GATE Exams Syllabus in Hindi

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GATE Exams Syllabus in Hindi

इस खंड में गेट सिलेबस का एक व्यापक भंडार एकीकृत किया गया है और उन सभी विषयों को शामिल किया गया है जो गेट पाठ्यक्रम में सूचीबद्ध हैं। पाठ्यक्रम की संरचना और विस्तृत सिलेबस के साथ उम्मीदवारों की बेहतर क्षमता के लिए, प्रस्तुतिकरण को अच्छी तरह से व्यवस्थित किया गया है। विषयों को तालिकाओं में संक्षेपित किया गया है और विवरण बुलेट बिंदुओं में समझाया गया है

यह गेट सिलेबस रिपॉजिटरी उन सभी उम्मीदवारों के लिए विशेष रूप से डिज़ाइन किया गया है जो गेट परीक्षा के लिए उपस्थित होने की योजना बना रहे हैं। यह शिक्षकों और अन्य निजी संस्थानों के लिए भी सहायक है जो GATE उम्मीदवारों को कक्षाएं प्रदान करते हैं। पाठ्यक्रम उन्हें अपनी पढ़ाई की योजना बनाने में मदद करेगा

ऐसी कोई शर्त नहीं है; GATE परीक्षा को क्रैक करने का इच्छुक कोई भी उम्मीदवार व्यापक रूप से और व्यवस्थित रूप से तैयार GATE सिलेबस का लाभ उठा सकता है.

GATE General Aptitude Syllabus

Common to All

Structure and Syllabus

Parts/Units Topic
Part A Verbal Ability
Unit 1 English Grammar
Unit 2 Sentence Completion
Unit 3 Verbal Analogies
Unit 4 Word Groups
Unit 5 Instructions
Unit 6 Critical Reasoning
Unit 7 Verbal Deduction
Part B Numerical Ability
Unit 8 Numerical Computation
Unit 9 Numerical Estimation
Unit 10 Numerical Reasoning
Unit 11 Data Interpretation

GATE Aerospace Engineering Syllabus

Subject Code: AE

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Topics (Core)
1 Linear Algebra
2 Calculus
3 Differential Equations
Topics (Special)
1 Fourier Series
2 Laplace Transforms
3 Numerical Methods for Linear and Nonlinear Algebraic Equations
4 Numerical Integration
5 Differentiation
Section B Flight Mechanics
Topics (Core)
1 Basics
2 Airplane performance
3 Static stability
Topics (Special)
1 Dynamic stability
2 Euler Angles
3 Equations of Motion
4 Aerodynamic Forces and Moments
5 Stability & Control Derivatives
6 Decoupling of Longitudinal and Lateral-Directional Dynamics
7 Longitudinal Modes
8 Lateral-Directional Modes
Section C Space Dynamics
Topics (Core)
1 Central Force Motion
2 Determination of Trajectory
3 Orbital Period in Simple Cases
Topics (Special)
1 Orbit Transfer
2 In-plane and Out-of-Plane
Section D Aerodynamics
Topics (Core)
1 Basic Fluid Mechanics
2 Airfoils and wings
3 Compressible Flows
Topics (Special)
1 Elementary Ideas of Viscous Flows Including Boundary Layers
2 Wind Tunnel Testing
3 Measurement and Visualization Techniques
Section E Structures
Topics (Core)
1 Strength of Materials
2 Flight Vehicle Structure
3 Structural Dynamics
Topics (Special)
1 Vibration of Beams
2 Theory of Elasticity
3 Equilibrium and compatibility equations, Airy’s stress function
Section F Propulsion
Topics (Core)
1 Basics
2 Thermodynamics of Aircraft Engines
3 Axial Compressors
4 Axial Turbines
5 Centrifugal Compressor
6 Rocket Propulsion
No Special Topic
NoteIn each of the following subjects the topics have been divided into two categories – Core Topics and Special Topics. The corresponding sections of the question paper will contain 90% of their questions on Core Topics and the remaining 10% on Special Topics.

Course Syllabus

Section A: Engineering Mathematics

Core Topics

Unit 1: Linear Algebra

  • Vector algebra

  • Matrix algebra

  • Systems of linear equations

  • Rank of a matrix

  • Eigenvalues and eigenvectors

Unit 2: Calculus

  • Functions of single variable

  • Limits

  • Continuity and differentiability

  • Mean value theorem

  • Chain rule

  • Partial derivatives

  • Maxima and minima

  • Gradient

  • Divergence and curl

  • Directional derivatives

  • Integration −

    • Line

    • surface and volume integrals

    • Theorems of Stokes

    • Gauss and Green

Unit 3: Differential Equations

  • First order linear and nonlinear differential equations

  • Higher order linear ODEs with constant coefficients

  • Partial differential equations and separation of variables methods

Section B: Flight Mechanics

Core Topics

Unit 1: Basics

  • Atmosphere −

    • Properties

    • Standard atmosphere

  • Classification of aircraft

  • Airplane (fixed wing aircraft) configuration and various parts

Unit 2: Airplane performance

  • Pressure altitude −

    • Equivalent

    • Calibrated

    • Indicated Air Speeds

  • Primary flight instruments −

    • Altimeter

    • ASI

    • VSI

    • Turn-bank indicator

    • Drag polar

    • Takeoff and landing

    • Steady climb & descent

    • Absolute and service ceiling

    • Cruise

    • cruise climb

    • Endurance or loiter

    • Load factor

    • Turning flight

    • V-n diagram

  • Winds −

    • Head

    • Tail

    • Cross winds

Unit 3: Static stability

  • Angle of attack, sideslip

  • Roll, pitch & yaw controls

  • Longitudinal stick fixed & free stability

  • Horizontal tail position and size

  • Directional stability

  • Vertical tail position and size

  • Dihedral stability

  • Wing dihedral

  • Sweep & position

  • Hinge moments, stick forces

Section C: Space Dynamics

Core Topics

  • Central force motion

  • Determination of trajectory

  • Orbital period in simple cases

Section D: Aerodynamics

Core Topics

Unit 1: Basic Fluid Mechanics

  • Conservation laws −

    • Mass

    • Momentum (Integral and differential form)

  • Potential flow theory −

    • Sources

    • Sinks

    • Doublets

    • Line vortex and their superposition

  • Viscosity −

    • Reynold's number

Unit 2: Airfoils and wings

  • Airfoil nomenclature

  • Aerodynamic coefficients −

  • Lift

  • Drag

  • Moment

  • Kutta-Joukoswki theorem −

    • Thin airfoil theory

    • Kutta condition

    • Starting vortex

  • Finite wing theory

    • Induced drag

  • Prandtl lifting line theory

  • Critical and drag divergence Mach number

Unit 3: Compressible Flows

  • Basic concepts of compressibility

    • Conservation equations

  • One dimensional compressible flows

    • Fanno flow

    • Rayleigh flow

  • Isentropic flows

    • Normal and oblique shocks

    • Prandtl-Meyer flow

  • Flow through nozzles and diffusers

Section E: Structures

Core Topics

  • Strength of Materials −

    • States of stress and strain

    • Stress and strain transformation

    • 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

    • Analysis of statically determinate and indeterminate trusses and beams

    • Elastic flexural buckling of columns

Unit 2: Flight vehicle structures

  • Characteristics of aircraft structures and materials

  • Torsion, bending and flexural shear of thin-walled sections

  • Loads on aircraft

Unit 3: Structural Dynamics

  • Free and forced vibrations of undamped and damped SDOF systems

  • Free vibrations of undamped 2-DOF systems

Section F: Propulsion

Core Topics

Unit 1: Basics

  • Thermodynamics

  • Boundary layers and heat transfer and combustion thermochemistry

Unit 2: Thermodynamics of aircraft engines

  • Thrust

  • Efficiency and engine performance of turbojet

  • Turboprop

  • Turbo shaft

  • Turbofan and ramjet engines

  • Thrust augmentation of turbojets and turbofan engines

  • Aerothermodynamics of non-rotating propulsion components such as −

    • Intakes

    • Combustor

    • Nozzle

Unit 3: Axial compressors

  • Angular momentum

  • Work and compression

  • Characteristic performance of a single axial compressor stage

  • Efficiency of the compressor

  • Degree of reaction

Unit 4: Axial turbines

  • Axial turbine stage efficiency

Unit 5: Centrifugal compressor

  • Centrifugal compressor stage dynamics

    • Inducer

    • Impeller

    • Diffuser

Unit 6: Rocket propulsion

  • Thrust equation and specific impulse

  • Vehicle acceleration

  • Drag

  • Gravity losses

  • Multi-staging of rockets

  • Classification of chemical rockets

  • Performance of solid and liquid propellant rockets

GATE Agricultural Engineering Syllabus

Subject Code: AG

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
1 Linear Algebra
2 Calculus
3 Vector Calculus
4 Differential Equations
5 Probability and Statistics
6 Numerical Methods
Section B Farm Machinery
1 Machine Design
2 Farm Machinery
Section C Farm Power
1 Sources of Power
2 Farm Power
3 Tractors and Powertillers
Section D Soil and Water Conservation Engineering
1 Fluid Mechanics
2 Soil Mechanics
3 Hydrology
4 Surveying and Leveling
5 Soil and Water Erosion
6 Watershed Management
Section E Irrigation and Drainage Engineering
1 Soil-Water-Plant Relationship
2 Irrigation Water Conveyance and Application Methods
3 Agricultural Drainage
4 Groundwater Hydrology
5 Wells and Pumps
Section F Agricultural Processing Engineering
1 Drying
2 Size Reduction and Conveying
3 Processing and By-product Utilization
4 Storage System
Section G Dairy and Food Engineering
1 Heat and Mass Transfer
2 Preservation of Food

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrices and determinants

  • Systems of linear equations

  • Eigen values and Eigen vectors

Unit 2: Calculus

  • Limit, continuity and differentiability

  • Partial derivatives

  • Maxima and minima

  • Sequences and series

  • Tests for convergence

    • Fourier series

    • Taylor series

Unit 3: Vector Calculus

  • Gradient; divergence and curl

  • Line, surface and volume integrals

  • Stokes, Gauss and Green’s theorems

Unit 4: Differential Equations

  • Linear and non-linear first order Ordinary Differential Equations (ODE)

  • Higher order linear ODEs with constant coefficients

  • Cauchy’s and Euler’s equations

  • Laplace transforms

  • Partial Differential Equations - Laplace, heat and wave equations

Unit 5: Probability and Statistics

  • Mean, median, mode and standard deviation

  • Random Variables

  • Poisson, normal and binomial distributions

  • Correlation and regression analysis

  • Tests of significance

  • Analysis of variance (ANOVA)

Unit 6: Numerical Methods

  • Solutions of linear and non-linear algebraic equations

  • Numerical integration - trapezoidal and Simpson’s rule

  • Numerical solutions of ODE

Section B: Farm Machinery

Unit 1: Machine Design

  • Design and selection of machine elements −

    • Gears

    • Pulleys

    • Chains and sprockets

    • Belts

  • Overload safety devices used in farm machinery

  • Measurement of force, torque, speed, displacement and acceleration on machine elements

Unit 2: 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

    • Threshing

    • Transport

  • Testing of agricultural machinery and equipment

  • Calculation of performance parameters −

    • Field capacity

    • Efficiency

    • Application rate and losses

  • Cost analysis of implements and tractors

Section C: Farm Power

Unit 1: Sources of Power

  • Sources of power on the farm −

    • Human

    • Animal

    • Mechanical

    • Electrical

    • Wind

    • Solar

    • Biomass

  • Bio-fuels

Unit 2: 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

    • 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

Unit 3: Tractors and Powertillers

  • Type, selection, maintenance and repair of tractors and powertillers

  • 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

  • Mechanical steering and hydraulic control systems used in tractors

  • Tractor tests and performance

  • Human engineering and safety in design of tractor and agricultural implements

Section D: Soil and Water Conservation Engineering

Unit 1: Fluid Mechanics

  • Ideal and real fluids −

    • properties of fluids

  • Hydrostatic pressure and its measurement

  • Hydrostatic forces on plane and curved surface

  • Continuity equation

  • Bernoulli’s theorem

  • Laminar and turbulent flow in pipes, darcy- weisbach and hazen-williams equations, moody’s diagram

  • Flow through orifices and notches

  • Flow in open channels

Unit 2: 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

Unit 3: Hydrology

  • Hydrological cycle and components

  • Meteorological parameters, their measurement and analysis of precipitation data

  • Runoff estimation

  • Hydrograph analysis −

    • Unit hydrograph theory and application

  • Stream flow measurement

  • Flood routing −

    • Hydrological reservoir

    • Channel routing

Unit 4: 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

  • Computation of areas and volume

Unit 5: Soil and Water Erosion

  • Mechanics of soil erosion −

    • Soil erosion types

    • Wind and water erosion

    • 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

Unit 6: Watershed Management

  • Watershed characterization

  • Land use capability classification

  • Rainwater harvesting structures

  • Check dams and farm ponds

Section E: Irrigation and Drainage Engineering

Unit 1: Soil-Water-Plant Relationship

  • Water requirement of crops

  • Consumptive use and evapotranspiration

  • Measurement of infiltration −

    • Soil moisture

    • Irrigation water infiltration

Unit 2: 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

Unit 3: Agricultural Drainage

  • Drainage coefficient −

    • Planning

    • Design and layout of surface

    • Sub-surface drainage systems

  • Leaching requirement and salinity control

  • Irrigation and drainage water quality and reuse

Unit 4: Groundwater Hydrology

  • Groundwater occurrence

  • Darcy’s Law, steady flow in confined and unconfined aquifers, evaluation of aquifer properties

  • Groundwater recharge

Unit 5: Wells and Pumps

  • Types of wells, steady flow through wells

  • Classification of pumps

  • Pump characteristics

  • Pump selection and installation

Section F: Agricultural Processing Engineering

Unit 1: Drying

  • Psychrometry – properties of air-vapors mixture

  • Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers

  • Hydrothermal treatment

  • Drying and milling of cereals, pulses and oilseeds

Unit 2: Size Reduction and Conveying

  • Mechanics and energy requirement in size reduction of granular solids

  • 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 grain cleaners

  • Centrifugal separation of solids, liquids and gases

Unit 3: Processing and By-product Utilization

  • Processing of −

    • Seeds

    • Spices

    • Fruits

    • Vegetables

  • By-product utilization from processing industries

Unit 4: Storage Systems

  • Controlled and modified atmosphere storage

  • Perishable food storage, godowns, bins and grain silos

Section G: Dairy and Food Engineering

Unit 1: 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

Unit 2: 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

GATE Architecture and Planning Syllabus

Subject Code: AR

Course Structure

Sections/Units Topics
Section A Architecture and Design
Section B Building Materials, Construction and Management
Section C Building and Structures
Section D Environmental Planning and Design
Section E Urban Design
Section F Urban Planning and Housing
Section G Planning Techniques and Management
Section H Services, Infrastructure and Transportation

Course Syllabus

Section A: Architecture and Design

  • Visual composition in 2D and 3D

  • Principles of Art and Architecture

  • Organization of space

  • Architectural Graphics

  • Computer Graphics – concepts of CAD, BIM, 3D modeling and Architectural rendition

  • Programming languages and automation.

  • Anthropometrics

  • Planning and design considerations for different building types;

  • Site planning

  • Circulation- horizontal and vertical

  • Barrier free design

  • Space Standards

  • Building Codes

  • National Building Code

  • Elements, construction, architectural styles and examples of different periods of −

    • Indian and Western History of Architecture

    • Oriental, Vernacular and Traditional architecture

    • Architectural developments since Industrial Revolution

    • Influence of modern art on architecture

    • Art nouveau, Eclecticism, International styles, Post Modernism, Deconstruction in architecture

    • Recent trends in Contemporary Architecture

    • Works of renowned national and international architects

Section B: Building Materials, Construction and Management

  • Behavioral characteristics and applications of different building materials viz. mud, timber, bamboo, brick, concrete, steel, glass, FRP, AAC, different polymers, composites

  • Building construction techniques, methods and details

  • Building systems and prefabrication of building elements

  • Principles of Modular Coordination, estimation, specification, valuation, professional practice

  • Construction planning and equipment

  • Project management techniques e.g. PERT, CPM etc.

Section C: Building and Structures

  • Principles of strength of materials

  • Design of structural elements in wood, steel and RCC

  • Elastic and Limit State design

  • Structural systems in RCC and Steel

  • Form and Structure

  • Principles of Pre-stressing

  • High Rise and Long Span structures, gravity and lateral load resisting systems

  • Principles and design of disaster resistant structures

Section D: Environmental Planning and Design

  • Ecosystem - natural and man-made ecosystem

  • Ecological principles

  • Concepts of Environmental Impact Analysis

  • Environmental considerations in planning and design

  • Thermal comfort, ventilation and air movement

  • Principles of lighting and illumination

  • Climate responsive design

  • Solar architecture

  • Principles of architectural acoustics

  • Green Building- Concepts and Rating

  • ECBC

  • Building Performance Simulation and Evaluation

  • Environmental pollution - types, causes, controls and abatement strategies

Section E: Urban Design

  • Concepts and theories of urban design

  • Public Perception

  • Townscape

  • Public Realm

  • Urban design interventions for sustainable development and transportation

  • Historical and modern examples of urban design

  • Public spaces, character, spatial qualities and Sense of Place

  • Elements of urban built environment – urban form, spaces, structure, pattern, fabric, texture, grain etc

  • Principles, tools and techniques of urban design

  • Urban renewal and conservation

  • Site planning

  • Landscape design

  • Development controls – FAR, densities and building bye laws

Section F: Urban Planning and Housing

Planning process

  • Types of plans −

    • Master Plan

    • City Development Plan

    • Structure

  • Plan −

    • Zonal Plan

    • Action Area Plan

    • Town Planning Scheme

    • Regional Plan

  • Salient concepts −

    • Theories and principles of urban planning

  • Sustainable urban development

  • Emerging concepts of cities −

    • Eco-City

    • Smart City

    • Transit Oriented

  • Development (TOD), SEZ, SRZ etc.


  • Concepts

  • Principles and examples of neighbourhood

  • Housing typologies

  • Slums

  • Affordable Housing

  • Housing for special areas and needs

  • Residential

  • Densities

  • Standards for housing and community facilities

  • National Housing Policies, Programs and Schemes

Section G: Planning Techniques and Management

Planning Techniques

  • Tools and techniques of Surveys −

    • Physical

    • Topographical

    • Land use

    • Socioeconomic Surveys

  • Methods of non-spatial and spatial data analysis

  • Graphic presentation of spatial data

  • Application of G.I.S. and Remote Sensing techniques in urban and regional planning

  • Decision support system and Land Information System


  • Urban Economics

  • Law of demand and supply of land and its use in planning

  • Social, Economic and environmental cost benefit analysis

  • Techniques of financial appraisal

  • Management of Infrastructure Projects

  • Development guidelines such as URDPFI

  • Planning Legislation and implementation – Land Acquisition Act, PPP etc.

  • Local self-governance

Section H: Services, Infrastructure and Transportation

Building Services

  • Water supply

  • Sewerage and drainage systems

  • Sanitary fittings and fixtures

  • Plumbing systems

  • Principles of internal and external drainage system

  • Principles of electrification of buildings

  • Intelligent Buildings

  • Elevators and Escalators - standards and uses

  • Air-Conditioning systems

  • Firefighting Systems

  • Building Safety and Security systems

Urban Infrastructure

  • Transportation

  • Water Supply

  • Sewerage

  • Drainage

  • Solid

  • Waste Management

  • Electricity

  • Communications

Process and Principles of Transportation Planning and Traffic Engineering

  • Road capacity

  • Traffic survey methods

  • Traffic flow characteristics

  • Traffic analyses and design considerations

  • Travel demand forecasting

  • Land-use – transportation - urban form inter-relationships Design of roads, intersections, grade separators and parking areas

  • Hierarchy of roads and level of service

  • Traffic and transport management and control in urban areas

  • Mass transportation planning

  • Paratransit and other modes of transportation

  • Pedestrian and slow moving traffic planning

  • Intelligent Transportation Systems

Principles of water supply and sanitation 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

    • Disposal

  • Recycling and Reuse of solid waste

  • Power Supply and Communication Systems, network, design and guidelines

GATE Biotechnology Syllabus

Subject Code: BT

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Section B General Biotechnology
Unit 1 Biochemistry
Unit 2 Microbiology
Unit 3 Cell Biology
Unit 4 Molecular Biology and Genetics
Unit 5 Analytical Techniques
Unit 6 Immunology
Unit 7 Bioinformatics
Section C Recombinant DNA Technology
Section D Plant and Animal Biotechnology
Section E Bioprocess Engineering and Process Biotechnology

Course Syllabus

Section A: 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

  • Differential Equations −

    • Linear and nonlinear first order ODEs

    • Higher order ODEs with constant coefficients

    • Cauchy’s and Euler’s equations

    • Laplace transforms

    • PDE-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 −

    • Solution of linear and nonlinear algebraic equations

    • Integration of trapezoidal and Simpson’s rule

    • Single and multistep methods for differential equations

Section B: General Biotechnology

Unit 1: Biochemistry

  • Biomolecules-structure and functions −

    • Biological membranes

    • Structure

    • Action potential

    • Transport processes

  • Enzymes −

    • Classification

    • Kinetics and mechanism of action

  • Basic concepts and designs of metabolism −

    • Carbohydrates

    • Lipids

    • Amino acids

    • Nucleic acids

    • Photosynthesis

    • Respiration

    • Electron transport chain

  • Bioenergetics

Unit 2: Microbiology

  • Viruses- structure and classification

  • Microbial classification and diversity (bacterial, algal and fungal)

  • Methods in microbiology

  • Microbial growth and nutrition

  • Aerobic and anaerobic respiration

  • Nitrogen fixation

  • Microbial diseases and host-pathogen interaction

Unit 3: Cell Biology

  • Prokaryotic and eukaryotic cell structure

  • Cell cycle and cell growth control

  • Cell-Cell communication

  • Cell signaling and signal transduction

Unit 4: Molecular Biology and Genetics

  • Molecular structure of genes and chromosomes

  • Mutations and mutagenesis

  • Nucleic acid replication, transcription, translation and their regulatory mechanisms in prokaryotes and eukaryotes

  • Mendelian inheritance

  • Gene interaction

  • Complementation

  • Linkage, recombination and chromosome mapping

  • Extra chromosomal inheritance

  • Microbial genetics (plasmids, transformation, transduction, conjugation)

  • Horizontal gene transfers and Transposable elements

  • RNA interference

  • DNA damage and repair

  • Chromosomal variation

  • Molecular basis of genetic diseases

Unit 5: Analytical Techniques

  • Principles of microscopy-light, electron, fluorescent and confocal

  • Centrifugation- high speed and ultra

  • Principles of spectroscopy −

    • UV

    • Visible

    • CD

    • IR

    • FTIR

    • Raman

    • MS

    • NMR

  • Principles of chromatography −

    • Ion exchange

    • Gel filtration

    • Hydrophobic interaction

    • Affinity

    • GC

    • HPLC

    • FPLC

  • Electrophoresis

  • Microarray

Unit 6: Immunology

  • History of Immunology

  • Innate, humoral and cell mediated immunity

  • Antigen

  • Antibody structure and function

  • Molecular basis of antibody diversity

  • Synthesis of antibody and secretion

  • Antigen-antibody reaction

  • Complement

  • Primary and secondary lymphoid organ

  • B and T cells and macrophages

  • Major histocompatibility complex (MHC)

  • Antigen processing and presentation

  • Polyclonal and monoclonal antibody

  • Regulation of immune response

  • Immune tolerance

  • Hypersensitivity

  • Autoimmunity

  • Graft versus host reaction

Unit 7: Bioinformatics

  • Major bioinformatics resources and search tools

  • Sequence and structure databases

  • Sequence analysis −

    • Biomolecular sequence file formats

    • Scoring matrices

    • Sequence alignment

    • Phylogeny

  • Data mining and analytical tools for genomic and proteomic studies

  • Molecular dynamics and simulations (basic concepts including force fields, protein-protein, protein-nucleic acid, protein-ligand interaction)

Section C: Recombinant DNA Technology

  • Restriction and modification enzymes

  • Vectors; plasmid, bacteriophage and other viral vectors, cosmids, Ti plasmid, yeast artificial chromosome

  • Mammalian and plant expression vectors

  • cDNA and genomic DNA library

  • Gene isolation, cloning and expression

  • Transposons and gene targeting

  • DNA labeling

  • DNA sequencing

  • Polymerase chain reactions

  • DNA fingerprinting

  • Southern and northern blotting

  • In-situ hybridization


  • Site-directed mutagenesis

  • Gene transfer technologies

  • Gene therapy

Section D: Plant and Animal Biotechnology

  • Totipotency

  • Regeneration of plants

  • Plant growth regulators and elicitors

  • Tissue culture and Cell suspension culture system −

    • Methodology

    • Kinetics of growth

    • Nutrient optimization

  • Production of secondary metabolites by plant suspension cultures

  • Hairy root culture

  • Transgenic plants

  • Plant products of industrial importance

Animal cell 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

Section E: Bioprocess Engineering and Process Biotechnology

  • Chemical engineering principles applied to biological system −

    • Principle of reactor design

    • Ideal and non-ideal multiphase bioreactors

    • Mass and heat transfer

  • Rheology of fermentation fluids, Aeration and agitation

  • Media formulation and optimization

  • Kinetics of microbial growth, substrate utilization and product formation

  • Sterilization of air and media

  • Batch, fed-batch and continuous processes

  • Various types of microbial and enzyme reactors

  • Instrumentation control and optimization

  • Unit operations in solid-liquid separation and liquid-liquid extraction

  • Process scale-up, economics and feasibility analysis

Engineering principle of bioprocessing

  • Upstream production and downstream

  • Bioprocess design and development from lab to industrial scale

  • Microbial, animal and plant cell culture platforms

  • Production of biomass and primary/secondary metabolites

  • Biofuels, Bioplastics, industrial enzymes, antibiotics

  • Large scale production and purification of recombinant proteins

  • Industrial application of chromatographic and membrane based bio-separation methods

  • Immobilization of biocatalysts (enzymes and cells) for bioconversion processes

  • Bioremediation-Aerobic and anaerobic processes for stabilization of solid/liquid wastes

GATE Chemical Engineering Syllabus

Subject Code: CH

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential equations
Unit 4 Complex variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Process Calculations and Thermodynamics
Section C Fluid Mechanics and Mechanical Operations
Section D Heat Transfer
Section E Mass Transfer
Section F Chemical Reaction Engineering
Section G Instrumentation and Process Control
Section H Plant Design and Economics
Section I Chemical Technology

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrix algebra

  • Systems of linear equations

  • Eigen values

  • Eigenvectors

Unit 2: 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

Unit 3: 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

Unit 4: Complex variables

  • Complex number

  • Polar form of complex number

  • Triangle inequality

Unit 5: 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

Unit 6: 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 B: Process Calculations and Thermodynamics

  • Steady and unsteady state mass and energy balances including multiphase −

    • Multicomponent

    • Reacting and non-reacting systems

  • Use of tie components −

    • Recycle

    • Bypass

    • 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

    • Activity coefficients

  • Phase equilibria −

    • Predicting VLE of systems

    • Chemical reaction equilibrium

Section C: Fluid Mechanics and Mechanical Operations

  • Fluid statics

  • Newtonian and non-Newtonian fluids

  • Shell-balances including differential form of Bernoulli equation and energy balance

  • Macroscopic friction factors

  • Dimensional analysis and similitude

  • Flow through pipeline systems

  • 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

  • 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 D: Heat Transfer

  • Steady and unsteady heat conduction

  • Convection and radiation

  • Thermal boundary layer and heat transfer coefficients

  • Boiling, condensation and evaporation

  • Types of heat exchangers and evaporators and their process calculations

  • Design of double pipe, shell and tube heat exchangers

  • Single and multiple effect evaporators

Section E: Mass Transfer

  • Fick’s laws

  • Molecular diffusion in fluids

  • Mass transfer coefficients

  • Film

  • Penetration

  • 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

    • Adsorption

Section F: Chemical Reaction Engineering

  • Theories of reaction rates

  • Kinetics of homogeneous reactions

  • Interpretation of kinetic data

  • Single and multiple reactions in ideal reactors

  • Non-ideal reactors

  • Residence time distribution

  • Single parameter model

  • Non-isothermal reactors

  • Kinetics of heterogeneous catalytic reactions

  • Diffusion effects in catalysis

Section G: Instrumentation and Process Control

  • Measurement of process variables

  • Sensors

  • Transducers and their dynamics

  • 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

  • Analysis of closed loop systems including stability

  • Frequency response

  • Controller tuning

  • Cascade and feed forward control

Section H: 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 compressors

  • Heat exchangers

  • Multistage contactors

Section I: 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 fibers)

GATE Chemistry Syllabus

Sections/Units Topics
Section A Physical Chemistry
Unit 1 Structure
Unit 2 Equilibrium
Unit 3 Kinetics
Unit 4 Surfaces and Interfaces
Section B Inorganic Chemistry
Unit 1 Main Group Elements
Unit 2 Transition Elements
Unit 3 Lanthanides and Actinides
Unit 4 Organometallics
Unit 5 Radioactivity
Unit 6 Bioinorganic Chemistry
Unit 7 Solids
Unit 8 Instrumental Methods of Analysis
Section C Organic Chemistry
Unit 1 Stereochemistry
Unit 2 Reaction Mechanisms
Unit 3 Organic Synthesis
Unit 4 Pericyclic Reactions and Photochemistry
Unit 5 Heterocyclic Compounds
Unit 6 Biomolecules
Unit 7 Spectroscopy

Course Syllabus

Section A: Physical Chemistry

Unit 1: Structure

  • Postulates of quantum mechanics

  • Time dependent and time independent Schrödinger equations

  • Born interpretation

  • Particle in a box

  • Harmonic oscillator

  • Rigid rotor

  • Hydrogen atom: atomic orbitals

  • Multi-electron atoms: orbital approximation

  • Variation and first order perturbation techniques

  • Chemical bonding: Valence bond theory and LCAO-MO theory

  • Hybrid orbitals

  • Applications of LCAO-MOT to H2+, H2 and other homonuclear diatomic molecules, heteronuclear diatomic molecules like HF, CO, NO, and to simple delocalized π – electron systems

  • Huckel approximation and its application to annular π – electron systems

  • Symmetry elements and operations

  • Point groups and character tables

  • Origin of selection rules for rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules

  • Einstein coefficients

  • Relationship of transition moment integral with molar extinction coefficient and oscillator strength

  • Basic principles of nuclear magnetic resonance: nuclear g factor, chemical shift, nuclear coupling

Unit 2: Equilibrium

  • Laws of thermodynamics

  • Standard states

  • Thermochemistry

  • Thermodynamic functions and their relationships −

    • Gibbs-Helmholtz and Maxwell relations

    • Van’t Hoff equation

  • Criteria of spontaneity and equilibrium

  • Absolute entropy

  • Partial molar quantities

  • Thermodynamics of mixing

  • Chemical potential

  • Fugacity, activity and activity coefficients

  • Chemical equilibria

  • Dependence of equilibrium constant on temperature and pressure

  • Non-ideal solutions

  • Ionic mobility and conductivity

  • Debye-Huckel limiting law

  • Debye-Huckel-Onsager equation

  • Standard electrode potentials and electrochemical cells

  • Potentiometric and conductometric titrations

  • Phase rule

  • Clausius Clapeyron equation

  • Phase diagram of one component systems: CO2, H2O, S

  • Two component systems −

    • Liquid-vapour system

    • Liquid-liquid system

    • Solid-liquid systems

  • Fractional distillation

  • Azeotropes and eutectics

  • Statistical thermodynamics −

    • Microcanonical and canonical ensembles

    • Boltzmann distribution

    • Partition functions

    • Thermodynamic properties

Unit 3: Kinetics

  • Transition state theory −

    • Eyring equation

    • Thermodynamic aspects

  • Potential energy surfaces and classical trajectories

  • Elementary, parallel, opposing and consecutive reactions

  • Steady state approximation

  • Mechanisms of complex reactions

  • Unimolecular reactions

  • Kinetics of polymerization and enzyme catalysis

  • Fast reaction kinetics: relaxation and flow methods

  • Kinetics of photochemical and photophysical processes

Unit 4: Surfaces and Interfaces

  • Physisorption and chemisorption

  • Langmuir, Freundlich and BET isotherms

  • Surface catalysis: Langmuir-Hinshelwood mechanism

  • Surface tension, viscosity

  • Self-assembly

  • Physical chemistry of colloids, micelles and macromolecules

Section B: Inorganic Chemistry

Unit 1: Main Group Elements

  • Hydrides, halides, oxides, oxoacids, nitrides, sulfides – shapes and reactivity

  • Structure and bonding of boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes

  • Allotropes of carbon

  • Chemistry of noble gases, pseudohalogens, and interhalogen compounds

  • Acid-base concepts

Unit 2: 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 diagrams

    • Charge-transfer spectra

  • Magnetic properties of transition metal complexes

  • Reaction mechanisms −

    • Kinetic and thermodynamic stability

    • Substitution and redox reactions

Unit 3: Lanthanides and Actinides

  • Recovery

  • Periodic properties

  • Spectra properties

  • Magnetic properties

Unit 4: Organometallics

  • 18-Electron rule

    • metal-alkyl

    • metal-carbonyl

    • metal-olefin and metalcarbene complexes

    • metallocenes

  • 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

Unit 5: Radioactivity

  • Decay processes

  • Half-life of radioactive elements

  • Fission and fusion processes

Unit 6: Bioinorganic Chemistry

  • Ion (Na+ and K+) transport

  • Oxygen binding

  • Transport and utilization

  • Electron transfer reactions

  • Nitrogen fixation

  • Metalloenzymes containing −

    • Magnesium

    • Molybdenum

    • Iron

    • Cobalt

    • Copper

    • Zinc

Unit 7: 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

  • Semiconductors

Unit 8: Instrumental Methods of Analysis

  • UV-visible spectrophotometry

  • NMR and ESR spectroscopy

  • Mass spectrometry

  • Chromatography including GC and HPLC

  • Electroanalytical methods −

    • Polarography

    • Cyclic voltammetry

    • Ion-selective electrodes

  • Thermoanalytical methods

Section C: Organic Chemistry

Unit 1: Stereochemistry

  • Chirality of organic molecules with or without chiral centres and determination of their absolute configurations

  • Relative stereochemistry in compounds having more than one stereogenic centre

  • Homotopic, enantiotopic and diastereotopic atoms, groups and faces

  • Stereoselective and stereospecific synthesis

  • Conformational analysis of acyclic and cyclic compounds

  • Geometrical isomerism

  • Configurational and conformational effects, and neighbouring group participation on reactivity and selectivity/specificity

Unit 2: Reaction Mechanisms

  • Basic mechanistic concepts −

    • Kinetic versus thermodynamic control

    • Hammond’s postulate and Curtin-Hammett principle

  • Methods of determining reaction mechanisms through identification of products, intermediates and isotopic labeling

  • Nucleophilic and electrophilic substitution reactions (both aromatic and aliphatic)

  • Addition reactions to carbon-carbon and carbon-heteroatom (N, O) multiple bonds

  • Elimination reactions

  • Reactive intermediates −

    • Carbocations

    • Carbanions

    • Carbenes

    • Nitrenes

    • Arynes

    • Free radicals

  • Molecular rearrangements involving electron deficient atoms

Unit 3: 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 and Si based reagents in organic synthesis

  • Carbon-carbon bond formation through coupling reactions - Heck, Suzuki, Stille and Sonogoshira

  • Concepts of multistep synthesis −

    • Retrosynthetic analysis

    • Strategic disconnections

    • Synthons and synthetic equivalents

  • 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), desymmetrization and use of chiral auxiliaries

  • Carbon-carbon bond forming reactions through enolates (including boron enolates), enamines and silyl enol ethers.

  • Michael addition reaction

  • Stereoselective addition to C = O groups (Cram and Felkin-Anh models)

Unit 4: Pericyclic Reactions and Photochemistry

  • Electrocyclic, cycloaddition and sigmatropic reactions

  • Orbital correlations - FMO and PMO treatments

  • Photochemistry of alkenes, arenes and carbonyl compounds

  • Photooxidation and photoreduction

  • Di-π-methane rearrangement, Barton reaction

Unit 5: Heterocyclic Compounds

  • Structure

  • Preparation

  • Properties and reactions of furan

  • Pyrrole

  • Thiophene

  • Pyridine

  • Indole

  • Quinolone

  • Isoquinoline

Unit 6: Biomolecules

  • Structure

  • Properties and reactions of mono- and di-saccharides

  • Physicochemical properties of amino acids

  • Chemical synthesis of peptides

  • Structural features of proteins

  • Nucleic acids

  • Steroids

  • Terpenoids

  • Carotenoids

  • Alkaloids

Unit 7: Spectroscopy

  • Applications of UV-visible, IR, NMR and Mass spectrometry in the structural determination of organic molecules

GATE Civil Engineering Syllabus

Subject Code: CE

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Ordinary Differential Equation (ODE)
Unit 4 Partial Differential Equation (PDE)
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Structural Engineering
Unit 1 Engineering Mechanics
Unit 2 Solid Mechanics
Unit 3 Structural Analysis
Unit 4 Construction Materials and Management
Unit 5 Concrete Structures
Unit 6 Steel Structures
Section C Geotechnical Engineering
Unit 1 Soil Mechanics
Unit 2 Foundation Engineering
Section D Water Resources Engineering
Unit 1 Fluid Mechanics
Unit 2 Hydraulics
Unit 3 Hydrology
Unit 4 Irrigation
Section E Environmental Engineering
Unit 1 Water and Waste Water
Unit 2 Air Pollution
Unit 3 Municipal Solid Wastes
Unit 4 Noise Pollution
Section F Transportation Engineering
Unit 1 Transportation Infrastructure
Unit 2 Highway Pavements
Unit 3 Traffic Engineering
Section G Geomatics Engineering

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrix algebra

  • Systems of linear equations

  • Eigen values and Eigen vectors

Unit 2: Calculus

  • Functions of single variable

  • Limit, continuity and differentiability

  • Mean value theorems

  • Local maxima and minima

  • Taylor and Maclaurin 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

  • Stokes

  • Gauss and Green’s theorems

Unit 3: Ordinary Differential Equation (ODE)

  • First order (linear and non-linear) equations

  • higher order linear equations with constant coefficients

  • Euler-Cauchy equations

  • Laplace transform and its application in solving linear ODEs

  • Initial and boundary value problems

Unit 4: 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.

Unit 5: Probability and Statistics

  • Definitions of probability and sampling theorems

  • Conditional probability

  • Discrete Random variables

  • Poisson and Binomial distributions

  • Continuous random variables

  • Normal and exponential distributions

  • Descriptive statistics - Mean, median, mode and standard deviation

  • Hypothesis testing

Unit 6: Numerical Methods

  • Accuracy and precision; error analysis

  • Numerical solutions of linear and non-linear algebraic equations

  • Least square approximation

  • 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 B: Structural Engineering

Unit 1: Engineering Mechanics

  • System of forces, free-body diagrams, equilibrium equations

  • Internal forces in structures

  • Friction and its applications

  • Kinematics of point mass and rigid body

  • Centre of mass

  • Euler’s equations of motion

  • Impulse-momentum

  • Energy methods

  • Principles of virtual work

Unit 2: Solid Mechanics

  • Bending moment and shear force in statically determinate beams

  • Simple stress and strain relationships

  • Theories of failures

  • Simple bending theory, flexural and shear stresses, shear centre

  • Uniform torsion, buckling of column, combined and direct bending stresses

Unit 3: 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

Unit 4: Construction Materials and Management

  • Construction Materials −

    • Structural steel – composition

    • Material properties and behavior

  • Concrete - constituents −

    • Mix design

    • Short-term and long-term properties

    • Bricks and mortar

    • Timber

    • Bitumen

  • Construction Management −

    • Types of construction projects

    • Tendering and construction contracts

    • Rate analysis and standard specifications

    • Cost estimation

    • Project planning and network analysis - PERT and CPM

Unit 5: Concrete Structures

  • Working stress, Limit state and Ultimate load design concepts

  • Design of beams, slabs, columns

  • Bond and development length

  • Prestressed concrete

  • Analysis of beam sections at transfer and service loads

Unit 6: Steel Structures

  • 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

  • Plastic analysis of beams and frames

Section C: Geotechnical Engineering

Unit 1: Soil Mechanics

  • Origin of soils, soil structure and fabric

  • Three-phase system and phase relationships, index properties

  • Unified and Indian standard soil classification system

  • Permeability - one dimensional flow, Darcy’s law

  • Seepage through soils - two-dimensional flow, flow nets, uplift pressure, piping

  • Principle of effective stress, capillarity, seepage force and quicksand condition

  • Compaction in laboratory and field conditions

  • One dimensional consolidation, time rate of consolidation

  • Mohr’s circle, stress paths, effective and total shear strength parameters, characteristics of clays and sand

Unit 2: Foundation Engineering

  • Sub-surface investigations −

    • Scope

    • Drilling bore holes

    • Sampling

    • Plate load test

    • Standard penetration

    • Cone penetration tests

  • Earth pressure theories - Rankine and Coulomb

  • Stability of slopes −

    • Finite and infinite slopes

    • Method of slices

    • Bishop’s method

  • Stress distribution in soils −

    • Boussinesq’s and Westergaard’s theories

    • 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 −

    • Types of piles

    • Dynamic and static formulae

    • Load capacity of piles in sands and clays

    • Pile load test

    • Negative skin friction

Section D: Water Resources Engineering

Unit 1: Fluid Mechanics

  • Properties of fluids, fluid statics

  • Continuity, momentum, energy and corresponding equations

  • Potential flow, applications of momentum and energy equations

  • Laminar and turbulent flow

  • Flow in pipes, pipe networks

  • Concept of boundary layer and its growth

Unit 2: Hydraulics

  • Forces on immersed bodies

  • Flow measurement in channels and pipes

  • Dimensional analysis and hydraulic similitude

  • Kinematics of flow, velocity triangles

  • Basics of hydraulic machines, specific speed of pumps and turbines

  • Channel Hydraulics −

    • Energy-depth relationships

    • Specific energy

    • Critical flow

    • Slope profile

    • Hydraulic jump

    • Uniform flow and gradually varied flow

Unit 3: Hydrology

  • Hydrologic cycle

  • Precipitation

  • Evaporation

  • Evapo-transpiration

  • Watershed

  • Infiltration

  • Unit hydrographs

  • Hydrograph analysis

  • Flood estimation and routing

  • Reservoir capacity

  • Reservoir and channel routing

  • Surface run-off models

  • Ground water hydrology - steady state well hydraulics and aquifers

  • Application of darcy’s law

Unit 4: Irrigation

  • Duty, delta, estimation of evapo-transpiration

  • Crop water requirements

  • Design of lined and unlined canals, head works, gravity dams and spillways

  • Design of weirs on permeable foundation

  • Types of irrigation systems, irrigation methods

  • Water logging and drainage

  • Canal regulatory works, cross-drainage structures, outlets and escapes

Section E: Environmental Engineering

Unit 1: Water and Waste Water

  • Quality standards, basic unit processes and operations for water treatment

  • Drinking water standards −

    • Water requirements

    • Basic unit operations and unit processes for surface water treatment

    • Distribution of water

  • Sewage and sewerage treatment, quantity and characteristics of wastewater

  • Primary, secondary and tertiary treatment of wastewater, effluent discharge standards

  • Domestic wastewater treatment −

    • Quantity of characteristics of domestic wastewater

    • Primary and secondary treatment

  • Unit operations and unit processes of domestic wastewater −

    • Sludge disposal

Unit 2: Air Pollution

Types of pollutants, their sources and impacts, air pollution meteorology, air pollution control, air quality standards and limits

Unit 3: Municipal Solid Wastes

  • Characteristics

  • Generation

  • Collection and transportation of solid wastes

  • Engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal)

Unit 4: Noise Pollution

  • Impacts of noise

  • Permissible limits of noise pollution

  • Measurement of noise

  • Control of noise pollution

Section F: Transportation Engineering

Unit 1: Transportation Infrastructure

  • Highway alignment and engineering surveys

  • Geometric design of highways −

    • Cross-sectional elements

    • Sight distances

    • Horizontal and vertical alignments

  • Geometric design of railway track

  • Airport runway length, taxiway and exit taxiway design

Unit 2: Highway Pavements

  • Highway materials - desirable properties and quality control tests

  • Design of bituminous paving mixes

  • Design factors for flexible and rigid pavements

  • Design of flexible pavement using IRC: 37-2012

  • Design of rigid pavements using IRC: 58-2011

  • Distresses in concrete pavements

Unit 3: Traffic Engineering

  • Traffic studies on flow, speed, travel time - delay and O-D study, PCU, peak hour factor, parking study, accident study and analysis, statistical analysis of traffic data

  • Microscopic and macroscopic parameters of traffic flow, fundamental relationships

  • Control devices, signal design by Webster’s method

  • Types of intersections and channelization

  • Highway capacity and level of service of rural highways and urban roads

Section G: 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:

    • Scale, flying height

    • Remote sensing - basics, platform and sensors, visual image interpretation

    • Basics of Geographical information system (GIS) and Geographical Positioning system (GPS)

GATE Computer Science and IT Syllabus

Subject Code: CS

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Discrete Mathematics
Unit 2 Linear Algebra
Unit 3 Calculus
Unit 4 Probability
Section B Digital Logic
Section C Computer Organization and Architecture
Section D Programming and Data Structures
Section E Algorithms
Section F Theory of Computation
Section G Compiler Design
Section H Operating System
Section I Databases
Section J Computer Networks

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Discrete Mathematics

  • Propositional and first order logic

    • Sets

    • Relations

    • Functions

    • Partial orders

    • Lattices

  • Groups

  • Graphs −

    • Connectivity

    • Matching

    • Coloring

  • Combinatorics −

    • Counting

    • Recurrence relations

    • Generating functions

Unit 2: Linear Algebra

  • Matrices

  • Determinants

  • System of linear equations

  • Eigenvalues and eigenvectors

  • LU decomposition

Unit 3: Calculus

  • Limits, continuity and differentiability

  • Maxima and minima

  • Mean value theorem

  • Integration

Unit 4: Probability

  • Random variables

  • Uniform, normal, exponential, poisson and binomial distributions

  • Mean, median, mode and standard deviation

  • Conditional probability

  • Bayes theorem

Section B: Digital Logic

  • Boolean algebra

  • Combinational and sequential circuits

  • Minimization. Number

  • representations and computer arithmetic (fixed and floating point)

Section C: Computer Organization and Architecture

  • Machine instructions and addressing modes

  • ALU, data-path and control unit

  • Instruction pipelining

  • Memory hierarchy −

    • Cache

    • Main memory and secondary storage

    • I/O interface (interrupt and DMA mode)

Section D: Programming and Data Structures

  • Programming in C

  • Recursion

  • Arrays, stacks, queues, linked lists, trees, binary search trees, binary heaps, graphs

Section E: Algorithms

  • Searching, sorting, hashing

  • Asymptotic worst case time and space complexity

  • Algorithm design techniques −

    • Greedy

    • Dynamic programming

    • Divide-and-conquer

  • Graph search, minimum spanning trees, shortest paths

Section F: Theory of Computation

  • Regular expressions and finite automata

  • Context-free grammars and push-down automata

  • Regular and contex-free languages, pumping lemma

  • Turing machines and undecidability

Section G: Compiler Design

  • Lexical analysis, parsing, syntax-directed translation

  • Runtime environments

  • Intermediate code generation

Section H: Operating System

  • Processes, threads, inter-process communication, concurrency and synchronization

  • Deadlock

  • CPU scheduling

  • Memory management and virtual memory

  • File systems

Section I: 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 J: Computer Networks

  • Concept of layering

  • LAN technologies (Ethernet)

  • Flow and error control techniques, switching

  • IPv4/IPv6, routers and routing algorithms (distance vector, link state)

  • TCP/UDP and sockets, congestion control

  • Application layer protocols (DNS, SMTP, POP, FTP, HTTP)

  • Basics of Wi-Fi

  • Network security −

    • Authentication

    • Basics of public key and private key cryptography

    • Digital signatures and certificates

    • Firewalls

GATE Ecology and Evolution Syllabus

Subject Code: EY

Course Structure

Sections/Units Topics
Section A Ecology
Unit 1 Population Ecology
Unit 2 Species Interactions
Unit 3 Community Ecology
Unit 4 Ecosystem Structure, Function and Services
Section B Evolution
Unit 1 Origin, Evolution and Diversification of Life
Unit 2 Types of Selection (Stabilizing, Directional etc.)
Unit 3 Life History Strategies
Unit 4 Origin of Genetic Variation
Unit 5 Molecular Evolution
Section C Mathematics and Quantitative Ecology
Unit 1 Mathematics and Statistics In Ecology
Unit 2 Statistical Hypothesis Testing
Section D Behavioural Ecology
Unit 1 Classical Ethology
Unit 2 Mating Systems

Course Syllabus

Section A: Ecology

Unit 1: Population Ecology

  • Metapopulation dynamics −

    • Growth rates

    • Density independent growth

    • Density dependent growth

    • Niche concept

Unit 2: Species Interactions

  • Plant-animal interactions −

    • Mutualism

    • Commensalism

    • Competition

    • Predation

  • Trophic interactions −

    • Functional ecology

    • Ecophysiology

    • Behavioural ecology

Unit 3: Community Ecology

  • Community assembly, organization and evolution

  • Biodiversity −

    • Species richness

    • Evenness and diversity indices

    • Endemism

    • Species-area relationships

Unit 4: Ecosystem Structure, Function and Services

  • Nutrient cycles

  • Biomes

  • Habitat ecology;

  • Primary and secondary productivity

  • Invasive species

  • Global and climate change

  • Applied ecology

Section B: Evolution

Unit 1: Origin, Evolution and Diversification of Life

  • Natural selection

  • Levels of selection

Unit 2: Types of selection (stabilizing, directional etc.)

  • Sexual selection

  • Genetic drift

  • Gene flow

  • Adaptation

  • Convergence

  • Species concepts

Unit 3: Life history strategies

  • Adaptive radiation

  • Biogeography and evolutionary ecology

Unit 4: Origin of genetic variation

  • Mendelian genetics

  • Polygenic traits, linkage and recombination

  • Epistasis, gene-environment interaction

  • Heritability

  • Population genetics

Unit 5: Molecular evolution

  • Molecular clocks

  • Systems of classification −

    • Cladistics

    • Phenetics

  • Molecular systematics

  • Gene expression and evolution

Section C: Mathematics and Quantitative Ecology

Unit 1: 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.)

Unit 2: 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 D: Behavioural Ecology

Unit 1: Classical Ethology

  • Neuroethology

  • Evolutionary ethology

  • Chemical

  • Acoustic and visual signaling

Unit 2: Mating systems

  • Sexual dimorphism

  • Mate choice

  • Parenting behaviour competition

  • Aggression

  • Foraging behavior

  • Predator–prey interactions

  • Sociobiology

  • Kin selection, altruism, costs and benefits of group-living

GATE Electrical Engineering Syllabus

Subject Code: EE

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Complex Variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Unit 7 Transform Theory
Section B Electric Circuits
Section C Electromagnetic Fields
Section D Signals and Systems
Section E Algorithms
Section F Electrical Machines
Section G Power Systems
Section H Control Systems
Section I Electrical and Electronic Measurements
Section J Analog and Digital Electronics
Section K Power Electronics

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrix Algebra

  • Systems of linear equations

  • Eigenvalues

  • Eigenvectors

Unit 2: 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

  • Green’s theorem

Unit 3: Differential equations

  • 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

Unit 4: Complex variables

  • Analytic functions

  • Cauchy’s integral theorem

  • Cauchy’s integral formula

  • Taylor series

  • Laurent series

  • Residue theorem

  • Solution integrals

Unit 5: 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

Unit 6: Numerical Methods

  • Solutions of nonlinear algebraic equations

  • Single and Multi-step methods for differential equations

Unit 7: Transform Theory

  • Fourier Transform

  • Laplace Transform

  • z-Transform

Section B: Electric Circuits

  • Network graph

  • KCL, KVL, Node and Mesh analysis

  • Transient response of dc and ac networks

  • Sinusoidal steady-state analysis

  • Resonance

  • Passive filter, Ideal current and voltage sources

  • Thevenin’s theorem

  • Norton’s theorem

  • Superposition theorem

  • Maximum power transfer theorem

  • Two-port networks

  • Three phase circuits

  • Power and power factor in ac circuits

Section C: 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 D: Signals and Systems

  • Representation of continuous and discrete-time signals

  • Shifting and scaling operations

  • Linear Time Invariant and Causal systems

  • Fourier series representation of continuous periodic signals

  • Sampling theorem

  • Applications of Fourier Transform

  • Laplace Transform and z-Transform

Section E: Electrical Machines

  • Single phase transformer −

    • Equivalent circuit

    • Phasor diagram

    • Open circuit and short circuit tests

    • Regulation and efficiency

  • Three phase transformers −

    • Connections

    • Parallel operation

  • Auto-transformer

  • Electromechanical energy conversion principles

  • DC machines −

    • Separately excited

    • Series and shunt

    • Motoring and generating mode of operation and their characteristics

    • Starting and speed control of dc motors

  • Three phase induction motors −

    • 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

    • Regulation and parallel operation of generators

    • Starting of synchronous motor

    • Characteristics

  • Types of losses and efficiency calculations of electric machines

Section F: Power Systems

  • Power generation concepts

  • ac and dc transmission concepts

  • Models and performance of transmission lines and cables

  • Series and shunt compensation

  • Electric field distribution and insulators

  • Distribution systems

  • Per-unit quantities

  • Bus admittance matrix

  • GaussSeidel 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 and distance protection

  • Circuit breakers

  • System stability concepts

  • Equal area criterion

Section G: 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

  • Routh-Hurwitz and Nyquist criteria

  • Bode plots, Root loci, Stability analysis, Lag, Lead and Lead-Lag compensators

  • P, PI and PID controllers

  • State space model

  • State transition matrix

Section H: 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 I: Analog and Digital Electronics

  • Characteristics of diodes, BJT, MOSFET

  • Simple diode circuits: clipping, clamping, rectifiers

  • Amplifiers: Biasing, Equivalent circuit and Frequency response

  • Oscillators and Feedback amplifiers

  • Operational amplifiers: Characteristics and applications

  • Simple active filters

  • VCOs and Timers

  • Combinational and Sequential logic circuits

  • Multiplexer

  • Demultiplexer

  • Schmitt trigger

  • Sample and hold circuits

  • A/D and D/A converters

  • 8085Microprocessor −

    • Architecture

    • Programming

    • Interfacing

Section H: Power Electronics

  • Characteristics of semiconductor power devices −

    • Diode

    • Thyristor

    • Triac

    • GTO

    • MOSFET

    • IGBT

  • DC to DC conversion −

    • Buck

    • Boost

    • Buck-Boost converters

  • Single and three phase configuration of uncontrolled rectifiers

  • Line commutated thyristor based converters

  • Bidirectional ac to dc voltage source converters

  • Issues of line current harmonics

  • Power factor

  • Distortion factor of ac to dc converters

  • Single phase and three phase inverters

  • Sinusoidal pulse width modulation

GATE Electronics and Communications Syllabus

Subject Code: EC

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Vector Analysis
Unit 5 Complex Analysis
Unit 6 Numerical Methods
Unit 7 Probability and Statistics
Section B Networks, Signals and Systems
Unit 1 Network Solution Methods
Unit 2 Continuous-time Signals
Section C Electronic Devices
Section D Analog Circuits
Section E Digital Circuits
Section F Control Systems
Section G Communications
Section H Electromagnetics

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Vector space, basis, linear dependence and independence

  • Matrix algebra

  • Eigen values and Eigen vectors

  • Rank, solution of linear equations −

    • Existence and uniqueness

Unit 2: 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

Unit 3: Differential Equations

  • 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

Unit 4: Vector Analysis

  • Vectors in plane and space

  • Vector operations

  • Gradient, Divergence and Curl

  • Gauss's, Green's and Stoke's theorems

Unit 5: Complex Analysis

  • Analytic functions

  • Cauchy's integral theorem

  • Cauchy's integral formula

  • Taylor's and Laurent's series

  • Residue theorem

Unit 6: Numerical Methods

  • Solution of nonlinear equations

  • Single and multi-step methods for differential equations

  • convergence criteria

Unit 7: Probability and Statistics

  • Mean, median, mode and standard deviation

  • Combinatorial probability

  • probability distribution functions −

    • Binomial

    • Poisson

    • Exponential

    • Normal

  • Joint and conditional probability

  • Correlation and regression analysis

Section B: Networks, Signals and Systems

Unit 1: Network Solution Methods

  • Nodal and mesh analysis

  • Network theorems −

    • Superposition

    • Thevenin and Norton’s

    • maximum power transfer

  • Wye-Delta transformation

  • Steady state sinusoidal analysis using phasors

  • Time domain analysis of simple linear circuits

  • Solution of network equations using Laplace transform

  • Frequency domain analysis of RLC circuits

  • Linear 2-port network parameters −

    • Driving point

    • Transfer functions

  • State equations for networks

Unit 2: Continuous-time signals

  • Fourier series and Fourier transform representations, sampling theorem and applications

  • Discrete-time signals −

    • Discrete-time Fourier transform (DTFT)

    • DFT

    • FFT

    • Z-transform

    • Interpolation of discrete-time signals

  • LTI systems −

    • Definition and properties

    • Causality

    • Stability

    • Impulse response

    • Convolution

    • Poles and zeros

    • Parallel and cascade structure

    • Frequency response

    • Group delay

    • Phase delay

    • Digital filter design techniques

Section C: Electronic Devices

  • Energy bands in intrinsic and extrinsic silicon

  • Carrier transport −

    • Diffusion current

    • Drift current

    • Mobility

    • 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

  • Integrated circuit fabrication process −

    • Oxidation

    • Diffusion

    • Ion implantation

    • Photolithography

    • Twin-tub CMOS process

Section D: Analog Circuits

  • Small signal equivalent circuits of diodes, BJTs and MOSFETs

  • Simple diode circuits −

    • Clipping

    • Clamping

    • Rectifiers

  • Single-stage BJT and MOSFET amplifiers −

    • Biasing

    • Bias stability

    • Mid-frequency small signal analysis

    • Frequency response

  • BJT and MOSFET amplifiers −

    • Multi-stage

    • Differential

    • Feedback

    • Power and operational

  • Simple op-amp circuits

  • Active filters

  • Sinusoidal oscillators −

    • Criterion for oscillation

    • Single-transistor

    • Opamp configurations

  • Function generators, wave-shaping circuits and 555 timers

  • Voltage reference circuits

  • Power supplies: ripple removal and regulation

Section E: Digital Circuits

  • Number systems

  • Combinatorial circuits −

    • Boolean algebra

    • Minimization of functions using Boolean identities and Karnaugh map

    • Logic gates and their static CMOS implementations

    • Arithmetic circuits

    • Code converters

    • Multiplexers

    • Decoders and PLAS

  • Sequential circuits −

    • Latches and flip-flops

    • Counters

    • Shift-registers

    • Finite state machines

  • Data converters −

    • Sample and hold circuits

    • ADCs and DACs

  • Semiconductor memories −

    • ROM

    • SRAM

    • DRAM

  • 8-bit microprocessor (8085) −

    • Architecture

    • Programming

    • Memory and I/O interfacing

Section F: 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 G: 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

    • Circuits for analog communications

  • Information theory −

    • Entropy

    • Mutual information

    • Channel capacity theorem

  • Digital communications −

    • PCM

    • DPCM

    • Digital modulation schemes

    • Amplitude

    • Phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding

    • Matched filter receiver

    • Calculation of bandwidth

    • SNR and BER for digital modulation

  • Fundamentals of error correction, Hamming codes

  • Timing and frequency synchronization, inter-symbol interference and its mitigation

  • Basics of TDMA, FDMA and CDMA

Section H: Electromagnetics

  • Electrostatics

  • 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

  • Waveguides −

    • Modes

    • Boundary conditions

    • Cut-off frequencies

    • Dispersion relations

  • Antennas −

    • Antenna types

    • Radiation pattern

    • Gain and directivity

    • Return loss

    • Antenna arrays

  • Basics of radar Light propagation in optical fibers

GATE Geology and Geophysics Syllabus

Subject Code: GG

Course Structure

Sections/Units Topics
Common Section
Unit 1 Earth and Planetary system
Unit 2 Weathering and soil formation
Unit 3 Introduction to remote sensing
Unit 4 Principles and applications of gravity
Section A Geology
Unit 1 Geomorphic processes and agents
Unit 2 Mechanism of rock deformation
Unit 3 Crystallography
Unit 4 Cosmic abundance of elements
Unit 5 Igneous rocks
Unit 6 Physico-chemical conditions of metamorphism and concept of metamorphic facies, grade and baric types
Unit 7 Morphology, classification and geological significance of important invertebrates, vertebrates, plant fossils and microfossils
Unit 8 Principles of Stratigraphy and concepts of correlation
Unit 9 Ore-mineralogy and optical properties of ore minerals
Unit 10 Engineering properties of rocks and soils
Section B Geophysics
Unit 1 The earth as a planet
Unit 2 Scalar and vector potential fields
Unit 3 Absolute and relative gravity measurements
Unit 4 Elements of Earth’s magnetic field
Unit 5 Conduction of electricity through rocks
Unit 6 Basic concept of EM induction in the earth
Unit 7 Seismic methods of prospecting
Unit 8 Geophysical signal processing
Unit 9 Principles and techniques of geophysical well-logging
Unit 10 Radioactive methods of prospecting and assaying
Unit 11 Basic concepts of forward and inverse problems

Course Syllabus

Common Section

Unit 1: Earth and Planetary system

  • Earth −

    • Size

    • Shape

    • Internal structure

    • Composition

  • Concept of isostasy

  • Elements of seismology −

    • Body and surface waves

    • Propagation of body waves in the earth’s interior

  • Gravitational field of the Earth −

    • Geomagnetism

    • Paleomagnetism

  • Continental drift −

  • Plate tectonics – relationship with earthquakes

  • Volcanism and mountain building

  • Continental and oceanic crust −

    • Composition

    • Structure

    • Thickness

Unit 2: Weathering and soil formation

  • Landforms created by −

    • River

    • Wind

    • Glacier

    • Ocean

    • Volcanoes

  • Basic structural geology −

    • Stress

    • Strain

    • 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 −

    • Mineralogy and classification of common igneous, sedimentary and metamorphic rocks

  • Geological time scale −

    • Geochronology and absolute time

  • Stratigraphic principles −

    • Major stratigraphic divisions of India

  • Geological and geographical distribution of −

    • Mineral in India

    • Coal in India

    • petroleum resources in India

Unit 3: Introduction to remote sensing

  • Engineering properties of rocks and soils

  • Ground water geology

Unit 4: Principles and applications of gravity

  • Magnetic, electrical, electromagnetic, seismic and radiometric methods of prospecting for oil, mineral and ground water

  • Introductory well logging

Section A: Geology

Unit 1: Geomorphic processes and agents

  • Development and evolution of landforms

  • Slope and drainage

  • Processes in deep oceanic and near-shore regions

  • Quantitative and applied geomorphology

Unit 2: Mechanism of rock deformation

  • Primary and secondary structures

  • Geometry and genesis of folds, faults, joints and unconformities

  • Cleavage, schistosity and lineation

  • Methods of projection

  • Tectonites and their significance

  • Shear zones

  • Superposed

  • Folding

  • Basement-cover relationship

Unit 3: Crystallography

  • Symmetry, forms and twinning

  • Crystal chemistry

  • Optical mineralogy, classification of minerals, diagnostic physical and optical properties of rock - forming minerals

Unit 4: 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 geochemical thermodynamics

  • Isotope geochemistry

  • Geochemistry of waters including solution equilibria and water-rock interaction

Unit 5: Igneous rocks

  • Classification, forms and textures

  • Magmatic differentiation

  • Binary and ternary phase diagrams

  • Major and trace elements as monitors of partial melting and magma evolutionary processes

  • Sedimentary rocks – texture and structure

  • sedimentary processes and environments, sedimentary facies, provenance and basin analysis

  • Metamorphic rocks – structures and textures

Unit 6: Physico-chemical conditions of metamorphism and concept of metamorphic facies, grade and baric types

  • Metamorphism of pelitic, mafic and impure carbonate rocks

  • Role of fluids in metamorphism

  • Metamorphic P-T-t paths and their tectonic significance

  • Association of igneous, sedimentary and metamorphic rocks with tectonic setting

  • Igneous and metamorphic provinces and important sedimentary basins of India

Unit 7: Morphology, classification and geological significance of important

  • Invertebrates

  • Vertebrates

  • Plant fossils

  • Microfossils

Unit 8: Principles of Stratigraphy and concepts of correlation

  • Lithostratigraphy, biostratigraphy and chronostratigraphy

  • Indian stratigraphy −

    • Precambrian

    • Phanerozoic

  • Overview of Himalayan Geology

Unit 9: Ore-mineralogy and optical properties of ore minerals

  • Ore forming processes vis-à-vis ore-rock association (magmatic, hydrothermal, sedimentary, supergene and metamorphogenic ores)

  • Fluid inclusions as an ore genetic tool

  • Coal and petroleum geology −

    • Marine mineral resources

  • Prospecting and exploration of economic mineral deposits −

    • Sampling

    • Ore reserve estimation

    • Geostatistics

    • Mining methods

  • Ore dressing and mineral economics

  • Origin and distribution of mineral −

    • Fossil and nuclear fuel deposits in India

Unit 10: Engineering properties of rocks and soils

  • Rocks as construction materials

  • Role of geology in the construction of engineering structures including −

    • Dams

    • Tunnels

    • Excavation sites

  • Natural hazards

  • Ground water geology −

    • Exploration

    • Well hydraulics

    • 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 B: Geophysics

Unit 1: 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

  • Geothermics and heat flow

  • Seismology and interior of the earth

  • Variation of density, velocity, pressure, temperature, electrical and magnetic properties of the earth

  • Earthquakes −

    • Causes and measurements

    • Magnitude and intensity

    • Focal mechanisms

    • Earthquake quantification

    • Source characteristics

    • Seismotectonics and seismic hazards

  • Digital seismographs

Unit 2: 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 theory

  • Eikonal equation

  • Ray theory

Unit 3: Absolute and relative gravity measurements

  • Gravimeters, land, airborne, shipborne and bore-hole gravity 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

Unit 4: Elements of Earth’s magnetic field

  • Units of measurement

  • Magnetic susceptibility of rocks and measurements

  • Magnetometer land, airborne and marine magnetic 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-geometrical shaped bodies

  • Depth estimates

  • Image processing concepts in processing of magnetic anomaly maps

  • Interpretation of processed magnetic anomaly data

  • Applications of gravity and magnetic methods for mineral and oil exploration

Unit 5: Conduction of electricity

  • Conduction of electricity through −

    • Rocks

    • Electrical conductivities of metals

    • Nonmetals

    • Rock forming minerals

    • Different rocks

  • Concepts of D.C. Resistivity measurement

  • Various electrode configurations for resistivity sounding and profiling

  • Application of filter theory

  • Type-curves over multi-layered structures

  • Dar-zarrouck parameters

  • Reduction of layers

  • Coefficient of anisotropy

  • Interpretation of resistivity field data

  • Equivalence and suppression

  • Self-potential and its origin

  • Field measurement

  • Induced polarization

  • Time and frequency domain ip measurements

  • Interpretation and applications of ip, ground-water exploration, mineral exploration, environmental and engineering applications

Unit 6: Basic concept of EM induction in the earth

  • Skin-depth

  • Elliptic polarization

  • In phase and quadrature components

  • Various EM methods, measurements in different source-receiver configurations

  • Earth’s natural electromagnetic field

  • Tellurics, magneto-tellurics

  • Geomagnetic depth sounding principles

  • Electromagnetic profiling

  • Time domain EM method

  • EM scale modeling

  • Processing of EM data and interpretation

  • Geological applications including groundwater, mineral and hydrocarbon exploration

Unit 7: Seismic methods of prospecting

  • 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, recording instruments (DFS), digital formats, field layouts

  • Seismic noises and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D and 3D seismic data acquisition, processing and interpretation

  • CDP stacking charts, binning, filtering, dip-move out, 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

  • Reservoir geophysics

Unit 8: Geophysical signal processing

  • Sampling theorem

  • Aliasing

  • Nyquist frequency

  • 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

Unit 9: Principles and technique

  • Principles and technique of −

    • Geophysical well-logging

    • SP

    • Resistivity

    • Induction

    • Gamma ray

    • Neutron

    • Density

    • Sonic

    • Temperature

    • Dip meter

    • Caliper

    • Nuclear magnetic

    • Cement bond logging

    • Micro-logs

  • Quantitative evaluation of formations from well logs

  • well hydraulics and application of geophysical methods for groundwater study

  • application of bore hole geophysics in ground water, mineral and oil exploration

Unit 10: Radioactive methods

  • Radioactive methods of −

    • 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

Unit 11: 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

  • Quasilinear and non-linear methods including Tikhonov’s regularization method, Singular Value Decomposition, Backus-Gilbert method, simulated annealing, genetic algorithms and artificial neural network

GATE Instrumental Engineering Syllabus

Subject Code: IN

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Analysis of complex variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Electric Circuits
Section C Signals and Systems
Section D Control Systems
Section E Analog Electronics
Section F Digital Electronics
Section G Measurements
Section H Sensors and Industrial Instrumentation
Section I Communication and Optical Instrumentation

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrix algebra

  • Systems of linear equations

  • Eigen values and Eigen

  • Vectors

Unit 2: 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

Unit 3: Differential equations

  • First order equation (linear and nonlinear)

  • Higher 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

Unit 4: Analysis of complex variables

  • Analytic functions

  • Cauchy’s integral theorem and integral formula

  • Taylor’s and Laurent’s series

  • Residue theorem

  • Solution of integrals

Unit 5: Probability and Statistics

  • Sampling theorems

  • Conditional probability

  • Mean, median, mode and standard deviation

  • Random variables

  • Discrete and continuous distributions

  • Normal, Poisson and binomial distributions

Unit 6: Numerical Methods

  • Matrix inversion

  • Solutions of non-linear algebraic equations

  • Iterative methods for solving differential equations

  • Numerical integration

  • Regression and correlation analysis

Section B: Electrical Circuits

Unit 1: Voltage and current sources

  • Independent, dependent, ideal and practical

  • V-i relationships of resistor, inductor, mutual inductor and capacitor

  • Transient analysis of RLC circuits with dc excitation

Unit 2: Kirchoff’s laws

  • Mesh and nodal analysis

  • Superposition

  • Thevenin

  • Norton

  • Maximum power

  • Transfer

  • Reciprocity theorems

Unit 3: 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

  • One-port and two-port networks

  • Driving point impedance and admittance

  • Open- and short circuit parameters

Section C: Signals and Systems

  • 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 D: 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, P-I, P-I-D, cascade, feedforward, and ratio controllers.

Section E: Analog Electronics

  • Characteristics and applications of −

    • Diode

    • Zener diode

    • BJT

    • MOSFET

  • Small signal analysis of transistor circuits, feedback amplifiers

  • Characteristics of operational amplifiers

  • Applications of opamps −

    • Difference amplifier

    • Adder

    • Subtractor

    • Integrator

    • Differentiator

    • Instrumentation amplifier

    • Precision rectifier

    • Active filters and other circuits

  • Oscillators, signal generators, voltage controlled oscillators and phase locked loop

Section F: Digital Electronics

  • Combinational logic circuits, minimization of Boolean functions

  • IC families: TTL and CMOS

  • Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flipflops, shift registers, timers and counters

  • Sample-and-hold circuit, multiplexer, analog-todigital (successive approximation, integrating, flash and sigma-delta) and digital-toanalog 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, 8-bit microprocessor and microcontroller: applications, memory and input-output interfacing

  • Basics of data acquisition systems

Section G: Measurements

  • SI units, systematic and random errors in measurement, expression of uncertainty - accuracy and precision index, propagation of errors

  • PMMC, MI and dynamometer type instruments −

    • DC potentiometer

    • Bridges for measurement of R, L and C, 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 H: 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 (differential pressure, 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

Section I: 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-, pulse shift keying for digital modulation

  • Optical sources and detectors − led, laser, photo-diode, light dependent resistor and their characteristics

  • Interferometer − applications in metrology

  • Basics of fiber optic sensing

GATE Mathematics Syllabus

Subject Code: MA

Course Structure

Sections/Units Topics
Section A Linear Algebra
Section B Complex Analysis
Section C Real Analysis
Section D Ordinary Differential Equations
Section E Algebra
Section F Functional Analysis
Section G Numerical Analysis
Section H Partial Differential Equations
Section I Topology
Section J Probability and Statistics
Section K Linear programming

Course Syllabus

Section A: Linear Algebra

  • Finite dimensional vector spaces

  • Linear transformations and their matrix representations −

    • Rank

    • Systems of linear equations

    • Eigenvalues and eigenvectors

    • Minimal polynomial

    • Cayley-hamilton theorem

    • Diagonalization

    • Jordan-canonical form

    • Hermitian

    • Skewhermitian

    • Unitary matrices

  • Finite dimensional inner product spaces −

    • Gram-Schmidt orthonormalization process

    • Self-adjoint operators, definite forms

Section B: Complex Analysis

  • Analytic functions, conformal mappings, bilinear transformations

  • complex integration −

    • Cauchy’s integral theorem and formula

    • Liouville’s theorem

    • Maximum modulus principle

  • Zeros and singularities

  • Taylor and Laurent’s series

  • Residue theorem and applications for evaluating real integrals

Section C: Real Analysis

  • Sequences and series of functions −

    • Uniform convergence

    • Power series

    • Fourier series

    • Functions of several variables

    • Maxima

    • Minima

  • Riemann integration −

    • Multiple integrals

    • Line

    • Surface and volume integrals

    • Theorems of green

    • Stokes

    • Gauss

  • Metric spaces −

    • Compactness

    • Completeness

    • Weierstrass approximation theorem

  • Lebesgue measure −

    • Measurable functions

  • Lebesgue integral −

    • Fatou’s lemma

    • Dominated convergence theorem

Section D: Ordinary Differential Equations

  • First order ordinary differential equations −

    • Existence and uniqueness theorems for initial value problems

    • Systems of linear first order ordinary differential equations

    • Linear ordinary differential equations of higher order with constant coefficients

  • Linear second order ordinary differential equations with variable coefficients

  • Method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method)

  • Legendre and Bessel functions and their orthogonal properties

Section E: Algebra

  • Groups, subgroups, normal subgroups, quotient groups and homomorphism theorems

  • Automorphisms

  • Cyclic groups and permutation groups

  • Sylow’s theorems and their applications

  • Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings and irreducibility criteria

  • Fields, finite fields, and field extensions

Section F: Functional Analysis

  • Normed linear spaces

  • Banach spaces

  • Hahn-Banach extension theorem

  • Open mapping and closed graph theorems

  • Principle of uniform boundedness

  • Inner-product spaces

  • Hilbert spaces

  • Orthonormal bases

  • Riesz representation theorem

  • Bounded linear operators

Section G: Numerical Analysis

  • Numerical solution of algebraic and transcendental equations −

    • Bisection

    • Secant method

    • Newton-Raphson method

    • Fixed point iteration

  • Interpolation −

    • Error of polynomial interpolation

    • Lagrange, newton interpolations

  • Numerical differentiation

  • Numerical integration −

    • Trapezoidal and Simpson Rules

  • Numerical solution of systems of linear equations −

    • Direct methods (Gauss Elimination, Lu Decomposition)

  • Iterative methods (Jacobi and Gauss-Seidel)

  • Numerical solution of ordinary differential equations

  • Initial value problems −

    • Euler’s method

    • Runge-Kutta methods of order 2

Section H: Partial Differential Equations

  • Linear and quasilinear first order partial differential equations −

    • Method of characteristics

  • Second order linear equations in two variables and their classification

  • Cauchy, Dirichlet and Neumann problems

  • Solutions of Laplace, wave in two dimensional Cartesian coordinates, interior and exterior Dirichlet problems in polar coordinates

  • Separation of variables method for solving wave and diffusion equations in one space variable

  • Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations

Section I: Topology

  • Basic concepts of topology

  • Bases

  • Subbases

  • Subspace topology

  • Order topology

  • Product topology

  • Connectedness

  • Compactness

  • Countability

  • Separation axioms

  • Urysohn’s lemma

Section J: Probability and Statistics

  • Probability space, conditional probability, Bayes theorem, independence, Random

  • Variables, joint and conditional distributions, standard probability distributions and their properties (Discrete uniform, Binomial, Poisson, Geometric, Negative binomial, Normal, Exponential, Gamma, Continuous uniform, Bivariate normal, Multinomial), expectation, conditional expectation, moments

  • Weak and strong law of large numbers, central limit theorem

  • Sampling distributions, UMVU estimators, maximum likelihood estimators

  • Interval estimation

  • Testing of hypotheses, standard parametric tests based on normal, distributions

  • Simple linear regression

Section H: Linear programming

  • Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, Big-M and two phase methods

  • Infeasible and unbounded LPP’s, alternate optima

  • Dual problem and duality theorems, dual simplex method and its application in post optimality analysis

  • Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems

  • Hungarian method for solving assignment problems