B) Material fractures elastically
• (C) Yield point is not well defined
• (D) Material is brittle

Aluminum alloy stress–strain curve shows

• (A) Sharp yield point
• (B) Large elastic region only
• (C) Brittle fracture
• (D) Smooth yielding

Quantum well lasers achieve lower threshold current because of

• (A) Larger active volume
• (B) Carrier confinement
• (C) Higher losses
• (D) Lower gain

The active medium in a semiconductor laser is

• (A) Insulator
• (B) Metal
• (C) p–n junction
• (D) Dielectric

Composites are designed primarily to

• (A) Combine desirable properties
• (B) Reduce cost
• (C) Improve conductivity only
• (D) Replace metals

Grain refinement improves strength mainly by

• (A) Increasing slip length
• (B) Increasing dislocation mobility
• (C) Hindering dislocation motion
• (D) Reducing elastic modulus

Which mechanism involves the movement of atoms to form a mirror image of the crystal structure across a plane?

• (A) Slip
• (B) Climbing
• (C) Creep
• (D) Twinning

Which material typically exhibits a distinct upper and lower yield point in its stress-strain curve?

• (A) Pure Aluminum
• (B) Mild Steel
• (C) Copper
• (D) Gray Cast Iron

During the recovery stage of annealing, which property changes the most significantly?

• (A) Grain size
• (B) Mechanical hardness
• (C) Electrical conductivity
• (D) Macroscopic shape

In which structure the Copper and Aluminum crystallize?

• (A) BCC
• (B) FCC
• (C) HCP
• (D) Simple Cubic

The area under the engineering stress-strain curve up to the point of fracture represents

• (A) Resilience
• (B) Elastic Modulus
• (C) Hardness
• (D) Toughness

Which of the following is not a mechanism of polymerization?

• (A) Addition
• (B) Condensation
• (C) Sintering
• (D) Ring-opening

In a fiber-reinforced composite, the primary role of the matrix is to

• (A) Carry the major load
• (B) Transfer stress to the fibers and protect them
• (C) Increase the density
• (D) Decrease the thermal conductivity

Electrical conductivity in metals primarily depends on

• (A) Number of free electrons
• (B) Atomic mass
• (C) Grain size
• (D) Lattice defects

Free electron theory treats conduction of electrons in metals as:

• (A) Classical gas of electrons
• (B) Bound electrons
• (C) Ion cores
• (D) Magnetic dipoles

The point on the stress-strain curve beyond which the material will not return to its original shape when the load is removed is called the:

• (A) Proportional Limit
• (B) Fracture Point
• (C) Ultimate Tensile Strength
• (D) Elastic Limit

The band gap of an intrinsic semiconductor increases with:

• (A) Temperature
• (B) Pressure
• (C) Doping
• (D) Time

Diamagnetic materials have:

• (A) Permanent magnetic moments
• (B) Magnetic susceptibility \(< 0\)
• (C) Magnetic susceptibility \(> 0\)
• (D) Hysteresis

The refractive index of a material is defined as:

• (A) Ratio of velocity of light in vacuum to velocity in material
• (B) Ratio of permittivity to permeability
• (C) Absorption coefficient of light
• (D) Polarization per unit field

A metal has one free electron per atom, density \(\rho = 0.97 g/cm^3\) and molar mass \(M = 39 g/mol\). Calculate the Fermi energy \(E_F\) of the metal:

• (A) \(4.5 eV\)
• (B) \(7.0 eV\)
• (C) \(5.5 eV\)
• (D) \(1.78 eV\)

A metal has free electron density \(n = 8.5 \times 10^{28} m^{-3}\) and relaxation time \(\tau = 2.5 \times 10^{-14} s\). Calculate its electrical conductivity (\(\sigma\)):

• (A) \(3.4 \times 10^7 S/m\)
• (B) \(2.0 \times 10^7 S/m\)
• (C) \(1.0 \times 10^7 S/m\)
• (D) \(5.0 \times 10^7 S/m\)

Which of the following best describes the general properties of Ceramics?

• (A) Soft and flexible
• (B) Brittle and insulating
• (C) Metallic and conductive
• (D) Ductile and malleable

Composite materials are typically made up of:

• (A) Single-phase materials
• (B) Matrix and reinforcement
• (C) Only polymers
• (D) Only metals

In composite materials, Matrices mainly function to:

• (A) Transfer load to reinforcement
• (B) Increase brittleness
• (C) Reduce density
• (D) Absorb light

Nanomaterials can be synthesized by the following approaches

• (1) \( Top-down approaches only \)
• (2) \( Bottom-up approaches only \)
• (3) \( Both Top-down and Bottom-up approaches \)
• (4) \( Only mechanical grinding \)

Dielectric constant of a material measures

• (1) \( Electrical conductivity \)
• (2) \( Polarizability in electric field \)
• (3) \( Magnetic susceptibility \)
• (4) \( Optical absorption \)

Soft magnetic materials are mainly used in

• (1) \( Permanent magnets \)
• (2) \( Transformers and cores \)
• (3) \( Optical devices \)
• (4) \( None of the above \)

Ferrimagnetic materials are found in

• (1) \( Iron oxides like magnetite \)
• (2) \( Copper \)
• (3) \( Silicon \)
• (4) \( Aluminium \)

Top-down approach in nanotechnology involves

• (1) \( Building from atoms \)
• (2) \( Electron-hole recombination \)
• (3) \( Chemical self-assembly \)
• (4) \( Breaking bulk material into nano-size \)

In band theory, metals have

• (1) \( Completely filled valence band and empty conduction band \)
• (2) \( Partially filled conduction band \)
• (3) \( Large band gap \)
• (4) \( No electrons \)

The critical temperature of a superconductor is the temperature at which

• (1) \( Resistance drops to zero \)
• (2) \( Magnetic susceptibility becomes zero \)
• (3) \( Dielectric constant diverges \)
• (4) \( Electron mobility decreases \)

The phenomenon where light is emitted from a material after the absorption of photons (excitation) is generally called

• (1) \( Luminescence \)
• (2) \( Refraction \)
• (3) \( Polarization \)
• (4) \( Dispersion \)

In a composite material, the phase that is continuous and surrounds the other phase is called the

• (1) \( Reinforcement \)
• (2) \( Matrix \)
• (3) \( Fiber \)
• (4) \( Dispersoid \)

The method commonly used for fabricating continuous fiber-reinforced polymer composites, specifically for making pipes or tanks is

• (1) \( Injection Molding \)
• (2) \( Filament Winding \)
• (3) \( Sintering \)
• (4) \( Blow Molding \)

As the size of a material reduces to the nanoscale, the surface area-to-volume ratio

• (1) \( Increases significantly \)
• (2) \( Decreases \)
• (3) \( Remains constant \)
• (4) \( Becomes zero \)

Above Curie temperature, a ferromagnetic material becomes

• (1) \( Diamagnetic \)
• (2) \( Superconducting \)
• (3) \( Paramagnetic \)
• (4) \( Antiferromagnetic \)

Which combination of mechanical properties is typically shown by Ceramics?

• (1) \( High ductility and low toughness \)
• (2) \( High hardness and high brittleness \)
• (3) \( Low hardness and high ductility \)
• (4) \( High tensile strength and high toughness \)

Concrete is a classic example of which type of composite?

• (1) \( Laminar composite \)
• (2) \( Particulate composite \)
• (3) \( Fiber-reinforced composite \)
• (4) \( Sandwich panel \)

Quantum confinement effects become significant when the size of the particle is comparable to the

• (1) \( Wavelength of visible light \)
• (2) \( Exciton Bohr radius \)
• (3) \( Mean free path of a gas molecule \)
• (4) \( Grain size of a metal \)

An inverting amplifier has a phase shift of

• (A) \(0^\circ\)
• (B) \(90^\circ\)
• (C) \(180^\circ\)
• (D) \(270^\circ\)

An op-amp adder sums voltages using

• (A) Voltage divider
• (B) Series connection of resistors
• (C) Inverting configuration
• (D) Differential pair

Integrator using op-amp uses

• (A) Resistor in feedback
• (B) Capacitor in feedback
• (C) Inductor in input
• (D) No feedback

Whenever a JFET operates above pinch-off voltage

• (A) Drain current starts decreasing
• (B) Drain current remains nearly constant
• (C) Depletion regions become smaller
• (D) Drain current increases steeply

A half-adder has

• (A) One input only
• (B) Two outputs only
• (C) Two inputs and two outputs
• (D) Three outputs

Basic function of ADC is to convert

• (A) Analog to Digital
• (B) Digital to Analog
• (C) Voltage to Current
• (D) Current to Voltage

BJT in common-emitter configuration has

• (A) High input, high output
• (B) Low input, high output
• (C) High input, low output
• (D) Low input, low output

DFT converts

• (A) Time domain to Frequency domain
• (B) Frequency domain to Time domain
• (C) Voltage to Current
• (D) Analog to Digital

CMOS technology is preferred for

• (A) Oscillators
• (B) Resistors
• (C) High power circuits
• (D) Low power circuits

The characteristic of an ideal operational amplifier is

• (A) Infinite input impedance and zero output impedance
• (B) Zero input impedance and infinite output impedance
• (C) Infinite input impedance and infinite output impedance
• (D) Zero input impedance and zero output impedance

Which of the following logic gate is known as a "Universal Gate"?

• (A) XOR
• (B) AND
• (C) NAND
• (D) OR

A CMOS inverter consists of

• (A) A PMOS pull-up and an NMOS pull-down network
• (B) An NMOS pull-up and a PMOS pull-down network
• (C) Two NMOS transistors
• (D) Two PMOS transistors

How many flip-flops are required to design a Mod-10 counter?

• (A) 3
• (B) 4
• (C) 10
• (D) 5

The process of converting a continuous-time signal into a discrete-time signal is called

• (A) Quantization
• (B) Sampling
• (C) Encoding
• (D) Aliasing

Charge Coupled Devices (CCDs) are primarily used in

• (A) High-power amplification
• (B) Digital Logic
• (C) Image sensing and signal processing
• (D) Voltage regulation

A 4-bit ripple counter uses flip-flops with a propagation delay of 50 ns each. The maximum clock frequency that can be used is:

• (A) \(5 MHz\)
• (B) \(10 MHz\)
• (C) \(20 MHz\)
• (D) \(50 MHz\)

A 10-bit ADC has a reference voltage of 10.24 V. The resolution (step size) of the converter is:

• (A) \(1 mV\)
• (B) \(10 mV\)
• (C) \(10.24 mV\)
• (D) \(100 mV\)

"Latch-up" in CMOS circuits is caused by the formation of parasitic:

• (A) Capacitors
• (B) Inductors
• (C) Thyristors (SCRs)
• (D) Resistors

A practical op-amp differentiator requires a small resistor in series with the input capacitor to:

• (A) Increase gain
• (B) Reduce input impedance
• (C) Improve stability and reduce high-frequency noise sensitivity
• (D) Increase bandwidth

In a MOSFET, if the source-to-body voltage \( V_{SB} > 0 \) (for NMOS), the threshold voltage \( V_T \):

• (A) Decreases
• (B) Increases
• (C) Remains constant
• (D) Becomes negative

D/A converter resolution improves with:

• (A) More bits
• (B) Lower voltage
• (C) Faster clock
• (D) Larger load

Digital signals for FFT are assumed:

• (A) Periodic
• (B) Non-periodic
• (C) Random
• (D) DC only

CMOS inverter output is LOW when input is:

• (A) LOW
• (B) HIGH
• (C) Floating
• (D) Zero current

A counter with modulus 8 has:

• (A) \(3 flip-flops\)
• (B) \(4 flip-flops\)
• (C) \(2 flip-flops\)
• (D) \(8 flip-flops\)

MOSFET cutoff occurs when:

• (A) \(V_{GS} < V_{th}\)
• (B) \(V_{GS} > V_{th}\)
• (C) \(V_{DS} = 0\)
• (D) \(V_{GS} = V_{DS}\)

The de Broglie wavelength of a particle is:

• (A) \(\frac{h}{p}\)
• (B) \(\frac{p}{h}\)
• (C) \(\frac{h^2}{p}\)
• (D) sqrt{frac{h}{p}}

The Schrödinger equation is:

• (A) \(H\psi = E\psi\)
• (B) \(F = ma\)
• (C) \(E = mc^2\)
• (D) \(pV = nRT\)

The time-independent Schrödinger equation is fundamentally an eigenvalue equation for which operator?

• (A) Momentum Operator
• (B) Hamiltonian Operator
• (C) Position Operator
• (D) Parity Operator

The ground state energy of the Hydrogen atom is approximately:

• (A) \(-1.5 eV\)
• (B) \(-3.4 eV\)
• (C) \(-13.6 eV\)
• (D) \(-54.4 eV\)

The wavefunction of a system of identical fermions must be:

• (A) Symmetric under particle exchange
• (B) Antisymmetric under particle exchange
• (C) Symmetric for spin, antisymmetric for space
• (D) Unrelated to exchange symmetry

The energy levels of a quantum harmonic oscillator are:

• (1) Degenerate
• (2) Equally spaced
• (3) Proportional to \(n^2\)
• (4) Continuous

Particles with integer spin are called:

• (1) Fermions
• (2) Bosons
• (3) Leptons
• (4) Baryons

The second-order correction to the energy of the ground state is always:

• (1) Zero
• (2) Imaginary
• (3) Positive
• (4) Negative

Harmonic oscillator potential is:

• (1) \(V = \frac{m\omega^2 x^2}{2}\)
• (2) \(V = mgh\)
• (3) \(V = kx\)
• (4) \(V = 0\)

The Born's approximation is applicable for:

• (1) High energy, low atomic number for scatterer
• (2) Low energy, low atomic number for scatterer
• (3) High energy, high atomic number for scatterer
• (4) Low energy, high atomic number for scatterer

The following are the centroidal coordinates of semicircular plane of \(16\pi\) cm diameter and is symmetric about \(x\)-axis.

• (1) \(\left(0, \frac{32}{3}\right)\)
• (2) \(\left(\frac{32}{3}, 0\right)\)
• (3) \(\left(0, \frac{16}{3}\right)\)
• (4) \(\left(\frac{16}{3}, 0\right)\)

The polar moment of inertia of a circular plane of diameter about its centroid is (in \(cm^4\)):

• (1) \(128\pi\)
• (2) \(156\pi\)
• (3) \(64\pi\)
• (4) \(312\pi\)

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is:

• (1) \(0.64\)
• (2) \(0.86\)
• (3) \(0.34\)
• (4) \(0.72\)

Which of the following has the highest specific heat capacity?

• (1) Copper
• (2) Iron
• (3) Aluminium
• (4) Water *(Note: Explicit target option implied by standard thermodynamic comparisons)*

A uniform cylinder of radius 10 cm and mass 20 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0 cm from the central longitudinal axis of the cylinder. What is the rotational inertia of the cylinder about the axis of rotation?

• (1) \(0.15 kg\)
• (2) \(0.21 kg\)
• (3) \(0.26 kg\)
• (4) \(0.17 kg\)

When a torque of 32.0 Nm is applied to a certain wheel, the wheel acquires an angular acceleration of 25.0 units. What is the rotational inertia of the wheel?

• (1) \(1.25 kg^2\)
• (2) \(1.28 kg^2\)
• (3) \(2.28 kg^2\)
• (4) \(2.25 kg^2\)

The minimum value of angular momentum by coupling three angular momenta \(1\), \(\frac{3}{2}\) and \(\frac{5}{2}\) is:

• (1) \(-5\)
• (2) \(\frac{1}{2}\)
• (3) \(0\)
• (4) \(1\)

If a particle has mass of 20 kg moves with an acceleration of \(2.5 m/s^2\), then the magnitude of force acting on the particle is (in \(kg/s^2\)):

• (1) \(25\)
• (2) \(50\)
• (3) \(75\)
• (4) \(100\)

The centre of gravity for a solid hemisphere about its diametral base having diameter 120 cm and is symmetric about y-axis is (in cm):

• (1) \(22.5\)
• (2) \(90\)
• (3) \(135\)
• (4) \(45\)

In a simple harmonic motion (SHM), the acceleration is proportional to:

• (1) Velocity
• (2) Displacement and opposite in direction
• (3) Time
• (4) Square of velocity

The driving force for heat conduction is called as:

• (1) Temperature gradient
• (2) Concentration gradient
• (3) Pressure gradient
• (4) Velocity gradient

Furnace efficiency is best defined as the ratio of

• (1) Heat input to heat output
• (2) Heat stored in stock to total heat input
• (3) Heat utilized by the stock to the heat released by the fuel
• (4) Heat losses to heat input

A Sankey diagram is primarily used to represent

• (1) Temperature distribution in a furnace
• (2) Pressure drops in a piping system
• (3) Energy balance and heat flow distribution
• (4) Electrical wiring diagrams

Saturated steam at 100 \(^\circ\)C condenses on the outside of a tube. Cold fluid enters the tube at 20 \(^\circ\)C and exits at 50 \(^\circ\)C. The value of the Log Mean Temperature Difference (in \(^\circ\)C) is:

• (1) 54.89
• (2) 63.83
• (3) 72.39
• (4) 89.36

Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being \(T_1 = 300\) K and \(T_2 = 350\) K. The heat capacity rates of the two fluids are \(C_1 = 1000\) W/K and \(C_2 = 400\) W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is (in kW)

• (1) 12
• (2) 15
• (3) 18
• (4) 10

Adding insulation to a cylindrical pipe with a radius smaller than the critical radius of insulation will

• (1) Decrease heat loss
• (2) Increase heat loss
• (3) Have no effect
• (4) Stop heat flow completely

The primary mode of heat transfer to the workpiece in a salt bath furnace is

• (1) Radiation
• (2) Convection (Liquid to Solid)
• (3) Conduction (Gas to Solid)
• (4) Induction

High excess air in a furnace combustion process generally

• (1) Increases furnace efficiency
• (2) Decreases furnace efficiency due to stack losses
• (3) Increases flame temperature
• (4) Reduces fuel consumption

Fourier's law of heat conduction relates

• (1) Heat flux to temperature gradient
• (2) Heat flux to pressure gradient
• (3) Heat flux to velocity gradient
• (4) Heat flux to density

Steady-state conduction implies

• (1) Temperature does not change with time
• (2) Temperature varies with time
• (3) Heat flux is zero
• (4) Convection occurs

Entropy of a perfect crystal at 0 K is

• (1) Negative
• (2) Infinity
• (3) Constant
• (4) Zero

Boltzmann equation relates

• (1) Entropy to the number of microstates \(S = k \ln \Omega\)
• (2) Enthalpy to pressure
• (3) Work to volume
• (4) Energy to temperature

Gibbs-Helmholtz equation relates

• (1) Gibbs free energy, enthalpy and temperature
• (2) Entropy and work
• (3) Internal energy and volume
• (4) Heat and temperature

Chemical potential is

• (1) Work done by system
• (2) Total enthalpy
• (3) Partial molar Gibbs free energy
• (4) Heat absorbed

Mixing entropy arises due to

• (1) Volume change
• (2) Heat transfer
• (3) Work done
• (4) Random distribution of components

Fundamental equation of state for ideal gas

• (1) \(PV = nRT\)
• (2) \(PV^2 = nRT\)
• (3) \(\frac{P}{V} = nRT\)
• (4) \(P + V = nRT\)

A heat engine receives 1000 J of heat from a reservoir at 1000 K and rejects 600 J of heat to a sink at 300 K. This engine is

• (1) Reversible
• (2) Irreversible
• (3) Impossible
• (4) Perfectly efficient

For a van der Waals gas, the internal energy U

• (1) Depends only on Temperature
• (2) Depends on both Temperature and Volume
• (3) Is zero
• (4) Depends only on Volume

For a unary (one component) system, the maximum number of phases that can coexist in equilibrium at the triple point is

• (1) 1
• (2) 2
• (3) 3
• (4) 0

Mixing two distinct ideal gases results in an increase in entropy primarily because of

• (1) Increase in internal energy
• (2) Increase in molecular interactions
• (3) Increase in spatial uncertainty
• (4) Chemical reaction between gases