Graduate Aptitude Test in Engineering (GATE)

Linear algebra
Vector algebra
Matrix algebra
Systems of linear equations
Rank of a matrix
Eigen values and Eigen vectors

Calculus
Functions of single variable
Limits
Continuity and differentiability
Mean value theorem
Chain rule
Partial derivatives
Maxima and minima
Gradient
Gradient, divergence and curl
Directional derivatives
Integration
Line
Line, surface & volume integrals
Theorems of stokes
Gauss and Green

Differential equations
First order linear and nonlinear differential equations
Higher order linear ODEs with constant coefficients
Partial differential equations and separation of variables methods

Fourier series

Laplace transforms

Numerical methods for linear and nonlinear algebraic equations

Numerical integration and differentiation

Atmosphere
Properties
Standard atmosphere
Classification of aircraft
Airplane (fixed wing aircraft) configuration and various parts

Airplane performance
Pressure altitude
Equivalent, calibrated, indicated air speeds
Primary flight instruments
Altimeter, ASI, VSI, turn-bank indicator
Drag polar
Take-off 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

Static stability
Angle of attack
Sideslip
Roll, pitch and 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

Dynamic stability
Euler angles
Equations of motion
Aerodynamic forces and moments
Stability & control derivatives
Decoupling of longitudinal and lateral-directional dynamics
Longitudinal modes
Lateral-directional modes

Central force motion, determination of trajectory and orbital period in simple cases

Orbit transfer

In-plane and out-of-plane

Basic fluid mechanics
Conservation laws: Mass, momentum (integral and differential form)
Potential flow theory: Sources, sinks, doublets, line vortex and their superposition, viscosity and Reynolds number

Airfoils and wings
Airfoil nomenclature
Aerodynamic coefficients
Lift, drag and moment
Kutta- Joukowski theorem
Thin airfoil theory
Kutta condition
Starting vortex
Finite wing theory
Induced drag
Prandtl lifting line theory
Critical and drag divergence Mach number

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

Elementary ideas of viscous flows including boundary layers

Wind tunnel testing

Measurement and visualization techniques

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, Mohr’s circle(stress), deflection of beams
Strain energy
Castigliano's principles
Analysis of statically determinate and indeterminate trusses and beams
Elastic flexural buckling of columns

Flight vehicle structures
Characteristics of aircraft structures and materials
Torsion, bending and flexural shear of thin-walled sections
Loads on aircraft

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

Vibration of beams

Theory of elasticity: Equilibrium and compatibility equations, Airy’s stress function

Thermodynamics

Boundary layers and heat transfer and combustion thermochemistry

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 and nozzle

Axial compressors
Angular momentum
Work and compression
Characteristic performance of a single axial compressor stage
Efficiency of the compressor and degree of reaction

Axial turbines
Axial turbine stage efficiency

Centrifugal compressor
Centrifugal compressor stage dynamics
Inducer
Impeller and diffuser

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

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
Tests for convergence
Fourier series
Taylor series

Vector calculus
Gradient
Gradient, divergence and curl
Line
Line, surface & volume integrals
Stokes, Gauss and Green’s theorems

Differential equations
Linear and non-linear first order ordinary differential equations
Higher order linear ODEs with constant coefficients
Cauchy's and Euler's equations
Laplace transforms
Partial differential equations - Laplace, heat and wave equations

Probability and Statistics
Mean
Median
Mean, median, mode & standard deviation
Random variables
Poisson, normal & binomial distributions
Correlation and regression analysis
Tests of significance
Analysis of variance (ANOVA)

Numerical methods
Solutions of linear and non-linear algebraic equations
Numerical integration - trapezoidal and Simpson's rule
Numerical solutions of ODE

Machine design
Design and selection of machine elements – Gears, pulleys, chains and sprockets and belts
Overload safety devices used in farm machinery
Measurement of force, torque, speed
Displacement and acceleration on machine elements

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 and transport
Testing of agricultural machinery and equipment
Calculation of performance parameters - Field capacity, efficiency, application rate and losses
Cost analysis of implements and tractors

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

Farm power
Thermodynamic principles of I.C. engines
I.C. engine cycles
Engine components
Fuels and combustion
Lubricants and their properties
I.C. engine systems – Fuel, cooling, lubrication, ignition, electrical, intake and exhaust
Selection, operation, maintenance and repair of I.C. engines
Power efficiencies and measurement
Calculation of power
Torque
Fuel consumption
Heat load and power losses

Tractors and power tillers
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 transmission system
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

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

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

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 and channel routing

Surveying and levelling
Measurement of distance and area
Instruments for surveying and levelling
Chain surveying
Methods of traversing
Measurement of angles and bearings
Plane table surveying
Types of levelling
Theodolite traversing
Contouring
Computation of areas and volume

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

Watershed management
Watershed characterization
Land use capability classification
Rainwater harvesting structures
Check dams and farm ponds

Soil-water-plant relationship
Water requirement of crops
Consumptive use and evapotranspiration
Measurement of infiltration
Soil moisture and irrigation water infiltration

Irrigation water conveyance and application methods
Design of irrigation channels and underground pipelines
Irrigation scheduling
Surface, sprinkler and micro irrigation methods, design and evaluation of irrigation methods
Irrigation efficiencies

Agricultural drainage
Drainage coefficient
Planning, design and layout of surface and sub-surface drainage systems
Leaching requirement and salinity control
Irrigation and drainage water quality and reuse

Groundwater hydrology
Groundwater occurrence
Darcy's law
Steady flow in confined and unconfined aquifers
Evaluation of aquifer properties
Groundwater recharge

Wells and pumps
Types of wells, steady flow through wells
Classification of pumps
Pump characteristics
Pump selection and installation

Drying
Psychrometry – properties of air-vapours mixture
Concentration and drying of liquid foods – evaporators, tray, drum and spray dryers
Hydrothermal treatment
Drying and milling of cereals
Pulses and oilseeds

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

Processing and by-product utilization
Processing of seeds, spices, fruits and vegetables
By-product utilization from processing industries

Storage systems
Controlled and modified atmosphere storage
Perishable food storage
Godowns
Bins and grain silos

Heat and mass transfer
Steady state heat transfer in conduction
Convection and radiation
Transient heat transfer in simple geometry
Working principles of heat exchangers
Diffusive and convective mass transfer
Simultaneous heat and mass transfer in agricultural processing operations
Material and energy balances in food processing systems
Water activity
Sorption and desorption isotherms

Preservation of food
Kinetics of microbial death – pasteurization and sterilization of milk and other liquid foods
Preservation of food by cooling and freezing
Refrigeration and cold storage basics and applications

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

Horizontal and vertical circulation

Barrier free design

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

Works of renowned national and international architects

Behavioural 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 equipments

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

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

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

Concepts and rating green building

ECBC

Building performance simulation and evaluation

Environmental pollution types

Environmental pollution causes

Controls and abatement strategies

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 and FAR

Development controls densities and building byelaws

Planning process

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

Housing

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

Physical tools and techniques of surveys

Topographical tools and techniques of surveys

Land use and socio economic 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, economical 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 planning legislation and implementation

Local self-governance

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 and standards and uses

Air-conditioning systems

Firefighting systems

Building safety and security systems

Urban infrastructure - Transportation, water supply, sewerage, drainage, solid waste management, electricity and 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 and transportation and urban form inter-relationships

Design of roads

Intersections

Grade separators and parking areas

Hierarchy of roads and level of service

Traffic, transport management and control in urban areas

Mass transportation planning

Para transits 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 and collection

Methods of solid waste management and transportation and disposal

Recycling and reuse of solid waste

Power supply and communication systems

Network, design and guidelines

Linear algebra
Matrices and determinants
Systems of linear equations
Linear algebra and Eigen values and Eigen vectors

Calculus
Calculus: Limits, continuity and differentiability
Partial derivatives, maxima and minima, sequences and series, test for convergence, Fourier series

Differential equations
Differential equations for linear and nonlinear first order ODEs
Differential equations higher order ODEs with constant coefficients
Differential equations Cauchy's and Euler's equations
Differential equations and Laplace transforms
Differential equations and PDE Laplace
Differential equations heat and wave equations

Probability and Statistics
Mean, median, mode and standard deviation, probability and statistics
Random variables for probability and statistics
Poisson probability and statistics
Probability and statistics normal and binomial distributions
Probability and statistics correlation and regression analysis

Numerical methods
Numerical methods solution of linear and nonlinear algebraic equations
Numerical methods integration of trapezoidal and Simpson's rule
Numerical methods single and multistep methods for differential equations

Biochemistry
Biomolecules-structure and functions
Biological membranes
Structure
Action potential and transport processes
Classification and enzymes
Kinetics and mechanism of action and enzymes
Basic concepts and designs of metabolism in carbohydrates, lipids, amino acids and nucleic acids
Photosynthesis
Respiration and electron transport chain
Bioenergetics

Microbiology
Structure and classification viruses
Microbial classification and diversity in bacterial, algal and fungal
Methods in microbiology
Microbial growth and nutrition
Aerobic and anaerobic respiration
Nitrogen fixation
Microbial diseases and host and pathogen interaction

Cell biology
Prokaryotic and eukaryotic cell structure
Cell cycle and cell growth control
Cell communication
Cell signalling and signal transduction

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
Plasmids of microbial genetics
Transformation of microbial genetics
Transduction of microbial genetics
Conjugation of microbial genetics
Horizontal gene transfer and transposable elements
RNA interference
DNA damage and repair
Chromosomal variation
Molecular basis of genetic diseases

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

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
Antigen processing and presentation
Polyclonal and monoclonal antibody
Regulation of immune response
Immune tolerance
Hypersensitivity
Autoimmunity
Graft versus host reaction

Bioinformatics
Major bioinformatic 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)

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 labelling
DNA Sequencing
Polymerase chain reactions
DNA fingerprinting
Southern and northern blotting
In-situ hybridization
RAPD
RFLP
Site-directed mutagenesis
Gene transfer technologies
Gene therapy

Plant and animal biotechnology
Totipotency
Regeneration of plants
Plant growth regulators and elicitors
Tissue culture and cell suspension culture system
Tissue culture and methodology
Tissue culture and kinetics of growth
Tissue culture and 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 and macro-carrier culture
Hybridoma technology
Stem cell technology
Animal cloning
Transgenic animals

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 for bioconversion processes
Bioremediation-aerobic and anaerobic processes for stabilization of solid / liquid wastes

Linear algebra
Matrix algebra
Systems of linear equations
Eigen values and Eigen vectors

Calculus
Functions of single variable
Limit
Continuity and differentiability
Mean value theorems
Local maxima and minima
Taylor and Maclaurin series
Evaluation of definite and indefinite integrals
Application of definite integral to obtain area and volume
Partial derivatives
Total derivative
Gradient
Gradient, divergence and curl
Vector identities
Directional derivatives
Line
Line, surface & volume integrals
Stokes, Gauss and Green’s theorems

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

Partial differential equation (PDE)
Fourier series
Separation of variables
Solutions of one dimensional diffusion equation
First and second order one-dimensional wave equation and two-dimensional Laplace equation

Probability and Statistics
Definitions of probability and sampling theorems
Conditional probability
Discrete random variables
Poisson and binomial distributions
Continuous random variables
Normal and exponential distributions
Descriptive statistics of mean, median, mode and standard deviation
Hypothesis testing

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

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

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

Structural analysis
Statically determinate and indeterminate structures by force/ energy methods
Method of superposition
Analysis of trusses
Arches
Beams
Cables and frames
Displacement methods: Slope deflection and moment distribution methods
Influence lines
Stiffness and flexibility methods of structural analysis

Construction materials and management
Construction materials: Structural steel - composition, material properties and behaviour
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

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

Steel structures
Working stress and limit state design concepts
Design of tension and compression members
Beams and beam of columns, column bases
Connections - Simple and eccentric, beam-column connections, plate girders and trusses
Plastic analysis of beams and frames

Soil mechanics
Origin of soils
Soil structure and fabric
Three-phase system and phase relationships
Three 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
One time rate of consolidation
Mohr's circle
Stress paths
Effective and total shear strength parameters
Characteristics of clays and sand

Foundation engineering
Sub-surface investigations: Scope, drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests
Earth pressure theories - Rankine and Coulomb
Stability of slopes - Finite and infinite slopes, method of slices and bishop's method
Stress distribution in soils - Boussinesq's and Westergaard's theories, pressure bulbs
Shallow foundations - Terzaghi's and Meyerhof'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

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

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

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

Irrigation
Duty, delta, estimation of evapotranspiration
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

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 waste water
Primary, secondary and tertiary treatment of waste water
Effluent discharge standards
Domestic waste water treatment
Quantity of characteristics of domestic waste water
Primary and secondary treatment
Unit operations and unit processes of domestic waste water
Sludge disposal

Air pollution
Types of pollutants
Their sources and impacts
Air pollution meteorology
Air pollution control
Air quality standards and limits

Municipal solid wastes
Characteristics
Generation, collection and transportation of solid wastes
Engineered systems for solid waste management reuse/ recycle, energy recovery, treatment and disposal

Noise pollution
Impacts of noise
Permissible limits of noise pollution
Measurement of noise and control of noise pollution

Transportation infrastructure
Highway alignment and engineering surveys
Geometric design of highways and horizontal and vertical alignments, cross-sectional elements
Geometric design of railway track
Airport runway length
Taxiway and exit taxiway design

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

Traffic engineering
Traffic studies on flow, speed
Traffic studies on travel time - delay and 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

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
Photogrammetry - scale, flying height
Remote sensing - Baics, platform and sensors, visual image interpretation
Remote sensing of platform and sensors
Remote sensing and visual image interpretation

GIS and GPS
Basics of geographical information system (GIS) and geographical positioning system (GPS)

Linear algebra
Matrix algebra
Systems of linear equations
Eigen values and Eigen vectors
Matrix algebra, systems of linear equations, eigen values and eigenvectors

Calculus
Functions of single variable
Limit
Continuity and differentiability
Taylor series
Mean value theorems
Evaluation of definite and improper integrals
Partial derivatives
Total derivative
Maxima and minima
Gradient
Gradient, divergence and curl
Vector identities
Directional derivatives
Line
Line, surface & volume integrals
Stokes, Gauss and Green’s theorems
Functions of single variable, limit, continuity and differentiability
Taylor series, mean value theorems, evaluation of definite and improper integrals
Partial derivatives, total derivative, maxima and minima
Gradient, divergence and curl, vector identities, directional derivatives
Line, surface and volume integrals, stokes, gauss and green’s theorems

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

Complex variables
Complex number
Polar form of complex number
Triangle inequality
Complex number, polar form of complex number, triangle inequality

Probability and Statistics
Definitions of probability and sampling theorems
Conditional probability
Mean
Median
Mean, median, mode & standard deviation
Random variables
Poisson, normal & binomial distributions
Linear regression analysis
Definitions of probability and sampling theorems, conditional probability, mean, median, mode and standard deviation
Random variables, poisson, normal and binomial distributions, linear regression analysis

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

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 and purge calculations
Gibb's phase rule and degree of freedom analysis
First and second laws of thermodynamics
Applications of first law to close and open systems
Second law and entropy
Thermodynamic properties of pure substances
Equation of state and residual properties
Properties of mixtures
Partial molar properties
Fugacity
Excess properties and activity coefficients
Phase equilibria
Predicting VLE of systems
Chemical reaction equilibrium

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 and pressure drop
Particle size and shape
Particle size distribution
Size reduction and classification of solid particles
Free and hindered settling
Centrifuge and cyclones
Thickening and classification
Filtration
Agitation and mixing
Conveying of solids

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

Mass transfer
Fick's laws
Molecular diffusion in fluids
Mass transfer coefficients
Film, penetration and surface renewal theories
Momentum, heat and mass transfer analogies
Stage-wise and continuous contacting and stage efficiencies
HTU & NTU concepts
Design and operation of equipment for distillation
Absorption
Leaching
Liquid-liquid extraction
Drying
Humidification
Dehumidification and adsorption

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

Instrumentation and process control
Measurement of process variables
Sensors, transducers and their dynamics
Process modelling 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

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

Chemical technology
Inorganic chemical industries (sulphuric acid, phosphoric acid, chloralkali industry)
Fertilizers (ammonia, urea, SSP and TSP)
Natural products industries (pulp and paper, sugar, oil, and fats)
Petroleum refining and petrochemicals
Polymerization industries (polyethylene, polypropylene, PVC and polyester synthetic fibres)

Steady and unsteady state mass and energy balances including multiphase

Multicomponent

Reacting and non-reacting systems

Use of tie components

Recycle

Bypass and purge calculations

Gibb’s phase rule and degree of freedom analysis

First and second laws of thermodynamics

Applications of first law to close and open systems

Second law and entropy

Thermodynamic properties of pure substances

Equation of state and residual properties

Properties of mixtures

Partial molar properties

Fugacity

Excess properties and activity coefficients

Phase equilibria

Predicting VLE of systems

Chemical reaction equilibrium

Multicomponent, reacting and non-reacting systems

Recycle, bypass and purge calculations

Equation of state and residual properties, properties of mixtures

Partial molar properties, fugacity, excess properties and activity coefficients

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 and pressure drop

Particle size and shape

Particle size distribution

Size reduction and classification of solid particles

Free and hindered settling

Centrifuge and cyclones

Thickening and classification

Filtration

Agitation and mixing

Conveying of solids

Fluid statics, newtonian and non-newtonian fluids

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

Fluctuating velocity, universal velocity profile and pressure drop

Particle size and shape, particle size distribution, size reduction and classification of solid particles

Thickening and classification, filtration, agitation and mixing

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

Steady and unsteady heat conduction, convection and radiation

Thermal boundary layer and heat transfer coefficients, boiling, condensation and evaporation

Design of double pipe, shell and tube heat exchangers, and single and multiple effect evaporators

Fick’s laws

Molecular diffusion in fluids

Mass transfer coefficients

Film

Penetration and surface renewal theories

Momentum

Heat and mass transfer analogies

Stage-wise and continuous contacting and stage efficiencies

HTU & NTU concepts

Design and operation of equipment for distillation

Absorption

Leaching

Liquid-liquid extraction

Drying

Humidification

Dehumidification and adsorption

Fick’s laws, molecular diffusion in fluids, mass transfer coefficients, film, penetration and surface renewal theories

Momentum, heat and mass transfer analogies

Design and operation of equipment for distillation, absorption, leaching, liquid-liquid extraction, drying, humidification, dehumidification and adsorption

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

Kinetics of homogeneous reactions, interpretation of kinetic data, single and multiple reactions in ideal reactors, non-ideal reactors

Residence time distribution, single parameter model

Measurement of process variables

Sensors

Transducers and their dynamics

Process modelling 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

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)

Analysis of closed loop systems including stability, frequency response, controller tuning, cascade and feed forward control

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

Cost indices, rate of return, payback period, discounted cash flow

Optimization in process design and sizing of chemical engineering equipments such as compressors, heat exchangers, multistage contactors

Inorganic chemical industries (sulphuric acid, phosphoric acid, chloralkali 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)

Inorganic chemical industries (sulfuric acid, phosphoric acid, chlor-alkali industry), fertilizers (Ammonia, Urea, SSP and TSP)

Discrete mathematics
Propositional and first order logic
Sets
Relations
Functions
Partial orders and lattices
Groups
Graphs: Connectivity, matching, coloring
Combinatorics: Counting, recurrence relations, generating functions

Linear algebra
Matrices
Determinants
System of linear equations
Eigen values and Eigen vectors
LU decomposition

Calculus
Limits
Continuity and differentiability
Maxima and minima
Mean value theorem
Integration

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

Digital logic
Boolean algebra
Combinational and sequential circuits
Minimization
Number representations and computer arithmetic of fixed and floating point

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 in interrupt and DMA mode

Programming and data structures
Programming in c, recursion
Arrays
Stacks
Queues
Linked lists
Trees
Binary search trees
Binary heaps
Graphs

Algorithms
Searching
Sorting
Hashing
Asymptotic worst case time and space complexity
Algorithm design techniques and greedy
Dynamic programming and divide and conquer
Graph search
Minimum spanning trees
Shortest paths

Theory of computation
Regular expressions and finite automata
Context-free grammar and push-down automata
Regular and context-free languages
Pumping lemma
Turing machines and undecidability

Compiler design
Lexical analysis
Parsing
Syntax-directed translation
Runtime environments
Intermediate code generation

Operating system
Processes
Threads
Inter‐process communication
Concurrency and synchronization
Deadlock
CPU scheduling
Memory management and virtual memory
File systems

Databases
ER‐model
Relational model: Relational algebra, tuple calculus, SQL
Integrity constraints, normal forms
File organization
Indexing of b and b+ trees
Transactions and concurrency control

Computer networks
Concept of layering
Lan technologies in Ethernet
Flow and error control techniques
Switching
IPV4/ IPV6
Routers and routing algorithms in distance vector, link state
TCP/UDP and sockets
Congestion control
Application layer protocols in 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

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-MO theory to h2+, h2 and other homonuclear diatomic molecules
Hetero nuclear 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

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
Potentiometric and conductometric titrations
Phase rule
Clausius-Clapeyron equation
Phase diagram of one component systems CO2, H2O, S
Two component systems: liquid-vapour, liquid-liquid and solid-liquid systems
Fractional distillation
Azeotropes and eutectics
Statistical thermodynamics
Microcanonical and canonical ensembles
Boltzmann distribution
Partition functions and thermodynamic properties

Kinetics
Transition state theory of 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 of relaxation and flow methods
Kinetics of photochemical and photophysical processes

Surfaces and interfaces
Physisorption and Chemisorption
Langmuir, Freundlich and BET isotherms
Surface catalysis and Langmuir-Hinshelwood mechanism
Surface tension
Viscosity
Self-assembly
Physical chemistry of colloids
Micelles and macromolecules

Main group elements
Hydrides
Halides (excluding fluoride)
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
Interhalogen compounds
Acid-base concepts

Transition elements
Coordination chemistry – structure and isomerism
Theories of bonding in 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

Lanthanides and actinides
Recovery
Periodic properties
Spectra and magnetic properties

Organometallics
18-electron rule
Metal-alkyl, metal-carbonyl, metal-olefin and metal- carbene complexes and 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

Radioactivity
Decay processes
Half-life of radioactive elements
Fission and fusion processes

Bioinorganic chemistry
Ion Na+ and K+ transport
Oxygen binding
Transport and utilization
Electron transfer reactions
Nitrogen fixation
Metallo enzymes containing magnesium
Molybdenum
Iron
Cobalt
Copper and zinc

Solids
Crystal systems and lattices
Miller planes
Crystal packing
Crystal defects
Bragg's law
Ionic crystals
Structures of ax, ax2, abx3 type compounds
Spinels
Band theory
Metals and semiconductors

Instrumental methods of analysis
UV-visible spectrophotometry
NMR and ESR spectroscopy
Mass spectrometry
Chromatography including GC and HPLC
Electroanalytical methods - Polarography, cyclic voltammetry, ion-selective electrodes
Thermo analytical methods

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
Neighbouring group participation on reactivity and selectivity/specificity

Reaction mechanisms
Basic mechanistic concepts – kinetic versus thermodynamic control
Hammond's postulate and Curtin-Hammett principle
Methods of determining reaction mechanisms through identification of products
Intermediates and isotopic labelling
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 and free radicals
Molecular rearrangements involving electron deficient atoms

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 Sonogashira
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 in cram and Felkin-Anh models models

Pericyclic reactions and photochemistry
Electrocyclic
Cycloaddition and sigmatropic reactions
Orbital correlations - FMO and PMO treatments
Photochemistry of alkenes
Arenes and carbonyl compounds
Photo-oxidation and photoreduction
Di-π-methane rearrangement
Barton reaction

Heterocyclic compounds
Structure
Preparation
Properties and reactions of furan
Pyrrole
Thiophene
Pyridine
Indole
Quinoline and Isoquinoline

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

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

Linear algebra
Vector space
Basis
Linear dependence and independence
Matrix algebra
Eigen values and Eigen vectors
Rank, solution of linear equations – existence and uniqueness

Calculus
Mean value theorems
Theorems of integral calculus
Evaluation of definite and improper integrals
Partial derivatives
Maxima and minima
Multiple integrals
Line
Line, surface & volume integrals
Taylor series

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

Vector analysis
Vectors in plane and space
Vector operations
Gradient
Gradient, divergence and curl
Gauss, Green and Stokes theorem

Complex analysis
Analytic functions
Cauchy's integral theorem
Cauchy's integral formula
Taylor's & Laurent's series
Residue theorem.

Numerical methods
Solution of nonlinear equations
Single and multi-step methods for differential equations
Convergence criteria

Probability and Statistics
Mean, median, mode and standard deviation
Combinatorial probability
Probability distribution functions - binomial, Poisson, exponential and normal
Joint and conditional probability
Correlation and regression analysis

Network solution methods
Nodal and mesh analysis
Network theorems - Thevenin and Norton's, superposition
Maximum power transfer of network theorems
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 of driving point and transfer functions
State equations for networks

Continuous-time signals
Fourier series and Fourier transform representations
Sampling theorem and applications
Discrete-time signals and Fourier transform (DTFT), DFT, FFT, Z-transform
Discrete-time and 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

Energy bands in intrinsic and extrinsic silicon

Carrier transport of diffusion current, drift current, mobility and resistivity

Generation and recombination of carriers

Poisson and continuity equations

P-N junction

Zener diode

BJT

MOS capacitor

MOSFET

LED

Photo diode and solar cell

Integrated circuit fabrication process: Oxidation, diffusion, ion implantation, photolithography

Twin-tub CMOS process

Small signal equivalent circuits of diodes

BJTS and MOSFETs

Simple diode circuits and clipping

Simple diode circuits of clamping and rectifiers

Single-stage BJT and MOSFET amplifiers: biasing, bias stability, mid-frequency small signal analysis and frequency response

BJT and MOSFET amplifiers: multi-stage, differential, feedback, power and operational

Simple op-amp circuits

Active filters

Sinusoidal oscillators and criterion for oscillation

Single-transistor and op amp configurations of sinusoidal oscillators

Function generators

Wave-shaping circuits and 555 timers

Voltage reference circuits

Power supplies for ripple removal and regulation

Number systems

Combinatorial circuits of 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 and finite state machines

Data converters: sample and hold circuits, ADCs and DACs

Semiconductor memories: ROM, SRAM, DRAM

Bit microprocessor (8085): architecture, programming, memory and I/O interfacing

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

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

Super heterodyne receivers of angle modulation

Circuits for analog communications

Information theory of entropy

Mutual information and channel capacity theorem

Digital communications of 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

Electrostatics

Maxwell’s equations: differential and integral forms and their interpretation

Boundary conditions, wave equation and poynting vector

Plane waves and properties of reflection and refraction

Polarization, phase and group velocity

Plane waves and properties of 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

Linear algebra
Matrix algebra
Systems of linear equations
Eigen values
Eigen vectors

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
Stoke's theorem
Gauss's theorem
Green's theorem, Stokes' theorem, and Gauss divergence theorem

Differential equations
First order equations of linear and nonlinear
Higher order linear differential equations with constant coefficients
Method of variation of parameters
Cauchy's equation
Euler's equation
Initial and boundary value problems
Partial differential equations
Method of separation of variables

Complex variables
Analytic functions
Cauchy's integral theorem
Cauchy's integral formula
Taylor series
Laurent series
Residue theorem
Solution integrals

Probability and Statistics
Sampling theorems
Conditional probability
Mean, mode, median and standard deviation
Random variables
Discrete and continuous distributions
Poisson distribution
Normal distribution
Binomial distribution
Correlation analysis
Regression analysis

Numerical methods
Solutions of nonlinear algebraic equations
Single and multi‐step methods for differential equations

Transform theory
Fourier transform
Laplace transform
Z‐transform

Electric circuits
Network graph
KCL
KVL
Node and mesh analysis
Transient response of DC and AC networks
Sinusoidal steady‐state analysis
Resonance
Passive filters
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

Electromagnetic fields
Coulomb's law
Electric field intensity
Electric flux density
Gauss's law
Divergence
Electric field and potential due to point
Plane, line 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
Magnetic circuits
Self and mutual inductance of simple configurations

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

Electrical machines
Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests
Regulation & 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 of induction
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

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
Gauss-Seidel and Newton-Raphson load flow methods
Voltage and frequency control
Power factor correction
Symmetrical components
Symmetrical and unsymmetrical fault analysis
Principles of over‐current
Differential and distance protection
Circuit breakers
System stability concepts
Equal area criterion

Control systems
Mathematical modelling 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

Electrical and electronic measurements
Bridges and potentiometers
Measurement of voltage
Current
Power
Energy and power factor
Instrument transformers
Digital voltmeters and multimeters
Time, phase and frequency measurement
Oscilloscopes
Error analysis

Analog and digital electronics
Characteristics of diodes, BJT, MOSFET
Simple diode circuits: clipping, clamping, rectifiers
Amplifiers and biasing
Equivalent circuit and frequency response of amplifiers
Oscillators and feedback amplifiers
Operational amplifiers and 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
8085 microprocessor and architecture

Power electronics
Characteristics of semiconductor power devices: diode, thyristor, TRIAC, GTO, MOSFET, IGBT
DC to DC conversion: buck, boost and 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

Earth and planetary system - size, shape, internal structure and composition of the earth

Concept of isostasy

Elements of seismology - body and surface waves, propagation of body waves in the earth’s interior

Gravitational field of the earth

Geomagnetism and paleomagnetism

Continental drift

Plate tectonics - relationship with earthquakes, volcanism and mountain building

Continental and oceanic crust - composition, structure and thickness

Weathering and soil formation

Landforms created by river, wind, glacier, ocean and volcanoes

Basic structural geology - stress, strain and material response

Brittle and ductile deformation

Nomenclature and classification of folds and faults

Crystallography – basic crystal symmetry and concept of point groups

Mineralogy – silicate crystal structure and determinative mineralogy of common rock forming minerals

Petrology – mineralogy

Classification of common igneous, sedimentary and metamorphic rocks

Geological time scale and geochronology and absolute time

Stratigraphic principles

Major stratigraphic divisions of India

Geological and geographical distribution of mineral, coal and petroleum resources of India

Introduction to remote sensing

Engineering properties of rocks and soils

Ground water geology

Principles and applications of gravity, magnetic, electrical, electromagnetic

Seismic and radiometric methods of prospecting for oil

Mineral and ground water

Introductory well logging

Geomorphic processes and agents

Development and evolution of landforms

Slope and drainage

Processes in deep oceanic and near-shore regions

Quantitative and applied geomorphology

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

Crystallography - symmetry, forms and twinning

Crystal chemistry

Optical mineralogy

Classification of minerals

Diagnostic physical and optical properties of rock - forming minerals

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

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

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

Morphology

Classification and geological significance of important invertebrates, vertebrates, plant fossils and microfossils

Principles of stratigraphy and concepts of correlation - lithostratigraphy, biostratigraphy and chronostratigraphy

Indian stratigraphy – Precambrian and Phanerozoic

Overview of Himalayan geology

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

Engineering properties of rocks and soils

Rocks as construction materials

Role of geology in the construction of engineering structures including dams, tunnels and excavation sites

Natural hazards

Ground water geology – exploration

Well hydraulics and water quality

Basic principles of remote sensing – energy sources and radiation principles

Atmospheric absorption

Interaction of energy with earth’s surface

Aerial-photo interpretation

Multispectral remote sensing in visible

Infrared

Thermal IR and microwave regions

Digital processing of satellite images

GIS – basic concepts, raster and vector mode operations