# (Syllabus) CSIR-UGC National Eligibility Test (NET) : Engineering Sciences

## Council of Scientific and Industrial Research

Human Resource Development Group

## CSIR-UGC National Eligibility Test (NET) for Junior Research
Fellowship

and Lecturer-ship

## Engineering Sciences

## PART A

General aptitude with emphasis on logical reasoning, graphical analysis, analytical and numerical ability, quantitative comparisons, series formation, puzzles, etc.

## PART B

### Mathematics And Engineering Aptitude

**Linear Algebra:** Algebra of matrices, inverse, rank,
system of linear equations, symmetric, skew-symmetric and orthogonal matrices.
Hermitian, skew-Hermitian and unitary matrices. eigenvalues and eigenvectors,
diagonalisation of matrices.

**Calculus: **Functions of single variable, limit,
continuity and differentiability, Mean value theorems, Indeterminate forms and
L'Hospital rule, Maxima and minima, Taylor's series, Newton’s method for finding
roots of polynomials. Fundamental and mean value-theorems of integral calculus.
Numerical integration by trapezoidal and Simpson’s rule. Evaluation of definite
and improper integrals, Beta and Gamma functions, Functions of two variables,
limit, continuity, partial derivatives, Euler's theorem for homogeneous
functions, total derivatives, maxima and minima, Lagrange method of multipliers,
double integrals and their applications, sequence and series, tests for
convergence, power series, Fourier Series, Half range sine and cosine series.

**Complex variables:** Analytic functions, Cauchy-Riemann
equations, Line integral, Cauchy's integral theorem and integral formula
Taylor’s and Laurent' series, Residue theorem and its applications.

**Vector Calculus:** Gradient, divergence and curl, vector
identities, directional derivatives, line, surface and volume integrals, Stokes,
Gauss and Green's theorems and their applications.

**Ordinary Differential:** First order equation (linear
and nonlinear), Second order linear differential equations with variable
coefficients, Variation of Equations parameters method, higher order linear
differential equations with constant coefficients, Cauchy-Euler's equations,
power series solutions, Legendre polynomials and Bessel's functions of the first
kind and their properties. Numerical solutions of first order ordinary
differential equations by Euler’s and Runge-Kutta methods.

**Probability:** Definitions of probability and simple theorems,
conditional probability, Bayes Theorem.

**Solid Body Motion and Fluid Motion:** Particle dynamics;
Projectiles; Rigid Body Dynamics; Lagrangian formulation; Eularian formulation;
Bernoulli’s Equation; Continuity equation; Surface tension; Viscosity; Brownian
Motion.

**Energetics: **Laws of Thermodynamics; Concept of Free
energy; Enthalpy, and Entropy; Equation of State; Thermodynamics relations.

**Electron Transport:** Structure of atoms, Concept of
energy level, Bond Theory; Definition of conduction, Semiconductor and
Insulators; Diode; Half wave & Full wave rectification; Amplifiers &
Oscillators; Truth Table.

**Electromagnetics:** Theory of Electric and Magnetic
potential & field; Biot & Savart’s Law; Theory of Dipole; Theory of Oscillation
of electron; Maxwell’s equations; Transmission theory; Amplitude & Frequency
Modulation.

**Materials: **Periodic table; Properties of elements;
Reaction of materials; Metals and non-Metals (Inorganic materials), Elementary
knowledge of monomeric and polymeric compounds; Organometallic compounds;
Crystal structure and symmetry,

Structure-property correlation-metals, ceramics, and polymers.

## PART C

### 1. COMPUTER SCIENCE AND INFORMATION TECHNOLOGY

**Basic Discrete Mathematics: **Counting principles, linear recurrence, mathematical induction, equation
sets, relations and function, predicate and propositional logic.

**Digital Logic:**Logic functions, Minimization, Design and synthesis of combinational and
sequential circuits; Number representation and computer arithmetic (fixed and
floating point).

**Computer Organization and Architecture:**Machine instructions and addressing modes, ALU and data-path, CPU control
design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction
pipelining, Cache and main memory, Secondary storage.

Programming and Data Structures:

Programming in C; Functions, Recursion, Parameter passing, Scope, Binding;
Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search
trees, Binary heaps.

**Algorithms:**Analysis, Asymptotic notation, Notions of space and time complexity, Worst
and average case analysis; Design: Greedy approach, Dynamic programming,
Divide-and conquer; Tree and graph traversals, Connected components, Spanning
trees, Shortest paths; Hashing, Sorting, Searching. Asymptotic analysis (best,
worst, average cases) of time and space, upper and lower bounds, Basic concepts
of complexity classes P, NP, NP-hard, NP-complete.

**Operating System:**Processes, Threads, Inter-process communication, Concurrency,
Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory,
File systems.

**Databases:**ER-model, Relational model (relational algebra, tuple calculus), Database
design (integrity constraints, normal forms), Query languages (SQL), File
structures (sequential files, indexing, B and B+ trees), Transactions and
concurrency control.

**Information Systems and Software Engineering:**information gathering, requirement and feasibility analysis, data flow
diagrams, process specifications, input/output design, process life cycle,
planning and managing the project, design, coding, testing, implementation,
maintenance.

### 2. ELECTRICAL SCIENCES

**Electric Circuits and Fields:**Node and mesh analysis, transient response of dc and ac networks, sinusoidal
steady-state analysis, resonance, basic filter concepts, ideal current and
voltage sources, Thevenin’s, Norton’s and Superposition and Maximum Power
Transfer theorems, two port networks, three phase circuits, measurement of power
in three phase circuits, Gauss Theorem, electric field and potential due to
point, line, plane and spherical charge distributions, Ampere’s and
Biot-Savart’s laws, inductance, dielectrics , capacitance.

**Electrical Machines: Magnetic circuits**

Magnetic circuits, Single phase transformer- equivalent circuit, phasor diagram,
tests, regulatio and efficiency, Three phase transformers- connections, parallel
operation, auto-transformer; energy conversion principles, DC Machines- types ,
starting and speed control of dc motors, Three phase induction motors-
principles, types, performance characteristics, starting and speed control ,
Single phase induction motors, synchronous machines performance, regulation and
parallel operation of synchronous machine operating as generators, starting and
speed control of synchronous motors and its applications, servo and stepper
motors.

**Power Systems:**Basic power generation concepts, transmission line models and performance,
cable performance, insulation, corona and radio interference , Distribution
systems, per-unit quantities, bus impedance and admittance matrices, load flow,
voltage and frequency control, power factor correction; unbalanced analysis,
symmetrical components, basic concepts of protection and stability; Introduction
to HVDC systems.

**Control Systems:**Principles of feedback control, transfer function, block diagrams, steady
state errors, Routh and Nyquist techniques, Bode plots, Root loci, Lag , Lead
and Lead-lag compensation; proportional, PI, PID controllers, state space model
, state transition matrix, controllability and observability.

**Power Electronics and Drives:**

Semiconductor Power devices - power diodes, power transistors, thyristors,
triacs, GTOs, MOSFETs, IGBTs – their characteristics and basic triggering
circuits; diode rectifiers, thyristor based line commutated ac to dc converters,
dc to dc converters – buck, boost, buck-boost, c`uk, flyback, forward, push-pull
converters, single phase and three phase dc to ac inverters and related pulse
width modulation techniques, stability of electric drives; speed control issues
of dc motors, induction motors and synchronous motors.

### 3. ELECTRONICS

**Analog Circuits and Systems:**Electronic devices: characteristics and small-signal equivalent circuits of
diodes, BJTs and MOSFETs. Diode circuits: clipping, clamping and rectifier.
Biasing and bias stability of BJT and FET amplifiers. Amplifiers: single-and
multi-stage, differential and operational, feedback, and power. Frequency
response of amplifiers. Op-amp circuits: voltage-to-current and
current-to-voltage converters, active filters, sinusoidal oscillators,
wave-shaping circuits, effect of practical parameters (input bias current, input
offset voltage, open loop gain, input resistance, CMRR). Electronic
measurements: voltage, current, impedance, time, phase, frequency measurements,
oscilloscope.

**Digital Circuits and Systems:**Boolean algebra and minimization of Boolean functions. Logic gates, TTL and
CMOS IC families. Combinatorial circuits: arithmetic circuits, code converters,
multiplexers and decoders. Sequential circuits: latches and flip-flops, counters
and shift-registers. Sample-and-hold circuits,ADCs, DACs. Microprocessors and
microcontrollers: number systems, 8085 and 8051 architecture, memory, I/O
interfacing, Serial and parallel communication.

**Signals and Systems:**Linear time invariant systems: impulse response, transfer function and
frequency response of first- and second order systems, convolution. Random
signals and noise: probability, random variables, probability density function,
autocorrelation, power spectral density. Sampling theorem, Discrete-time
systems: impulse and frequency response, IIR and FIR filters.

**Communications:**

Amplitude and angle modulation and demodulation, frequency and time division
multiplexing. Pulse code modulation, amplitude shift keying, frequency shift
keying and pulse shift keying for digital modulation. Bandwidth and SNR
calculations. Information theory and channel capacity.

### 4. MATERIALS SCIENCE

**Structure:**

Atomic structure and bonding in materials. Crystal structure of materials,
crystal systems, unit cells and space lattices, miller indices of planes and
directions, packing geometry in metallic, ionic and covalent solids. Concept of
amorphous, single and polycrystalline structures and their effect on properties
of materials. Imperfections in crystalline solids and their role in influencing

various properties.

**Diffusion: **Fick's laws and application of diffusion.

**Metals and Alloys:**

Solid solutions, solubility limit, phase rule, binary phase diagrams,
intermediate phases, intermetallic compounds, iron-iron carbide phase diagram,
heat treatment of steels, cold, hot working of metals, recovery,
recrystallization and grain growth. Microstrcture, properties and applications
of ferrous and non-ferrous alloys.

**Ceramics, Polymers, & Composites:**

Structure, properties, processing and applications of ceramics. Classification,
polymerization, structure and properties, processing and applications.
Properties and applications of various composites.

**Materials Characterization Tools:**

X-ray diffraction, optical microscopy, scanning electron microscopy and
transmission electron microscopy, differential thermal analysis, differential
scanning calorimetry.

**Materials Properties: **

Stress-strain diagrams of metallic, ceramic and polymeric materials, modulus of
elasticity, yield strength, tensile strength, toughness, elongation, plastic
deformation, viscoelasticity, hardness, impact strength, creep, fatigue, ductile
and brittle fracture.

Heat capacity, thermal conductivity, thermal expansion of materials. Concept of
energy band diagram for materials - conductors, semiconductors and insulators,
intrinsic and extrinsic semiconductors, dielectric properties. Origin of
magnetism in metallic and ceramic materials, paramagnetism, diamagnetism,
antiferro magnetism, ferromagnetism, ferrimagnetism, magnetic hysterisis.

**Environmental Degradation:**

Corrosion and oxidation of materials, prevention.

### 5. FLUID MECHANICS

**Fluid Properties:**

Relation between stress and strain rate for Newtonian fluids; Buoyancy,
manometry, forces on submerged bodies.

**Kinematics**

Eulerian and Lagrangian description of fluid motion, strain rate and vorticity;
concept of local and convective accelerations, steady and unsteady flows

**Control Volume Based Analysis**

Control volume analysis for mass, momentum and energy. Differential equations of
mass and momentum (Euler equation), Bernoulli's equation and its applications,
Concept of fluid rotation.

**Potential flow: **

Vorticity, Stream function and Velocity potential function; Elementary flow
fields and principles of superposition, potential flow past a circular cylinder.

**Dimensional analysis:**

Concept of geometric, kinematic and dynamic similarity, Non-dimensional numbers
and their usage.

**Viscous Flows**

Navier-Stokes Equations; Exact Solutions; Couette Flow, Fully-developed pipe
flow, Hydrodynamic lubrication, Basic ideas of Laminar and Turbulent flows,
Prandtl-mixing length, Friction factor, Darcy-Weisbach relation, Simple pipe
networks.

**Boundary Layer**

Qualitative ideas of boundary layer, Boundary Layer Equation; Separation,
Streamlined and bluff bodies, drag and lift forces.

**Measurements**

Basic ideas of flow measurement using venturimeter, pitot-static tube and
orifice plate.

### 6. SOLID MECHANICS

Equivalent force systems; free-body diagrams; equilibrium equations; analysis of determinate trusses and frames; friction; simple particle dynamics; plane kinematics and kinetics; workenergy and impulse-momentum principles;

Stresses and strains; principal stresses and strains; Mohr's circle; generalized Hooke's Law; thermal strain.

Axial, shear and bending moment diagrams; axial, shear and bending stresses; deflection of beams (symmetric bending); Torsion in circular shafts; thin walled pressure vessels. Energy methods (Catigliano’s theorems) for analysis. Combined axial, bending and torsional action; Theories of failure. Buckling of columns.

Free vibration of single degree of freedom systems.

### 7. THERMODYNAMICS

**Basic Concepts:**

Continuum, macroscopic approach, thermodynamic system (closed and open or
control volume); thermodynamic properties and equilibrium; state of a system,
state diagram, path and process; different modes of work; Zeroth law of
thermodynamics; concept of temperature; heat.

**First Law of Thermodynamics:**

Energy, enthalpy, specific heats, first law applied to closed systems and open
systems (control volumes), steady and unsteady flow analysis.

**Second Law of Thermodynamics:**

Kelvin-Planck and Clausius statements, reversible and irreversible processes,
Carnot theorems, thermodynamic temperature scale, Clausius inequality and
concept of entropy, principle of increase of entropy, entropy balance for closed
and open systems, exergy (availability) and irreversibility, non-flow and flow
exergy.

**Properties of Pure Substances:**

Thermodynamic properties of pure substances in solid, liquid and vapor phases,
P-V-T behaviour of simple compressible substances, phase rule, thermodynamic
property tables and charts, ideal and real gases, equations of state,
compressibility chart.

**Thermodynamic Relations:**

T-ds relations, Maxwell equations, Joule-Thomson coefficient, coefficient of
volume expansion, adiabatic and isothermal compressibilities, Clapeyron
equation.

**Thermodynamic cycles:**

Carnot vapour power cycle; simple Rankine cycle, reheat and regenerative Rankine
cycle; Air standard cycles: Otto cycle, Diesel cycle, simple Brayton cycle,
Brayton cycle with regeneration, reheat and intercooling; vapour-compression
refrigeration cycle.

**Ideal Gas Mixtures:**

Dalton's and Amagat's laws, calculations of properties (internal energy,
enthalpy, entropy), airwater vapour mixtures and simple thermodynamic processes
involving them.

Courtesy: CSIR-UGC

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