An exam known as the Graduate Aptitude Test in Engineering (GATE) is administered to candidates seeking admission to Indian Institutes of Technology (IITs), National Institutes of Technology (NITs), Indian Institutes of Information Technology (IIITs), and other colleges and universities throughout India for Master of Engineering (ME), Masters in Technology (MTech), and direct PhD programs. Additionally, it provides entry to flourishing research and public sector enterprises (PSUs). ONGC, NTPC, GAIL, HPCL, PGCIL, BHEL, BSNL, NHPC, BARC, DRDO, and other PSUs and research organizations are among those that use GATE scores to offer employment.

The GATE Committee, which consists of faculty members from IISc, Bangalore, and the other seven IITs, administers and conducts the GATE examination nationwide in eight zones on behalf of the National Coordinating Board, Department of Education, Ministry of Human Resources Development.

EXAM PATTERN

GATE NEGAVTIVE MARKING

Before taking the exam, candidates are advised to familiarize themselves with the GATE exam's negative marking scheme. The GATE 2024 exam will have negative markings. Understanding the negative marking could improve their scorecard and results. We have included the GATE 2024 negative marking scheme below to provide an idea of how the GATE negative marking scheme works.

Negative grades won't be applied to MSQ or NAT questions.

Gate multiple-choice question marks will be deducted. There will be a mark deduction for each incorrect response.

SYLLABUS

GENERAL APTITUDE SYLLABUS

This paper is common for all.

VERBAL APTITUDE-  Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech are all part of basic English grammar. Basic vocabulary: contextualized words, idioms, and phrases comprehension and reading Story progression.

QUANTITATIVE APTITUDE- Data visualization tools include 2- and 3-dimensional plots, maps, tables, and data graphs (bar graphs, pie charts, and other graphs displaying the data). Calculating and estimating numbers: powers, exponents, logarithms, ratios, percentages, permutations, combinations, and series Calculus and geometric shapes Basic probability and statistics.

ANALYTICAL APTITUDE- Logic includes reasoning, numerical relationships, analogy, and inference and deduction.

SPATIAL APTITUDE- Transformations of shapes: assembly, mirroring, scaling, translation, rotation, and grouping  Two- and three-dimensional paper folding, cutting, and patterning.

EXAM PATTERN OF GATE

There are two sections on the GATE Exam Question Paper for every subject. There are ten questions in the General Aptitude (GA) section of the exams that are required. Out of these 10, five questions are worth one mark, and the remaining five are worth two each. Thus, the GA portion of a paper receives a total of 15 marks.

The mode of exam is offline, which means it is Computer Based Test (CBT)

Exam Duration is 3hours and the questions will be MCQs based.

There are two sections in GA which are General Aptitude and Candidate’s Selected Subjects.

GATE SYLLABUS IN OTHER FIELDS

1 Aerospace Engineering

2 Agriculture Engineering

3 Architecture and planning Engineering

4 Biotechnology Engineering

5 Civil Engineering

6 Chemical Engineering

7 Computer Science Engineering (CSE)

8 Chemistry Engineering (CY)

9 Electronic and Communication Engineering (ECE)

10 Electrical Engineering (EE)

11 Ecology and Evolution (EY)

12 Geology and Geophysics (GG)

13 Instrumentation Engineering (IN)

14 Mathematics (MA)
15 Mechanical Engineering (ME)

16 Mining Engineering (MN)

17 Metallurgical Engineering (MT)

18 Petroleum Engineering (PE)

19 Physics (PH)

20 Production and Industrial Engineering (PI)

21 Textile Engineering and Fiber Science Engineering (TF)

22 Statistics Engineering (ST)

23Bio Medical Engineering (BM)

24 Engineering Science (XE)

25 Life Science  Engineering (XL)

26 Humanities and Social Science Engineering (XH)

27 Environmental Science and Engineering (ES)

28 Geomatics Engineering (GE)

29 Naval Architecture and Marine Engineering (NM)

Meanwhile, few new subjects were introduced and added in the syllabus.

1 Environment Science and Engineering (ES)

2 Humanities and Social Science Engineering (XH) in Economics/ English/ Linguistics/ Philosophy/ Psychology and Sociology.

3 Naval Architecture and Marine Engineering (NM)

4 Geomatics Engineering (GE)

UNDERGRADUATE COURSE

1 AEROSPACE ENGINEERING (AG) SYLLABUS

One of the main area of engineering that deals with the creation of aircraft and spacecraft is aerospace engineering. The graduate Aptitude Test in Engineering (GATE) exam’s first or primary paper is also known as Aerospace Engineering (AE). Exam authorities typically post the brochure and the GATE Aerospace Engineering 2023 syllabus on their official website.

There are six sections under the designated subjects, with the topic under each section split into two categories, according to the updated GATE syllabus for Aerospace Engineering 2023.

SECTION 1

ENGINEERING MATHEMATICS

Core Topics

Linear Algebra- Algebraic Vectors, matrix algebra, linear equation systems, matrix rank, eigenvalues, and eigenvectors.

Calculus- Single-variable functions, boundaries, continuity and differentiability, mean value theorem, chain rule, partial derivatives, gradient, divergence and curl, and directional derivatives and discussed. Combination, integrals for lines, surfaces and volumes. The strokes, Gauss and Green theorems.

Differential Equations- first order linear and nonlinear differential equations, higher order linear ODEs with constant coefficients. Partial differential equations and separation of variables methods.

Special Topics

Fourier Series, Laplace Transforms, Numerical Methods for linear and nonlinear algebraic equations, Numerical integration and differentiation, complex analysis, probability and statistics.

SECTION 2

FLIGHT MECHANICS

Atmosphere- Properties standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts. Pressure altitude; equivalent, calibrated, indicated air speeds; primary flight instruments: Altimeter, ASI, VSI, Turn-bank Indicator. Angle of attack, sideslip; Roll, pitch and yaw controls. Aerodynamic forces and moments.

Airplane Performance- Drag polar; takeoff and landing; steady climb and descent; absolute and service ceiling; range and endurance, load factor, turning flight, V-n Diagram, winds; head, tail and cross winds.

Static Stability- Stability and Control derivation; longitudinal stick fixed and free stability; horizontal tail position and size; directional stability, vertical tail position and size; lateral stability. Wing dihedral, sweep and position; hinge moments, stick forces.

Dynamic stability

Euler angles; Equations of motion; Decoupling of  longitudinal and lateral-directional dynamics; longitudinal models; lateral-directional modes.

SECTION  3

SPACE DYNAMICS

Central force motion, determination of trajectory and orbital period in simple cases. Kepler’s laws; escape velocity. And there is no special topics.

SECTION 4

AERODYNAMICS

Basic Fluid Mechanics- Conservation laws: Mass, momentum and energy (Integral and Differential form); Dimensional analysis and dynamic similarity.

Potential Flow theory- sources, sinks, doublets, line vortex and their superposition. Elementary idea of viscous flows, including boundary  layers.

Airfoils and wings- Airfoil nomenclature; Aerodynamic Coefficient: lift, drag and moment; kutta-Joukoswki theorem; Thin airfoil theory, starting vortex; finite wing theory: Induced drag, Prandtl lifting line theory; critical and drag divergence Mach number.

Compressible Flows- Basic concepts of compressibility, one- dimensional compressibility, one- dimensional compressible flows, Isentropic flows, Isentropic flows, fanno flow, Rayleigh flow; Normal and oblique shocks, Prandti-Meyer flow; Flow through nozzles and diffusers.

Wind Tunnel Testing- Measurement and visualization techniques. Shock- boundary layer interaction.

SECTION 5

STRUCTURES

Strength of Materials- Stress and Strain: Three-dimensional transformations, Mohr’s circle, principal stresses, three-dimensional Hooke’s law, Plane stress and strain. Failure theories: Maximum stress, Tresca Von Mises. Strain energy. Castigliano’s principles. Statically determinate and indeterminate trusses and beams. Elastic Flexural buckling of columns.

Flight Vehicle Structure-  characteristics of aircraft structure and materials. Torsion, bending and shear of thin-walled sections. Loads on aircraft.

Structural Dynamics- Free and forced vibrations of undamped and damped SDOF systems. Free vibrations of undamped 2- DOF systems.

Vibration of beams- Theory of elasticity: Equilibrium and Compatibility equations, Airy’s stress function section.

SECTION 6

PROPULSION

Basic- Thermodynamics, boundary layers, heat transfer, combustion and thermochemistry.

Aerothermodynamics of aircraft engines: Thrust, efficiency, range, Brayton cycle.

Engine performance: ramjet, turbojet, turbofan, turboprop and turboshaft engines. Afterburners.

Turbomachinery: Axial compressors, Angular momentum, work and compression, characteristic performance of a single axial compressor stage, efficiency of the compressor characteristic performance of a single axial compressor stage, efficiency of the compressor and degree of reaction, multi-staging.

Centrifugal Compressor: stages dynamics, inducer, impeller and diffuser.

Axial Turbines- stage performance.

Rockets: Thrust equation and specific impulse, rocket performance. Multi-staging. Chemical rockets. Performance of solid and liquid propellant rockets.

Aerothermodynamics of non-rotating propulsion components such as intakes, combustor and nozzle. Turbine blade cooling. Compressor-turbine matching, Surge and stall.

2 ARCHITECTURE AND PLANNING (AR) SYLLABUS

Plans, organizes and overseas research and development projects; it also acts as a clearinghouse for information pertaining to Agriculture Engineering. It works on the development and demonstration of technologies for the mechanization of agriculture during production and after employing both conventional and non- conventional energy sources. This includes the mechanization of drainage and irrigation systems, as well as the post-harvest and value adding of agriculture products and byproducts. Its responsibility includes five institutes, six AICRPs, two AINPs and four CRPs.

PART A (Common)

Section 1: Architecture Planning and Design

Architectural Graphics; Visual composition in 2D and 3D; Computer application in Architecture and Planning; Anthropometrics; Organization of space; Circulation- horizontal and vertical; Space Standards; Universal design; Building byelaws; Codes and standards;

Section 2: Construction and Management

Project management techniques e.g., PERT, CPM etc.; Estimation and Specification; Professional practice and ethics; Form and structure; principles and design of disaster resistant structure; Temporary structure for rehabilitation.

Section 3: Environment Planning and Design

Natural and man-mad ecosystem; Ecological principles; Environmental consideration in Planning and design; environment pollution- types, causes, controls and abatement strategies; sustainable development, goals and strategies; climate change and built environment; climate responsive design.

Section 4: Urban Design Landscape and conservation

Historical and modern examples of urban design; Elements of urban built environment – urban form, spaces, structure, pattern, fabric, texture, grain etc.; Concepts and theories of urban design; Principles, tools and techniques of urban design; Public spaces, character, spatial qualities and Sense of Place; Urban design interventions for sustainable development and transportation;
Development controls – FAR, densities and building byelaws.; Urban renewal and conservation; heritage conservation; historical public spaces and gardens; Landscape design; Site planning.

Section 5: Planning Process

Salient concepts, theories and principles of urban planning; concepts of cities – Eco-City, Smart City; Concepts and theories by trendsetting planners and designers; Ekistics; Urban sociology; Social, Economic and environmental cost benefit analysis; Methods of non-spatial and spatial data analysis; Development guidelines such as URDPFI;

Section 6: Housing

Housing Typologies; Concepts, principles and examples of neighborhood; Residential densities; Affordable housing; Real estate valuation

Section 7: Services and Infrastructure

Firefighting Systems; Building Safety and Security systems; Building Management Systems; Water treatment; Water supply and distribution system; Water harvesting systems; Principles, Planning and Design of storm water drainage system; Sewage disposal methods; Methods of solid waste
management – collection, transportation and disposal; Recycling and Reuse of solid waste; Land use – transportation – urban form inter-relationships; Design of roads, intersections, grade separators and parking areas; Hierarchy of roads and level of service; Para-transits and other modes of transportation, Pedestrian and slow moving traffic planning.

PART B1

Section 1- History and Contemporary Architecture

Principles of Art and Architecture; World History of Architecture: Egyptian, Greco-Roman classical period, Byzantine, Gothic, Renaissance, Baroque-Rococo, etc.; Recent trends in Contemporary Architecture: Art nouveau, Art Deco, Eclecticism, International styles, Post Modernism, Deconstruction in architecture, etc.; Influence of Modern art and Design in Architecture; Indian
vernacular and traditional Architecture, Oriental Architecture; Works of renowned national and international architects.

Section 2- Building Construction and Structure systems

Building construction techniques, methods and details; Building systems and prefabrication of building elements; Principles of Modular Coordination; Construction planning and equipment; Building material characteristics and applications; Principles of strength of materials; Alternative building materials; Foundations; Design of structural elements with different materials; Elastic and Limit State design; Structural systems; Principles of Pre-stressing; High Rise and Long Span structures, gravity and lateral load resisting systems.

Section 3- Building Service and Sustainability

Solar architecture; Thermal, visual and acoustic comfort in built environments; Natural and Mechanical ventilation in buildings; Air-Conditioning systems; Sustainable building strategies; Building Performance Simulation and Evaluation; Intelligent Buildings; Water supply; Sewerage and drainage systems; Sanitary fittings and fixtures; Plumbing systems; Principles of internal and external drainage system; Principles of electrification of buildings; Elevators and Escalators – standards and uses.

PART B2

Section1- Regional and Settlement Planning

Regional delineation; settlement hierarchy; Types and hierarchy of plans; Various schemes and programs of central government; Transit Oriented Development (TOD), SEZ, SRZ etc.; Public Perception and user behavior; National Housing Policies, Programs and Schemes. ; Slums, Squatters and informal housing; Standards for housing and community facilities; Housing for special areas and needs.

Section 2- Planning Techniques and Management

Application of G.I.S and Remote Sensing techniques in urban and regional planning; Tools and techniques of Surveys – Physical, Topographical, Land use and Socio-economic Surveys; Urban Economics, Law of demand and supply of land and its use in planning; Graphic presentation of spatial data; Local self-governance, Panchayati raj institutions; Planning Legislation and implementation – Land Acquisition Act, PPP etc.; Decision support system and Land Information System; Urban geography and Econometrics; Management of Infrastructure Projects; Demography and equity in planning.

Section 3- Infrastructure Planning

Process and Principles of Transportation Planning and Traffic Engineering; Road capacity and Travel demand forecasting; Traffic survey methods, Traffic flow Analysis; Traffic analyses and design considerations; Traffic and transport management and control in urban areas; Mass transportation planning; Intelligent Transportation Systems; Urban and Rural Infrastructure System Network

3 BIOTECHNOLOGY ENGINEERING

Biological technology a combination of biotechnology and engineering, engineering is regarded as an interdisciplinary field. The subjects of biology, physics, chemistry and engineering are combined with their varied features and lessons learned. This course teaches applicants how to handle complicated procedures and use technology to tackle biotechnological issues. After competing this degree, graduate is referred to as biotechnology engineering, and it is their job to create new items like medicines and innovative treatments that are vital to survival.

Section 1: Engineering Mathematics

Linear Algebra- Matrices and determinants- systems of linear equation; Eigen values and Eigen vectors.

Calculus- Limits, continuity and differentiability: Partial derivatives, maxima and minima; sequences and series, Test for convergence.

Differential Equations- Linear and nonlinear first order ODEs, higher order ODEs with constant Coefficients; Cauchy’s and Euler’s equation; Laplace transforms.

Probability and Statistics- Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis

Numerical Methods- Solution of linear and nonlinear algebraic equations; Integration by trapezoidal and Simpson’s rule; Single step method for differential equations.

Section 2: General Biology

Biochemistry- Biomolecules: structure and function; Biological membranes – structure, membrane channel and pumps, molecular motors, action potential and transport processes; Basic concepts and regulation of metabolism of carbohydrates, lipids, amino acids and nucleic acids; Photosynthesis, respiration and electron transport chain. Enzymes – Classification, catalytic and regulatory strategies; Enzyme kinetics – Michaelis- Menten equation; Enzyme inhibition – competitive, non-competitive and uncompetitive inhibition.

Microbiology- Bacterial classification and diversity; Microbial Ecology – microbes in marine, freshwater and terrestrial ecosystems; Microbial interactions; Viruses – structure and classification; Methods in microbiology; Microbial growth and nutrition; Nitrogen fixation; Microbial diseases and host-pathogen interactions; Antibiotics and antimicrobial resistance.

Immunology-  Innate and adaptive immunity, humoral and cell mediated immunity; Antibody structure and function; Molecular basis of antibody diversity; T cell and B cell development; Antigen-antibody reaction; Complement; Primary and secondary lymphoid organs; Major histocompatibility complex (MHC); Antigen processing and presentation; Polyclonal and monoclonal antibody; Regulation of immune response; Immune tolerance; Hypersensitivity; Autoimmunity; Graft versus host reaction; Immunization and vaccines.

Section 3: Genetics, Cellular and Molecular Biology

Genetics and Evolutionary Biology- Mendelian inheritance; Gene interaction; Complementation; Linkage, recombination and chromosome mapping; Extra chromosomal inheritance; Microbial genetics – transformation, transduction and conjugation; Horizontal gene transfer and transposable elements; Chromosomal variation; Genetic disorders; Population genetics; Epigenetics; Selection and inheritance; Adaptive and neutral evolution; Genetic drift; Species and speciation.

Cell Biology- Prokaryotic and eukaryotic cell structure; Cell cycle and cell growth control; Cell-cell communication; Cell signaling and signal transduction; post-translational modifications; Protein trafficking; Cell death and autophagy; Extra-cellular matrix.

Molecular Biology- Molecular structure of genes and chromosomes; Mutations and mutagenesis; Regulation of gene expression; Nucleic acid – replication, transcription, splicing, translation and their regulatory mechanisms; non-coding and micro-RNA; RNA interference; DNA damage and repair.

Section 4: Fundamentals of Biological Engineering

Engineering principles applied to biological systems- Material and energy balances for reactive and non-reactive systems; Recycle, bypass and purge processes; Stoichiometry of growth and product formation; Degree of reduction, electron balance, theoretical oxygen demand.

Classical thermodynamics and Bioenergetics- Laws of thermodynamics; Solution thermodynamics; Phase equilibria, reaction equilibria; Ligand binding; Membrane potential; Energetics of metabolic pathways, oxidation and reduction reactions.

Transport Processes- Newtonian and non-Newtonian fluids, fluid flow – laminar and turbulent; Mixing in bioreactors, mixing time; Molecular diffusion and film theory; Oxygen transfer and uptake in bioreactor, Kla and its measurement; Conductive and convective heat transfer, LMTD, overall heat transfer coefficient; Heat exchangers.

Section 5: Bioprocess Engineering and Process Biotechnology

Bioreaction engineering- Rate law, zero and first order kinetics; Ideal reactors – batch, mixed flow and plug flow; Enzyme immobilization, diffusion effects – Thiele modulus, effectiveness factor, Dam Koehler number; Kinetics of cell growth, substrate utilization and product formation; Structured and unstructured models; Batch, fed-batch and continuous processes; Microbial and enzyme reactors; Optimization and scale up.

Upstream and Downstream Processing-  Media formulation and optimization; Sterilization of air and media; Filtration – membrane filtration, ultrafiltration; Centrifugation – high speed and ultra; Cell disruption; Principles of chromatography – ion exchange, gel filtration, hydrophobic interaction, affinity, GC, HPLC and FPLC; Extraction, adsorption and drying.

Instrumentation and process control- Pressure, temperature and flow measurement devices; Valves; First order and second order systems; Feedback and feed forward control; Types of controllers – proportional, derivative and integral control, tuning of controllers.

Section 6: Plant, Animal and Microbial Biotechnology

Plants: Totipotency; Regeneration of plants; Plant growth regulators and elicitors; Tissue culture and cell suspension culture system – methodology, kinetics of growth and nutrient optimization; Production of secondary metabolites; Hairy root culture; Plant products of industrial importance; Artificial seeds; Soma clonal variation; Protoplast, protoplast fusion – somatic hybrid and cybrid; Transgenic plants – direct and indirect methods of gene transfer techniques; Selection marker and reporter gene; Plastid transformation.

Animal: Culture media composition and growth conditions; Animal cell and tissue preservation; Anchorage and non-anchorage dependent cell culture; Kinetics of cell growth; Micro & macro-carrier culture; Hybridoma technology; Stem cell technology; Animal cloning; Transgenic animals; Knock-out and knock-in animals.

Microbes: Culture media composition and growth conditions; Animal cell and tissue preservation; Anchorage and non-anchorage dependent cell culture; Kinetics of cell growth; Micro & macro-carrier culture; Hybridoma technology; Stem cell technology; Animal cloning; Transgenic animals; Knock-out and knock-in animals.

Section 7: Recombinant DNA technology and other Tool in Biotechnology

Recombinant DNA technology- Restriction and modification enzymes; Vectors – plasmids, bacteriophage and other viral vectors, Cosmides, Ti plasmid, bacterial and yeast artificial chromosomes; Expression vectors; cDNA and genomic DNA library; Gene isolation and cloning, strategies for production of recombinant proteins; Transposons and gene targeting

Molecular tools- Polymerase chain reaction; DNA/RNA labelling and sequencing; Southern and northern blotting; In-situ hybridization; DNA fingerprinting, RAPD, RFLP; Site-directed mutagenesis; Gene transfer technologies; CRISPR-Cas; Biosensing and biosensors.

Analytical tools- Principles of microscopy – light, electron, fluorescent and confocal; Principles of spectroscopy – UV, visible, CD, IR, fluorescence, FT-IR, MS, NMR; Electrophoresis; Micro-arrays; Enzymatic assays; Immunoassays – ELISA, RIA, immunohistochemistry; immunoblotting; Flow cytometry; Whole genome and Chip sequencing.

Computational tools- Bioinformatics resources and search tools; Sequence and structure databases; Sequence analysis – sequence file formats, scoring matrices, alignment, phylogeny; Genomics, proteomics, metabolomics; Gene prediction; Functional annotation; Secondary structure and 3D structure prediction; Knowledge discovery in Biochemical databases; Metagenomics; Metabolic engineering and systems Biology.

4 CIVIL ENGINEERING (CE)

One of the main disciplines for GATE 2023 is civil engineering. Consequently, candidates taking the GATE civil Engineering paper are aware of the important of the GATE Civil Syllabus 2023. The topic and idea covered in the GATE Exam syllabus for Civil Engineering serve as the foundation for the exam questions. Understanding the GATE 2023 syllabus for Civil Engineering (CE) can benefit students by improving their test-taking strategies and facilitating more effective study planning. The GATE curriculum for Civil Engineering will assist applicants in better organizing their exam preparation by emphasizing areas of weakness.

There are seven primary sections in the GATE 2023 Civil Engineering (CE) syllabus. The GATE syllabus. The GATE syllabus for Civil Engineering covers the following topics: Geotechnical engineering, engineering mathematics, structural engineering, geotechnical engineering, environment engineering, transportation engineering and geomatics engineering.

SYLLABUS

Section 1: Engineering Mathematics

Linear Algebra- Matrix algebra; Systems of linear equations; Eigen values and Eigen vectors.

Calculus- Functions of single variable; Limit, continuity and differentiability; Mean value theorems, local maxima and minima; Taylor series; Evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume; Partial derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities; Directional derivatives; Line, Surface and Volume integrals.

Ordinary Differential Equation (ODE)-  First order (linear and nonlinear) equations; higher order linear equation with constant coefficients; Euler-Cauchy equations; initial and boundary value problems.

Partial Differential Equation (PDE)- Fourier series; separation of variables; solutions of one- dimensional diffusion equation; first and second order one-dimensional wave equation and two-dimensional Laplace equation.

Probability and Statistics- Sampling theorems; Conditional probability; Descriptive statistics – Mean, median, mode and standard deviation; Random Variables – Discrete and Continuous, Poisson and Normal Distribution; Linear regression.

Numerical Methods- Error analysis. Numerical solutions of linear and non-linear algebraic equations; Newton’s and Lagrange polynomials; numerical differentiation; Integration by trapezoidal and Simpson’s rule;  Single and multi-step methods for first order differential equations.

Section 2: Structural Engineering

Engineering Mechanics- System of forces, free-body diagrams, equilibrium equations; Internal forces in structures; Frictions and its applications; Centre of mass; Free Vibrations of undamped SDOF system.

Solid Mechanics- Bending moment and shear force in statically determinate beams; Simple stress and strain relationships; Simple bending theory, flexural and shear stresses, shear center; Uniform torsion, Transformation of stress; buckling of column, combined and direct bending stresses.

Structural Analysis- Statically determinate and indeterminate structures by force/ energy methods; Method of superposition; Analysis of trusses, arches, beams, cables and frames.

Displacement Methods- Slope deflection and moment distribution methods; Influence lines; Stiffness and flexibility methods of structural analysis.

Construction Materials and Management- Construction Materials: Structural Steel – Composition, material properties and behavior; Concrete – Constituents, mix design, short-term and long-term properties.

Construction Management- Types of construction projects; Project planning and network analysis – PERT and CPM; Cost estimation.

Concrete Structures- Working stress and Limit state design concepts; Design of beams, slabs, columns; Bond and development length; Pre stressed concrete beams.

Steel Structure- Working stress and Limit state design concepts; Design of tension and compression members, beams and beam- columns, column bases; Connections – simple and eccentric, beam-column connections, plate girders and trusses; Concept of plastic analysis – beams and frames.

Section 3: GEOTECHNICAL ENGINEERING

Soil Mechanics- Three-phase system and phase relationships, index properties; Unified and Indian standard soil classification system; Permeability – one dimensional flow, Seepage through soils – two – dimensional flow, flow nets, uplift pressure, piping, capillarity, seepage force; Principle of effective stress and quicksand condition; Compaction of soils; One- dimensional consolidation, time rate of consolidation; Shear Strength, Mohr’s circle, effective and total shear strength parameters, Stress-Strain characteristics of clays and sand; Stress paths.

Foundation Engineering - surface investigations – Drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theories – Rankine and Coulomb; Stability of slopes –Finite and infinite slopes, Bishop’s method; Stress distribution in soils – Bossiness’s theory; Pressure bulbs, Shallow foundations – Terzaghi’s and Meyerhoff’s bearing capacity theories, effect of water table; Combined footing and raft foundation; Contact pressure; Settlement analysis in sands and clays; Deep foundations – dynamic and static formulae, Axial load capacity of piles in sands and clays, pile load test, pile under lateral loading, pile group efficiency, negative skin friction.

SECTION 4: WATER RESOURCES ENGINEERING

Fluid Mechanics- Properties of fluids, fluid statics; Continuity, momentum and energy equations and their applications; Potential flow, Laminar and turbulent flow; Flow in pipes, pipe networks; Concept of boundary layer and its growth; Concept of lift and drag.

Hydraulics- Forces on immersed bodies; Flow measurement in channels and pipes; Dimensional analysis and hydraulic similitude; Channel Hydraulics – Energy-depth relationships, specific energy, critical flow, hydraulic jump, uniform flow, gradually varied flow and water surface profiles.

Hydrology- Hydrologic cycle, precipitation, evaporation, vapor-transpiration, watershed, infiltration, unit hydrographs, hydrograph analysis, reservoir capacity, flood estimation and routing, surface run-off models, groundwater hydrology – steady state well hydraulics and aquifers; Application of Darcy’s Law.

Irrigation- Types of irrigation systems and methods; Crop water requirements – Duty, delta, vapor-transpiration; Gravity Dams and Spillways; Lined and unlined canals, Design of weirs on permeable foundation; cross drainage structures.

SECTION 5: ENVIRONMENTAL ENGINEERING

Water and Waste Water Quality and Treatment- Basics of water quality standards – Physical, chemical and biological parameters; Water quality index; Unit processes and operations; Water requirement; Water distribution system; Drinking water treatment. Sewerage system design, quality of domestic wastewater primary and secondary treatment. Efficient discharge standards; Sludge disposal; Reuse of treated sewage for different applications.

Air Pollution- Types of pollutants, their sources and impacts, air pollution control, air quality standards, Air quality Index and limits.

Municipal Solid Wastes- Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal).

SECTION 6: TRANSPORTATION ENGINEERING

Transportation Engineering- Geometric design of highways – cross-sectional elements, sight distances, horizontal and vertical alignments. Geometric design of railway Track- speed and Cant.

Concept of airport runway length, calculations and corrections; taxiway and exit taxiway design.

Highway Pavements- Highway materials – desirable properties and tests; Desirable properties of bituminous paving mixes; Design factors for flexible and rigid pavements; Design of flexible and rigid pavement using IRC codes.

Traffic Engineering- Traffic studies on flow and speed, peak hour factor, accident study, statistical analysis of traffic data; Microscopic and macroscopic parameters of traffic flow, fundamental relationships; Traffic signs; Signal design by Webster’s method; Types of intersections; Highway capacity.

SECTION 7: GEOMATICS ENGINEERING

Principles of surveying; Errors and their adjustment; Maps – scale, coordinate system; Distance and angle measurement – Levelling and trigonometric levelling; Traversing and triangulation survey; Total station; Horizontal and vertical curves. Photogrammetry and Remote sensing- Scale, flying height; Basics of remote sensing and GIS.

5 CHEMICAL ENGINEERING

The creation and manufacturing of goods by chemical processes is the focus of chemical engineering. This involve creating machinery, methods and procedures for processing, mixing and compounding chemicals as well as refining raw materials. Chemical engineers strive to maintain and enhance processes that are developed in the lab and transform them into useful application for the commercial manufacture of products. They rely on arithmetic, physics and chemical- the three fundamentals of engineering. There is also the growing importance of biology.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

Calculus- Functions of single variable, Limit, continuity and differentiability, Taylor series, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

Differential Equations-  First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one-dimensional heat and wave equations and Laplace equation.

Complex Variables- Complex number, polar form of complex number, triangle inequality. Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions, Linear regression analysis.

Numerical Methods- Numerical solutions of linear and non-linear algebraic equations. Integration by trapezoidal and Simpson’s rule. Single and multi-step methods for numerical solution of differential equations.

SECTION 2: PROCESS CALCULATION S AND THERMODYNAMICS

Steady and unsteady state mass and energy balances including multiphase, multi-component, reacting and non-reacting systems. Use of tie components; recycle, bypass and purge calculations; Gibb’s phase rule and degree of freedom analysis.

First and Second laws of thermodynamics. Applications of first law to close and open systems. Second law and Entropy. Thermodynamic properties of pure substances: Equation of State and residual properties, properties of mixtures: partial molar properties, fugacity, excess properties and activity coefficients; phase equilibria; predicting VLE of systems; chemical reaction equilibrium.

SECTION 3: FLUID MECHANICS AND MECHANICAL OPERATOINS

Fluid statics, surface tension, Newtonian and non-Newtonian fluids, transport properties, shell-balances including differential form of Bernoulli equation and energy balance, equation of continuity, equation of motion, equation of mechanical energy, Macroscopic friction factors, dimensional analysis and similitude, flow through pipeline systems, velocity profiles, flow meters, pumps and compressors, elementary boundary layer theory, flow past immersed bodies including packed and fluidized beds, Turbulent flow: fluctuating velocity, universal velocity profile and pressure drop.

Particle size and shape, particle size distribution, size reduction and classification of solid particles; free and hindered settling; centrifuge and cyclones; thickening and classification, filtration, agitation and mixing; conveying of solids.

SECTION 5: MASS TRANSFER

Fick’s laws, molecular diffusion in fluids, mass transfer coefficients, film, penetration and surface renewal theories; momentum, heat and mass transfer analogies; stage-wise and continuous contacting and stage efficiencies; HTU & NTU concepts; design and operation of equipment for distillation, absorption, leaching, liquid-liquid extraction, drying, humidification, dehumidification and adsorption, membrane separations (micro- filtration, ultra-filtration, nano-filtration and reverse osmosis).

SECTION 6: CHEMICAL REACTION ENGINEERING

Theories of reaction rates; kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, kinetics of enzyme reactions (Michaelis-Menten and Monod models), non-ideal reactors; residence time distribution, single parameter model; non-isothermal reactors; kinetics of heterogeneous catalytic reactions; diffusion effects in catalysis; rate and performance equations for catalyst deactivation.

SECTION 7: INSTRUMENTATION AND PROCESS CONTROL

Measurement of process variables; sensors and transducers; P&ID equipment symbols; process modeling and linearization, transfer functions and dynamic responses of various systems, systems with inverse response, process reaction curve, controller modes (P, PI, and PID); control valves; transducer dynamics; analysis of closed loop systems including stability, frequency response, controller tuning, cascade and feed forward control.

SECTION 8: PLANT DESIGN AND ECONOMICS

Principles of process economics and cost estimation including depreciation and total annualized cost, cost indices, rate of return, payback period, discounted cash flow, optimization in process design and sizing of chemical engineering equipment such as heat exchangers and multistage contactors.

SECTION 9: CHEMICAL TECHNOLOGY

Inorganic chemical industries (sulfuric acid, phosphoric acid, chlor-alkali industry), fertilizers (Ammonia, Urea, SSP and TSP); natural products industries (Pulp and Paper, Sugar, Oil, and Fats); petroleum refining and petrochemicals; polymerization industries (polyethylene, polypropylene, PVC and polyester synthetic fibres).

6 COMPUTER SCIENCE ENGINEERING (CSE)

Many schools provide an attractive education in computer science and engineering that combines the logical and scientific parts of technology and computer. Students can learn about coding, programming languages, software application, algorithms, operation systems, database management systems, etc. while pursuing computer science and IT engineering. But in order to become a tech-savvy engineer, you must hone your abilities. This is the main reason why candidates are gravitating into post-graduation programs and searching for the best website to find trustworthy information regarding the exam, the GATE syllabus for CBSE (Computer Science Engineering), the exam structure, etc.

SYLLABUS

Engineering Mathematics, Digital Logic, Computer organization and Architecture, programming and Data structures, Algorithms, Theory of Computation, Compiler Design, Operating System, Databases, and Computer Networks are the ten sections that make up the GATE 2023 CSE syllabus. If students wish to ace the test, they must thoroughly study each of these sections.

SECTION 1: ENGINEERING MATHEMATICS

Discrete Mathematics- Propositional and first order logic. Sets, relations, functions, partial orders and lattices. Monoids, Groups. Graphs: connectivity, matching, coloring. Combinatorics: counting, recurrence relations, generating functions.

Linear Algebra- Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition.

Calculus- Limits, continuity and differentiability. Maxima and minima. Mean value theorem. Integration.

Probability- Random variables. Uniform, normal, exponential, poisson and binomial
distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem.

SECTION 2: DIGITAL LOGIC

Boolean algebra. Combinational and sequential circuits. Minimization. Number representations and computer arithmetic (fixed and floating point).

SECTION 3: COMPUTER ORGANIZATION AND ARCHITECTURE

Machine instructions and addressing modes. ALU, data-path and control unit. Instruction pipelining, pipeline hazards. Memory hierarchy: cache, main memory and secondary storage; I/O interface (interrupt and DMA mode).

SECTION 4: PROGRAMMING AND DATA STRUCTURES

Programming in C. Recursion. Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs.

SECTION 5: ALGORITHMS

Searching, sorting, hashing. Asymptotic worst-case time and space complexity. Algorithm design techniques: greedy, dynamic programming and divide-and-conquer. Graph  traversals, minimum spanning trees, shortest paths

SECTION 6: THEORY OF COMPUTATION

Regular expressions and finite automata. Context-free grammars and push-down automata. Regular and context-free languages, pumping lemma. Turing machines and undecidability.

SECTION 7: COMPILER DESIGN

Lexical analysis, parsing, syntax-directed translation. Runtime environments. Intermediate code generation. Local optimization, Data flow analyses: constant propagation, liveness analysis, common subexpression elimination.

SECTION 8: OPERATING SYSTEM

System calls, processes, threads, inter-process communication, concurrency and synchronization. Deadlock. CPU and I/O scheduling. Memory management and virtual memory. File systems.

SECTION 9: DATABASES

ER-model. Relational model: relational algebra, tuple calculus, SQL. Integrity constraints, normal forms. File organization, indexing (e.g., B and B+ trees). Transactions and concurrency control.

SECTION 10: COMPUTER NETWORKS

Concept of layering: OSI and TCP/IP Protocol Stacks; Basics of packet, circuit and virtual circuit switching; Data link layer: framing, error detection, Medium Access Control, Ethernet bridging; Routing protocols: shortest path, flooding, distance vector and link state routing; Fragmentation and IP addressing, IPv4, CIDR notation, Basics of IP support protocols (ARP, DHCP, ICMP), Network Address Translation (NAT); Transport layer: flow control and congestion control, UDP, TCP, sockets; Application layer protocols: DNS, SMTP, HTTP, FTP, Email.

7 CHEMISTRY ENGINEERING (CY)

Science includes Chemistry; therefore, the GATE Chemistry paper is denoted by the code CY. Candidate may pick between the two papers, XL (Life Science) and CH (Chemical Engineering), if they choose this as their first paper. The chemistry paper, code XL-P, is also accessible as a secondary paper in the interim. For those applicants who choose to take the XL subject, this is required.

SYLLABUS

Three primary components comprise the GATE Chemistry syllabus (CY). The three main subjects covered in the syllabus are organic, inorganic, and physical chemistry. Atomic structure and periodicity, structure and bonding, s, p, and d block elements, chemistry equilibrium, electrochemistry, reaction kinetics, thermodynamics, structure- reactivity correlations, organic reaction mechanisms, and the chemistry of biomolecules are among the major subjects covered in the nine sections that make up chemistry.

SECTION 1: PHYSICAL CHEMISTRY

Structure-  Postulates of quantum mechanics. Operators. Time dependent and time independent Schrödinger equations. Born interpretation. Dirac bra-kept notation. Particle in a box: infinite and finite square wells; concept of tunnelling; particle in 1D, 2D and 3D-box; applications. Harmonic oscillator: harmonic and anharmonic potentials; Hermite polynomials. Rotational motion: Angular momentum operators, Rigid rotor. Hydrogen and hydrogen-like atoms : atomic orbitals; radial distribution function. Multi-electron atoms: orbital approximation; electron spin; Pauli exclusion principle; slater determinants. Approximation Methods: Variation method and secular determinants; first order perturbation techniques. Atomic units. Molecular structure and Chemical bonding: Born-Oppenheimer approximation; Valence bond theory and linear combination of atomic orbitals –molecular orbital (LCAO-MO) theory. Hybrid orbitals. Applications of LCAO-MO theory to H₂+, H₂; molecular orbital theory (MOT) of homo- and heteronuclear diatomic molecules. Hickel approximation and its application to annular π– electron systems.

Group Theory- Symmetry elements and operations; Point groups and character tables; Internal coordinates and vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using symmetry aspects.

Spectroscopy-  Atomic spectroscopy; Russell-Saunders coupling; Term symbols and spectral details; origin of selection rules. Rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Line broadening. Einstein’s coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance: gyromagnetic ratio; chemical shift, nuclear coupling.

Equilibrium- Laws of thermodynamics. Standard states. Thermochemistry. Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, Gibbs-Duhem equation, van’t Hoff equation. Criteria of spontaneity and equilibrium. Absolute entropy. Partial molar quantities. Thermodynamics of mixing. Chemical potential. Fugacity, activity and activity coefficients. Ideal and non-ideal solutions, Raoul’s Law and Henry’s Law, Chemical equilibria. Dependence of equilibrium constant on temperature and pressure. Ionic mobility and conductivity. Debye-Hickel limiting law. Debye-Hückel-Onsager equation. Standard electrode potentials and electrochemical cells. Nernst Equation and its application, relationship between Electrode potential and thermodynamic quantities, Potentiometric and conductometric titrations. Phase rule. Clausius- Clapeyron equation. Phase diagram of one component systems: CO2, H2O, S; two component systems: liquid- vapor, liquid-liquid and solid-liquid systems. Fractional distillation. Azeotropes and eutectics. Statistical thermodynamics: microcanonical, canonical and grand canonical ensembles, Boltzmann distribution, partition functions and thermodynamic properties.

Kinetics-  Elementary, parallel, opposing and consecutive reactions. Steady state approximation. Mechanisms of complex reactions. Unimolecular reactions. Potential energy surfaces and classical trajectories, Concept of Saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of photochemical and photophysical processes.

Surfaces and Interfaces- Physisorption and chemisorption. Langmuir, Freundlich and Brunauer–Emmett–Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity. Self-assembly. Physical chemistry of colloids, micelles and macromolecules.

SECTION 2: INORGANIC CHEMISTRY

Main Group Elements- Hydrides, halides, oxides, oxoacids, nitrides, sulfides – shapes and reactivity. Structure and bonding of boranes, car boranes, silicones, silicates, boron nitride, borazines and phosphagens. Allotropes of carbon, phosphorous and Sulphur. Industrial synthesis of compounds of main group elements. Chemistry of noble gases, pseudo halogens, and interhalogen compounds. Acid-base concepts and principles (Lewis, Brønsted, HSAB and acid-base catalysis).

Transition Elements- Coordination chemistry – structure and isomerism, theories of bonding (VBT, CFT, and MOT). Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion. Electronic spectra of transition metal complexes: spectroscopic term symbols, selection rules, Orgel and Tanabe-Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra. Magnetic properties of transition metal complexes. Ray-Dutt and Bailar twists, Reaction mechanisms: kinetic and thermodynamic stability, substitution and redox reactions. Metal-metal multiple bond.

Lanthanides and Actinides- Recovery. Periodic properties, spectra and magnetic properties.

Organometallics-  18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metal- carbene complexes and metallocene’s. Fluxionality in organometallic complexes. Types of organometallic reactions. Homogeneous catalysis – Hydrogenation, hydroformylation, acetic acid synthesis, metathesis and olefin oxidation. Heterogeneous catalysis – Fischer- Tropsch reaction, Ziegler-Natta polymerization.

Radioactivity- Detection of radioactivity, Decay processes, half-life of radioactive elements, fission and fusion processes.

Bioinorganic Chemistry- Ion (Na+ and K+) transport, oxygen binding, transport and utilization, electron transfer reactions, nitrogen fixation, metalloenzymes containing magnesium, molybdenum, iron, cobalt, copper and zinc.

Solids- Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structures of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors.

Instrumental Methods of Analysis- UV-visible, fluorescence and FTIR spectrophotometry, NMR and ESR spectroscopy, mass spectrometry, atomic absorption spectroscopy, Mossbauer spectroscopy (Fe and Sn) and Xray crystallography. Chromatography including GC and HPLC. Electroanalytical methods- polarography, cyclic voltammetry, ion-selective electrodes. Thermoanalytical methods.

SECTION 3: ORGANIC CHEMISTRY

Stereochemistry- Chirality and symmetry of organic molecules with or without chiral centers and determination of their absolute configurations. Relative stereochemistry in compounds having more than one stereo genic center. Homotopic, enantiotropic and diastrophic atoms, groups and faces. Stereoselective and stereospecific synthesis. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism and optical isomerism. Configurational and conformational effects, atropoisomeric, and neighboring group participation on reactivity and selectivity/specificity.

Reaction Mechanisms- Basic mechanistic concepts – kinetic versus thermodynamic control, Hammond’s postulate and Curtin-Hammett principle. Methods of determining reaction mechanisms through kinetics, identification of products, intermediates and isotopic labelling. Linear free-energy relationship – Hammett and Taft equations. Nucleophilic and electrophilic substitution reactions (both aromatic and aliphatic). Addition reactions to carbon-carbon and carbon-heteroatom (N and O) multiple bonds. Elimination reactions. Reactive intermediates – carbocations, carbanions, carbenes, nitrenes, arynes and free radicals. Molecular rearrangements.

Organic Synthesis- Synthesis, reactions, mechanisms and selectivity involving the following classes of compounds – alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids, esters, nitriles, halides, nitro compounds, amines and amides. Uses of Mg, Li, Cu, B, Zn, P, S, Sn and Si based reagents in organic synthesis. Carbon-carbon bond formation through coupling reactions – Heck, Suzuki, Stille, Sonogoshira, Negishi, Kumada, Hiyama, Tsuji-Trost, olefin metathesis and McMurry. Concepts of multistep synthesis – retrosynthetic analysis, strategic disconnections, synthons and synthetic equivalents. Atom economy and Green Chemistry, Umpolung reactivity – formyl and acyl anion equivalents. Selectivity in organic synthesis – chemo-,regio- and stereoselectivity. Protection and deprotection of functional groups. Concepts of asymmetric synthesis – resolution (including enzymatic), dememorization and use of chiral auxiliaries, organocatalytic. Carbon and carbon-heteroatom bond forming reactions through enolates (including boron enolates), enamines and silyl enol ethers. Stereoselective addition to C=O groups (Cram, Prelog and Ferkin-Anh models).

Pericyclic Reaction and Photochemistry- Electrocyclic, cycloaddition and sigma tropic reactions. Orbital correlations – FMO and PMO treatments, Woodward-Hoffmann rule. Photochemistry of alkenes, arenes and carbonyl compounds. Photooxidation and photoreduction. Di-π-methane rearrangement, Barton-McCombie reaction, Norrish type-I and II cleavage reaction.

Heterocyclic compounds- Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole, quinoline and is quinoline.

Biomolecules- Structure, properties and reactions of mono- and di-saccharides, physicochemical properties of amino acids, chemical synthesis of peptides, chemical structure determination of peptides and proteins, structural features of proteins, nucleic acids, lipids, steroids, terpenoids, carotenoids, and alkaloids.

Experimental techniques in organic chemistry- Optical rotation (polarimetry). Applications of various chromatographic techniques such as thin-layer, column, HPLC and GC. Applications of UV-visible, IR, NMR and Mass spectrometry in the structural determination of organic molecules.

8 ELECTRONICS AND COMMUNICATION ENGINEERING (ECE)

Communication and electronics Engineering works with integrated circuits (ICs), circuits, and communication devices such as transmitters and receivers. Basic electronics, voice and video (such as transmitters and receivers. Basic electronics, voice and video (such as AM, FM and DTH), digital and analog data transmission and reception, microprocessors, satellite communication, microwave engineering, antennae, and wave progression are also covered. It attempts to increase student’s understanding of fundamental ideas and theories in order to better prepare them for their professional careers as analysts, system implementers, operators, producers, and maintainers of various applications in the field of communications and electronics engineering.

Provides pupils with excellent employment opportunities. After earning their degree, students can readily find employment in the manufacturing sector as well as in service- related field like system support, consulting, data communication, entertainment, broadcasting and research and development. The candidates may also work with contemporary multimedia service provides that use online broadcasting and video conferencing to communicating information in real time.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and eigenvectors, rank, solution of linear equations- existence and uniqueness.

Calculus- Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

Different Equation-  First order equations (linear and nonlinear), higher order linear differential equations, Cauchy’s and Euler’s equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.

Vector Analysis- Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss’s, Green’s and Stokes’ theorems.

Complex Analysis- Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem.

Probability and Statistics- Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability.

SECTION 2: NETWORKS, SINGNALS AND SYSTEMS

Circuit Analysis- Node and mesh analysis, superposition, Thevenin’s theorem, Norton’s theorem, reciprocity. Sinusoidal steady state analysis: phasors, complex power, maximum power transfer.
Time and frequency domain analysis of linear circuits: RL, RC and RLC circuits, solution of network equations using Laplace transform.
Linear 2-port network parameters, wye-delta transformation.

Continuous-time signals- Fourier series and Fourier transform, sampling theorem and applications.

Discrete-time signals-  DTFT, DFT, z-transform, discrete-time processing of continuous-time signals.
LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeroes, frequency response, group delay, phase delay.

SECTION 3: ELECTRONC DEVICES

Energy bands in intrinsic and extrinsic semiconductors, equilibrium carrier concentration, direct and indirect band-gap semiconductors.

Carrier transport- diffusion current, drift current, mobility and resistivity, generation and recombination of carriers, Poisson and continuity equations.

P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photo diode and solar cell.

SECTION 4: ANALOG CIRCUITS

Diode Circuit- clipping, clamping and rectifiers.

BJT and MOSFET amplifiers- biasing, AC coupling, small signal analysis frequency response.

Current mirrors and differential amplifiers.

Op-amp Circuits- Amplifiers, summers, differentiators, integrators, active filters, Schmitt triggers and oscillators.

SECTION 5: DIGITAL CIRCUITS

Number Representations- binary, integer and floating-point-numbers.

Combinatorial Circuits- Boolean algebra, minimization of function using Boolean identities and Karnaugh map, logic gates ad their static CMOS implementations, arithmetic circuits, code converters multiplexers, decodes.

Sequential Circuit- latches and flip-flops, counters, shift-registers, finite state machines, propagation delay, setup and hold time, critical path delay.

Data Converters- sample and hold circuit, ADCs and DACs.

Semiconductor Memories- ROM, SRAM, DRAM

Computer Organization- Machine instructions and addressing modes, ALU, data-path and control unit, instruction pipe lining.

SECTION 6: CONTROL SYSTEMS

Basic control system components; Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and lag-lead compensation; State variable model and solution of state equation of LTI systems.

SECTION 7: COMMUNICATIONS

Random Processes- autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems.

Analog Communications- amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers.

Information theory- entropy, mutual information and channel capacity theorem.

Digital Communication- PCM, DPCM, digital modulation schemes (ASK, PSK, FSK, QAM), bandwidth, inter-symbol interference, MAP, ML detection, matched filter receiver, SNR and BER.

Fundamentals of error correction, Hamming codes, CRC. SECTION 8: ELECTROMAGNETICS

Maxwell’s Equations- differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector.

Plane Waves and Properties- reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth.

Transmission Lines- equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart.

Rectangular and circular waveguides, light propagation in optical fibres, dipole and monopole antennas, linear antenna arrays.

9 ELECTRICAL ENGINEERING (EE)

Engineering that deals with the design, analysis, and application of devices and machinery that require electricity in any form is known as electricity in any form is known as electricity in any form is known as electricity engineering. Consequently, electromagnetism is also included. The 19^th century saw the widespread generation and distributing of electricity, which led to the beginning of commercialization and the recognition of electrical engineering as a profession. Nevertheless, there are many different subfields within this area of engineering, including as computer engineering, photonics, electronics, telecommunication and more. Even so, electrical engineering is thought signal proceeding and instrumentation.

BRANCHES IN ELECTRICAL ENGINEERING

Power Engineering- Electric power generation, transmission, and distribution are the subjects of power engineering, often known as power system engineering. Transformers, motors, and generators are fundamental to this branch of engineering. In order to ensure safety and prevent any power outages, power engineering responsibly provide smooth working operation.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrix Algebra, Systems of linear equations, Eigenvalues,
Eigenvectors.

Calculus-  Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Divergence theorem, Green’s theorem.

Differential Equation- First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.

Complex Variation- Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.

Probability and Statistics-  Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.

SECTION 2: ELECTRIC CIRCUITS

Network Elements- ideal voltage and current sources, dependent sources, R, L, C, M elements; Network solution methods: KCL, KVL, Node and Mesh analysis; Network Theorems: Thevenin’s, Norton’s, Superposition and Maximum Power Transfer theorem; Transient response of dc and ac networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in ac circuits.

SECTION 3: ELECTROMAGNETIC FIELDS

Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot-Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

SECTION 4: SIGNALS AND SYSTEMS

Representation of continuous and discrete time signals, shifting and scaling properties, linear time invariant and causal systems, Fourier series representation of continuous and discrete time periodic signals, sampling theorem, Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform. R.M.S. value, average value calculation for any general periodic waveform.

SECTION 5: ELECTRICAL MACHINES

Single Phase transformer- equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency; Three-phase transformers: connections, vector groups, parallel operation; Auto-transformer, Electromechanical energy conversion principles; DC machines: separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of dc motors; Three-phase induction machines: principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control; Operating principle of single-phase induction motors; Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors; Types of losses and efficiency calculations of electric machines.

SECTION 6: POWER SYSTEMS

Basic concepts of electrical power generation, ac and dc transmission concepts, Models and performance of transmission lines and cables, Economic Load Dispatch (with and without considering transmission losses), Series and shunt compensation, Electric field distribution and insulators, Distribution systems, Per-unit quantities, Bus admittance matrix, Gauss- Seidel and Newton-Raphson load flow methods, Voltage and Frequency
control, Power factor correction, Symmetrical components, Symmetrical and
unsymmetrical fault analysis, Principles of over-current, differential, directional and distance protection; Circuit breakers, System stability concepts, Equal area criterion.

SECTION 7: CONTROL SYSTEMS

Mathematical modeling and representation of systems, Feedback principle, transfer function, Block diagrams and Signal flow graphs, Transient and Steady-state analysis of linear time invariant systems, Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci, Lag, Lead and Lead-Lag compensators; P, PI and PID controllers; State space model, Solution of state equations of LTI systems.

SECTION 8: ELECTRICAL AND ELECTRONIC MEASUREMENTS

Bridges and Potentiometers, Measurement of voltage, current, power, energy and power factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement; Oscilloscopes, Error analysis.

SECTION 9: ANALOG AND DIGITAL ELECTRONICS

Simple diode Circuits- clipping, clamping, rectifiers; Amplifiers: biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; operational amplifiers: characteristics and applications; single stage active filters, Active Filters: Sallen Key, Butterworth, VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers, Schmitt triggers, sample and hold circuits, A/D and D/A converters.

SECTION 10: POWER ELECTRONICS

Static V-I characteristics and firing/gating circuits for Thyristor, MOSFET, IGBT; DC to DC conversion: Buck, Boost and Buck-Boost Converters; Single and three-phase configuration of uncontrolled rectifiers; Voltage and Current commutated Thyristor based converters; Bidirectional ac to dc voltage source converters; Magnitude and Phase of line current harmonics for uncontrolled and thyristor based converters; Power factor and Distortion Factor of ac to dc converters; Single-phase and three-phase voltage and current source inverters, sinusoidal pulse width modulation.

10 ECOLOGY AND EVOLUTION ENGINEERING (EY)

The GATE syllabus for Ecology and Evolution 2023 contains all graduation-level questions, with the key disciplines accounting for 85% of the syllabus. The General Aptitude section provides the remaining fifteen percent.

SECTION 1: ECOLOGY

Fundamental concepts: Abiotic and biotic components; scales (population, species, community, ecosystems, biomes); niches and habitats

Population ecology: Population growth rates (density dependent/independent); metapopulation ecology (colonization, persistence, extinction, patches, sources, sinks); age- structured populations

Interactions: Types (mutualism, symbiosis, commensalism, competition, parasitism, predation, etc.); ecophysiology (physiological adaptations to abiotic environment); prey- predator interactions (Lotka-Volterra equation etc.)

Community ecology: Community assembly, organization and succession; species richness, evenness and diversity indices, species-area relationships; theory of island biogeography

Eco systems structure and function: trophic levels and their interactions; nutrient cycles; primary and secondary productivity.

SECTION 2: EVOLUTION

History of Evolutionary thought: Lamarckism; Darwinism; Modern Synthesis

Fundamentals- Variation; heritability; natural selection; fitness and adaptation; types of selection (stabilizing, directional, disruptive)

Diversity of life- Origin and history of life on earth; diversity and classification of life; systems of classification (cladistics and phenetics)

Life history strategies- Allocation of resources; trade-offs; r/K selection; semelparity and iteroparity

Interactions- Coevolution (co-adaptations, arms race, Red Queen hypothesis, co- speciation); prey-predator interactions (mimicry, crypsis, etc.)

Population and Quantitative genetics- Origins of genetic variation; Mendelian genetics; Hardy-Weinberg equilibrium; drift; selection (one-locus two-alleles model); population genetic structure (panmixia, gene flow, FST); polygenic traits; gene-environment interactions (phenotypic plasticity); heritability

Molecular evolution and phylogenetics- Neutral theory; molecular clocks; rates of evolution; phylogenetic reconstruction; molecular systematics

Macroevolution- Species concepts and speciation; adaptive radiation; convergence; biogeography.

SECTION 3: MATHEMATICS AND QUANTITATIVE ECOLOGY

Mathematics and statistics in ecology: Simple functions (linear, quadratic, exponential, logarithmic, etc.); concept of derivatives and slope of a function; permutations and combinations; basic probability (probability of random events; sequences of events, etc.); frequency distributions and their descriptive statistics (mean, variance, coefficient of variation, correlation, etc.).

Statistical hypothesis testing: Concept of p-value; Type I and Type II error, test statistics like t-test and Chi-square test; basics of linear regression and ANOVA.

SECTION 4: BEHAVIOURAL ECOLOGY

Classical Ethology: Instinct; fixed action pattern; imprinting; learnt behavior; proximate and ultimate questions

Sensory ecology: Neuroethology; communication (chemical, acoustic and visual signaling); recognition systems

Foraging ecology: Foraging behavior; optimal foraging theory

Reproduction: Cost of sex; sexual dimorphism; mate choice; sexual selection (runaway selection, good-genes, handicap principle, etc.); sexual conflict; mating systems; parental care

Social living: Costs and benefits of group-living (including responses to predators); effect of competition (scramble and contest) on group formation; dominance relationships; eusociality; kin selection; altruism; reciprocity; human behavior.

SECTION 5: APPLIED ECOLOGY AND EVOLUTION

Biodiversity and conservation: Importance of conserving biodiversity; ecosystem services; threats to biodiversity; invasive species; in-situ conservation (endemism, biodiversity hotspots, protected areas); ex-situ conservation; conservation genetics (genetic diversity, inbreeding depression); DNA fingerprinting and DNA barcoding.

Disease ecology and evolution: Epidemiology; zoonotic diseases; antibiotic resistance; vector control.

Plant and animal breeding: Marker assisted breeding; genetic basis of economically important traits.

Global climate change: Causes; consequences; mitigation.

11 GEOLOGY AND GEOPHYSICS ENGINERING

Studying the composition, structure, and other physical characteristic of the earth are the fields of geology and geophysicists. Finding and advising on the extraction of minerals, petroleum, and ground water are possible tasks for a geologist or geophysicist. Seismic, magnetic, electrical, thermal and oceanic activity detection, monitoring and forecasting are possible jobs.

SECTION 1- Earth and planetary system – terrestrial planets and moons of the solar system; size, shape, internal structure and composition of the earth; concept of isostasy; elements of seismology – body and surface waves, propagation of body waves in the earth’s interior; Heat flow within the earth; Gravitational field of the Earth; geomagnetism and paleomagnetism; continental drift; plate tectonics – relationship with earthquakes, volcanism and mountain building; continental and oceanic crust – composition, structure and thickness.

Weathering and soil formation; landforms created by river, wind, glacier, ocean and volcanoes.

Basic structural geology – stress, strain and material response; brittle and ductile deformation; nomenclature and classification of folds and faults.

Crystallography – basic crystal symmetry and concept of point groups. Mineralogy – silicate crystal structure and determinative mineralogy of common rock forming minerals.

Petrology of common igneous, sedimentary and metamorphic rocks.

Geological timescale; Geochronology and absolute time. Stratigraphic principles; major stratigraphic divisions of India.

Mineral, coal and petroleum resources of India.

Introduction to remote sensing.

Engineering properties of rocks and soils.

Elements of hydrogeology.

Principles and applications of gravity, magnetic, electrical, electromagnetic, seismic and radiometric methods of prospecting for oil, mineral and groundwater; introductory well logging.

SECTION 2 (1)- Geomorphology – Geomorphic processes and agents; development and evolution of landforms in continental and oceanic settings; tectonic geomorphology.

Structural geology – Forces and mechanism of rock deformation; primary and secondary structures; geometry and genesis of planar and linear structures (bedding, cleavage, schistosity, lineation); folds, faults, joints and unconformities; Stereographic projection; shear zones, thrusts and superposed folding; basement-cover relationship. Interpretation of geological maps.

Crystallography and mineralogy- Elements of crystal symmetry, form and twinning; crystallographic projection; crystal chemistry; classification of minerals, physical and optical properties of rock- forming minerals.

Geochemistry – Cosmic abundance of elements; meteorites; geochemical evolution of the earth; geochemical cycles; distribution of major, minor and trace elements in crust and mantle; elements of high temperature and low temperature geochemical thermodynamics; isotopic evolution of the crust and the mantle, mantle reservoirs; geochemistry of water and water-rock interaction.

Igneous petrology – Classification, forms, textures and genesis of common igneous rocks; magmatic differentiation; binary and ternary phase diagrams; major and trace elements as monitors of partial melting and magma evolutionary processes. Mantle plumes, hotspots and large igneous provinces.

Sedimentology– Texture, structure and sedimentary processes; petrology of common sedimentary rocks; Sedimentary facies and environments, cyclicities in sedimentary succession; provenance and basin analysis. Important sedimentary basins of India

Metamorphic petrology – Structures and textures of metamorphic rocks. Physic-chemical conditions of metamorphism and concept of metamorphic facies, grade and baric types; chemigraphic projections; metamorphism of politic, mafic and impure carbonate rocks; role of bulk composition including fluids in metamorphism; thermobarometer and metamorphic P-T-t paths, and their tectonic significance.

Paleobiology – Diversity of life through time, mass extinctions- causes and effects; taphonomy – processes of fossilization. Taxonomy. Morphology and functional morphology of invertebrates (bivalves, brachiopods, gastropods, echinoids, ammonites); microfossils (foraminifera, Ostracoda, conodonts, Bryozoa); Vertebrate paleontology (Equus, Proboscidea, Human); Paleobotany (plant, spores, pollens). Basic concepts of ecology/paleoecology; classification – ecological and taxonomic schemes (diversity and richness). Fossils and paleoenvironments.

Stratigraphy – Principles of stratigraphy and concepts of correlation; Lithostratigraphy, biostratigraphy and chronostratigraphic. Principles of sequence stratigraphy and applications. Stratigraphy of peninsular and extra-peninsular India. Boundary problems in Indian stratigraphy.

Resource geology – Ore-mineralogy; ore forming processes vis-à-vis ore-rock association (magmatic, hydrothermal, sedimentary, supergene and meta morphogenic ores); fluid inclusions as ore genetic tools. Coal and petroleum geology; marine mineral resources. Prospecting and exploration of economic mineral deposits – sampling, ore reserve estimation, egotistic, mining methods. Ore dressing and mineral economics. Distribution of mineral, fossil and nuclear fuel deposits in India.

Global tectonics – Plate motions, driving mechanisms, plate boundaries, supercontinent cycles.

Applied geology – Physic-mechanical properties of rocks and soils; rock index tests; Rock failure criteria (Mohr-Coulomb, Griffith and Hoek-Brown criteria); shear strength of rock discontinuities; rock mass classifications (RMR and Q Systems); in-situ stresses; rocks as construction materials; geological factors in the construction of engineering structures including dams, tunnels and excavation sites. Analysis of slope stability.

Natural hazards (landslide, volcanic, seism genic, coastal) and mitigation. Principles of climate change Hydrogeology – Groundwater flow and exploration, well hydraulics and water quality.

Basic principles of remote sensing – energy sources and radiation principles, atmospheric absorption, interaction of energy with earth’s surface, aerial-photo interpretation, multispectral remote sensing in visible, infrared, thermal IR and microwave regions, digital processing of satellite images. GIS – basic concepts, raster and vector mode operations.

SECTION 2 (2)- Solid-Earth Geophysics – The earth as a planet; different motions of the earth; gravity field of the earth, Clairaut’s theorem, size and shape of earth; geomagnetic field, paleomagnetism; Geothermic and heat flow; seismology and interior of the earth; variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth.

Geodesy – Gravitational Field of the Earth; Geoid; Ellipsoid; Geodetic Reference Systems; Datum; Everest (1830) and WGS 84 (1984) systems; GPS and DGPS; Levelling and Surveying.

Earthquake Seismology – Elements of elasticity theory- stress and strain tensors, Generalized Hooke’s Law; Body and Surface Waves; Rotational, dilatational, irrotational and equivalently waves. Reflection and refraction of elastic waves; Inhomogeneous and evanescent waves and bounded waves;

Eikon Equation and Ray theory; earthquakes-causes and measurements, magnitude and intensity, focal mechanisms; earthquake quantification, source characteristics, seismotectonic and seismic hazards; digital seismographs, Earthquake statistics, wave propagation in elastic media, quantifying earthquake source from seismological data. Elements of Seismic Tomography.

Potential and Time Varying Fields – Scalar and vector potential fields; Laplace, Maxwell and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green’s theorem; Image theory; integral equations in potential and time varying field theory.

Gravity Methods – Absolute and relative gravity measurements; Gravimeters; Land, airborne, shipborne and bore-hole gravity surveys; Tensorial Gravity sensors and surveys; various corrections for gravity data reduction – free air, Bouguer and isostatic anomalies; density estimates of rocks; regional and residual gravity separation; principle of equivalent stratum; data enhancement techniques, upward and downward continuation; derivative maps, wavelength filtering; preparation and analysis of gravity maps; gravity anomalies and their interpretation – anomalies due to geometrical and irregular shaped bodies, depth rules, calculation of mass.

Magnetic Methods – Elements of Earth’s magnetic field, units of measurement, magnetic susceptibility of rocks and measurements, magnetometers and magnetic gradiometers, Land, airborne and marine magnetic and magnetic gradiometer surveys, Various corrections applied to magnetic data, IGRF, Reduction to Pole transformation, Poisson’s relation of gravity and magnetic potential field, preparation of magnetic maps, upward and downward continuation, magnetic anomalies due to geometrical and irregular shaped bodies; Image processing concepts in processing of magnetic anomaly maps; Depth rules; Interpretation of processed magnetic anomaly data; derivative, analytic signal and Euler Depth Solutions. Applications of gravity and magnetic methods for mineral and oil exploration.

Electrical Methods – Conduction of electricity through rocks, electrical conductivities of metals, non- metals, rock forming minerals and different rocks, concepts of D.C. resistivity measurement and depth of investigation; Apparent Resistivity and Apparent Chargeability, Concept of Negative Apparent Resistivity and Negative Apparent Chargeability; Theory of Reciprocity, Sounding and Profiling, Various electrode arrangements, application of linear filter theory, Sounding curves over multi-layered earth, Dar-Sarouk parameters, reduction of layers, Triangle of anisotropy, interpretation of resistivity field data, Principles of equivalence and suppression, self-potential method and its origin; Electrical Resistivity Tomography (ERT); Induced polarization, time and frequency domain IP measurements; interpretation and applications of SP, resistivity and IP data sets for ground-water exploration, mineral exploration, environmental and engineering applications.

Electromagnetic Methods -Geo-electromagnetic spectrum; Biot Savart’s Law; Maxwell’s Equation, Helmets Equation, Basic concept of EM induction in the earth, Skin-depth, elliptic polarization, in- phase and quadrature components, phasor diagrams; Response function and response parameters; Ground and Airborne Methods, measurements in different source-receiver configurations; Earth’s natural electromagnetic methods-telluric, geomagnetic depth sounding and magnetotellurics; Electromagnetic profiling and Sounding,  Time domain EM method; EM scale modeling, processing of EM data and interpretation; Ground Penetrating Radar (GPR) Methods; Effect of conducting overburden; Geological applications including groundwater, mineral environmental and hydrocarbon exploration.

Seismic methods – Elastic properties of earth materials; Reflection, refraction and CDP surveys; land and marine seismic sources, generation and propagation of elastic waves, velocity – depth models, geophones, hydrophones, digital recording systems, digital formats, field layouts, seismic noise and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D, 3D and 4D seismic data acquisition, processing and interpretation; CDP stacking charts, binning, filtering, static and dynamic corrections, Digital seismic data processing, seismic deconvolution and migration methods, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismic, VSP, AVO, multi- component seismic and seismic interferometry. Reservoir geophysics- Rock Physics and Petrophysics.

Geophysical Survey Design.

Geophysical signal processing – sampling theorem, Nyquist frequency, aliasing, Fourier series, periodic waveform, Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, auto correlation, cross correlation, convolution, deconvolution, principles of digital filters, windows, poles and zeros.

Geophysical Well Logging – Principles and techniques of geophysical well-logging, SP,resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic resonance- longitudinal and transverse relaxation, CPMG sequence, porosity characterization, cement bond logging, micro-logs. Pulsed Neutron Devices and Spectroscopy; Multi-Array and Triaxial Induction Devices; Quantitative evaluation of formations from well logs; Logging while drilling; High angle and horizontal wells; Clay Quantification; Lithology and Porosity Estimation; Saturation and Permeability Estimation; application of bore hole geophysics in ground water, mineral and oil exploration.

Radioactive Methods – Prospecting and assaying of mineral (radioactive and non-radioactive) deposits, half-life, decay constant, radioactive equilibrium, G M counter, scintillation detector, semiconductor devices, application of radiometric for exploration, assaying and radioactive waste disposal.

Geophysical Inversion – Basic concepts of forward and inverse problems, Ill-posedness of inverse problems, condition number, non-uniqueness and stability of solutions; L1, L2 and Lp norms, overdetermined, underdetermined and mixed determined inverse problems, quasi- linear and non-linear methods including Tikhonov’s regularization method, Singular Value Decomposition, Backus-Gilbert method, simulated annealing, genetic algorithms, swarm intelligence, machine learning and artificial neural networks. Statistics of misfit and likelihood, Bayesian construction of posterior probabilities, sparsity promoting L1 optimization. Ambiguity and uncertainty in geophysical interpretation.

12 INSTRUMENTATION ENGINEERING (IN)

The creation of control systems, particularly in the electrical and pneumatic domain, is under the purview of instrumentation engineering. Engineering specializing in instrumentation design, develop, install, and maintain machinery monitoring and control systems. They set up automated procedures to increase production’s dependability, efficiency and safety.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrix algebra, systems of linear equations, consistency and rank, Eigen values and Eigen vectors.

Calculus- Mean value theorems, theorems of integral calculus, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes, Gauss and Green’s theorems.

Differential Equations- First order equation (linear and nonlinear), second order linear differential equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s equations, initial and boundary value problems, solution of partial differential equations: variable separable method.

Analysis of Complex Variables- Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’s series, residue theorem, solution of integrals.

Probability and Statistics- Sampling theorems, conditional probability, mean, median, mode, standard deviation and variance; random variables: discrete and continuous distributions: normal, Poisson and binomial distributions.

Numerical Methods- Matrix inversion, solutions of non-linear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis.

SECTION 2: ELECTRICITY AND MAGNETISM

Coulomb’s Law, Electric Field Intensity, Electric Flux Density, Gauss’s Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

SECTION 3: ELECTRICAL CIRCUITS AND MACHINES

Voltage and Current Sources-  independent, dependent, ideal and practical; v-I relationships of resistor, inductor, mutual inductance and capacitor; transient analysis of RLC circuits with dc excitation.

Kirchoff’s laws, mesh and nodal analysis, superposition, Thevenin, Norton, maximum power transfer and reciprocity theorems.

Peak-, average- and rms values of ac quantities; apparent-, active- and reactive powers; phasor analysis, impedance and admittance; series and parallel resonance, locus diagrams, realization of basic filters with R, L and C elements. transient analysis of RLC circuits with ac excitation.

One-port and two-port networks, driving point impedance and admittance, open-, and short circuit parameters.

Single Phase Transformer- equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency; Three phase induction motors: principle of operation, types, performance, torque-speed characteristics, no-load and blocked rotor tests, equivalent circuit, starting and speed control; Types of losses and efficiency calculations of electric machines.

SECTION 4: SIGNALS AND SYSTEMS

Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer function, frequency response of first and second order linear time invariant systems, impulse response of systems; convolution, correlation. Discrete time system: impulse response, frequency response, pulse transfer function; DFT and FFT; basics of IIR and FIR filters.

SECTION 5: CONTROL SYSTEMS

Feedback principles, signal flow graphs, transient response, steady-state-errors, bode plot, phase and gain margins, Routh and Nyquist criteria, root loci, design of lead, lag and lead-lag compensators, state-space representation of systems; time-delay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo and stepper motors, servo valves; on-off, P, PI, PID, cascade, feedforward, and ratio controllers, tuning of PID controllers and sizing of control valves.

SECTION 6: ANALOG ELECTRONICS

Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal analysis of transistor circuits, feedback amplifiers. Characteristics of ideal and practical operational amplifiers; applications of pumps: adder, subtractor, integrator, differentiator, difference amplifier, instrumentation amplifier, precision rectifier, active filters, oscillators, signal generators, voltage-controlled oscillators and phase locked loop, sources and effects of noise and interference in electronic circuits.

SECTION 7: DIGITAL ELECTRONICS

Combinational logic circuits, minimization of Boolean functions. IC families: TTL and CMOS. Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flip flops, shift registers, timers and counters; sample-and-hold circuit, multiplexer, analog-to-digital (successive approximation, integrating, flash and sigma-delta) and digital-to-analog converters (weighted R, R-2R ladder and current steering logic). Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/settling time); basics of number systems, Embedded Systems: Microprocessor and microcontroller applications, memory and input-output interfacing; basics of data acquisition systems, basics of distributed control systems (DCS) and programmable logic controllers (PLC).

SECTION 8: MEASUREMENTS

SI units, standards (R,L,C, voltage, current and frequency), systematic and random errors in measurement, expression of uncertainty – accuracy and precision, propagation of errors, linear and weighted regression.
Bridges: Wheatstone, Kelvin, Megohm, Maxwell, Anderson, Schering and Wien for measurement of R, L, C and frequency, Q-meter. Measurement of voltage, current and power in single and three phase circuits; ac and dc current probes; true rms meters, voltage and current scaling, instrument transformers, timer/counter, time, phase and frequency measurements, digital voltmeter, digital multimeter; oscilloscope, shielding and grounding.

SECTION 9: SENSORS AND INDUSTRIAL INSTRUMENTATION

Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal conditioning circuits; transducers for industrial instrumentation: displacement (linear and angular), velocity, acceleration, force, torque, vibration, shock, pressure (including low pressure), flow (variable head, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters) 

temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer and semiconductor); liquid level, pH, conductivity and viscosity measurement. 4-20 Mateo-wire transmitter.

SECTION 10- COMMUNICATION AND OPTICAL INSTRUMENTATION

Amplitude- and frequency modulation and demodulation; Shannon’s sampling theorem, pulse code modulation; frequency and time division multiplexing, amplitude-, phase-, frequency-, quadrature amplitude, pulse shift keying for digital modulation; optical sources and detectors: LED, laser, photo-diode, light dependent resistor, square law detectors and their characteristics; interferometer: applications in metrology; basics of fibre optic sensing. UV-VIS Spectrophotometers, Mass spectrometer.

13 MATHEMATICS ENGINEERING (MA)

A subfield of applied mathematics known as “ engineering mathematics” studies mathematical strategies and tactics that are frequently employed in engineering and business. In addition to disciplines like engineering physics and engineering geology, which may fall under the broader umbrella of engineering science, engineering mathematics is an interdisciplinary subject driven by the needs of engineers to overcome limitations in order to be productive in their work and to address theoretical, practice and other consideration outside of their area of expertise.

SECTION 1: CALCULUS

Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications to area, volume and surface area; Vector Calculus: gradient, divergence and curl, Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

SECTION 2: LINEAR ALGEBRA

Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigenvalues and eigenvectors, diagonalization, minimal polynomial, Cayley-Hamilton Theorem, Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices; diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms.

SECTION 3: REAL ANALYSIS

Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence, Ascoli-Arzela theorem; Eigenstress approximation theorem; contraction mapping principle, Power series; Differentiation of functions of several variables, Inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.

SECTION 4: COMPLEX ANALYSIS

Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, radius of convergence, Taylor’s series and Laurent’s series; Residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; Conformal mappings, Mobius transformations.

SECTION 5: ORDINARY DIFFERENTIAL EQUATIONS

First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients; Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first order ordinary differential equations, Sturm’s oscillation and separation theorems, Sturm-Liouville eigenvalue problems, Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.

SECTION 6: ALGEBRA

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Group actinomycoses theorems and their applications; Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, Eisenstein’s irreducibility criterion; Fields, finite fields, field extensions, algebraic extensions, algebraically closed fields.

SECTION 7: FUNCTIONAL ANALYSIS

Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem,Riesz representation theorem, spectral theorem for compact self-adjoint operators.

SECTION 8: NUMERICAL ANALYSIS

Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), Iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices; Numerical solutions of nonlinear equations: bisection method, secant method, Newton-Raphson method, fixed point iteration; Interpolation: Lagrange and Newton forms of interpolating polynomial, Error in polynomial interpolation of a function; Numerical differentiation and error, Numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, Mathematical errors involved in numerical integration formulae; Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2

SECTION 9: PARTIAL DIFFERENTIAL EQUATIONS

Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable; Wave equation: Cauchy problem and d’Alembert formula, domains of dependence and influence, non-homogeneous wave equation; Heat equation: Cauchy problem; Laplace and Fourier transform methods.

SECTION 10: TOPOLOGY

Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

SECTION 11: LINEAR PROGRAMMING

Linear programming models, convex sets, extreme points; Basic feasible solution, graphical method, simplex method, two phase methods, revised simplex method ; Infeasible and unbounded linear programming models, alternate optima; Duality theory, weak duality and strong duality; Balanced and unbalanced transportation problems, Initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel’s approximation method); Optimal solution, modified distribution method; Solving assignment problems, Hungarian method.

14 MECHANICAL ENGINEERING (ME)

The application of engineering ideas and problem-solving methods to any object, from design to manufacture and marketable product, is known as mechanical engineering. By using the concepts of motion, energy, and force to their work, mechanical engineers make sure that their designs operate in a safe, dependable and cost- competitive manner.

An impact is made by mechanical engineers. This is due to the fact that professions in mechanical engineering are focused on developing technologies that satisfy human demands. Many mechanical engineers have contributed to the betterment of humanity by working on almost every product or service that exists today.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.

Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.

Differential equations: First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace’s equations.

Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series.

Probability and Statistics: Definitions of probability, sampling theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.

SECTION 2: APPLIED MECHANICS AND DESIGN

Engineering Mechanics: Free-body diagrams and equilibrium; friction and its applications including rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc.; trusses and frames; virtual work; kinematics and dynamics of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations; Lagrange’s equation.

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; concept of shear center; 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 SN 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.

SECTION 3: FLUID MECHANICS AND THERMAL SCIENCE

Fluid Mechanics: Fluid properties; fluid statics, 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; basics of compressible fluid flow.

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 network analysis.

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 relations.

Applications: Power Engineering: Air and gas compressors; vapor and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles.

Refrigeration and air-conditioning: Vapor and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines; steam and gas turbines.

SECTION 4: MATERIALS, MANUFACTURING, AND INDUSTRIAL ENGINEERING

Engineering Materials: Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials.

Casting, Forming and Joining Processes: Different types of castings, design of patterns, molds 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, jigs and fixtures; abrasive machining processes; NC/CNC machines and CNC programming.

Metrology and Inspection: limits, fits and tolerances: linear and angular measurements; comparators; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly; concepts of coordinate-measuring machine (CMM).

Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools; additive manufacturing.

Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning; lean manufacturing.

Inventory Control: Deterministic models; safety stock inventory control systems.

Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

15 MINING ENGINEERING (MN)

The process of extracting minerals from the ground, above, underground, or open pits is known as mining in the engineering field. Mineral processing, exploration, excavation, geology, metallurgy, geotechnical engineering, and surveying are just a few of the numerous fields that mining engineering is related to. From resource exploration and discovery to mine design, plan development, production, and operations to mine closure, a mining engineer can oversee any stage of the mining process.

SECTION1 : ENGINEERING MATHEMATICS

Linear Algebra- Matrices and Determinants; Inverse and Rank of matrix; Systems of linear equations; Eigen values and Eigen vectors. Cayley-Hamilton Theorem.

Calculus- Limit, continuity and differentiability- Partial Derivatives; Mean value theorems; Indeterminate forms and L’ Hospital’s rule; Maxima and minima; Taylor’s theorem; Sequences and series; Test for convergence; Fourier series.

Vector Calculus- Gradient; Divergence and Curl; Line; surface and volume integrals; Stokes, Gauss and Green’s theorems.

Differential Equations- Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations.

Probability and Statistics- Measures of central tendency and dispersion; hypothesis testing; Binomial, Poisson, exponential and normal distributions; Correlation and regression analysis.

Numerical Methods- Solutions of linear algebraic equations; Interpolation; Integration of trapezoidal and Simpson’s rule; Single and multi-step methods for differential equations.

SECTION 2: MINING GEOLOGY, MINE DEVELOPMENT AND SURVEYING

Mining Geology- Minerals, Rocks and their Origin, Classification, Ore Genesis; Structural Geology.

Mine Development- Methods of access to deposits; Underground drivage’s; Drilling methods and machines; Explosives and energetics, blasting devices, blast design practices; Rock-Tool Interaction applicable to mechanical cutting systems and their selection.

Mine Surveying- Levels and levelling, theodolite, tacheometry, triangulation; Contouring; Errors and adjustments; Correlation; Underground surveying; Curves; Photogrammetry; EDM, Total Station, GPS, Basics of GIS and remote sensing

SECTION 3: GEOMECHANICS AND GROUND CONTROL

Engineering Mechanics- Equivalent force systems, Equation of equilibrium, two dimensional frames and trusses, free body diagrams, friction forces, Partial kinematics and dynamics and Bean analysis.

Geomechanics- Geo-technical properties of rocks, Rock mass classification, Instrumentation and in-situ stress measurement techniques, theories of rock failure, ground vibration, stress distribution around mine opening, Subsidence and Slope stability.

Ground Control- Design of pillars, Roof supporting system, Mine filling, Strate Control and Monitoring Plan.

SECTION 4: MINING METHODS AND MACHINERY

Mining Methods- Surface mining; layout, development, loading, transportation and mechanization, continuous surface, mining systems, highwall mining, underground coal mining, bord and pillar systems, room and pillar mining, longwall mining, thick seam mining methods, underground metal mining, open, supported and caved stopping methods, stope mechanization, ore handling systems.

Mining Machinery- Generation and transmission of mechanical, hydraulic and pneumatic power, materials handling; wire ropes, haulages, conveyors, face and development machinery, hoisting systems, pumps; comminution methods and machinery.

SECTION 5: SURFACE ENVIORNMENT, MINE VENTILATION AND UNDERGROUND HAZARDS

Surface Environment- Air, water and soil pollution: Standards of quality, causes and dispersion of contamination and control; Noise pollution and control; Land reclamation; EIA.

Mine Ventilation- Underground atmosphere; Heat load sources and thermal environment, air cooling; Mechanics of airflow, distribution, natural and mechanical ventilation; Mine fans and their usage; Auxiliary ventilation; Ventilation survey and planning; Ventilation networks.

Underground Hazards- Mine Gases, Methane drainage; Underground hazards from fires, explosions, dust and inundation; Rescue apparatus and practices; Safety management plan; Accident data analysis; assessment; My lighting; My legislation; Occupational health and safety

SECTION 6: MINERAL ECONOMICS, MINE PLANNING, SYSTEMS ENGINEERING

Mineral Economics- Mineral resource classification; Discounted cash flow analysis; My valuation; Mineral taxation.

Mine Planning- Sampling methods, practices and interpretation; Reserve estimation techniques: Basics of geostatistics and quality control; Optimization of facility location; Mine planning and its components, Determination of mine size and my life; Ultimate pit configuration and its determination, Optimum mill cut-off grade and its determination, Stope planning, Design of haul road, Selection of mining system vis-à-vis equipment system.

Systems Engineering- Concepts of reliability; Reliability of simple systems; Maintainability and availability; Linear programming, transportation and assignment problems; Network analysis; Inventory models; Queuing theory; Decision trees.

16 METALLURGICAL ENGINEERING (MT)

A subfield of engineering called metallurgy is concerned with the in-depth study of different metals and how they are used in everyday life. Metal is a major component in practically every element of modern life. It includes a variety of studies on unusual materials, both pure and mixed, with applications  across a range of industries. Metallurgical engineering is one of the most significant engineering specialties since contemporary application demand materials with high strength and low weight in addition to other requirements. Metallurgical engineering careers contribute significantly to the advancement of our society. Candidates that have chosen to major in metallurgical engineering thoroughly research the properties, bonding, and diverse environment aspects of metal. Professional with extensive expertise in the extraction, refinement and recycling of metal are known as metallurgical engineers. Metal could be employed in machinery and other industrial applications in inventive ways that they used to. Significant influence is exerted on adjacent engineering domains by the work of metallurgical engineers.

The subjects are divided into seven division, according to the GATE Metallurgy Syllabus, which includes Engineering Mathematics, Metallurgical Thermodynamics, Transport Phenomena and Rate Processes, Processing Minerals and Extractive Metallurgy. The three field of mechanical, physical and manufacturing metallurgy

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.

Calculus- Limit, Continuity and Differentiability; Partial derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.

Vector Calculus- Gradient; Divergence and Curl; Line, Surface and volume integrals; Stokes, Gauss and Green’s theorems.

Differential Equations- Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –Laplace, one dimensional heat and wave equations.

Probability and Statistics- Definitions of probability and sampling theorems, conditional probability, Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Analysis of experimental data; linear least squares method.

Numerical Methods- Solutions of linear and non-linear (Bisection, Secant, Newton- Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations.

SECTION 2: METALLURGICAL THERMODYNAMICS

Laws of thermodynamics- First law – energy conservation, Second law – entropy; Enthalpy, Gibbs and Helmholtz free energy; Maxwell’s relations; Chemical potential; Applications to metallurgical systems, solutions, ideal and regular solutions; Gibbs phase rule, phase equilibria, binary phase diagram and lever rule, free-energy vs. composition diagrams; Equilibrium constant, Activity, Ellingham and phase stability diagrams; Thermodynamics of point defects, surfaces and interfaces, adsorption and segregation phenomena.

Electrochemistry- Single electrode potential, Electrochemical cells, Nernst equation, Potential-pH diagrams.

SECTION 3: TRANSPORT PHENOMENA AND RATE PROCESSES

Momentum transfer- Concept of viscosity, shell balances, Bernoulli’s equation, mechanical energy balance equation, flow past plane surfaces and through pipes.

Heat transfer- Conduction, Fourier’s Law, 1-D steady state conduction.

Convection- Heat transfer coefficient relations for forced convection.

Radiation- Black body radiation, Stefan-Boltzmann Law, Kirchhoff’s Law.

Mass transfer- Diffusion and Fick’s laws, Mass transfer coefficients.

Dimensional analysis- Buckingham Pi theorem, Significance of dimensionless numbers.

Basic laws of chemical kinetics-  First order reactions, reaction rate constant, Arrhenius relation, heterogeneous reactions, oxidation kinetics.

Electrochemical kinetics- Polarization.

SECTION 4: MINERAL PROCESSING AND EXTRACTING METTALLURGY

Comminution techniques- Size classification, Flotation, Gravity and other methods of mineral beneficiation; Agglomeration: sintering, pelletizing and briquetting.

Material and Energy balances in metallurgical processes- Principles and processes for the extraction of non- ferrous metals – aluminum, copper and titanium.

Iron and steel making- Material and heat balance in blast furnace; Structure and properties of slags and molten salts – basicity of slags – sulphone and phosphate capacity of slags; Production of metallurgical coke.

Other methods of iron making- (COREX, MIDRE)

Primary steelmaking- Basic oxygen furnace, process dynamics, oxidation reactions, electric arc furnace.

Secondary steelmaking- Ladle process – deoxidation, argon stirring, desulphurization, inclusion shape control, principles of degassing methods; Basics of stainless-steel manufacturing.

Continuous Casting- Fluid flow in the tundish and mould, heat transfer in the mould, segregation, inclusion control.

SECTION 5: PHYSICAL METALLURGY

Chemical Bonding- Ionic, covalent, metallic, and secondary bonding in materials, Crystal structure of solids – metals and alloys, ionic and covalent solids, and polymers.

X-ray Diffraction – Bragg’s law, optical metallography, principles of SEM imaging.

Crystal Imperfections- Point, line and surface defects; Coherent, semi-coherent and incoherent interfaces.

Diffusion in solids- Diffusion equation, steady state and error function solutions; Examples- homogenization and carburization; Kirkendall effect; Uphill diffusion; Atomic models for interstitial and substitutional diffusion; Pipe diffusion and grain boundary diffusion.

Phase transformation- Driving force, Homogeneous and heterogeneous nucleation, growth kinetics.

Solidification in isomorphous- eutectic and peritectic systems, cast structures and macro segregation, dendritic solidification and constitutional supercooling, coring and micro segregation.

Solid state transformations- Precipitation, spinodal decomposition, ordering, massive transformation, discontinuous precipitation, eutectoid transformation, diffusion less transformations; Precipitate coarsening, Gibbs-Thomson effect.

Principles of heat treatment of steels- TTT and CCT diagrams; Surface hardening treatments; Recovery, recrystallization and grain growth; Heat treatment of cast iron and aluminum alloys.

Electronic, magnetic and optical properties of materials.

Basic forms of corrosion and its prevention.

SECTION 6: MECHANICAL METALLURGY

Strain tensor and stress tensor, Representation by Mohr’s circle, elasticity, stiffness and compliance tensor, Yield criteria, Plastic deformation by slip and twinning.

Dislocation theory: Edge, screw and mixed dislocations, source and multiplication of dislocations, stress fields

around dislocations; Partial dislocations, dislocation interactions and reactions.

Strengthening mechanisms: Work/strain hardening, strengthening due to grain boundaries, solid solution, precipitation and dispersion.

Fracture behavior, Griffith theory, linear elastic fracture mechanics, fracture toughness, fractography, ductile to brittle transition.

Fatigue: Cyclic stress strain behavior – low and high cycle fatigue, crack growth.

Mechanisms of high temperature deformation and failure; creep and stress rupture, stress exponent and activation energy.

SECTION 7: MANUFACTURING PROCESSES

Metal casting- Mould design involving feeding, gating and rise ring, casting practices, casting defects.

Hot, warm and cold working of metals- Metal forming -fundamentals of metal forming processes of rolling, forging, extrusion, wire drawing and sheet metal forming, defects in forming.

Metal joining- Principles of soldering, brazing and welding, welding metallurgy, defects in welded joints in steels and aluminum alloys.

Powder metallurgy- production of powders, compaction and sintering.

Non-destructive Testing (NDT)- Dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle inspection methods.

17 PETROLEUM ENGINEERING (PE)

The exploration and invention of the oil and gas extraction process are central to courses in petroleum engineering, also known as oil engineering, is multidisciplinary and connected to geoscience. The activities of the Petroleum Engineering course include developing methods to inject water, chemicals, gases or stream into an oil and gas fields; and keeping an eye on the installation, operation and maintenance of oilfield equipment. The fact that there are numerous petroleum firms functioning all over the world gives petroleum engineering more opportunities. These engineers create cutting-edge machinery to produce hydrocarbons from offshore oil and gas fields and oil shale. Candidates may choose to pursue an MTech or PhD in petroleum engineering to further their research, or they may choose to pursue a BTech in petroleum engineering.

Linear Algebra -  Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.

Calculus- Functions of single variable, Limit, continuity and differentiability, Taylor series, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

Differential equations- First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one-dimensional heat and wave equations and LaPlace equation.

Complex variables- Complex number, polar form of complex number, triangle inequality.

Probability and Statistics- Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions, Linear regression analysis.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations. Integration by trapezoidal and Simpson’s rule. Single and multi-step methods for numerical solution of differential equations.

Petroleum Exploration- : Classification and description of some common rocks with special reference to clastic and nonelastic reservoir rocks. Origin, migration and accumulation of Petroleum. Petroleum exploration methods.

Oil and Gas Well Drilling Technology- Well planning. Drilling method. Drilling rigs Rig operating systems. Drilling fluid’s function and properties. Drilling fluid maintenance equipment. Oil & gas well cementing operations. Drill bit types and their applications. Drill string & Casing string function, operations, selection & design. Drilling problems, their control & remedies. Directional drilling tools. Directional survey. Application of horizontal, multilateral, extended reach, slim wells.

Reservoir Engineering- Petrophysical properties of reservoir rocks. Coring and core analysis. Reservoir fluid properties. Phase behavior of hydrocarbon system. Flow of fluids through porous media. Water and gas coning. Reservoir pressure measurements. Reservoir drives, drive mechanics and recovery factors. Reserve estimation &techniques.

Petroleum Production Operation- Well equipment’s. Well completion techniques. Well production problems and mitigation. Well servicing & Workover operations. Workover & completion fluids. Formation damage. Well stimulation techniques. Artificial lift techniques. Field processing of oil & gas. Storage and transportation of petroleum and petroleum products. Metering and measurements oil & gas. Production system analysis & optimization. Production testing. Multiphase flow in tubing and flow-lines. Nodal system analysis. Pressure vessels, storage tanks, shell and tube heat exchangers, pumps and compressors, LNG value chain.

Offshore Drilling and Production Practices- Offshore oil and gas operations & ocean environment. Offshore fixed platforms, offshore mobile units, Station keeping methods like mooring & dynamic positioning system. Offshore drilling from fixed platform, jack-up, ships and semi submersibles. Use of conductors and risers. Offshore well completion. Deep water applications of subsea technology. Offshore production: Oil processing platforms, water injection platforms, storage, SPM and SBM transportation and utilities. Deep water drilling rig. Deep water production system. Emerging deep-water technologies.

Petroleum Formation Evaluation- : Evaluation of petrophysical of sub-surface formations: Principles applications, advantages and disadvantages of SP, resistivity, radioactive, acoustic logs and types of tools used. Evaluation of CBL/VDL, USIT, SFT, RFT. Production logging tools, principles, limitations and applications. Special type of logging tools. Casing inspection tools (principles, applications and limitations), Formations micro scanner (FMS), NMR logging principles. Standard log interpretation methods. Cross-plotting methods.

Oil and Gas Well Testing- Diffusivity equation, derivation & solutions. Radius of investigation. Principle of superposition. Horner’s approximation. Drill Stem Testing. Pressure Transient Tests: Drawdown and build up test analysis. Wellbore effects. Multilayer reservoirs. Injection well testing. Multiple well testing. Interference testing, Pulse testing, well-test analysis by use of type curves. Gas well testing.

Health Safety and Environment in Petroleum Industry- Health hazards in Petroleum Industry: Toxicity, Physiological, Asphyxiation, respiratory and skin effect of petroleum hydrocarbons, sour gases. Safety System: Manual & automatic shutdown system, blow down systems. Gas detection system. Fire detection and suppression systems. Personal protection system & measures. HSE Policies. Disaster & crisis management in Petroleum Industry. Environment: Environment concepts, impact on eco-system, air, water and soil. The impact of drilling & production operations on environment, Environmental transport of petroleum wastes. Offshore environmental studies. Offshore oil spill and oil spill control. Waste treatment methods.

Enhanced Oil Recovery Techniques- Basic principles and mechanism of EOR, Screening of EOR process. Concept of pattern flooding, recovery efficiency, permeability heterogeneity. Macroscopic and microscopic displacement efficiency. EOR methods: Chemical flooding, Miscible flooding, Thermal recoveries (steam stimulation, hot water & steam flooding, in-situ combustion), Microbial EOR.

Latest Trends in Petroleum Engineering- Coal bed methane, shale gas, oil shale, gas hydrate, and heavy oil.

18 PHYSICS ENGINEERING (PH)

A course in engineering physics is designed for students who are interested in both research and engineering. It combines the study of novel concepts in physics with applied science and engineering to develop a course that enables students learn about them collectively while also investigating and analyzing their application. You can study a variety of subjects concurrently in an engineering physics course, which gives you a variety of employment opportunities. A highly regarded degree that distinguishes itself from other engineering degree and has the potential to be very rewarding, the Engineering Physics course is incredibly broad and sophisticated.

SECTION 1: MATHEMATICAL PHYSICS

Vector Calculus- linear vector space: basis, orthogonality and completeness; matrices; similarity transformations, diagonalization, eigenvalues and eigenvectors; linear differential equations: second order linear differential equations and solutions involving special functions; complex analysis: Cauchy-Riemann conditions, Cauchy’s theorem, singularities, residue theorem and applications; Laplace transform, Fourier analysis; elementary ideas about tensors: covariant and contravariant tensors.

SECTION 2: CLASSICAL MECHANICS

Lagrangian Formulation- D’Alembert’s principle, Euler-Lagrange equation, Hamilton’s principle, calculus of variations; symmetry and conservation laws; central force motion: Kepler problem and Rutherford scattering; small oscillations: coupled oscillations and normal modes; rigid body dynamics: inertia tensor, orthogonal transformations, Euler angles, Torque free motion of a symmetric top; Hamiltonian and Hamilton’s equations of motion; Liouville’s theorem; canonical transformations: action-angle variables, Poisson brackets, Hamilton- Jacobi equation.

Special theory of relativity- Lorentz transformations, relativistic kinematics, mass-energy equivalence.

SECTION 3: ELECTROMAGNETIC THEORY

Solutions of electrostatic and magnetostatic problems including boundary value problems; method of images; separation of variables; dielectrics and conductors; magnetic materials; multipole expansion; Maxwell’s equations; scalar and vector potentials; Coulomb and Lorentz gauges; electromagnetic waves in free space, non-conducting and conducting media; reflection and transmission at normal and oblique incidences; polarization of electromagnetic waves; Poynting vector, Poynting theorem, energy and momentum of electromagnetic waves; radiation from a moving charge.

SECTION 4: QUANTUM MECHANICS

Postulates of quantum mechanics; uncertainty principle; Schrodinger equation; Dirac Bra-Ket notation, linear vectors and operators in Hilbert space; one dimensional potentials: step potential, finite rectangular well, tunneling from a potential barrier, particle in a box, harmonic oscillator; two and three dimensional systems: concept of degeneracy; hydrogen atom; angular momentum and spin; addition of angular momenta; variational method and WKB approximation, time independent perturbation theory; elementary scattering theory, Born approximation; symmetries in quantum mechanical systems.

SECTION 5: THERMODYNAMICS AND STATISTICAL PHYSICS

Laws of thermodynamics; microstates and microstates; phase space; ensembles; partition function, free energy, calculation of thermodynamic quantities; classical and quantum statistics; degenerate Fermi gas; black body radiation and Planck’s distribution law; Bose-Einstein condensation; first and second order phase transitions, phase equilibria, critical point.

SECITON 6: ATOMIC AND MOLECULAR PHYSICS

Spectra of one-and many-electron atoms; spin-orbit interaction: LS and jj couplings; fine and hyperfine structures; Zeeman and Stark effects; electric dipole transitions and selection rules; rotational and vibrational spectra of diatomic molecules; electronic transitions in diatomic molecules, Franck-Condon principle; Raman effect; EPR, NMR, ESR, X-ray spectra; lasers: Einstein coefficients, population inversion, two and three level systems.

SECTION 7: SOLID STATE PHYSICS

Elements of crystallography; diffraction methods for structure determination; bonding in solids; lattice vibrations and thermal properties of solids; free electron theory; band theory of solids: nearly free electron and tight binding models; metals, semiconductors and insulators; conductivity, mobility and effective mass; Optical properties of solids; Kramer’s-Kroni relation, intra- and inter-band transitions; dielectric properties of solid; dielectric function, polarizability, ferroelectricity; magnetic properties of solids; Dia, para, ferro, antihero and ferry-magnetism, domains and magnetic anisotropy; superconductivity: Type-I and Type II superconductors, Meissner effect, London equation, BCS Theory, flux quantization.

SECTION 8: ELECTRONICS

Semiconductors in equilibrium- electron and hole statistics in intrinsic and extrinsic semiconductors; metal semiconductor junctions; Ohmic and rectifying contacts; PN diodes, bipolar junction transistors, field effect transistors; negative and positive feedback circuits; oscillators, operational amplifiers, active filters; basics of digital logic circuits, combinational and sequential circuits, flip-flops, timers, counters, registers, A/D and D/A conversion.

SECTION 9: NUCLEAR AND PARTICLE PHYSICS

Nuclear radii and charge distributions, nuclear binding energy, electric and magnetic moments; semi-empirical mass formula; nuclear models; liquid drop model, nuclear shell model; nuclear force and two nucleon problem; alpha decay, beta-decay, electromagnetic transitions in nuclei; Rutherford scattering, nuclear reactions, conservation laws; fission and fusion; particle accelerators and detectors; elementary particles; photons, baryons, mesons and leptons; quark model; conservation laws, isospin symmetry, charge conjugation, parity and time-reversal invariance.

19 AGRICULTURAL ENGINEERING

Creating, development and refining farm machinery, equipment and technology to increase farm productivity is known as agriculture engineering. Ensuring sustainable and environmentally friendly farming is their main objective. The environmental implication of intensive agriculture, sustainable agriculture production, pollution control, managing natural resources, and handling agriculture goods after harvests are just a few of the problems they assess and resolve using their engineering expertise.

They may design and construct various agriculture infrastructure, such as storage facilities, water reservoirs and dams, even if their primary focus is on agriculture land and equipment. Agriculture engineering is abroad field that combines farming with cutting edge technologies such as artificial intelligence. It blends agriculture ideas with aspects of mechanical, civil, electrical and chemical engineering.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrices and determinants, linear and orthogonal transformations, Caley-Hamilton theorem; Eigenvalues and Eigenvectors, solutions of linear equations.

Calculus- Limit, continuity and differentiability; partial derivatives; homogeneous function – Euler’s theorem on homogeneous functions, total differentiation; maxima and minima of function with several independent variables; sequences and series – infinite series, tests for convergence; Fourier, Taylor and Maclaurin series.

Vector Calculus- Vector differentiation, scalar and vector point functions, vector differential operators – del, gradient; divergence and curl; physical interpretations-line, surface and volume integrals; Stokes, Gauss and Green’s theorems.

Differential Equations- Linear and non-linear first order Ordinary Differential Equations (ODE); homogeneous differential equations, higher order linear ODEs with constant coefficients; Laplace transforms and their inverse; Partial Differential Equations - Laplace, heat and wave equations.

Probability and statistics- Mean, median, mode and standard deviation; random variables; Poisson, normal and binomial distributions; correlation and regression analysis

Numerical Methods- Mean, median, mode and standard deviation; random variables; Poisson, normal and binomial distributions; correlation and regression analysis.

SECTION 2: FARM MACHINERY

Machine Design- Design and selection of machine elements – gears, pulleys, chains and sprockets and belts; overload safety devices used in farm machinery; measurement of force, stress, torque, speed, displacement and acceleration on machine elements - shafts, couplings, keys, bearings and knuckle joints.

Farm Machinery- : Soil tillage; forces acting on a tillage tool; hitch systems and hitching of tillage implements; functional requirements, principles of working, construction and operation of manual, animal and power operated equipment for tillage, sowing, planting, fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing calculation of performance parameters - field capacity, efficiency, application rate and losses; cost analysis of implements and tractors.

SECTION 3: FARM POWER

Sources of Power- Sources of power on the farm - human, animal, mechanical, electrical, wind, solar and biomass; bio-fuels

Farm Power- Thermodynamic principles of I.C. engines; I.C. engine cycles; engine components; fuels and combustion; lubricants and their properties; I.C. engine systems – fuel, cooling, lubrication, ignition, electrical, intake and exhaust; selection, operation, maintenance and repair of I.C. engines; power efficiencies and measurement; calculation of power, torque, fuel consumption, heat load and power losses; performance index, cost analysis of implements and tractors.

Tractors and Power Tillers- Type, selection, maintenance and repair of tractors and power tillers; tractor clutches and brakes; power transmission systems – gear trains, differential, final drives and power take-off; mechanics of tractor chassis; traction theory; three point hitches - free link and restrained link operations; steering and hydraulic control systems used in tractors; tractor tests and performance; human engineering and safety considerations in design of tractor and agricultural implements.

SECTION 4: SOIL AND WATER CONSERVATION ENGINEERING

Fluid Mechanics- Ideal and real fluids, properties of fluids; hydrostatic pressure and its measurement; continuity equation, kinematics and dynamics of flow; Bernoulli’s theorem; laminar and turbulent flow in pipes, DarcyWeisbach and Hazen-William’s equations, Moody’s diagram; flow through orifices, weirs and notches; flow in open channels, dimensional analysis – concepts of geometric dimensionless numbers.

Soil Mechanics- Engineering properties of soils; fundamental definitions and relationships; index properties of soils; permeability and seepage analysis; shear strength, Mohr’s circle of stress, active and passive earth pressures; stability of slopes, Terzaghi’s one dimensional soil consolidation theory.

Hydrology- Hydrological cycle and measurement of its components; meteorological parameters and their measurement; analysis of precipitation data; runoff estimation; hydrograph analysis, unit hydrograph theory and application; streamflow measurement; flood routing, hydrological reservoir and channel routing, Infiltration – indices and equations, drought and its classification.

Surveying and Leveling- Measurement of distance and area; instruments for surveying and leveling; chain surveying, methods of traversing; measurement of angles and bearings, plane table surveying; types of leveling; theodolite traversing; contouring; total station, introduction to GPS survey, computation of areas and volume.

Soil and Water Erosion- Mechanics of soil erosion - wind and water erosion: soil erosion types, factors affecting erosion; soil loss estimation; biological and engineering measures to control erosion; terraces and bunds; vegetative waterways; gully control structures, drop, drop inlet and chute spillways; earthen dams.

Watershed Management- Watershed characterization and land use capability classification; water budgeting in watershed, rainwater harvesting, check dams and farm ponds.

SECTION 5: IRRIGATION AND DRAINAGE ENGINEERING

Soil-Water-Plant Relationship- Water requirement of crops; consumptive use and evapotranspiration; measurement of infiltration, soil moisture and irrigation water infiltration.

Irrigation Water Conveyance and Application Methods- Design of irrigation channels and underground pipelines; irrigation scheduling; surface, sprinkler and micro irrigation methods, design and evaluation of irrigation methods; irrigation efficiencies.

Agricultural Drainage- Drainage coefficient; planning, design and layout of surface and sub-surface drainage systems; leaching requirement and salinity control; irrigation and drainage water quality and reuse; nonconventional drainage system.

Groundwater Hydrology- Groundwater occurrence; Darcy’s Law, steady and unsteady flow in confined and unconfined aquifers, groundwater exploration techniques; overview of groundwater recharge estimation and artificial recharge techniques.

Wells and Pumps- Types of wells, steady flow through wells; design and construction of water wells; classification of pumps; pump characteristics; pump selection and installation.

SECTION 6: AGRICULTURAL PROCESS ENGINEERING

Engineering Properties of agriculture produce- Physical, thermal, frictional, rheological and electrical properties.

Evaporation and Drying- Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers; hydrothermal treatments; drying and milling of cereals, pulses and oilseeds; drying kinetics; psychrometry – properties of air-water vapor mixture.

Size Reduction and Material Handling- Mechanics and energy requirement in size reduction of agriculture produce; particle size analysis for comminuted solids; size separation by screening; fluidization of granular solids-pneumatic, bucket, screw and belt conveying; cleaning and grading; effectiveness of separation; centrifugal separation of solids, liquids and gases; homogenization; filtration and membrane separation.

Processing of Agriculture Produce- Processing of seeds, spices, fruits and vegetables; value addition of agriculture produces.

Storage Systems- Controlled and modified atmosphere storage; perishable food storage, God owns, bins and grain silos, packaging material and machines.

SECTION 7: DAIRY AND FOOD ENGINEERING

Heat and Mass Transfer- Steady state heat transfer in conduction, convection and radiation; transient heat transfer in simple geometry; working principles of heat exchangers; diffusive and convective mass transfer; simultaneous heat and mass transfer in agricultural processing operations; material and energy balances in food processing systems; water activity, sorption and desorption isotherms.

Preservation of Food- Kinetics of microbial death – pasteurization and sterilization of milk and other liquid foods; preservation of food by cooling and freezing; refrigeration and cold storage basics and applications.

20 PRODUCTION AND INDUSTRIAL ENGINEERING  (PI)

The multidisciplinary engineering field of industrial and production engineering (IPE) encompasses the field of manufacturing technology, engineering sciences, management science, and complex process, system or organization optimization. It is focused on comprehending and utilizing engineering procedures in production methods and manufacturing operation. The history of Industrial engineering begins with the industrial revolution, which was sir Adam Smith, Henry Ford, Eli Whitney, Frank and Lilian Gilbreth, Henry Gantt, F.W. Taylor, and others. Automation and robotics became widely used in industrial and production engineering after the 1970s, as the field expanded globally. Three fields are included in industrial and production engineering: management science, industrial engineering, and mechanical engineering, which is where production engineering originates.

SECTION 1: ENGINEERING MATHEMATICS

Linear Algebra- Matrix algebra, Systems of linear equations, Eigen values and Eigen vectors.

Calculus- Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives; Line, Surface and Volume integrals; Stokes, Gauss and Green’s theorems.

Differential Equations- First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms.

Complex Variables- Analytic functions, Cauchy’s integral theorem, Taylor series.

Probability and Statistics- Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Linear regression, Random variables, Poisson, normal, binomial and exponential distributions.

Numerical Methods- Numerical solutions of linear and nonlinear algebraic equations, Integration by trapezoidal and Simpson’s rules, Single and multi-step methods for differential equations.

SECTION 2: GENERAL ENGINEERING

Engineering Materials- Structure, physical and mechanical properties, and applications of common engineering materials (metals and alloys, semiconductors, ceramics, polymers, and composites – metal, polymer and ceramic based); Iron-carbon equilibrium phase diagram; Heat treatment of metals and alloys and its influence on mechanical properties; Stress-strain behavior of metals and alloys.

Applied Mechanics- equivalent force systems, free body concepts, equations of equilibrium; Trusses; Strength of materials – stress, strain and their relationship; Failure theories; Mohr’s circle (stress); Deflection of beams, bending and shear stresses; Euler’s theory of columns; Thick and thin cylinders; Torsion.

Theory of Machines and Design- Analysis of planar mechanisms, cams and followers; Governors and fly wheels; Design of bolted, riveted and welded joints; Interference/shrink fit joints; Friction and lubrication; Design of shafts, keys, couplings, spur gears, belt drives, brakes and clutches; Pressure vessels.

Thermal and Fluids Engineering- Fluid mechanics – fluid statics, Bernoulli’s equation, flow through pipes, laminar and turbulent flows, equations of continuity and momentum, capillary action; Dimensional analysis; Thermodynamics – zeroth, first and second laws of thermodynamics, thermodynamic systems and processes, calculation of work and heat for systems and control volumes; Air standard cycles; Heat transfer – basic applications of conduction, convection and radiation.

SECTION 3: MANUFACTURING PROCESSES 1

Casting- Types of casting processes and applications; Sand casting: patterns – types, materials and allowances; molds and cores–materials, making, and testing; design of gating system and riser; casting techniques of cast iron, steels, and non-ferrous metals and alloys; analysis of solidification and microstructure development; Other casting techniques: Pressure die casting, Centrifugal casting, Investment casting, Shell mold casting; Casting defects and their inspection by non-destructive testing.

Metal Forming- Stress-strain relations in elastic and plastic deformation; von Mises and Tresca yield criteria, Concept of flow stress; Hot, warm and cold working; Bulk forming processes – forging, rolling, extrusion and wire drawing; Sheet metal working processes – blanking, punching, bending, stretch forming, spinning and deep drawing; Ideal work and slab analysis; Defects in metal working and their causes.

Joining of Materials- Classification of joining processes; Principles of fusion welding processes using different heat sources (flame, arc, resistance, laser, electron beam), Heat transfer and associated losses; Arc welding processes – SMAW, GMAW, GTAW, plasma arc, submerged arc welding processes; Principles of solid state welding processes – friction welding, friction stir welding, ultrasonic welding; Welding defects – causes and inspection; Principles of adhesive joining, brazing and soldering processes.

Power Processing- Production of metal/ceramic powders, compaction and sintering of metals and ceramic powders, Cold and hot isostatic pressing.

Polymers and Composites- Polymer processing – injection, compression and blow molding, extrusion, calendaring and thermoforming; Molding of composites.

SECTION 4: MANUFACTURING  PROCESSES II

Machining- Orthogonal and oblique machining, Single point cutting tool and tool signature, Chip formation, cutting forces, Merchant’s analysis, Specific cutting energy and power; Machining parameters and material removal rate; tool materials, Tool wear and tool life; Thermal aspects of machining, cutting fluids, machinability; Economics of machining; Machining processes – turning, taper turning, thread cutting, drilling, boring, milling, gear cutting, thread production; Finishing processes – grinding, honing, lapping and super-finishing.

Machine Tools- Lathe, milling, drilling and shaping machines – construction and kinematics; Jigs and fixtures –principles, applications, and design.

Advanced Manufacturing- Principles and applications of USM, AJM, WJM, AWJM, EDM and Wire EDM, LBM, EBM, PAM, CHM, ECM; Effect of process parameters on material removal rate, surface roughness and power consumption; Additive manufacturing techniques.

Computer Integrated Manufacturing- Basic concepts of CAD and CAM, Geometric modeling, CNC; Automation in Manufacturing; Industrial Robots – configurations, drives and controls; Cellular manufacturing and FMS – Group Technology, CAPP.

SECTION 5: QUALITY AND RELIABILITY

Metrology and Inspection- Accuracy and precision; Types of errors; Limits, fits and tolerances; Gauge design, Interchangeability, Selective assembly; Linear, angular, and form measurements (straightness, flatness, roundness, runout and cylindricity) by mechanical and optical methods; Inspection of screw threads and gears; Surface roughness measurement by contact and non-contact methods.

Quality Management-  concept and costs; Statistical quality control – process capability analysis, control charts for variables and attributes and acceptance sampling; Six sigma; Total quality management; Quality assurance and certification – ISO 9000, ISO14000.

Reliability and Maintenance- Reliability, availability and maintainability; Distribution of failure and repair times; Determination of MTBF and MTTR, Reliability models; Determination of system reliability; Preventive and predictive maintenance and replacement, Total productive maintenance.

SECTION 6: INDUSTRIAL ENGINEERING

Product Design and Development- Principles of product design, tolerance design; Quality and cost considerations; Product life cycle; Standardization, simplification, diversification; Value engineering and analysis; Concurrent engineering; Design for “X”.

Work System Design- Taylor’s scientific management, Gilbreth’s contributions; Productivity – concepts and measurements; Method study, Micro-motion study, Principles of motion economy; Work measurement – time study, Work sampling, Standard data, PMTS; Ergonomics; Job evaluation and merit rating.

Facility Design- Facility location factors and evaluation of alternate locations; Types of plant layout and their evaluation; Computer aided layout design techniques; Assembly line balancing; Materials handling systems.

SECTION 7: OPERATIONS RESEARCH AND OPERATIONS MANAGEMENT

Operation Research- Linear programming – problem formulation, simplex method, duality and sensitivity analysis; Transportation and assignment models; Integer programming; Constrained and unconstrained nonlinear optimization; Markovian queuing models; Simulation – manufacturing applications.

Engineering Economy and Casting- Elementary cost accounting and methods of depreciation; Break-even analysis; Techniques for evaluation of capital investments; Financial statements; Activity based costing.

Production Control- Forecasting techniques – causal and time series models, moving average, exponential smoothing, trend and seasonality; Aggregate production planning; Master production scheduling; MRP, MRP-II and ERP; Routing, scheduling and priority dispatching; Push and pull production systems, concepts of Lean and JIT manufacturing systems; Logistics, distribution, and supply chain management; Inventory – functions, costs, classifications, deterministic inventory models, quantity discount; Perpetual and periodic inventory control systems.

Project Management- Scheduling techniques – Gantt chart, CPM, PERT and GERT.

21 TEXTILE ENGINEERING AND FIBRE SCIENCE ENGINEERING (TF)

This area of engineering contributes to the production of fabric, textiles, days, textures and pattern utilized in the apparel business. A course on textile engineering may address the theories, regulations, and scientific methods that support the production of various fabrics, yarns and apparel materials. It also entails studying the fundamental of polymer analysis and evaluation, which are applied in the production of textile fabrics. Producers of Synthetic fibers frequently refer to the process of manipulating polymers to create fibers with a variety of performance characteristics as “fiber engineering,” while in recent years, the term “fabric engineering” has signed popularity to refer to the use of fabric as membranes in technical application like composite structure and architecture.

ENGINEERING MATHEMATICS

Linear Algebra- Matrices and Determinants; Systems of linear equations; Eigenvalues and Eigenvectors

Calculus- Limit, continuity and differentiability; Successive differentiation; Partial differentiation; Maxima and minima; Errors and approximations; Definite and improper integrals; Sequences and series; Test for convergence; Power series; Taylor series.

Differential Equations- First order linear and non-linear differential equations; Higher order linear differential equations with constant coefficients; Euler-Cauchy equation; Partial differential equations; Wave and heat equations; Laplace’s equation

Probability and Statistics-  Random variables; Poisson, binomial and normal distributions; Mean, mode, median, standard deviation; Confidence interval; Test of hypothesis; Correlation analysis; Regression analysis; Analysis of variance; Control charts.

Numerical Methods- Numerical solutions of linear and non-linear algebraic equations; Numerical integration by trapezoidal and Simpson’s rules; Single-step and multi-step numerical methods for differential equations.

TEXTILE ENGINEERING AND FIBRE SCIENCE

TEXTILE FIBRES

Classification of textile fibres; Essential requirements of fibre forming polymers; Gross and fine structures of natural fibres like cotton, wool, silk; Introduction to basifies; Properties and uses of natural and man-made fibres including carbon, aramid and ultra-high molecular weight polyethylene fibres; Physical and chemical methods of fibre and blend identification and blend analysis. Molecular architecture, amorphous and crystalline phases, glass transition, plasticization, crystallization, melting, factors affecting Tag and Tm; Polymerization of nylon-6, nylon-66, poly (ethylene terephthalate), polyacrylonitrile and polypropylene; Melt spinning processes for PET, polyamide and polypropylene; Preparation of spinning dope; Principles of wet spinning, dry spinning, dry-jet-wet spinning and gel spinning; Spinning of acrylic, viscose and other regenerated cellulosic fibres such as polynomic and lyocell; Post spinning operations such as drawing, heat setting, tow-to-top conversion; Spin finish composition and applications; Different texturing methods. Methods of investigating fibre structure such as density, x-ray diffraction, birefringence, optical and electron microscopy such as SEM and TEM, I.R. spectroscopy, thermal methods such as DSC, DMA, TMA and TGA; Structure and morphology of man-made fibres; Mechanical properties of fibres; Moisture sorption of fibres; Fibre structure-property correlation.

YARN MANUFACTURE, YARN STRUCTURE AND PROPERTIES

Principles of ginning; Principles of opening, cleaning and blending; Working principles of modern blow room machines; Fundamentals of carding; Conventional vs. modern carding machine; Card setting; Card clothing; Periodic mass variation in card sliver; Card autoleveller; Principles of roller drawing; Roller arrangements in drafting systems; Periodic mass variation in drawn sliver; Drawframeautoleveller; Principles of cotton combing; Combing cycle and mechanisms; Recent developments in combing machine; Principles of drafting, twisting, and bobbin building in roving formation; Modern developments in roving machine; Principles of drafting, twisting and cop building in ring spinning; Causes of end breakages; Modern developments in ring spinning machine; Working principles of ring doubler and two-for-one twister; Relationship between single yarn twist and folded yarn twist; Principles of compact, rotor, air-jet, air-vortex, friction, core, wrap and twist-less spinning processes. Influence of fibre geometry, fibre configuration and fibre orientation in yarn; Fibre packing density of yarn; Yarn diameter; Yarn twist and its relation to yarn strength; Helical arrangement of fibres in yarns; Yarn contraction; Fibre migration in yarns; Stress-strain relation in yarn; Mass irregularity of yarn; Structure-property relationship in ring, compact, rotor, air-jet and friction spun yarns.

FABRIC MANUFACTURE, STRUCTURE AND PROPERTIES

Principles of winding processes; Classification of winding methods; Patterning mechanism; Yarn clearers and tensioners; Different systems of yarn splicing; Warping objectives and classification; Different types of warping creels; Features of beam and sectional warping machines; Different sizing systems; Sizing of spun and filament yarns; Drawing-in process; Principles of pirn winding. Primary and secondary motions of loom; Shedding motion; Positive and negative shedding mechanisms; Type of sheds; Tappet, dobby and jacquard shedding; Weft insertion; Mechanics of weft insertion with shuttle; Shuttle picking and checking; Beat-up; Kinematics of sley; Loom timing diagram; Cam designing; Effect of sley setting and cam profile on fabric formation; Take-up and Let-off motions; Warp and weft stop motions; Warp protection; Weft replenishment; Principles of weft insertion systems of shuttle-less weaving machines such as projectile, rapier, water-jet and air-jet; Principles of functioning of multiphase and circular looms; Types of selvedges. Basic woven fabric constructions and their derivatives; Crepe, cord, terry, gauze, leno and double cloth constructions; Drawing and lifting plans. Fundamentals of weft knitting; Classification of weft knitting technologies; Weft knitted constructions such as plain, rib, interlock and purl; Different knit stitches such as loop, tuck and float. Principle of warp knitting; Classification of warp knitting technologies; Swinging and slogging motion of guide bar; Basic warp knit construction such as pillar, tricot, atlas, inlay and nets. Fibre preparation processes for nonwovens; Web formation and bonding processes; Spun-bonding and melt blowing technologies; Applications of nonwoven fabrics. Principles of braiding; Type of braids; Maypole braiding technology. Peirce’s equations for plain woven fabric geometry; Elastic model of plain-woven fabric; Thickness, cover and maximum set of woven fabrics; Geometry of plain weft knitted loop; Munden’s constants and tightness factor for plain weft knitted fabrics; Geometry of tubular braids.

TEXTILE TESTING

Sampling techniques for fibres, yarns and fabrics; Sample size and sampling errors. Moisture in textiles; Fibre length, fineness, crimp, maturity and trash content; Tensile testing of fibres; High volume fibre testing. Linear density of sliver, roving and yarn; Twist and hairiness of yarn; Tensile testing of yarns; Evenness testing; Fault measurement and analysis of yarns. Fabric thickness, compressibility, stiffness, shear, drape, crease recovery, tear strength, bursting strength, pilling and abrasion resistance; Tensile testing of fabrics; Objective evaluation of low stress mechanical characteristics; Air permeability; Wetting and wicking; Water-vapor transmission through fabrics; Thermal resistance of fabrics.

CHEMICAL PROCESSING

Impurities in natural fibre; Singeing; Chemistry and practice of preparatory processes for cotton; Preparatory processing of wool and silk; Mercerization of cotton; Preparatory processes for manmade fibres and their blends; Optical brightening agent. Classification of dyes; Dyeing of cotton, wool, silk, polyester, nylon and acrylic with appropriate classes of dyes; Dyeing of polyester/cotton and polyester/wool blends; Dyeing machines; Dyeing processes and machines for cotton knitted fabrics; Dye-fibre interaction; Introduction to thermodynamics and kinetics of dyeing; Brief idea about the relation between color and chemical constitution; Beer-Lambert’s law; Kubelka-Munk theory and its application in color measurement; Methods for determination of wash, light and rubbing fastness. Methods of printing such as roller printing and screen printing; Preparation of printing paste; Various types of thickeners; Printing auxiliaries; Direct styles of printing of (I) cotton with reactive dyes, (ii) wool, silk, nylon with acid and metal complex dyes, (iii) polyester with disperse dyes; Resist and discharge printing of cotton, silk and polyester; Pigment printing; Transfer printing of polyester; Inkjet printing; Printing faults. Mechanical finishing of cotton; Stiff, soft, wrinkle resistant, water repellent, flame retardant and enzyme (biopolishing) finishing of cotton; Milling, dequantizing and shrink resistant finishing of wool; Antistatic and soil release finishing; Heat setting of synthetic fabrics; Minimum application techniques. Pollution control and treatment of effluents.

22 STATISTICS ENGINEERING (ST)

The creation of software and programming for use in statistical modeling and graphic analysis is the focus of statistical engineering. In order to solve a problem at work, a statistical engineer’s job is to integrate the ideas and concepts from both engineering and statistics. To develop practical solution to boost an organization or business’s efficiency, they must evaluate data with the aid of advanced computer tools and write a final report based on their findings.

CALCULUS- Finite, countable and uncountable sets; Real number system as a complete ordered field, Archimedean property; Sequences of real numbers, convergence of sequences, bounded sequences, monotonic sequences, Cauchy criterion for convergence; Series of real numbers, convergence, tests of convergence, alternating series, absolute and conditional convergence; Power series and radius of convergence; Functions of a real variable: Limit, continuity, monotone functions, uniform continuity, differentiability, Rolle’s theorem, mean value theorems, Taylor’s theorem, L’ Hospital rules, maxima and minima, Riemann integration and its properties, improper integrals; Functions of several real variables: Limit, continuity, partial derivatives, directional derivatives, gradient, Taylor’s theorem, total derivative, maxima and minima, saddle point, method of Lagrange multipliers, double and triple integrals and their applications.

MATRIX THEORY- Subspaces of ℝ