GATE Exam 2025 - Counselling (Started), Result, Scorecard, Answer Key, Cutoff, Admission Process

Engineering mathematics: Unit 01

• Vector algebra, matrix algebra, systems of linear equations, rank of a matrix, eigen values and eigen vectors

Engineering mathematics: Unit 02

• 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

Engineering mathematics: Unit 03

• First order linear and nonlinear differential equations, higher order linear ODEs with constant coefficients
• Partial differential equations and separation of variables methods

Engineering mathematics: Unit 04

Engineering mathematics: Unit 05

Engineering mathematics: Unit 06

Engineering mathematics: Unit 07

Engineering mathematics: Unit 08

Engineering mathematics: Unit 09

Flight mechanics: Unit 01

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

Flight mechanics: Unit 02

• Drag polar; takeoff and landing; steady climb and descent; absolute and service ceiling; range and endurance, load factor, turning flight, V-N diagram
• Winds: Head, tail, and cross winds

Flight mechanics: Unit 03

• Stability and control derivatives; longitudinal stick fixed and free stability; horizontal tail position and size; directional stability, vertical tail position, and size; lateral stability
• Wing dihedral, sweep, and position; hinge moments, stick forces

Flight mechanics: Unit 04

• Euler angles; equations of motion; decoupling of longitudinal and lateral-directional dynamics; longitudinal modes; lateral-directional modes

Space dynamics: Unit 01

Space dynamics: Unit 02

Space dynamics: Unit 03

Space dynamics: Unit 04

Aerodynamics: Unit 01

• Conservation laws: Mass, momentum, and energy (integral and differential form); dimensional analysis and dynamic similarity; potential flow theory: Sources, sinks, doublets, line vortex, and their superposition
• Elementary ideas of viscous flows including boundary layers

Aerodynamics: Unit 02

• 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

Aerodynamics: Unit 03

• Basic concepts of compressibility, one-dimensional compressible flows, isentropic flows, fanno flow, Rayleigh flow; normal and oblique shocks, Prandtl-Meyer flow; flow through nozzles and diffusers

Aerodynamics: Unit 04

• Measurement and visualization techniques
• Shock-boundary layer interaction

Structures: Unit 01

• Stress and strain: Three-dimensional transformations, Mohr's circle, principal stresses, three-dimensional Hooke's law, plane stress and strain
• Failure theories: Maximum stress, Tresca and Von Mises
• Strain energy
• Castigliano's principles
• Statically determinate and indeterminate trusses, and beams
• Elastic flexural buckling of columns

Structures: Unit 02

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

Structures: Unit 03

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

Structures: Unit 04

Structures: Unit 05

• Equilibrium and compatibility equations, Airy's stress function

Propulsion: Unit 01

• Thermodynamics, boundary layers, heat transfer, combustion and thermochemistry

Propulsion: Unit 02

• Thrust, efficiency, range
• Brayton cycle
• Engine performance: Ramjet, turbojet, turbofan, turboprop, and turboshaft engines
• Afterburners

Propulsion: Unit 03

• Axial compressors: Angular momentum, work, and compression, characteristic performance of a single axial compressor stage, efficiency of the compressor and degree of reaction, multi-staging
• Centrifugal compressor: Stage dynamics, inducer, impeller, and diffuser
• Axial turbines: Stage performance

Propulsion: Unit 04

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

Propulsion: Unit 05

Propulsion: Unit 06

Propulsion: Unit 07

Propulsion: Unit 08

Engineering mathematics: Unit 01

• Matrices and determinants, linear and orthogonal transformations, Cayley-Hamilton theorem; eigen values and eigen vectors, solutions of linear equations

Engineering mathematics: Unit 02

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

Engineering mathematics: Unit 03

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

Engineering mathematics: Unit 04

• Linear and non-linear first order ordinary differential equations (ODE); homogeneous differential equations, higher order linear ODEs with constant coefficients; Laplace transforms and their inverse; partial differential equations
• Laplace, heat and wave equations

Engineering mathematics: Unit 05

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

Engineering mathematics: Unit 06

• Solutions of linear and non-linear algebraic equations; numerical integration-trapezoidal and Simpson's rule; numerical solutions of ODEs

Farm machinery: Unit 01

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

Farm machinery: Unit 02

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

Farm power: Unit 01

• Sources of power on the farm-human, animal, mechanical, electrical, wind, solar and biomass; biofuels

Farm power: Unit 02

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

Farm power: Unit 03

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

Soil and water conservation engineering: Unit 01

• Ideal and real fluids, properties of fluids; hydrostatic pressure and its measurement; continuity equation, kinematics, and dynamics of flow; Bernoulli's theorem; laminar and turbulent flow in pipes, Darcy-Weisbach and Hazen-Williams equations
• Moody's diagram; flow through orifices, weirs and notches; flow in open channels, dimensional analysis-concepts of geometric dimensionless numbers

Soil and water conservation engineering: Unit 02

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

Soil and water conservation engineering: Unit 03

• Hydrological cycle and measurement of its components; meteorological parameters and their measurement; analysis of precipitation data; runoff estimation; hydrograph analysis, unit hydrograph theory and application; stream flow measurement; flood routing
• Hydrological reservoir and channel routing, infiltration-indices and equations, drought and its classification

Soil and water conservation engineering: Unit 04

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

Soil and water conservation engineering: Unit 05

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

Soil and water conservation engineering: Unit 06

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

Irrigation and drainage engineering: Unit 01

• Water requirement of crops; consumptive use and evapotranspiration; measurement of infiltration, soil moisture, and irrigation water infiltration

Irrigation and drainage engineering: Unit 02

• Design of irrigation channels and underground pipelines; irrigation scheduling; surface, sprinkler and micro irrigation methods, design and evaluation of irrigation methods; irrigation efficiencies

Irrigation and drainage engineering: Unit 03

• 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; non-conventional drainage system

Irrigation and drainage engineering: Unit 04

• Groundwater occurrence; Darcy's law, steady and unsteady flow in confined and unconfined aquifers, groundwater exploration techniques; overview of groundwater recharge estimation and artificial recharge techniques

Irrigation and drainage engineering: Unit 05

• Types of wells, steady flow through wells; design and construction of water wells; classification of pumps; pump characteristics; pump selection and installation

Agricultural process engineering: Unit 01

• Physical, thermal, frictional, rheological, and electrical properties

Agricultural process engineering: Unit 02

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

Agricultural process engineering: Unit 03

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

Agricultural process engineering: Unit 04

• Processing of seeds, spices, fruits, and vegetables; value addition of agriculture produce

Agricultural process engineering: Unit 05

• Controlled and modified atmosphere storage; perishable food storage, godowns, bins and grain silos, packaging material and machines

Dairy and food engineering: Unit 01

• 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

Dairy and food engineering: Unit 02

• 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

Architecture, planning, and design: Unit 01

Architecture, planning, and design: Unit 02

Architecture, planning, and design: Unit 03

Architecture, planning, and design: Unit 04

Architecture, planning, and design: Unit 05

Architecture, planning, and design: Unit 06

Architecture, planning, and design: Unit 07

Architecture, planning, and design: Unit 08

Architecture, planning, and design: Unit 09

Architecture, planning, and design: Unit 10

Construction and management: Unit 01

Construction and management: Unit 02

Construction and management: Unit 03

Construction and management: Unit 04

Construction and management: Unit 05

Construction and management: Unit 06

Environmental planning and design: Unit 01

Environmental planning and design: Unit 02

Environmental planning and design: Unit 03

Environmental planning and design: Unit 04

Environmental planning and design: Unit 05

Environmental planning and design: Unit 06

Environmental planning and design: Unit 07

Urban design, landscape, and conservation: Unit 01

Urban design, landscape, and conservation: Unit 02

Urban design, landscape, and conservation: Unit 03

Urban design, landscape, and conservation: Unit 04

Urban design, landscape, and conservation: Unit 05

Urban design, landscape, and conservation: Unit 06

Urban design, landscape, and conservation: Unit 07

Urban design, landscape, and conservation: Unit 08

Urban design, landscape, and conservation: Unit 09

Urban design, landscape, and conservation: Unit 10

Urban design, landscape, and conservation: Unit 11

Urban design, landscape, and conservation: Unit 12

Planning process: Unit 01

Planning process: Unit 02

Planning process: Unit 03

Planning process: Unit 04

Planning process: Unit 05

Planning process: Unit 06

Planning process: Unit 07

Planning process: Unit 08

Planning process: Unit 09

Housing: Unit 01

Housing: Unit 02

Housing: Unit 03

Housing: Unit 04

Housing: Unit 05

Services and infrastructure: Unit 01

Services and infrastructure: Unit 02

Services and infrastructure: Unit 03

Services and infrastructure: Unit 04

Services and infrastructure: Unit 05

Services and infrastructure: Unit 06

Services and infrastructure: Unit 07

Services and infrastructure: Unit 08

Services and infrastructure: Unit 09

Services and infrastructure: Unit 10

Services and infrastructure: Unit 11

Services and infrastructure: Unit 12

Services and infrastructure: Unit 13

Services and infrastructure: Unit 14

Services and infrastructure: Unit 15

History and contemporary architecture: Unit 01

History and contemporary architecture: Unit 02

• Egyptian, Greco-Roman classical period, Byzantine, Gothic, Renaissance, Baroque-Rococo, etc

History and contemporary architecture: Unit 03

• Art nouveau, art Deco, eclecticism, international styles, post modernism, deconstruction in architecture, etc

History and contemporary architecture: Unit 04

History and contemporary architecture: Unit 05

History and contemporary architecture: Unit 06

History and contemporary architecture: Unit 07

Building construction and structural systems: Unit 01

Building construction and structural systems: Unit 02

Building construction and structural systems: Unit 03

Building construction and structural systems: Unit 04

Building construction and structural systems: Unit 05

Building construction and structural systems: Unit 06

Building construction and structural systems: Unit 07

Building construction and structural systems: Unit 08

Building construction and structural systems: Unit 09

Building construction and structural systems: Unit 10

Building construction and structural systems: Unit 11

Building construction and structural systems: Unit 12

Building construction and structural systems: Unit 13

Building construction and structural systems: Unit 14

Building services and sustainability: Unit 01

Building services and sustainability: Unit 02

Building services and sustainability: Unit 03

Building services and sustainability: Unit 04

Building services and sustainability: Unit 05

Building services and sustainability: Unit 06

Building services and sustainability: Unit 07

Building services and sustainability: Unit 08

Building services and sustainability: Unit 09

Building services and sustainability: Unit 10

Building services and sustainability: Unit 11

Building services and sustainability: Unit 12

Building services and sustainability: Unit 13

Building services and sustainability: Unit 14

Regional and settlement planning: Unit 01

Regional and settlement planning: Unit 02

Regional and settlement planning: Unit 03

Regional and settlement planning: Unit 04

Regional and settlement planning: Unit 05

Regional and settlement planning: Unit 06

Regional and settlement planning: Unit 07

Regional and settlement planning: Unit 08

Regional and settlement planning: Unit 09

Regional and settlement planning: Unit 10

Planning techniques and management: Unit 01

Planning techniques and management: Unit 02

Planning techniques and management: Unit 03

Planning techniques and management: Unit 04

Planning techniques and management: Unit 05

Planning techniques and management: Unit 06

Planning techniques and management: Unit 07

Planning techniques and management: Unit 08

Planning techniques and management: Unit 09

Planning techniques and management: Unit 10

Planning techniques and management: Unit 11

Planning techniques and management: Unit 12

Infrastructure planning: Unit 01

Infrastructure planning: Unit 02

Infrastructure planning: Unit 03

Infrastructure planning: Unit 04

Infrastructure planning: Unit 05

Infrastructure planning: Unit 06

Infrastructure planning: Unit 07

Infrastructure planning: Unit 08

Infrastructure planning: Unit 09

Engineering mathematics: Unit 01

• Matrices and determinants; systems of linear equations; eigen values and eigen vectors

Engineering mathematics: Unit 02

• Limits, continuity, and differentiability; partial derivatives, maxima and minima; sequences and series; test for convergence

Engineering mathematics: Unit 03

• Linear and nonlinear first order ODEs, higher order ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms

Engineering mathematics: Unit 04

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

Engineering mathematics: Unit 05

• Solution of linear and nonlinear algebraic equations; integration by trapezoidal and Simpson's rule; single step method for differential equations

General biology: Unit 01

• Biomolecules-structure and function; biological membranes-structure, membrane channels, and pumps, molecular motors, action potential and transport processes; basic concepts and regulation of metabolism of carbohydrates, lipids
• Amino acids and nucleic acids; photosynthesis, respiration, and electron transport chain
• Enzymes-classification, catalytic, and regulatory strategies; enzyme kinetics-Michaelis-Menten equation; enzyme inhibition-competitive, non-competitive, and uncompetitive inhibition

General biology: Unit 02

• Bacterial classification and diversity; microbial ecology-microbes in marine, freshwater, and terrestrial ecosystems; microbial interactions; viruses-structure and classification; methods in microbiology; microbial growth and nutrition; nitrogen fixation
• Microbial diseases and host-pathogen interactions; antibiotics and antimicrobial resistance

General biology: Unit 03

• Innate and adaptive immunity, humoral and cell mediated immunity; antibody structure and function; molecular basis of antibody diversity; T cell and B cell development; antigen-antibody reaction; complement; primary and secondary lymphoid organs
• Major histocompatibility complex (MHC); antigen processing and presentation; polyclonal and monoclonal antibody; regulation of immune response; immune tolerance; hyper sensitivity; autoimmunity; graft versus host reaction; immunization and vaccines

Genetics, cellular, and molecular biology: Unit 01

• Mendelian inheritance; gene interaction; complementation; linkage, recombination, and chromosome mapping; extra chromosomal inheritance; microbial genetics-transformation, transduction, and conjugation; horizontal gene transfer and transposable elements
• Chromosomal variation; genetic disorders; population genetics; epigenetics; selection and inheritance; adaptive and neutral evolution; genetic drift; species and speciation

Genetics, cellular, and molecular biology: Unit 02

• Prokaryotic and eukaryotic cell structure; cell cycle and cell growth control; cell-cell communication; cell signaling and signal transduction; post-translational modifications; protein trafficking; cell death and autophagy; extra-cellular matrix

Genetics, cellular, and molecular biology: Unit 03

• Molecular structure of genes and chromosomes; mutations and mutagenesis; regulation of gene expression; nucleic acid-replication, transcription, splicing, translation and their regulatory mechanisms; Non-coding and micro RNA; RNA interference
• DNA damage and repair

Fundamentals of biological engineering: Unit 01

• Material and energy balances for reactive and non-reactive systems; recycle, bypass and purge processes; stoichiometry of growth and product formation; degree of reduction, electron balance, theoretical oxygen demand

Fundamentals of biological engineering: Unit 02

• Laws of thermodynamics; solution thermodynamics; phase equilibrium, reaction equilibrium; ligand binding; membrane potential; energetics of metabolic pathways, oxidation, and reduction reactions

Fundamentals of biological engineering: Unit 03

• Newtonian and non-Newtonian fluids, fluid flow-laminar and turbulent; mixing in bioreactors, mixing time; molecular diffusion and film theory; oxygen transfer and uptake in bioreactor, kLa and its measurement; conductive and convective heat transfer, LMTD
• Overall heat transfer coefficient; heat exchangers

Bioprocess engineering and process biotechnology: Unit 01

• Rate law, zero, and first order kinetics; ideal reactors-batch, mixed flow and plug flow; enzyme immobilization, diffusion effects-Thiele modulus, effectiveness factor, Damkohler number; kinetics of cell growth
• Substrate utilization and product formation; structured and unstructured models; batch, fed-batch, and continuous processes; microbial and enzyme reactors; optimization and scale up

Bioprocess engineering and process biotechnology: Unit 02

• Media formulation and optimization; sterilization of air and media; filtration-membrane filtration, ultra filtration; centrifugation-high speed and ultra; cell disruption; principles of chromatography-ion exchange, gel filtration, hydrophobic interaction
• Affinity, GC, HPLC, and FPLC; extraction, adsorption, and drying

Bioprocess engineering and process biotechnology: Unit 03

• Pressure, temperature, and flow measurement devices; valves; first order and second order systems; feedback and feed forward control; types of controllers-proportional, derivative, and integral control, tuning of controllers

Plant, animal, and microbial biotechnology: Unit 01

• Totipotency; regeneration of plants; plant growth regulators and elicitors; tissue culture and cell suspension culture system-methodology, kinetics of growth and nutrient optimization; production of secondary metabolites; hairy root culture
• Plant products of industrial importance; artificial seeds; somaclonal variation; protoplast, protoplast fusion-somatic hybrid and cybrid; transgenic plants-direct and indirect methods of gene transfer techniques; selection marker and reporter gene
• Plastid transformation

Plant, animal, and microbial biotechnology: Unit 02

• 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; knock-out and knock-in animals

Plant, animal, and microbial biotechnology: Unit 03

• Production of biomass and primary/ secondary metabolites-biofuels, bioplastics, industrial enzymes, antibiotics; large scale production and purification of recombinant proteins and metabolites; clinical-, food-, and industrial microbiology
• Screening strategies for new products

Recombinant DNA technology and other tools in biotechnology: Unit 01

• Restriction and modification enzymes; vectors-plasmids, bacteriophage, and other viral vectors, cosmids, Ti plasmid, bacterial and yeast artificial chromosomes; expression vectors; cDNA and genomic DNA library; gene isolation and cloning
• Strategies for production of recombinant proteins; transposons and gene targeting

Recombinant DNA technology and other tools in biotechnology: Unit 02

• Polymerase chain reaction; DNA/ RNA labelling and sequencing; southern and northern blotting; in-situ hybridization; DNA fingerprinting, RAPD, RFLP; site-directed mutagenesis; gene transfer technologies; CRISPR-cas; biosensing and biosensors

Recombinant DNA technology and other tools in biotechnology: Unit 03

• Principles of microscopy-light, electron, fluorescent, and confocal; principles of spectroscopy-UV, visible, CD, IR, fluorescence, FT-IR, MS, NMR; electrophoresis; micro-arrays; enzymatic assays; immunoassays-ELISA, RIA, immunohistochemistry
• Immunoblotting; flow cytometry; whole genome and ChIP sequencing

Recombinant DNA technology and other tools in biotechnology: Unit 04

• Bioinformatics resources and search tools; sequence and structure databases; sequence analysis-sequence file formats, scoring matrices, alignment, phylogeny; genomics, proteomics, metabolomics; gene prediction; functional annotation
• Secondary structure and 3D structure prediction; knowledge discovery in biochemical databases; metagenomics; metabolic engineering and systems biology

Engineering mathematics: Unit 01

• Matrix algebra; systems of linear equations; eigen values and eigen vectors

Engineering mathematics: Unit 02

• Functions of single variable; limit, continuity, and differentiability; mean value theorems, local maxima and minima; Taylor series; evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume
• Partial derivatives; total derivative; gradient, divergence and curl, vector identities; directional derivatives; line, surface and volume integrals

Engineering mathematics: Unit 03

• First order (linear and non-linear) equations; higher order linear equations with constant coefficients; Euler-Cauchy equations; initial and boundary value problems

Engineering mathematics: Unit 04

• Fourier series; separation of variables; solutions of one-dimensional diffusion equation; first and second order one-dimensional wave equation and two-dimensional Laplace equation

Engineering mathematics: Unit 05

• Sampling theorems; conditional probability; descriptive statistics-mean, median, mode and standard deviation; random variables-discrete and continuous, Poisson and normal distribution; linear regression

Engineering mathematics: Unit 06

• Error analysis
• Numerical solutions of linear and non-linear algebraic equations; Newton's and Lagrange polynomials; numerical differentiation; integration by trapezoidal and Simpson's rule; single and multi-step methods for first order differential equations

Structural engineering: Unit 01

• System of forces, free-body diagrams, equilibrium equations; internal forces in structures; frictions and its applications; centre of mass; free vibrations of undamped SDOF system

Structural engineering: Unit 02

• Bending moment and shear force in statically determinate beams; simple stress and strain relationships; simple bending theory, flexural and shear stresses, shear centre; uniform torsion, transformation of stress; buckling of column
• Combined and direct bending stresses

Structural engineering: Unit 03

• 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

Structural engineering: Unit 04

• Construction materials: Structural steel-composition, material properties and behaviour; concrete-constituents, mix design, short-term and long-term properties
• Construction management: Types of construction projects; project planning and network analysis-PERT and CPM; cost estimation

Structural engineering: Unit 05

• Working stress and limit state design concepts; design of beams, slabs, columns; bond and development length; prestressed concrete beams

Structural engineering: Unit 06

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

Geotechnical engineering: Unit 01

• Three-phase system and phase relationships, index properties; unified and Indian standard soil classification system; permeability-one dimensional flow, seepage through soils-two-dimensional flow, flow nets, uplift pressure, piping, capillarity
• Seepage force; principle of effective stress and quicksand condition; compaction of soils; one-dimensional consolidation, time rate of consolidation; shear strength, Mohr's circle, effective and total shear strength parameters
• Stress-strain characteristics of clays and sand; stress paths

Geotechnical engineering: Unit 02

• Sub-surface investigations-drilling bore holes, sampling, plate load test, standard penetration and cone penetration tests; Earth pressure theories-Rankine and Coulomb; stability of slopes-finite and infinite slopes, Bishop's method
• Stress distribution in soils-Boussinesq's theory; pressure bulbs, shallow foundations-Terzaghi 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-dynamic and static formulae, axial load capacity of piles in sands and clays, pile load test, pile under lateral loading, pile group efficiency, negative skin friction

Water resources engineering: Unit 01

• Properties of fluids, fluid statics; continuity, momentum and energy equations and their applications; potential flow, laminar and turbulent flow; flow in pipes, pipe networks; concept of boundary layer and its growth; concept of lift and drag

Water resources engineering: Unit 02

• Forces on immersed bodies; flow measurement in channels and pipes; dimensional analysis and hydraulic similitude; channel hydraulics-energy-depth relationships, specific energy, critical flow, hydraulic jump, uniform flow
• Gradually varied flow and water surface profiles

Water resources engineering: Unit 03

• Hydrologic cycle, precipitation, evaporation, evapo-transpiration, watershed, infiltration, unit hydrographs, hydrograph analysis, reservoir capacity, flood estimation and routing, surface run-off models
• Ground water hydrology-steady state well hydraulics and aquifers; application of Darcy's law

Water resources engineering: Unit 04

• Types of irrigation systems and methods; crop water requirements-duty, delta, evapo-transpiration; gravity dams and spillways; lined and unlined canals, design of weirs on permeable foundation; cross drainage structures

Environmental engineering: Unit 01

• Basics of water quality standards-physical, chemical, and biological parameters; water quality index; unit processes and operations; water requirement; water distribution system; drinking water treatment
• Sewerage system design, quantity of domestic wastewater, primary and secondary treatment
• Effluent discharge standards; sludge disposal; reuse of treated sewage for different applications

Environmental engineering: Unit 02

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

Environmental engineering: Unit 03

• Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal)

Transportation engineering: Unit 01

• Geometric design of highways-cross-sectional elements, sight distances, horizontal and vertical alignments
• Geometric design of railway Track-speed and cant
• Concept of airport runway length, calculations and corrections; taxiway and exit taxiway design

Transportation engineering: Unit 02

• Highway materials-desirable properties and tests; desirable properties of bituminous paving mixes; design factors for flexible and rigid pavements; design of flexible and rigid pavement using IRC codes

Transportation engineering: Unit 03

• Traffic studies on flow and speed, peak hour factor, accident study, statistical analysis of traffic data; microscopic and macroscopic parameters of traffic flow, fundamental relationships; traffic signs; signal design by Webster's method
• Types of intersections; highway capacity

Geomatics engineering: Unit 01

Geomatics engineering: Unit 02

Geomatics engineering: Unit 03

• Scale, coordinate system

Geomatics engineering: Unit 04

• Levelling and trigonometric levelling

Geomatics engineering: Unit 05

Geomatics engineering: Unit 06

Geomatics engineering: Unit 07

Geomatics engineering: Unit 08

• Scale, flying height

Geomatics engineering: Unit 09

Engineering mathematics: Unit 01

• Matrix algebra, systems of linear equations, eigen values and eigen vectors

Engineering mathematics: Unit 02

• 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

Engineering mathematics: Unit 03

• 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

Engineering mathematics: Unit 04

• Complex number, polar form of complex number, triangle inequality

Engineering mathematics: Unit 05

• Definitions of probability and sampling theorems, conditional probability, mean, median, mode and standard deviation, random variables, Poisson, normal and binomial distributions, linear regression analysis

Engineering mathematics: Unit 06

• 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

Process calculations and thermodynamics: Unit 01

Process calculations and thermodynamics: Unit 02

Process calculations and thermodynamics: Unit 03

Process calculations and thermodynamics: Unit 04

Process calculations and thermodynamics: Unit 05

Process calculations and thermodynamics: Unit 06

Process calculations and thermodynamics: Unit 07

Process calculations and thermodynamics: Unit 08

Process calculations and thermodynamics: Unit 09

Process calculations and thermodynamics: Unit 10

• Equation of state and residual properties

Process calculations and thermodynamics: Unit 11

• Partial molar properties, fugacity, excess properties and activity coefficients

Process calculations and thermodynamics: Unit 12

• Predicting VLE of systems; chemical reaction equilibrium

Fluid mechanics and mechanical operations: Unit 01

Fluid mechanics and mechanical operations: Unit 02

Fluid mechanics and mechanical operations: Unit 03

Fluid mechanics and mechanical operations: Unit 04

Fluid mechanics and mechanical operations: Unit 05

Fluid mechanics and mechanical operations: Unit 06

Fluid mechanics and mechanical operations: Unit 07

Fluid mechanics and mechanical operations: Unit 08

Fluid mechanics and mechanical operations: Unit 09

Fluid mechanics and mechanical operations: Unit 10

Fluid mechanics and mechanical operations: Unit 11

Fluid mechanics and mechanical operations: Unit 12

Fluid mechanics and mechanical operations: Unit 13

Fluid mechanics and mechanical operations: Unit 14

Fluid mechanics and mechanical operations: Unit 15

Fluid mechanics and mechanical operations: Unit 16

Fluid mechanics and mechanical operations: Unit 17

• Fluctuating velocity, universal velocity profile and pressure drop

Fluid mechanics and mechanical operations: Unit 18

Fluid mechanics and mechanical operations: Unit 19

Fluid mechanics and mechanical operations: Unit 20

Fluid mechanics and mechanical operations: Unit 21

Fluid mechanics and mechanical operations: Unit 22

Fluid mechanics and mechanical operations: Unit 23

Fluid mechanics and mechanical operations: Unit 24

Fluid mechanics and mechanical operations: Unit 25

Fluid mechanics and mechanical operations: Unit 26

Heat transfer: Unit 01

Heat transfer: Unit 02

Heat transfer: Unit 03

Heat transfer: Unit 04

Heat transfer: Unit 05

Heat transfer: Unit 06

Heat transfer: Unit 07

Heat transfer: Unit 08

Heat transfer: Unit 09

Mass transfer: Unit 01

Mass transfer: Unit 02

Mass transfer: Unit 03

Mass transfer: Unit 04

Mass transfer: Unit 05

Mass transfer: Unit 06

Mass transfer: Unit 07

Mass transfer: Unit 08

Mass transfer: Unit 09

Mass transfer: Unit 10

Mass transfer: Unit 11

Mass transfer: Unit 12

Mass transfer: Unit 13

Mass transfer: Unit 14

Mass transfer: Unit 15

Mass transfer: Unit 16

Mass transfer: Unit 17

Chemical reaction engineering: Unit 01

Chemical reaction engineering: Unit 02

Chemical reaction engineering: Unit 03

Chemical reaction engineering: Unit 04

Chemical reaction engineering: Unit 05

Chemical reaction engineering: Unit 06

Chemical reaction engineering: Unit 07

Chemical reaction engineering: Unit 08

Chemical reaction engineering: Unit 09

Chemical reaction engineering: Unit 10

Chemical reaction engineering: Unit 11

Chemical reaction engineering: Unit 12

Instrumentation and process control: Unit 01

Instrumentation and process control: Unit 02

Instrumentation and process control: Unit 03

Instrumentation and process control: Unit 04

Instrumentation and process control: Unit 05

Instrumentation and process control: Unit 06

Instrumentation and process control: Unit 07

Instrumentation and process control: Unit 08

Instrumentation and process control: Unit 09

Instrumentation and process control: Unit 10

Instrumentation and process control: Unit 11

Instrumentation and process control: Unit 12

Instrumentation and process control: Unit 13

Instrumentation and process control: Unit 14

Plant design and economics: Unit 01

Plant design and economics: Unit 02

Plant design and economics: Unit 03

Plant design and economics: Unit 04

Plant design and economics: Unit 05

Plant design and economics: Unit 06

Chemical technology: Unit 01

Chemical technology: Unit 02

Chemical technology: Unit 03

Chemical technology: Unit 04

Chemical technology: Unit 05

Engineering mathematics: Unit 01

• Propositional and first order logic
• Sets, relations, functions, partial orders and lattices
• Monoids, groups
• Graphs: Connectivity, matching, colouring
• Combinatorics: Counting, recurrence relations, generating functions

Engineering mathematics: Unit 02

• Matrices, determinants, system of linear equations, eigen values and eigen vectors, LU decomposition

Engineering mathematics: Unit 03

• Limits, continuity, and differentiability
• Maxima and minima
• Mean value theorem
• Integration

Engineering mathematics: Unit 04

• Random variables
• Uniform, normal, exponential, poisson and binomial distributions
• Mean, median, mode and standard deviation
• Conditional probability and baye's theorem

Computer science and information technology: Unit 01

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

Computer science and information technology: Unit 02

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

Computer science and information technology: Unit 03

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

Computer science and information technology: Unit 04

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

Computer science and information technology: Unit 05

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

Computer science and information technology: Unit 06

• Lexical analysis, parsing, syntax-directed translation
• Runtime environments
• Intermediate code generation
• Local optimisation, data flow analyses: Constant propagation, liveness analysis, common subexpression elimination

Computer science and information technology: Unit 07

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

Computer science and information technology: Unit 08

• 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

Computer science and information technology: Unit 09

• Concept of layering: OSI and TCP/IP protocol stacks; basics of packet, circuit and virtual circuit-switching; data link layer: Framing, error detection, medium access control, ethernet bridging
• Routing protocols: Shortest path, flooding, distance vector and link state routing; fragmentation and IP addressing, IPv4, CIDR notation, basics of IP support protocols (ARP, DHCP, ICMP), network address translation (NAT)
• Transport layer: Flow control and congestion control, UDP, TCP, sockets; application layer protocols: DNS, SMTP, HTTP, FTP, Email

Physical chemistry: Unit 01

• Postulates of quantum mechanics
• Operators
• Time dependent and time independent Schrödinger equations
• Born interpretation
• Dirac bra-ket notation
• Particle in a box: Infinite and finite square wells; concept of tunnelling; particle in 1D, 2D and 3D-box; applications
• Harmonic oscillator: Harmonic and anharmonic potentials; hermite polynomials
• Rotational motion: Angular momentum operators, rigid rotor
• Hydrogen and hydrogen-like atoms: Atomic orbitals; radial distribution function
• Multi-electron atoms: Orbital approximation; electron spin; Pauli exclusion principle; slater determinants
• Approximation methods: Variation method and secular determinants; first order perturbation techniques
• Atomic units
• Molecular structure and chemical bonding: Born-Oppenheimer approximation; valence bond theory and linear combination of atomic orbitals-molecular orbital (LCAO-MO) theory
• Hybrid orbitals
• Applications of LCAO-MO theory to H2 +, H2; molecular orbital theory (MOT) of homo- and heteronuclear diatomic molecules
• Hückel approximation and its application to annular π– electron systems
• Group theory: Symmetry elements and operations; point groups and character tables; internal coordinates and vibrational modes; symmetry adapted linear combination of atomic orbitals (LCAO-MO); construction of hybrid orbitals using symmetry aspects
• Spectroscopy: Atomic spectroscopy; Russell-Saunders coupling; term symbols and spectral details; origin of selection rules. Rotational, vibrational, electronic and Raman spectroscopy of diatomic and polyatomic molecules. Line broadening
• Spectroscopy: Einstein's coefficients. Relationship of transition moment integral with molar extinction coefficient and oscillator strength. Basic principles of nuclear magnetic resonance: Gyromagnetic ratio; chemical shift, nuclear coupling

Physical chemistry: Unit 02

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

Physical chemistry: Unit 03

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

Physical chemistry: Unit 04

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

Inorganic chemistry: Unit 01

• 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, phosphorous and sulphur
• Industrial synthesis of compounds of main group elements
• Chemistry of noble gases, pseudohalogens, and interhalogen compounds
• Acid-base concepts and principles (Lewis, Brønsted, HSAB and acid-base catalysis)

Inorganic chemistry: Unit 02

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

Inorganic chemistry: Unit 03

• Recovery
• Periodic properties, spectra and magnetic properties

Inorganic chemistry: Unit 04

• 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

Inorganic chemistry: Unit 05

• Detection of radioactivity, decay processes, half-life of radioactive elements, fission and fusion processes

Inorganic chemistry: Unit 06

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

Inorganic chemistry: Unit 07

• 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

Inorganic chemistry: Unit 08

• UV-visible, fluorescence and FTIR spectrophotometry, NMR and ESR spectroscopy, mass spectrometry, atomic absorption spectroscopy, Mössbauer spectroscopy (Fe and Sn) and X-ray crystallography
• Chromatography including GC and HPLC
• Electroanalytical methods-polarography, cyclic voltammetry, ion-selective electrodes
• Thermoanalytical methods

Organic chemistry: Unit 01

• Chirality and symmetry 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 and optical isomerism
• Configurational and conformational effects, atropisomerism, and neighbouring group participation on reactivity and selectivity/ specificity

Organic chemistry: Unit 02

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

Organic chemistry: Unit 03

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

Organic chemistry: Unit 04

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

Organic chemistry: Unit 05

• Structure, preparation, properties and reactions of furan, pyrrole, thiophene, pyridine, indole, quinoline and isoquinoline

Organic chemistry: Unit 06

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

Organic chemistry: Unit 07

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

Engineering mathematics: Unit 01

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

Engineering mathematics: Unit 02

• 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

Engineering mathematics: Unit 03

• 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

Engineering mathematics: Unit 04

• Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stokes' theorems

Engineering mathematics: Unit 05

• Analytic functions, Cauchy's integral theorem, Cauchy's integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem

Engineering mathematics: Unit 06

• Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability

Networks, signals, and systems: Unit 01

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

Networks, signals, and systems: Unit 02

• Fourier series and Fourier transform, sampling theorem and applications

Networks, signals, and systems: Unit 03

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

Electronic devices: Unit 01

Electronic devices: Unit 02

Electronic devices: Unit 03

Electronic devices: Unit 04

• Diffusion current, drift current, mobility and resistivity, generation and recombination of carriers, Poisson and continuity equations

Electronic devices: Unit 05

Electronic devices: Unit 06

Electronic devices: Unit 07

Electronic devices: Unit 08

Electronic devices: Unit 09

Electronic devices: Unit 10

Electronic devices: Unit 11

Analog circuits: Unit 01

• Clipping, clamping and rectifiers

Analog circuits: Unit 02

• Biasing, ac coupling, small signal analysis, frequency response
• Current mirrors and differential amplifiers

Analog circuits: Unit 03

• Amplifiers, summers, differentiators, integrators, active filters, Schmitt triggers and oscillators

Digital circuits: Unit 01

• Binary, integer and floating-point-numbers

Digital circuits: Unit 02

• Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders

Digital circuits: Unit 03

• Latches and flip-flops, counters, shift-registers, finite state machines, propagation delay, setup and hold time, critical path delay

Digital circuits: Unit 04

• Sample and hold circuits, ADCs and DACs

Digital circuits: Unit 05

• ROM, SRAM, DRAM

Digital circuits: Unit 06

• Machine instructions and addressing modes, ALU, data-path and control unit, instruction pipelining

Control systems: Unit 01

Control systems: Unit 02

Control systems: Unit 03

Control systems: Unit 04

Control systems: Unit 05

Control systems: Unit 06

Control systems: Unit 07

Control systems: Unit 08

Control systems: Unit 09

Control systems: Unit 10

Control systems: Unit 11

Communications: Unit 01

• Autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems

Communications: Unit 02

• Amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers

Communications: Unit 03

• Entropy, mutual information and channel capacity theorem

Communications: Unit 04

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

Communications: Unit 05

Communications: Unit 06

Communications: Unit 07

Electromagnetics: Unit 01

• Differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector

Electromagnetics: Unit 02

• Reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth

Electromagnetics: Unit 03

• Equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart

Electromagnetics: Unit 04

Electromagnetics: Unit 05

Electromagnetics: Unit 06

Electromagnetics: Unit 07

Engineering mathematics: Unit 01

• Matrix algebra, systems of linear equations, eigen values, eigen vectors

Engineering mathematics: Unit 02

• Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, directional derivatives, line integral, surface integral
• Volume integral, Stokes's theorem, Gauss's theorem, divergence theorem, Green's theorem

Engineering mathematics: Unit 03

• 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

Engineering mathematics: Unit 04

• Analytic functions, Cauchy's integral theorem, Cauchy's integral formula, Taylor series, Laurent series, residue theorem, solution integrals

Engineering mathematics: Unit 05

• 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

Electric circuits: Unit 01

• Ideal voltage and current sources, dependent sources, R, L, C, M elements

Electric circuits: Unit 02

• KCL, KVL, node and mesh analysis

Electric circuits: Unit 03

• Thevenin's, Norton's, superposition and maximum power transfer theorem; transient response of dc and ac networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation
• Complex power and power factor in ac circuits

Electromagnetic fields: Unit 01

Electromagnetic fields: Unit 02

Electromagnetic fields: Unit 03

Electromagnetic fields: Unit 04

Electromagnetic fields: Unit 05

Electromagnetic fields: Unit 06

Electromagnetic fields: Unit 07

Electromagnetic fields: Unit 08

Electromagnetic fields: Unit 09

Electromagnetic fields: Unit 10

Electromagnetic fields: Unit 11

Electromagnetic fields: Unit 12

Electromagnetic fields: Unit 13

Electromagnetic fields: Unit 14

Electromagnetic fields: Unit 15

Electromagnetic fields: Unit 16

Electromagnetic fields: Unit 17

Electromagnetic fields: Unit 18

Signals and systems: Unit 01

Signals and systems: Unit 02

Signals and systems: Unit 03

Signals and systems: Unit 04

Signals and systems: Unit 05

Signals and systems: Unit 06

Signals and systems: Unit 07

Electrical machines: Unit 01

• Equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency

Electrical machines: Unit 02

• Connections, vector groups, parallel operation

Electrical machines: Unit 03

Electrical machines: Unit 04

Electrical machines: Unit 05

• Separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of dc motors

Electrical machines: Unit 06

• Principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control

Electrical machines: Unit 07

Electrical machines: Unit 08

• Cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors

Electrical machines: Unit 09

Power systems: Unit 01

Power systems: Unit 02

Power systems: Unit 03

Power systems: Unit 04

Power systems: Unit 05

Power systems: Unit 06

Power systems: Unit 07

Power systems: Unit 08

Power systems: Unit 09

Power systems: Unit 10

Power systems: Unit 11

Power systems: Unit 12

Power systems: Unit 13

Power systems: Unit 14

Power systems: Unit 15

Power systems: Unit 16

Power systems: Unit 17

Power systems: Unit 18

Power systems: Unit 19

Power systems: Unit 20

Control systems: Unit 01

Control systems: Unit 02

Control systems: Unit 03

Control systems: Unit 04

Control systems: Unit 05

Control systems: Unit 06

Control systems: Unit 07

Control systems: Unit 08

Control systems: Unit 09

Control systems: Unit 10

Control systems: Unit 11

Control systems: Unit 12

Control systems: Unit 13

Control systems: Unit 14

Control systems: Unit 15

Electrical and electronic measurements: Unit 01

Electrical and electronic measurements: Unit 02

Electrical and electronic measurements: Unit 03

Electrical and electronic measurements: Unit 04

Electrical and electronic measurements: Unit 05

Electrical and electronic measurements: Unit 06

Electrical and electronic measurements: Unit 07

Electrical and electronic measurements: Unit 08

Electrical and electronic measurements: Unit 09

Electrical and electronic measurements: Unit 10

Electrical and electronic measurements: Unit 11

Analog and digital electronics: Unit 01

• Clipping, clamping, rectifiers

Analog and digital electronics: Unit 02

• Biasing, equivalent circuit and frequency response

Analog and digital electronics: Unit 03

Analog and digital electronics: Unit 04

• characteristics and applications

Analog and digital electronics: Unit 05

Analog and digital electronics: Unit 06

Analog and digital electronics: Unit 07

Analog and digital electronics: Unit 08

Analog and digital electronics: Unit 09

Analog and digital electronics: Unit 10

Analog and digital electronics: Unit 11

Analog and digital electronics: Unit 12

Analog and digital electronics: Unit 13

Analog and digital electronics: Unit 14

Power electronics: Unit 01

Power electronics: Unit 02

Power electronics: Unit 03

Power electronics: Unit 04

• Buck, boost, and buck-boost converters

Power electronics: Unit 05

Power electronics: Unit 06

Power electronics: Unit 07

Power electronics: Unit 08

Power electronics: Unit 09

Power electronics: Unit 10

Power electronics: Unit 11

Common section: Unit 01

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

Common section: Unit 02

Common section: Unit 03

Common section: Unit 04

• Stress, strain and material response; brittle and ductile deformation; nomenclature and classification of folds and faults

Common section: Unit 05

• Basic crystal symmetry and concept of point groups
• Mineralogy-silicate crystal structure and determinative mineralogy of common rock forming minerals

Common section: Unit 06

Common section: Unit 07

Common section: Unit 08

Common section: Unit 09

Common section: Unit 10

Common section: Unit 11

Common section: Unit 12

Common section: Unit 13

Common section: Unit 14

Common section: Unit 15

Common section: Unit 16

Geology: Unit 01

• Geomorphic processes and agents; development and evolution of landforms in continental, and oceanic settings; tectonic geomorphology

Geology: Unit 02

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

Geology: Unit 03

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

Geology: Unit 04

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

Geology: Unit 05

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

Geology: Unit 06

• Texture, structure, and sedimentary processes; petrology of common sedimentary rocks; sedimentary facies and environments, cyclicities in sedimentary succession; provencance and basin analysis
• Important sedimentary basins of India

Geology: Unit 07

• Structures and textures of metamorphic rocks
• Physicochemical conditions of metamorphism and concept of metamorphic facies, grade and baric types; chemographic projections; metamorphism of pelitic, mafic and impure carbonate rocks; role of bulk composition including fluids in metamorphism
• Thermobarometry and metamorphic P-T-t paths, and their tectonic significance

Geology: Unit 08

• Diversity of life through time, mass extinctions-causes and effects; taphonomy-processes of fossilization
• Taxonomy
• Morphology and functional morphology of invertebrates (bivalves, brachiopods, gastropods, echinoids, ammonites); microfossils (foraminifera, ostracoda, conodonts, bryozoa); vertebrate paleonology (equus, probicidea, human)
• Paleobotany (plant, spores, pollens)
• Basic concepts of ecology/ paleoecology; classification-ecological and taxonomic schemes (diversity and richness)
• Fossils and paleoenvironments

Geology: Unit 09

• Principles of stratigraphy and concepts of correlation; lithostratigraphy, biostratigraphy, and chronostratigraphy
• Principles of sequence stratigraphy and applications
• Stratigraphy of peninsular and extra-peninsular India
• Boundary problems in Indian stratigraphy

Geology: Unit 10

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

Geology: Unit 11

• Plate motions, driving mechanisms, plate boundaries, supercontinent cycles

Geology: Unit 12

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

Geology: Unit 13

Geology: Unit 14

• Groundwater flow and exploration, well hydraulics and water quality

Geology: Unit 15

• 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

Geophysics: Unit 01

• 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

Geophysics: Unit 02

• Gravitational field of the earth; geoid; ellipsoid; geodetic reference systems; datum; Everest (1830) and WGS 84 (1984) systems; GPS and DGPS; levelling and surveying

Geophysics: Unit 03

• Elements of elasticity theory-stress and strain tensors, generalized Hooke's law; body and surface waves; rotational, dilatational, irrotational, and equivolumnal waves
• Reflection and refraction of elastic waves; inhomogeneous and evanescent waves, and bounded waves; Eikonal equation and ray theory; earthquakes causes and measurements, magnitude and intensity, focal mechanisms; earthquake quantification
• Source characteristics, seismotectonics, and seismic hazards; digital seismographs, earthquake statistics, wave propagation in elastic media, quantifying earthquake source from seismological data
• Elements of seismic tomography

Geophysics: Unit 04

• Scalar and vector potential fields; Laplace, Maxwell, and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green's theorem; image theory
• Integral equations in potential and time-varying field theory

Geophysics: Unit 05

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

Geophysics: Unit 06

• Elements of Earth's magnetic field, units of measurement, magnetic susceptibility of rocks and measurements, magnetometers, and magnetic gradiometers, land, airborne and marine magnetic, and magnetic gradiometer surveys
• Various corrections applied to magnetic data, IGRF, reduction to Pole transformation, Poisson's relation of gravity, and magnetic potential field, preparation of magnetic maps, upward and downward continuation
• Magnetic anomalies due to geometrical and irregular shaped bodies; image processing concepts in processing of magnetic anomaly maps; depth rules; interpretation of processed magnetic anomaly data; derivative
• Analytic signal and Euler depth solutions
• Applications of gravity and magnetic methods for mineral, and oil exploration

Geophysics: Unit 07

• Conduction of electricity through rocks, electrical conductivities of metals, non-metals, rock forming minerals and different rocks, concepts of DC resistivity measurement and depth of investigation; apparent resistivity and apparent chargeability
• Concept of negative apparent resistivity and negative apparent chargeability; theory of reciprocity, sounding and profiling, various electrode arrangements, application of linear filter theory, sounding curves over multi-layered earth
• Dar-Zarrouk parameters, reduction of layers, triangle of anisotropy, interpretation of resistivity field data, principles of equivalence and suppression, self-potential method and its origin; electrical resistivity tomography (ERT); induced polarization
• Time and frequency domain IP measurements; interpretation and applications of SP, resistivity and IP data sets for ground-water exploration, mineral exploration, environmental and engineering applications

Geophysics: Unit 08

• Geoelectromagnetic spectrum; Biot Savart's law; Maxwell's equation, Helmholtz equation, basic concept of EM induction in the earth, skin-depth, elliptic polarization, in-phase and quadrature components, phasor diagrams
• Response function and response parameters; ground and airborne methods, measurements in different source-receiver configurations; Earth's natural electromagnetic methods-tellurics, geomagnetic depth sounding and magnetotellurics
• Electromagnetic profiling and sounding, time domain EM method; EM scale modelling, processing of EM data and interpretation; ground penetrating radar (GPR) methods; effect of conducting overburden; geological applications including groundwater
• Mineral environmental and hydrocarbon exploration

Geophysics: Unit 09

• Elastic properties of earth materials; reflection, refraction, and CDP surveys; land and marine seismic sources, generation, and propagation of elastic waves, velocity-depth models, geophones, hydrophones, digital recording systems, digital formats
• Field layouts, seismic noise, and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D, 3D, and 4D seismic data acquisition, processing and interpretation; CDP stacking charts, binning, filtering
• Static and dynamic corrections, digital seismic data processing, seismic deconvolution and migration methods, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP, AVO, multi
• Component seismics and seismic interferometry
• Reservoir geophysics-rock physics and petrophysics
• Geophysical survey design

Geophysics: Unit 10

• Sampling theorem, Nyquist frequency, aliasing, Fourier series, periodic waveform, Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, auto correlation, cross correlation, convolution, deconvolution
• Principles of digital filters, windows, poles, and zeros

Geophysics: Unit 11

• Principles and techniques of geophysical well-logging, SP, resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic resonance-longitudinal and transverse relaxation, CPMG sequence
• Porosity characterization, cement bond logging, micro-logs
• Pulsed neutron devices and spectroscopy; multi-array and triaxial induction devices; quantitative evaluation of formations from well logs; logging while drilling; high angle and horizontal wells; clay quantification; lithology and porosity estimation
• Saturation and permeability estimation; application of bore hole geophysics in ground water, mineral, and oil exploration

Geophysics: Unit 12

• Prospecting and assaying of mineral (radioactive and non-radioactive) deposits, half-life, decay constant, radioactive equilibrium, GM counter, scintillation detector, semiconductor devices, application of radiometric for exploration
• Assaying and radioactive waste disposal

Geophysics: Unit 13

• Basic concepts of forward and inverse problems, ill-posedness of inverse problems, condition number, non-uniqueness and stability of solutions; L1, L2, and Lp norms, overdetermined, underdetermined, and mixed determined inverse problems
• Quasi-linear and non-linear methods including Tikhonov's regularization method, singular value decomposition, Backus-Gilbert method, simulated annealing, genetic algorithms, swarm intelligence, machine learning, and artificial neural networks
• Statistics of misfit and likelihood, Bayesian construction of posterior probabilities, sparsity promoting L1 optimization
• Ambiguity and uncertainty in geophysical interpretation

Engineering mathematics: Unit 01

• Matrix algebra, systems of linear equations, consistency and rank, eigen values and eigen vectors

Engineering mathematics: Unit 02

• 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

Engineering mathematics: Unit 03

• First order equation (linear and nonlinear), second order linear differential equations with constant coefficients, method of variation of parameters, Cauchy's and Euler's equations, initial and boundary value problems
• Solution of partial differential equations: variable separable method

Engineering mathematics: Unit 04

• Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent's series, residue theorem, solution of integrals

Engineering mathematics: Unit 05

• Sampling theorems, conditional probability, mean, median, mode, standard deviation and variance; random variables: Discrete and continuous distributions: Normal, Poisson and binomial distributions

Engineering mathematics: Unit 06

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

Instrumentation engineering: Unit 01

• 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

Instrumentation engineering: Unit 02

• Voltage and current sources: Independent, dependent, ideal and practical; V-I relationships of resistor, inductor, mutual inductance and capacitor; transient analysis of RLC circuits with DC excitation
• Kirchhoff's laws, mesh and nodal analysis, superposition, Thevenin, Norton, maximum power transfer and reciprocity theorems
• Peak-, average- and RMS values of ac quantities; apparent-, active- and reactive powers; phasor analysis, impedance and admittance; series and parallel resonance, locus diagrams, realization of basic filters with R, L and C elements
• Transient analysis of RLC circuits with AC excitation
• One-port and two-port networks, driving point impedance and admittance, open-, and short circuit parameters
• Single phase transformer: Equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency
• Three phase induction motors: Principle of operation, types, performance, torque-speed characteristics, no-load and blocked rotor tests, equivalent circuit, starting and speed control; types of losses and efficiency calculations of electric machines

Instrumentation engineering: Unit 03

• 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

Instrumentation engineering: Unit 04

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

Instrumentation engineering: Unit 05

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