VITREE Syllabus 2025: Check VIT Ph.D. Subject-Wise Syllabus Here

Statistics 

Definitions | Scope and Limitations - Sampling methods | Collection of data-Classification and Tabulation | Frequency distribution | Diagrammatic and graphical representation | Measures of Central Tendency - Mean, median, mode Partition values (Median, quartile, Deciles and percentiles) | Measures of Dispersion- Coefficient of variation- Skewness and Kurtosis 

Correlation- and regressions 

Scatter diagram-Coefficient of correlation – Rank correlation- Lines of linear regression – Partial correlation multiple correlation - Multiple linear regressions 

Probability 

Events - Addition Law of probabilities – Conditional Probabilities-Multiplication Law of probabilities - Baye’s Theorem – random variable – Discrete-continuous-cumulative distribution function-probability mass function probability density function - mathematical expectation. Binomial and Poisson’s distributions. Tests of hypothesis- small and large samples tests- chi-square test- Analysis of variance (ANOVA) 

Accounting for financial decisions 

Managerial accounting – analysis of financial statements – ratio analysis – budgetary control – marginal costing – inventory valuation 

Business Research Methodology 

Business research methods – development of research methodology – research plan – data collection – sampling techniques – qualitative research – quantitative analysis – report writing 

Banking and Insurance 

Central banking – commercial banks – development banks – non-banking financial institutions – modern banking – development of insurance – risk management and role of insurance – legal aspects – types of insurance products – customers services – marketing and distribution 

Marketing Management 

Foundations of marketing – selection of markets – product decisions – pricing decisions – distribution decisions – communication decisions – impact of competition on strategy – reaching consumers directly – analyzing markets 

Human Resource and Organizational Behavior 

Human resource planning – training development and career management – motivation perspectives – managing ethical issues in HRM – organizational behavior – individual perspective – group dynamics – dynamics of organization. 

Strength of Materials  

Analysis of statically determinate trusses, arches, beams, cables and frames, displacements in statically determinate structures and analysis of statically indeterminate structures by force/ energy methods, analysis by displacement methods (slope deflection method), influence lines for determinate and indeterminate structures. Bending moment and shear force in statically determinate beams. Simple stress and strain relationship Stress and strain in two dimensions, principal stresses, stress transformation, Mohr’s circle. Simple bending theory, flexural and shear stresses, unsymmetrical bending, shear center 

Reinforced Concrete Structures 

Concrete Technology- properties of concrete, basics of mix design. Concrete design-basic working stress and limit state design concepts, analysis of ultimate load capacity and design of members subjected to flexure, shear, compression and torsion by limit state methods. Basic elements of pre-stressed concrete, analysis of beam sections at transfer and service loads 

Steel Structures 

Analysis and design of tension and compression members, beams and beam columns, column bases. Connections simple and eccentric, beam-column connections, plate girders and trusses. Plastic analysis of beams and frames 

Geotechnical Engineering  

Soil classification, three - phase system, fundamental definitions, relationship and interrelationships, permeability and seepage, effective stress principle, consolidation, compaction, shear strength. Sub-surface investigations- scope, drilling bore holes, sampling, penetration tests, plate load test. Earth pressure theories, effect of water table, layered soils. Foundation types foundation design requirements. Shallow foundations bearing capacity, effect of shape, water table and other factors, stress distribution, settlement analysis in sands and clays. Deep foundations - pile types, dynamic and static formulae, load capacity of piles in sands and clays, negative skin friction 

Water Resources Engineering  

Properties of fluids, principle of conservation of mass, momentum, energy and corresponding equations, potential flow, applications of momentum and Bernoulli’s equation, laminar and turbulent flow, flow in pipes, pipe networks. Concept of boundary layer and its growth. Uniform flow, critical flow and gradually varied flow in channels, specific energy concept, hydraulic jump. Forces on immersed bodies, flow measurements in channels, tanks and pipes. Dimensional analysis and hydraulic modeling. Kinematics of flow, velocity triangles and specific speed of pumps and turbines. Hydrologic cycle, rainfall, evaporation, infiltration, stage discharge relationships, unit hydrographs, flood estimation, reservoir capacity, reservoir and channel routing. Well hydraulics. Duty, delta, estimation of evapo-transpiration. Crop water requirements. Types of irrigation system, irrigation methods 

Environmental Engineering  

Quality standards, basic unit processes and operations for water treatment. Drinking water standards, water requirements, basic unit operations and unit processes for surface water treatment, distribution of water. Primary, secondary and tertiary treatment of wastewater, sludge disposal, effluent discharge standards. Air pollutants – Types, their sources and impacts. Air pollution meteorology, air pollution control, air quality standards and limits. Municipal Solid Wastes -Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management. Noise Pollution - impacts of noise, permissible limits of noise pollution, measurement of noise and control of noise pollution 

Transportation Engineering 

Highway Planning - Geometric design of highways, testing and specifications of paving materials, design of flexible and rigid pavements. Traffic Engineering - Traffic characteristics, theory of traffic flow, intersection design, traffic signs and signal design, highway capacity 

Micro Economic Analysis 

Utility Analysis - Law of Diminishing Marginal Utility -Law of Equi-Marginal Utility - Theory of Demand – Law of Demand - Indifference Curve Analysis - Marginal Rate of Substitution - Consumers equilibrium – Income effect - Price effect and Substitution effect (Hicks Allen Eugene Slutsky method). 

Micro Economic Analysis 

Theory of Production – Law of Variable Proportions and Returns to Scale; Producers equilibrium, Elasticity of substitution - Production function: Linear-Homogenous production function, Cobb – Douglas Production function; Theory of cost – Different concepts of costs – short run – long run behavior of cost; Revenue concepts: Average, Marginal and Total Revenue, revenue curves under different market conditions; Market structure and pricing – Different types of Market – characteristics - Pricing and output under different forms of markets 

Macro-Economic Analysis 

National Income Analysis - Four sector model - Determination of output and employment - Classical approach and Keynesian approach - Theories of consumption – Multiplier – Accelerator 

Macro-Economic Analysis 

Theories Inflation – causes – consequences of inflation – Demand for money – Supply of money – Determinants of money supply - High-powered money, Money multiplier - Macroeconomic Equilibrium - Relative roles of monetary and fiscal policies 

International Economic Analysis 

Theories of International trade - Mercantilism - Absolute Advantage of trade, Comparative Advantage theory & Heckscher-Ohlin theory - Structure of India’s Exports – Imports – Balance of payments – Tariff – Terms of Trade – Protection – Free trade – Foreign Exchange Rate Mechanism - Trade Policy and Reforms in India. 

Legal Research Methodology 

Legal research Methods - Sociological Research methods - Empirical research in Law Theory - Hypothesis-Null hypothesis - Research Plan-Research proposal- Research problem 

Constitutional Law 

Important aspects of the Constitutional Law including leading cases on Constitutional Law 

Jurisprudence 

Different Schools of Law - Critical analysis of law 

Criminal Law 

General Principles of Criminal law 

Tort law 

Remedies available under Tort law with leading cases 

Emerging issues in Law 

IPR, Cyber Law, International Law, Contracts, Justice Education, Justice Administration, Labour and Industrial law, Personal and Administrative Law 

Heat-Transfer 

Modes of heat transfer; one dimensional heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, radiative heat transfer, black and grey surfaces, shape factors; heat exchanger performance, LMTD and NTU methods 

Thermodynamics 

Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle. irreversibility and availability; behavior of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion 

Machining and Machine Tool Operations 

Mechanics of machining, 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, principles of design of jigs and fixtures 

Mechatronics System Design 

Pneumatic and hydraulic systems; Eletro-pneumatic and electro-hydraulic systems; Pneumatic, hydraulic and electric motors and actutators; Concepts of microcontrollers, Feedback devices; Point-to-point, continuous-path and servo control; Types of CNC machines and robots. Programmable logic controllers; CNC and robot programming. Some current developments in modern machine tools, robotics, mechatronics; Basic topics related to micro-electro mechanical systems (MEMS) 

Computer Aided Engineering 

Finite Element Methods; Computational Fluid Dynamics; Mechanical Systems Simulation; Tools for conventional mechanisms and MEMS design 

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 and assembly 

Automotive Engineering 

Development in Bio-fuels, other alternative fuels and hydrogen as future fuel; Emission standards; Electronic injection systems; Passenger comfort and safety devices; Indian auto industry and Automotive vehicles in Indian market 

Introduction to Psychology 

Definition, Nature and Scope of psychology; Historical perspective; sub-fields and applications, methods of psychology; Schools of Psychology 

Psychological theories 

Learning theories, Models of Memory, Cognitive Strategies, Motivation theories, Current theories of emotion, Existential and humanistic theories of personality, Stress and coping Strategies 

Research Methodology 

Meaning, Aims, characteristics and types, Research Process, types of Research Design, Sampling, types and uses, Research Hypothesis, Methods of Data Collection, Tools and Techniques of data collection, Psychological Scaling, Sources of bias in psychological testing, Data Analysis and Report writing 

Statistics 

Introduction, Importance, Scope, Function and Limitations. Research Designs: Correlational, factorial, randomized block, matched group, quasi experimental, time series design, ANOVA: Randomized and repeated, Measures of Central tendency, Measures of Dispersion, Correlational analysis: Partial, multiple and regression analysis, Factor analysis and Chi Square Analysis 

English Communication  

15 

Statistics and Probability  

15 

Technical 

70