Welcome to the Doctoral Programme
Syllabus for Ph.D. Entrance Exam
The entrance examination shall contain both objective
and subjective type of questions. The syllabus for the written entrance examination
shall consist of 50% of research aptitude/methodology and 50% shall be subject-specific.
Research aptitude/methodology part shall be of generic nature, intended to assess
the research aptitude of the candidate. This part primarily shall contain questions
to test research aptitude, reasoning ability, graphical analysis, analytical and
numerical ability, data interpretation, quantitative aptitude of the candidate.
While, subject-specific syllabus for each branch is given below:
Computer Science & Engineering
Computer Science & Engineering
- Computer Programmeming: Fundamental Programmeming constructs, Decision
and control statements, Arrays, Strings, Functions, Recursion, Dynamic memory allocation,
Composite data types (Structures and Unions)
- Discrete Mathematical Structures: Boolean algebra, Propositional
and first order logic, Sets, Relations, Functions, Partial orders and lattices,
Groups and Rings, Trees, Graphs (Connectivity, Matching, Coloring), Combinatorics
(Counting, Recurrence relations, Generating functions)
- Data Structures: Time and Space complexity of algorithms, Asymptotic
analysis, Big `O’ and other notations, Stacks, Queues, Linked lists (Singly, Doubly
and Circular), Trees, Binary search trees, AVL tree, Heaps, Hashing and Graphs
- Algorithms: Complexity analysis, Searching, Sorting, Algorithm
design techniques (Greedy, Dynamic Programmeming and Divide‐and‐conquer), Graph search,
Minimum spanning tree, Shortest path
- Computer Organization and Architecture: Machine instructions and
addressing modes. ALU, Data‐path and Control unit, Instruction pipelining, Memory
hierarchy (Cache, Main memory and Secondary storage), I/O interface (Interrupt and
- Operating Systems: Processes, Threads, Inter‐process communication,
Concurrency and Synchronization, Deadlock, CPU scheduling, Memory management and
- Database Management Systems: ER‐model, Relational model, Relational
algebra, Tuple calculus, SQL, Integrity constraints, Normal forms, File organization,
Indexing, Transactions and Concurrency control
- Computer Networks: OSI Reference Model and TCP/IP Network Architecture,
Ethernet and WiFi, Access Control, Flow and Error control, Network devices, Switching,
IPv4, IPv6, Routing algorithms, TCP/UDP and Sockets, Congestion control, Application
layer protocols (DNS, SMTP, POP, FTP, HTTP)
- Theory of Computation: Regular expressions and finite automata,
Context-free grammars and push-down automata, Regular and context-free languages,
Turing machine and Undecidability
Electronics & Communication Engineering
Electronics & Communication Engineering
- Digital Design: Number Systems & Codes, Boolean Algebra and Minimization
Techniques, Digital CMOS Logic, Combinatorial Circuits & Systems, Sequential Circuits
& Systems, Finite State Machines.
- Analog Electronics: Circuit Theorems and KCL/KVL, Op-amp, RC, RLC
Circuits, Physics of transistors, Characteristics and biasing of BJT, Small signal
(incremental) equivalent circuits, CE, CB and CC amplifiers, Difference Amplifier
Design, Oscillators and Filters: Bode plots, Clipping, Clamping and other Non-Linear
Op-Amp applications, Power supplies, DAC: Principles and Circuits, ADC: Principles
- Signals and Systems : Linear Time-Invariant (LTI) systems: Discrete
and Continuous, Fourier representation of periodic signals, Fourier Transform of
aperiodic signals, Laplace and z-transform, Linear Feedback Systems.
- Digital Signal Processing: Transform analysis of LTI systems, Structures
for Discrete Time systems, FIR Filter Design Techniques, FFT, Multi-rate Digital
Signal Processing, Adaptive Signal Processing, Stochastic signals, Wiener Filtering,
LMS and RMS algorithms, Spectral Estimation.
- Basic Analog and Digital Communication: Bandwidth of AM/SSB/FM
analog signals, SNR of FM system, DM/ADM/PCM, signal-to-quantization noise ratio.,
PSK/DPSK/QAM /OFDM systems,BER and Q-function, Error Correcting Codes: Block codes
and convolutional codes
- Probability and Matrices Algebra: Random variables, Distributions,
Mean and variance, Conditional probability, Bayes’ theorem, Correlation, Covariance,
Central limit theorem, Matrix multiplication, Gaussian elimination, Determinant,
Inverse of matrix, Eigenvalues and Eigenvectors, Matrix diagonalization
Mechanical & Mechatronics Engineering
Mechanical & Mechatronics Engineering
- Mechanics of Materials: Stress and strain, elastic constants, Poisson's
ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force
and bending moment diagrams; bending and shear stresses; deflection of beams; torsion
of circular shafts; Euler’s theory of columns; energy methods; thermal stresses;
strain gauges and rosettes; testing of materials with universal testing machine;
testing of hardness and impact strength.
- Theory of Machines: Displacement, velocity and acceleration analysis
of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains;
flywheels and governors; balancing of reciprocating and rotating masses; gyroscope.
Vibrations: Free and forced vibration of single degree of freedom systems, effect
of damping; vibration isolation; resonance; critical speeds of shafts.
- Machine Design: Design for static and dynamic loading; failure
theories; fatigue strength and the S-N diagram; principles of the design of machine
elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding
contact bearings, brakes and clutches, springs.
- Fluid Mechanics and Turbomachinery: Fluid properties; fluid statics,
manometry, buoyancy, forces on submerged bodies, stability of floating bodies; control-volume
analysis of mass, momentum and energy; fluid acceleration; differential equations
of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous
flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through
pipes, head losses in pipes, bends and fittings. Impulse and reaction principles,
velocity diagrams, Pelton-wheel, Francis and Kaplan turbines.
- Heat-Transfer: Modes of heat transfer; one dimensional heat conduction,
resistance concept and electrical analogy, heat transfer through fins; unsteady
heat conduction, lumped parameter system, Heisler's charts; thermal boundary layer,
dimensionless parameters in free and forced convective heat transfer, heat transfer
correlations for flow over flat plates and through pipes, effect of turbulence;
heat exchanger performance, LMTD and NTU methods; radiative heat transfer, Stefan
Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation
- Thermodynamics: Thermodynamic systems and processes; properties
of pure substances, behavior of ideal and real gases; zeroth and first laws of thermodynamics,
calculation of work and heat in various processes; second law of thermodynamics;
thermodynamic property charts and tables, availability and irreversibility; thermodynamic
- Engineering Materials: Structure and properties of engineering
materials, phase diagrams, heat treatment, stress-strain diagrams for engineering
- Forming and Joining Processes: Different types of castings, design
of patterns, moulds and cores; solidification and cooling; riser and gating design.
Plastic deformation and yield criteria; fundamentals of hot and cold working processes;
load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing,
deep drawing, bending) metal forming processes; principles of powder metallurgy.
Principles of welding, brazing, soldering and adhesive bonding.
- Machining and Machine Tool Operations: Mechanics of machining;
basic machine tools; single and multi-point cutting tools, tool geometry and materials,
tool life and wear; economics of machining; principles of non-traditional machining
processes; principles of work holding, design of jigs and fixtures.
- Metrology and Inspection: Limits, fits and tolerances; linear and
angular measurements; comparators; gauge design; interferometry; form and finish
measurement; alignment and testing methods; tolerance analysis in manufacturing
- Production Planning and Control: Forecasting models, aggregate
production planning, scheduling, materials requirement planning. Inventory Control:
Deterministic models; safety stock inventory control systems.
- Operations Research: Linear Programmeming, simplex method, transportation
assignment, network flow models, simple queuing models, PERT and CPM.
- Classical Mechanics : Conservation of linear momentum, energy,
and angular momentum, Lagrangian, action principle, Euler-Lagrange equations, Lagrangian
formalism, Generalized coordinates, Hamiltonian, Hamilton’s equations of motion,
Phase space and phase trajectories, Hamiltonian systems and Liouville’s theorem,
Canonical transformations, Poisson brackets.
- Electrodynamics : Electrostatics, Gauss law and its application,
Magnetostatics, Electromotive force, Faraday laws, Maxwell equations, wave equation,
electromagnetic waves in vacuum, wave equation for E and B, scalar and vector potential,
gauge transformations, electric and magnetic field in matter, Polarization, magnetization.
- Quantum Mechanics : Basic principles of quantum mechanics, Probabilities
and probability amplitudes, linear vector spaces, Eigen states and eigenvalues,
wave function, Heisenberg uncertainty principle, Schrödinger equation, one dimensional
potential problems, linear harmonic oscillator, Orbital angular momentum operators,
spherical harmonics, hydrogen atom problem. Charged particle in a uniform constant
magnetic field, Time independent perturbation theory, Time dependent perturbation
theory, variational methods.
- Statistical Mechanics : First law of thermodynamics, Second law
of thermodynamics, Third law of thermodynamics, microcanonical ensemble, canonical
ensemble, grand canonical ensemble, quantum statistics, phase diagrams, phase equilibria
and phase transitions.
- Mathematical Methods : Orthogonal and curvilinear coordinates,
Scalar and vector fields, Vector differential operators, Gauss’ theorem, Green’s
theorem, Stokes theorem and their applications, Laplace and Poisson equations, Linear
vector spaces and representations, Elements of complex variables, various special
functions, Fourier analysis, Fourier transforms, and Laplace transforms.
- Linear Algebra: Linear transformations; Finite dimensional vector
spaces and their matrix representations, rank; systems of linear equations, eigen
vectors and eigen values, minimal polynomial, Cayley-Hamilton Theroem, Hermitian,
diagonalisation, Skew-Hermitian and unitary matrices; Gram-Schmidt orthonormalization
process, Finite dimensional inner product spaces, self-adjoint operators.
- Complex Analysis: Analytic functions, bilinear transformations;
conformal mappings; complex integration: Cauchy’s integral theorem and formula;
Liouville’s theorem, maximum modulus principle; Laurent’s and Taylor’s series; residue
theorem and applications for evaluating real integrals.
- Real Analysis: Sequences and series of functions, power series,
uniform convergence, Fourier series, functions of several variables, minima, maxima
; multiple integrals, Riemann integration, surface, line and volume integrals, theorems
of Green, Gauss and stokes; metric spaces, completeness, Weierstrass approximation
theorem, Lebesgue measure, compactness; measurable functions, Fatou’s lemma, Lebesgue
integral, dominated convergence theorem.
- Ordinary Differential Equations: First order ordinary differential
equations, existence and uniqueness theorems, linear ordinary differential equations
of higher order with constant coefficients; systems of linear first order ordinary
differential equations; linear second order ordinary differential equations with
variable coefficients; method of Laplace transforms for solving ordinary differential
equations, Legendre and Bessel functions and their orthogonality; series solutions.
- Algebra: Normal subgroups and automorphisms; homomorphism theorems
; Group actions, Sylow’s theorems and their applications; Euclidean domains, unique
factorization domains and Principle ideal domains .Prime ideals and maximal ideals
in commutative rings; finite fields, Fields
- Functional Analysis: Hahn-Banach extension theorem, Banach spaces
,open mapping and closed graph theorems, Hilbert spaces, principle of uniform boundedness,
orthonormal bases, Riesz representation theorem, bounded linear operators.
- Numerical Analysis: Numerical solution of algebraic and transcendental
equations: secant method, bisection, Newton-Raphson method, fixed point iteration;
interpolation: Lagrange error of polynomial interpolation, Newton interpolations;
numerical differentiation; numerical integration: Trapezoidal and Simpson rules,
Gauss Legendre quadrature, least square polynomial approximation; method of undetermined
parameters; numerical solution of systems of linear equations: direct methods (LU
decomposition ,Gauss elimination,); iterative methods (Gauss-Seidel and Jacobi);
matrix eigen value problems: power method, numerical solution of ordinary differential
equations: initial value problems: Euler’s method, Runge-Kutta methods, Taylor series
- Partial Differential Equations: Linear and quasi linear first order
partial differential equations, method of characteristics; second order linear equations
in two variables and their classification; Dirichlet, Cauchy and Neumann problems;
solutions of Laplace, diffusion and wave equations in two variables; Fourier transform,
Fourier series and Laplace transform methods of solutions for the above equations.
- Topology: Basic concepts of topology, connectedness, product topology,
compactness, countability and separation axioms, Urysohn’s Lemma.
- Probability and Statistics: Probability space, Bayes theorem, conditional
probability, independence, joint and conditional distributions, Random variables,
standard probability distributions and their properties, conditional expectation,
expectation,moments; strong and weak law of large numbers, Sampling distributions,
central limit theorem ,UMVU estimators, maximum likelihood estimators, standard
parametric tests based on normal, Testing of hypotheses, X2, t, F– distributions;
Linear regression; Interval estimation.
- Linear Programmeming: Linear Programmeming problem and its formulation,
convex sets and their properties, basic feasible solution, graphical method ,simplex
method, big-M and two phase methods; unbounded LPP’s and infeasible, alternate optima;
Dual problem and duality theorems, dual simplex method and its application in post
optimality analysis; unbalanced and balanced transportation problems, Hungarian
method for solving assignment problems, u -u method for solving transportation problems.
Humanities and Social Sciences (HSS)
- General Psychology: Scope of Psychology and Methods, Systems and
Theories in Psychology, Physiological Basis of Behaviour, Self and Personality,
Perception, Intelligence, Thinking and Language, Learning, Memory, Motivation.
- Social Psychology: Scope of Social Psychology and Methods, Social
Cognition, Social Perception, Social Influence (Conformity, Compliance and Obedience),
Attitude and Attitude Change, Aggression, Pro-Social Behaviour, Prejudice, Group
Dynamics, Inter-Group Relations.
- Research Methods: Scientific Research: Paradigms and Rigour; Quantitative
Research (Hypothesis Testing, Methods and Designs, Psychometrics); Qualitative Research
(Paradigms and Methodologies, Types of Methodologies, Criteria of Rigor).
- Statistics in Psychology: Descriptive and Inferential Statistics
used in behavioral sciences.
- Research Methodology: Meaning, Purpose & Steps of Research; Problem
Identification; Theory and its Role in Research; Ethics in Research. Research Methods:
Experimental and Non-Experimental; Laboratory Experiments; Field Experiments; Field
Research, Survey; Ethnography and Case Study. Concept & Types of Sampling APA style
of Report Writing.
- Micro Economics: Demand Analysis – Marshallian, Hicksian and revealed Preference Approaches – Theory of Production and Costs – Pricing and Output under different forms of Market Structure – Factor Pricing Analysis – Elements of General Equilibrium and New Welfare Economics.
- Macro Economics: Determination of Output and Employment – Classical Approach, Keynesian Approach and Consumption Hypotheses – Demand for Money – Fisher and Cambridge Versions, Approaches of Keynesian, Friedman, Patinkin, Baumol and Tobin – Supply of Money – Philips Curve Analysis – Business Cycles – Models of Samuelson, Hicks and Kaldor – Macro-Economic Equilibrium – Relative Roles of Monetary and Fiscal Policies.
- Development and Planning: Economic Growth, Economic Development and Sustainable Vicious Circle of Poverty– Measurement of Development: Conventional, HDI and Quality of Life Indices – Theories of Development – Classical, Marx and Schumpeter – Economic Growth – Harrod-Domar Model, Instability of Equilibrium, Neoclassical Growth – Solow’s Model, Steady State Growth – Approaches to Development: Balanced Growth, Critical Minimum Effect, Big Push, Unlimited Supply of Labour, Low Income Equilibrium Trap – Indicators and Measurement of Poverty – Importance of Agriculture and Industry in Economic Development – Choice of Techniques and Appropriate Technology – Investment Criteria – Trade as an engine of growth - Planning in India
- Public Finance: Role of the Government in Economic Activity - Allocation, Distribution and Stabilization Functions - Private, Public and Merit Goods – The Public Budgets: Kinds of Budgets, Concepts of Budget Deficits; Balanced Budget Multiplier - Budgets of the Union Government in India - Public Expenditure: Hypotheses, Effects and Evaluation - Public Revenue - Theories of taxation- Different Approaches - Tax burden, incidence and effects of taxation; elasticity and Buoyancy; Taxable Capacity - Public Debt: Sources, Effects, Burden and Its Management - Fiscal Federalism: Theory and Problems, Problems of Centre-State Financial Relations in India – Fiscal Policy: Neutral and Compensatory and Functional Finance, Balanced Budget Multiplier.
- Indian Economy: Basic Economic Indicators – National Income, Performance of different Sectors – Trends in Prices and Money Supply – Agriculture: Institutional and Technological aspects, New Agricultural Policy – Industry: New Industrial Policy and Liberalization – Money and Banking: Concepts of Money Supply, Inflation, Monetary Policy and Fiscal Sector Reforms – Public Finance: Trends in Revenue and Expenditure of the Central and State Governments, Public Debt, Analysis of Union Budget – Foreign Trade: Trends, Balance of Payments and Trade Reforms – Poverty, Unemployment, Migration and Environment.
- International Economics: Theories of International Trade - Concept and types of terms of trade - Theories of exchange rate determination - Balance of payments – Absorption and Monetary approaches for adjustment in the Balance of Payments – Foreign Trade Multiplier – Tariffs and Non-Tariff barriers - International trade and financial institutions: IMF, World Bank & WTO
- Industrial and Labour Economics: Industrial structure and economic growth - Pattern of industrialization - Public and Private; large and small industries - Theories of Industrial location: Indian experience - Industrial Productivity-Measurement, Partial and total trends - Industrial Finance in India - Industrial Labour -Problems, Policies and reforms in India - Economic Reforms and industrial growth
- Environmental Economics: Economy-Environment interaction – Economic development and Environmental stress - Environmental Kuznet’s curve hypothesis – Sustainable development - Environmental Cost-Benefit Analysis for Sustainable Development - Approaches to Environmental Accounting - Theory of Externality and Public Goods - Pigovian taxes – Coase Theorem – Techniques of Environmental Valuation - Theories of Optimal use of Exhaustible and Renewable resources - Energy and Environment - Trade and environment – International Environmental issues
- Statistical Methods: Measures of Central tendency, Dispersion, Skewness and Kurtosis – Elementary Theory of Probability – Binomial, Poisson and Normal Distributions – Simple Correlation and Regression analysis – Statistical Inferences – Applications, Sampling Distributions (t, chi-square and F tests) – Sampling of Attributes – Testing of hypothesis – Index Numbers and Time Series Analysis – Sampling and Census Methods – Types of Sampling and Errors.
- Econometrics: Assumption and Properties of Classical Linear Regression Model, BLUE Property, Gauss-markov Theorem, Inference of Simple and Multiple Linear Regression Model, Problems of Multicollinearity, Heteroskedasticity and Autocorrelation, Estimation with Dummy Variables, Basics of Simultaneous Equation Modelling
- Chaucer to Shakespeare
- Jacobean to Restoration Period
- Augustan Age: 18th Century Literature
- Romantic Period
- Victorian Period
- Modern Period
- 20th Century and Contemporary British Literature
- European Literature from 18th to 20th Century
- New Literatures in English
- American and other non-British Literatures
- Indian Writing in English
- Literary Theory and Criticism (up to T.S. Eliot)
- Contemporary Literary Theory
- Cultural Studies
- Prosody and Rhetoric
- Literary Comprehension
Applied Linguistics and ELT)
- Applied Linguistics (Structuralism, Chomsky, Halliday)
- Language Acquisition (L1/L2)
- Discourse Analysis
- Fundamentals of Phonetics and Phonological Theory
- Generative Syntax, Semantics and Morphology
- Contemporary English Grammar
- English Language Teaching (Pedagogic Methods, Approaches and Techniques), Critical
Theories, Trends and Movements
- Communicative Approach to Language Teaching (CLT)
- Language Testing and Assessment
- Error Analysis, Contrastive Analysis
- English for Academic/ Specific purposes (EAP/ESP)
- Curriculum Designing