GATE 2021 Exam - Result, Scorecard, Cutoff, Answer Key
Updated on 5th Mar, 2021
Result Date 22 Mar, 2021
Latest Update for GATE
- 1 day ago:
GATE 2021 answer key objection closed. Check GATE result date and previous year's GATE cutoff.
- 1 day ago: GATE 2021 answer key objections now open.
- 26 Feb 2021:
GATE Official Answer Key 2021 released by IIT Bombay on February 26. Download now!
About GATE 2021
GATE 2021 - IIT Bombay will release the GATE 2021 result on March 22, 2021, along with the final answer key. The official GATE answer key 2021 was released on February 26. Objections to the GATE 2021 answer keys were accepted from March 1 to 4. GATE 2021 exam was conducted by the Indian Institute of Technology (IIT) Bombay successfully on February 6, 7, 13 & 14. The scorecard of GATE will be valid for three years after the date of release. There will be no common counselling for GATE 2021. For IIT admissions, the candidates will have to register through COAP. Meanwhile, for NIT admissions, the candidates will have to apply through CCMT. Various PSUs will also open their recruitment process for GATE qualified candidates.
Latest GATE 2021 Updates: GATE answer key 2021 released on Feb 26. Also, check GATE cutoff.
The admit card of GATE was released online on January 8 at appsgate.iitb.ac.in. Candidates can download the admit card/hall ticket from the GOAPS website by using the GATE 2021 login credentials. GATE 2021 registered candidates were provided with a chance to change preferred exam cities on December 14 and 15. The authorities have released the GATE 2021 mock test on the official website on November 25. IIT Bombay has increased 11 new exam cities in the list of GATE exam centres 2021.
GATE 2021 eligibility criteria have also be relaxed due to the covid-19 situation. As per the announcement, candidates in their third year of an undergraduate degree will be eligible for the exam. Also, the GATE 2021 exam will have two new subjects - Humanities and Social Science (XH) and Environmental Science and Engineering (ES). The humanities and social science syllabus will be available on the official information brochure. Also, the environmental science and engineering GATE 2021 syllabus can be checked from the GATE 2021 official brochure.
GATE 2021 exam - Snippets
- GATE 2021 exam was conducted in fully computer-based mode.
- The exam authorities has introduced two new papers - ES (Environmental Science and Engineering) and XH (Humanities and Social Sciences) in Economics / English / Linguistics / Philosophy / Psychology / Sociology.
- The total number of subjects was 27.
- The syllabus of GATE was also revised.
- No age limit to appear for the GATE exam 2021.
- GATE 2021 scorecard will be valid for three years.
What is GATE exam?
Graduate Aptitude Test in Engineering (GATE) is conducted to shortlist candidates for admission in PG engineering courses. The scores are also taken into consideration during PSU recruitments. GATE is conducted jointly by the seven IITs (Bombay, Delhi, Guwahati, Kharagpur, Madras, Roorkee, and Kanpur) and the Indian Institute of Science (IISc) Bangalore. IIT Bombay has announced all the important dates of examination.
GATE 2021 Highlights
| Full Exam Name | Graduate Aptitude Test in Engineering |
| Short Exam Name | GATE |
| Conducting Body | Indian Institute of Technology Bombay |
| Frequency of Conduct | Once a year |
| Exam Level | National Level Exam |
| Languages | English |
| Mode of Application | Online |
| Application Fee (General) | 1500 Rs [Online] |
| Mode of Exam | Online |
| Mode of Counselling | Online |
| Participating Colleges | 1065 |
| Exam Duration | 3 Hours |
Download all details about GATE 2021
GATE 2021 Important Dates
Stay up-to date with Exam Notification and News
Upcoming Dates and Events
18 Mar, 2021
Answer Key - Final answer key | Mode: Online
22 Mar, 2021
Result | Mode: Online
Past Dates and Events
01 Mar, 2021 - 04 Mar, 2021
Answer Key - Objections | Mode: Online
26 Feb, 2021
Answer Key | Mode: Online
14 Feb, 2021
Exam - Forenoon - ME-1, XH | Mode: Online
14 Feb, 2021
Exam - Afternoon - ME-2, MT | Mode: Online
13 Feb, 2021
Exam - Afternoon - CS-2, XE, XL | Mode: Online
13 Feb, 2021
Exam - Forenoon - CS-1, MA, BT, CH, TF | Mode: Online
07 Feb, 2021
Exam - Afternoon - EC, PE, ES, ST, PI | Mode: Online
07 Feb, 2021
Exam - Forenoon - EE, GG, AG, EY | Mode: Online
06 Feb, 2021
Exam - Forenoon - CE-1, IN, CY | Mode: Online
06 Feb, 2021
Exam - Afternoon - CE-2, PH, AR, BM, AE, MN | Mode: Online
08 Jan, 2021
Admit Card | Mode: Online
14 Dec, 2020 - 15 Dec, 2020
Choice of Exam City - Last chance to change | Mode: Online
25 Nov, 2020
Mock Test - Start Date | Mode: Online
17 Nov, 2020 - 23 Nov, 2020
Application Correction - Reopened | Mode: Online
28 Oct, 2020 - 13 Nov, 2020
Application Correction | Mode: Online
08 Oct, 2020 - 14 Oct, 2020
Late Fee Application | Mode: Online
11 Sep, 2020 - 08 Oct, 2020
Application | Mode: Online
26 Jul, 2020
Advertisement | Mode: Online
GATE 2021 eligibility criteria has been relaxed due to the covid-19 situation. As per the announcement, candidates in their third year of an undergraduate degree will be eligible for the GATE exam 2021. Also, with the addition of humanities and social science, non-science graduates from arts and commerce can also apply for GATE 2021.
There are some important parameters that the candidates are expected to meet to be eligible for GATE 2021. These eligibility criteria are set up by the authorities and the candidates are advised to check them before filling out the application form. Various factors such as age, academics, nationality, and more are involved in the eligibility criteria of GATE 2021.
Age Limit: There is no age limit for GATE 2021.
Nationality: Candidates should be of Indian nationality. However, candidates from Bangladesh, Ethiopia, Nepal, Sri Lanka, Singapore and United Arab Emirate (UAE) would also be eligible to apply.
Academic Qualification: No minimum pass percentage has been specified by the authorities for GATE 2021. However, the candidates must meet the criteria related to the qualifying exam as explained below.
Qualifying Exam Details
Qualifying Degree | Qualifying Degree / Examination | Description | Year of Qualification not later than |
B.E./ B.Tech./ B.Pharm. | Candidate must be a Bachelor in Engineering/Technology (4 years after 10+2 or 3 years after B.Sc./ Diploma in Engineering / Technology) | Qualified or in pre-final/final year | 2022 |
B.Arch. | Candidate must have completed Bachelor of Architecture (5 years course) | Qualified or in pre-final/final year | 2022 |
B.Sc. (Research)/ B.S.
| Candidate need to have completed a Bachelor of Science degree (Post-Diploma/ 4 years after 10+2) | Qualified or in pre-final/final year | 2022 |
Pharm.D. (after 10+2) | Candidate must have completed 6 years programme having internship or residency training during the sixth year as part of it | Qualified or in pre-final/final year ```` | 2022 |
M.Sc./ M.A./ MCA or equivalent
| Candidates need to have Masters in Science, Mathematics, Statistics, Computer Applications, or equivalent | Qualified or in pre-final/final year | 2022 |
Int. M.E./ M.Tech. (Post-B.Sc.)
| Candidates should have done Post-BSc Integrated Master’s degree in Engineering or Technology (4 years programme) | Qualified or currently in 2nd/3rd /4th year | 2022 |
Int. M.E./ M.Tech. or Dual Degree (after Diploma or 10+2) | Candidates should have completed Integrated Master’s degree programme or Dual Degree in Engineering or Technology (5 years programme) | Qualified or in pre-final/final year | 2022 |
Int. M.Sc./ Int. B.S.-M.S. | Candidates applying must have completed Integrated M.Sc. or 5 years integrated B.S.-M.S. program | Qualified or in pre-final/final year | 2022 |
Professional Society Examinations* (equivalent to B.E/ B.Tech/ B.Arch.) | Candidates need to have completed B.E./ B.Tech./ B.Arch. Equivalent examinations of Professional Societies, recognized by MHRD/UPSC/AICTE (e.g., AMIE by Institution of professional courses Engineers-India, AMICE by the Institute of Civil Engineers-India) | Completed Section A or equivalent professional course | NA |
NOTE: *Candidates who possess certification from any of the professional societies must ensure that those examinations conducted by the societies are approved by MHRD/ AICTE as equivalent to B.E./ B.Tech./ B.Arch.
Mode of Application : Online
Mode of Payment : Net Banking | Credit Card | Debit Card
GATE application form 2021 correction facility was closed on November 23. Earlier, the correction facility was open from October 28 to November 13, 2020. Candidates had to visit the GOAPS 2021 portal at appsgate.iitb.ac.in to make changes in category, exam city, gender, and choice of GATE paper. GATE application form 2021 was released on September 11 at gate.iitb.ac.in. GATE 2021 registration last date with late fees was extended till October 14.
Candidates could also visit the GATE 2021 official website for filling the application form. The GATE registration was supposed to start on September 14 but it started on September 11. The last date to fill the GATE application form without a late fee was October 8 (5 PM). To participate in the entrance examination, the candidates had to register, fill out the required personal, contact and academic details, upload scanned documents, and also pay the required application fee.
GATE 2021 Registration Window
How to fill GATE Application Form 2021
Step 1 - Registration: Candidates had to visit the GOAPS portal for GATE registration 2021. Candidates have to use their name, country of residence, email address and mobile number for applying to GATE exam 2021. A password also had to be generated for future log-in. An enrollment number was generated on successful registration.
Step 2 - Filling of Application Form: Next, the candidates had to provide their valid personal, academic and communication details. The preferred GATE paper along with two exam centres (one from their zone and the other from another zone) also had to be selected by the candidates.
Step 3 - Uploading of Documents: After the details were filled, the candidates had to upload their photograph, signature and category certificate (if applicable) as per the specifications mentioned by the authorities.
Step 4 - Fee Payment: Finally, the candidates had to pay the required application fee of GATE 2021 in online mode (net banking/credit card/debit card).
GATE 2021 Registration Fee
Category | Amount (September 11 to 30) | Fees during the period of extension (October 1 to 7) |
Male (General, OBC and Others) | Rs. 1,500 | Rs. 2,000 |
SC/ ST/ PwD | Rs. 750 | Rs. 1,250 |
Female candidates | Rs. 750 | Rs. 1,250 |
International Students of Dubai and Singapore | US$ 100 | US$ 120 |
International Students of Addis Ababa, Colombo, Dhaka and Kathmandu | US$ 50 | US$ 70 |
GATE 2021 Application Form Correction Facility
IIT, Bombay has closed the GATE application form correction facility on the official website of GATE (GOAPS). Candidates had to log in to the website and make necessary corrections in the application form. They could make changes like category, gender, exam paper, and city. If any of the GATE 2021 registered candidates want to change the choice of exam city, no fee is required. For any other changes, additional charges would be applicable.
How to edit GATE Application Form 2021
You can check the steps below to know how to make changes in the GATE 2021 Application Form,
- Goto the GOAPS website - appsgate.iitb.ac.in
- Login to the website by using email ID/enrollment number and password.
- Now, you can make necessary changes by paying the required fee- gender, category, exam paper & city.
- Click on the Submit button.
Previous Year’s GATE Zone-Wise Registrations
Name of IITs | Registration Numbers |
1,73,965 | |
1,31,287 | |
1,30,522 | |
1,18,951 | |
1,14,794 | |
73,618 | |
62,340 | |
52,553 | |
Total | 8,58,030 |
Application Fees
| Category | Quota | Mode | Gender | Amount |
|---|---|---|---|---|
| SC, OBC, ST, General | PWD | Online | Female, Transgender, Male | ₹ 750 |
| OBC, General | Online | Transgender, Male | ₹ 1500 | |
| SC, ST | Online | Transgender, Male | ₹ 750 | |
| SC, OBC, ST, General | Online | Female | ₹ 750 |
GATE E-books and Sample Papers
GATE 2021 Syllabus
GATE Aerospace Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
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, divergence and curl, directional derivatives |
| Integration, line, surface, and 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 |
|---|
Complex analysis |
|---|
Probability and Statistics |
|---|
Flight mechanics
Flight mechanics: Unit 01
Basics |
|---|
| Atmosphere: Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts |
| Pressure altitude; equivalent, calibrated, indicated air speeds; primary flight instruments: Altimeter, ASI, VSI, turn-bank indicator |
| Angle of attack, sideslip; roll, pitch and yaw controls |
| Aerodynamic forces and moments |
Airplane performance |
|---|
| Drag polar; takeoff and landing; steady climb and descent; absolute and service ceiling; range and endurance, load factor, turning flight, V-N diagram |
| Winds: Head, tail, and cross winds |
Static stability |
|---|
| Stability and control 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 |
Dynamic stability |
|---|
| Euler angles; equations of motion; decoupling of longitudinal and lateral-directional dynamics; longitudinal modes; lateral-directional modes |
Space dynamics
Space dynamics: Unit 01
Central force motion |
|---|
Determination of trajectory and orbital period in simple cases |
|---|
Kepler's laws |
|---|
Escape velocity |
|---|
Aerodynamics
Aerodynamics: Unit 01
Basic fluid mechanics |
|---|
| Conservation laws: Mass, momentum, and energy (integral and differential form); dimensional analysis and dynamic similarity; potential flow theory: Sources, sinks, doublets, line vortex, and their superposition |
| Elementary ideas of viscous flows including boundary layers |
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, one-dimensional compressible flows, isentropic flows, fanno flow, Rayleigh flow; normal and oblique shocks, Prandtl-Meyer flow; flow through nozzles and diffusers |
Wind tunnel testing |
|---|
| Measurement and visualization techniques |
| Shock-boundary layer interaction |
Structures
Structures: Unit 01
Strength of materials |
|---|
| Stress and strain: Three-dimensional transformations, Mohr's circle, principal stresses, three-dimensional Hooke's law, plane stress and strain |
| Failure theories: Maximum stress, Tresca and Von Mises |
| Strain energy |
| Castigliano's principles |
| Statically determinate and indeterminate trusses, and beams |
| Elastic flexural buckling of columns |
Flight vehicle structures |
|---|
| Characteristics of aircraft structures and materials |
| Torsion, bending, and shear of thin-walled sections |
| Loads on aircraft |
Structural dynamics |
|---|
| Free and forced vibrations of undamped and damped SDOF systems |
| Free vibrations of undamped 2-DOF systems |
Vibration of beams |
|---|
Theory of elasticity |
|---|
| Equilibrium and compatibility equations, Airy's stress function |
Propulsion
Propulsion: Unit 01
Basics |
|---|
| Thermodynamics, boundary layers, heat transfer, combustion and thermochemistry |
Aerothermodynamics of aircraft engines |
|---|
| Thrust, efficiency, range |
| Brayton cycle |
| Engine performance: Ramjet, turbojet, turbofan, turboprop, and turboshaft engines |
| Afterburners |
Turbo machinery |
|---|
| 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 |
Rockets |
|---|
| Thrust equation and specific impulse, rocket performance |
| Multi-staging |
| Chemical rockets |
| Performance of solid and liquid propellant rockets |
Aerothermodynamics of non-rotating propulsion components such as intakes, combustor, and nozzle |
|---|
Turbine blade cooling |
|---|
Compressor-turbine matching |
|---|
Surge and stall |
|---|
GATE Agricultural Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
|---|
| Matrices and determinants, linear and orthogonal transformations, Cayley-Hamilton theorem; eigen values and eigen vectors, solutions of linear equations |
Calculus |
|---|
| Limit, continuity, and differentiability; partial derivatives; homogeneous function-Euler's theorem on homogeneous functions, total differentiation; maxima and minima of function with several independent variables; sequences and series-infinite series |
| Tests for convergence; Fourier, Taylor, and Maclaurin series |
Vector calculus |
|---|
| Vector differentiation, scalar and vector point functions, vector differential operators-del, gradient; divergence and curl; physical interpretations-line, surface and volume integrals; Stokes, Gauss, and Green's theorems |
Differential equations |
|---|
| Linear and non-linear first order ordinary differential equations (ODE); homogeneous differential equations, higher order linear ODEs with constant coefficients; Laplace transforms and their inverse; partial differential equations |
| Laplace, heat and wave equations |
Probability and Statistics |
|---|
| Mean, median, mode, and standard deviation; random variables; Poisson, normal and binomial distributions; correlation and regression analysis |
Numerical methods |
|---|
| Solutions of linear and non-linear algebraic equations; numerical integration-trapezoidal and Simpson's rule; numerical solutions of ODEs |
Farm machinery
Farm machinery: Unit 01
Machine design |
|---|
| Design and selection of machine elements-gears, pulleys, chains and sprockets, and belts; overload safety devices used in farm machinery; measurement of force, stress, torque, speed, displacement and acceleration on machine elements-shafts, couplings |
| Keys, bearings, and knuckle joints |
Farm machinery |
|---|
| Soil tillage; forces acting on a tillage tool; hitch systems and hitching of tillage implements; functional requirements, principles of working, construction and operation of manual, animal, and power operated equipment for tillage, sowing, planting |
| Fertilizer application, inter-cultivation, spraying, mowing, chaff cutting, harvesting and threshing calculation of performance parameters-field capacity, efficiency |
| Application rate and losses; cost analysis of implements and tractors |
Farm power
Farm power: Unit 01
Sources of power |
|---|
| Sources of power on the farm-human, animal, mechanical, electrical, wind, solar and biomass; biofuels |
Farm power |
|---|
| 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 |
Tractors and power tillers |
|---|
| Type, selection, maintenance and repair of tractors, and power tillers; tractor clutches and brakes; power transmission systems-gear trains, differential, final drives and power take-off; mechanics of tractor chassis; traction theory; three point hitches |
| Free link and restrained link operations; steering and hydraulic control systems used in tractors; tractor tests and performance; human engineering and safety considerations in design of tractor, and agricultural implements |
Soil and water conservation engineering
Soil and water conservation engineering: Unit 01
Fluid mechanics |
|---|
| Ideal and real fluids, properties of fluids; hydrostatic pressure and its measurement; continuity equation, kinematics, and dynamics of flow; Bernoulli's theorem; laminar and turbulent flow in pipes, 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 mechanics |
|---|
| Engineering properties of soils; fundamental definitions and relationships; index properties of soils; permeability and seepage analysis; shear strength, Mohr's circle of stress, active and passive earth pressures; stability of slopes |
| Terzaghi's one dimensional soil consolidation theory |
Hydrology |
|---|
| Hydrological cycle and measurement of its components; meteorological parameters and their measurement; analysis of precipitation data; runoff estimation; hydrograph analysis, unit hydrograph theory and application; stream flow measurement; flood routing |
| Hydrological reservoir and channel routing, infiltration-indices and equations, drought and its classification |
Surveying and leveling |
|---|
| Measurement of distance and area; instruments for surveying and leveling; chain surveying, methods of traversing; measurement of angles and bearings, plane table surveying; types of leveling; theodolite traversing; contouring; total station |
| Introduction to GPS survey, computation of areas and volume |
Soil and water erosion |
|---|
| Mechanics of soil erosion-wind and water erosion: Soil erosion types, factors affecting erosion; soil loss estimation; biological and engineering measures to control erosion; terraces and bunds; vegetative waterways; gully control structures, drop |
| Drop inlet and chute spillways; earthen dams |
Watershed management |
|---|
| Watershed characterization and land use capability classification; water budgeting in watershed, rainwater harvesting, check dams and farm ponds |
Irrigation and drainage engineering
Irrigation and drainage engineering: Unit 01
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; non-conventional drainage system |
Groundwater hydrology |
|---|
| Groundwater occurrence; Darcy's law, steady and unsteady flow in confined and unconfined aquifers, groundwater exploration techniques; overview of groundwater recharge estimation and artificial recharge techniques |
Wells and pumps |
|---|
| Types of wells, steady flow through wells; design and construction of water wells; classification of pumps; pump characteristics; pump selection and installation |
Agricultural process engineering
Agricultural process engineering: Unit 01
Engineering properties of agriculture produce |
|---|
| Physical, thermal, frictional, rheological, and electrical properties |
Evaporation and drying |
|---|
| Concentration and drying of liquid foods-evaporators, tray, drum, and spray dryers; hydrothermal treatments; drying and milling of cereals, pulses and oilseeds; drying kinetics; psychrometry-properties of air-water vapor mixture |
Size reduction and material handling |
|---|
| Mechanics and energy requirement in size reduction of agriculture produce; particle size analysis for comminuted solids; size separation by screening; fluidization of granular solids-pneumatic, bucket, screw and belt conveying; cleaning and grading |
| Effectiveness of separation; centrifugal separation of solids, liquids and gases; homogenization; filtration and membrane separation |
Processing of agriculture produce |
|---|
| Processing of seeds, spices, fruits, and vegetables; value addition of agriculture produce |
Storage systems |
|---|
| Controlled and modified atmosphere storage; perishable food storage, godowns, bins and grain silos, packaging material and machines |
Dairy and food engineering
Dairy and food engineering: Unit 01
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 |
GATE Architecture and Planning Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Architecture, planning, and design
Architecture, planning, and design: Unit 01
Architectural graphics |
|---|
Visual composition in 2D and 3D |
|---|
Computer application in architecture and planning |
|---|
Anthropometrics |
|---|
Organization of space |
|---|
Circulation-horizontal and vertical |
|---|
Space standards |
|---|
Universal design |
|---|
Building byelaws |
|---|
Codes and standards |
|---|
Construction and management
Construction and management: Unit 01
Project management techniques example PERT, CPM, etc |
|---|
Estimation and specification |
|---|
Professional practice and ethics |
|---|
Form and structure |
|---|
Principles and design of disaster resistant structures |
|---|
Temporary structures for rehabilitation |
|---|
Environmental planning and design
Environmental planning and design: Unit 01
Natural and man-made ecosystem |
|---|
Ecological principles |
|---|
Environmental considerations in planning and design |
|---|
Environmental pollution-types, causes, controls, and abatement strategies |
|---|
Sustainable development, goals, and strategies |
|---|
Climate change and built environment |
|---|
Climate responsive design |
|---|
Urban design, landscape, and conservation
Urban design, landscape, and conservation: Unit 01
Historical and modern examples of urban design |
|---|
Elements of urban built environment-urban form, spaces, structure, pattern, fabric, texture, grain etc |
|---|
Concepts and theories of urban design |
|---|
Principles, tools, and techniques of urban design |
|---|
Public spaces, character, spatial qualities, and sense of place |
|---|
Urban design interventions for sustainable development and transportation |
|---|
Development controls-FAR, densities, and building byelaws |
|---|
Urban renewal and conservation |
|---|
Heritage conservation |
|---|
Historical public spaces and gardens |
|---|
Landscape design |
|---|
Site planning |
|---|
Planning process
Planning process: Unit 01
Salient concepts |
|---|
Theories and principles of urban planning |
|---|
Concepts of cities-eco-city, smart city |
|---|
Concepts and theories by trendsetting planners, and designers |
|---|
Ekistics |
|---|
Urban sociology |
|---|
Social, economic, and environmental cost benefit analysis |
|---|
Methods of non-spatial and spatial data analysis |
|---|
Development guidelines such as URDPFI |
|---|
Housing
Housing: Unit 01
Housing typologies |
|---|
Concepts, principles, and examples of neighbourhood |
|---|
Residential densities |
|---|
Affordable housing |
|---|
Real estate valuation |
|---|
Services and infrastructure
Services and infrastructure: Unit 01
Firefighting systems |
|---|
Building safety and security systems |
|---|
Building management systems |
|---|
Water treatment |
|---|
Water supply and distribution system |
|---|
Water harvesting systems |
|---|
Principles, planning, and design of storm water drainage system |
|---|
Sewage disposal methods |
|---|
Methods of solid waste management-collection, transportation, and disposal |
|---|
Recycling and reuse of solid waste |
|---|
Land use-transportation, urban form inter relationships |
|---|
Design of roads, intersections, grade separators, and parking areas |
|---|
Hierarchy of roads and level of service |
|---|
Para-transits and other modes of transportation |
|---|
Pedestrian and slow moving traffic planning |
|---|
History and contemporary architecture
History and contemporary architecture: Unit 01
Principles of art and architecture |
|---|
World history of architecture |
|---|
| Egyptian, Greco-Roman classical period, Byzantine, Gothic, Renaissance, Baroque-Rococo, etc |
Recent trends in contemporary architecture |
|---|
| Art nouveau, art Deco, eclecticism, international styles, post modernism, deconstruction in architecture, etc |
Influence of modern art and design in architecture |
|---|
Indian vernacular and traditional architecture |
|---|
Oriental architecture |
|---|
Works of renowned national and international architects |
|---|
Building construction and structural systems
Building construction and structural systems: Unit 01
Building construction techniques, methods, and details |
|---|
Building systems and prefabrication of building elements |
|---|
Principles of modular coordination |
|---|
Construction planning and equipment |
|---|
Building material characteristics and applications |
|---|
Principles of strength of materials |
|---|
Alternative building materials |
|---|
Foundations |
|---|
Design of structural elements with different materials |
|---|
Elastic and limit state design |
|---|
Structural systems |
|---|
Principles of pre-stressing |
|---|
High rise and long span structures |
|---|
Gravity and lateral load resisting systems |
|---|
Building services and sustainability
Building services and sustainability: Unit 01
Solar architecture |
|---|
Thermal, visual, and acoustic comfort in built environments |
|---|
Natural and mechanical ventilation in buildings |
|---|
Air-conditioning systems |
|---|
Sustainable building strategies |
|---|
Building performance simulation and evaluation |
|---|
Intelligent buildings |
|---|
Water supply |
|---|
Sewerage and drainage systems |
|---|
Sanitary fittings and fixtures |
|---|
Plumbing systems |
|---|
Principles of internal and external drainage system |
|---|
Principles of electrification of buildings |
|---|
Elevators and escalators-standards and uses |
|---|
Regional and settlement planning
Regional and settlement planning: Unit 01
Regional delineation |
|---|
Settlement hierarchy |
|---|
Types and hierarchy of plans |
|---|
Various schemes and programs of central government |
|---|
Transit oriented development (TOD), SEZ, SRZ etc |
|---|
Public perception and user behaviour |
|---|
National housing policies, programs, and schemes |
|---|
Slums, squatters, and informal housing |
|---|
Standards for housing and community facilities |
|---|
Housing for special areas and needs |
|---|
Planning techniques and management
Planning techniques and management: Unit 01
Application of GIS and remote sensing techniques in urban, and regional planning |
|---|
Tools and techniques of surveys-physical, topographical, land use, and socio-economic surveys |
|---|
Urban economics |
|---|
Law of demand and supply of land and its use in planning |
|---|
Graphic presentation of spatial data |
|---|
Local self-governance |
|---|
Panchayati raj institutions |
|---|
Planning legislation and implementation-land acquisition act, PPP, etc |
|---|
Decision support system and land information system |
|---|
Urban geography and econometrics |
|---|
Management of infrastructure projects |
|---|
Demography and equity in planning |
|---|
Infrastructure planning
Infrastructure planning: Unit 01
Process and principles of transportation planning, and traffic engineering |
|---|
Road capacity and travel demand forecasting |
|---|
Traffic survey methods |
|---|
Traffic flow analysis |
|---|
Traffic analyses and design considerations |
|---|
Traffic and transport management, and control in urban areas |
|---|
Mass transportation planning |
|---|
Intelligent transportation systems |
|---|
Urban and rural infrastructure system network |
|---|
GATE Biotechnology Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
|---|
| Matrices and determinants; systems of linear equations; eigen values and eigen vectors |
Calculus |
|---|
| Limits, continuity, and differentiability; partial derivatives, maxima and minima; sequences and series; test for convergence |
Differential equations |
|---|
| Linear and nonlinear first order ODEs, higher order ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms |
Probability and Statistics |
|---|
| Mean, median, mode, and standard deviation; random variables; Poisson, normal, and binomial distributions; correlation and regression analysis |
Numerical methods |
|---|
| Solution of linear and nonlinear algebraic equations; integration by trapezoidal and Simpson's rule; single step method for differential equations |
General biology
General biology: Unit 01
Biochemistry |
|---|
| 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 |
Microbiology |
|---|
| Bacterial classification and diversity; microbial ecology-microbes in marine, freshwater, and terrestrial ecosystems; microbial interactions; viruses-structure and classification; methods in microbiology; microbial growth and nutrition; nitrogen fixation |
| Microbial diseases and host-pathogen interactions; antibiotics and antimicrobial resistance |
Immunology |
|---|
| Innate and adaptive immunity, humoral and cell mediated immunity; antibody structure and function; molecular basis of antibody diversity; T cell and B cell development; antigen-antibody reaction; complement; primary and secondary lymphoid organs |
| Major histocompatibility complex (MHC); antigen processing and presentation; polyclonal and monoclonal antibody; regulation of immune response; immune tolerance; hyper sensitivity; autoimmunity; graft versus host reaction; immunization and vaccines |
Genetics, cellular, and molecular biology
Genetics, cellular, and molecular biology: Unit 01
Genetics and evolutionary biology |
|---|
| Mendelian inheritance; gene interaction; complementation; linkage, recombination, and chromosome mapping; extra chromosomal inheritance; microbial genetics-transformation, transduction, and conjugation; horizontal gene transfer and transposable elements |
| Chromosomal variation; genetic disorders; population genetics; epigenetics; selection and inheritance; adaptive and neutral evolution; genetic drift; species and speciation |
Cell biology |
|---|
| Prokaryotic and eukaryotic cell structure; cell cycle and cell growth control; cell-cell communication; cell signaling and signal transduction; post-translational modifications; protein trafficking; cell death and autophagy; extra-cellular matrix |
Molecular biology |
|---|
| Molecular structure of genes and chromosomes; mutations and mutagenesis; regulation of gene expression; nucleic acid-replication, transcription, splicing, translation and their regulatory mechanisms; Non-coding and micro RNA; RNA interference |
| DNA damage and repair |
Fundamentals of biological engineering
Fundamentals of biological engineering: Unit 01
Engineering principles applied to biological systems |
|---|
| Material and energy balances for reactive and non-reactive systems; recycle, bypass and purge processes; stoichiometry of growth and product formation; degree of reduction, electron balance, theoretical oxygen demand |
Classical thermodynamics and bioenergetics |
|---|
| Laws of thermodynamics; solution thermodynamics; phase equilibrium, reaction equilibrium; ligand binding; membrane potential; energetics of metabolic pathways, oxidation, and reduction reactions |
Transport processes |
|---|
| Newtonian and non-Newtonian fluids, fluid flow-laminar and turbulent; mixing in bioreactors, mixing time; molecular diffusion and film theory; oxygen transfer and uptake in bioreactor, kLa and its measurement; conductive and convective heat transfer, LMTD |
| Overall heat transfer coefficient; heat exchangers |
Bioprocess engineering and process biotechnology
Bioprocess engineering and process biotechnology: Unit 01
Bioreaction engineering |
|---|
| Rate law, zero, and first order kinetics; ideal reactors-batch, mixed flow and plug flow; enzyme immobilization, diffusion effects-Thiele modulus, effectiveness factor, 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 |
Upstream and downstream processing |
|---|
| 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 |
Instrumentation and process control |
|---|
| Pressure, temperature, and flow measurement devices; valves; first order and second order systems; feedback and feed forward control; types of controllers-proportional, derivative, and integral control, tuning of controllers |
Plant, animal, and microbial biotechnology
Plant, animal, and microbial biotechnology: Unit 01
Plants |
|---|
| Totipotency; regeneration of plants; plant growth regulators and elicitors; tissue culture and cell suspension culture system-methodology, kinetics of growth and nutrient optimization; production of secondary metabolites; hairy root culture |
| Plant products of industrial importance; artificial seeds; 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 |
Animals |
|---|
| 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 |
Microbes |
|---|
| 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
Recombinant DNA technology and other tools in biotechnology: Unit 01
Recombinant DNA technology |
|---|
| 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 |
Molecular tools |
|---|
| Polymerase chain reaction; DNA/ RNA labelling and sequencing; southern and northern blotting; in-situ hybridization; DNA fingerprinting, RAPD, RFLP; site-directed mutagenesis; gene transfer technologies; CRISPR-cas; biosensing and biosensors |
Analytical tools |
|---|
| Principles of microscopy-light, electron, fluorescent, and confocal; principles of spectroscopy-UV, visible, CD, IR, fluorescence, FT-IR, MS, NMR; electrophoresis; micro-arrays; enzymatic assays; immunoassays-ELISA, RIA, immunohistochemistry |
| Immunoblotting; flow cytometry; whole genome and ChIP sequencing |
Computational tools |
|---|
| Bioinformatics resources and search tools; sequence and structure databases; sequence analysis-sequence file formats, scoring matrices, alignment, phylogeny; genomics, proteomics, metabolomics; gene prediction; functional annotation |
| Secondary structure and 3D structure prediction; knowledge discovery in biochemical databases; metagenomics; metabolic engineering and systems biology |
GATE Civil Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
|---|
| Matrix algebra; systems of linear equations; eigen values and eigen vectors |
Calculus |
|---|
| Functions of single variable; limit, continuity, and differentiability; mean value theorems, local maxima and minima; Taylor series; evaluation of definite and indefinite integrals, application of definite integral to obtain area and volume |
| Partial derivatives; total derivative; gradient, divergence and curl, vector identities; directional derivatives; line, surface and volume integrals |
Ordinary differential equation (ODE) |
|---|
| First order (linear and non-linear) equations; higher order linear equations with constant coefficients; Euler-Cauchy equations; initial and boundary value problems |
Partial differential equation (PDE) |
|---|
| Fourier series; separation of variables; solutions of one-dimensional diffusion equation; first and second order one-dimensional wave equation and two-dimensional Laplace equation |
Probability and Statistics |
|---|
| Sampling theorems; conditional probability; descriptive statistics-mean, median, mode and standard deviation; random variables-discrete and continuous, Poisson and normal distribution; linear regression |
Numerical methods |
|---|
| Error analysis |
| Numerical solutions of linear and non-linear algebraic equations; Newton's and Lagrange polynomials; numerical differentiation; integration by trapezoidal and Simpson's rule; single and multi-step methods for first order differential equations |
Structural engineering
Structural engineering: Unit 01
Engineering mechanics |
|---|
| System of forces, free-body diagrams, equilibrium equations; internal forces in structures; frictions and its applications; centre of mass; free vibrations of undamped SDOF system |
Solid mechanics |
|---|
| Bending moment and shear force in statically determinate beams; simple stress and strain relationships; simple bending theory, flexural and shear stresses, shear centre; uniform torsion, transformation of stress; buckling of column |
| Combined and direct bending stresses |
Structural analysis |
|---|
| Statically determinate and indeterminate structures by force/ energy methods; method of superposition; analysis of trusses, arches, beams, cables and frames; displacement methods: Slope deflection and moment distribution methods; Influence lines |
| Stiffness and flexibility methods of structural analysis |
Construction materials and management |
|---|
| Construction materials: Structural steel-composition, material properties and 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 |
Concrete structures |
|---|
| Working stress and limit state design concepts; design of beams, slabs, columns; bond and development length; prestressed concrete beams |
Steel structures |
|---|
| Working stress and Limit state design concepts; design of tension and compression members, beams and beam-columns, column bases; connections-simple and eccentric, beam-column connections, plate girders and trusses |
| Concept of plastic analysis-beams and frames |
Geotechnical engineering
Geotechnical engineering: Unit 01
Soil mechanics |
|---|
| Three-phase system and phase relationships, index properties; unified and Indian standard soil classification system; permeability-one dimensional flow, seepage through soils-two-dimensional flow, flow nets, uplift pressure, piping, capillarity |
| Seepage force; principle of effective stress and quicksand condition; compaction of soils; one-dimensional consolidation, time rate of consolidation; shear strength, Mohr's circle, effective and total shear strength parameters |
| Stress-strain characteristics of clays and sand; stress paths |
Foundation engineering |
|---|
| 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
Water resources engineering: Unit 01
Fluid mechanics |
|---|
| Properties of fluids, fluid statics; continuity, momentum and energy equations and their applications; potential flow, laminar and turbulent flow; flow in pipes, pipe networks; concept of boundary layer and its growth; concept of lift and drag |
Hydraulics |
|---|
| Forces on immersed bodies; flow measurement in channels and pipes; dimensional analysis and hydraulic similitude; channel hydraulics-energy-depth relationships, specific energy, critical flow, hydraulic jump, uniform flow |
| Gradually varied flow and water surface profiles |
Hydrology |
|---|
| Hydrologic cycle, precipitation, evaporation, 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 |
Irrigation |
|---|
| 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
Environmental engineering: Unit 01
Water and waste water quality and treatment |
|---|
| Basics of water quality standards-physical, chemical, and biological parameters; water quality index; unit processes and operations; water requirement; water distribution system; drinking water treatment |
| Sewerage system design, quantity of domestic wastewater, primary and secondary treatment |
| Effluent discharge standards; sludge disposal; reuse of treated sewage for different applications |
Air pollution |
|---|
| Types of pollutants, their sources and impacts, air pollution control, air quality standards, air quality index and limits |
Municipal solid wastes |
|---|
| Characteristics, generation, collection and transportation of solid wastes, engineered systems for solid waste management (reuse/ recycle, energy recovery, treatment and disposal) |
Transportation engineering
Transportation engineering: Unit 01
Transportation infrastructure |
|---|
| Geometric design of highways-cross-sectional elements, sight distances, horizontal and vertical alignments |
| Geometric design of railway Track-speed and cant |
| Concept of airport runway length, calculations and corrections; taxiway and exit taxiway design |
Highway pavements |
|---|
| Highway materials-desirable properties and tests; desirable properties of bituminous paving mixes; design factors for flexible and rigid pavements; design of flexible and rigid pavement using IRC codes |
Traffic engineering |
|---|
| Traffic studies on flow and speed, peak hour factor, accident study, statistical analysis of traffic data; microscopic and macroscopic parameters of traffic flow, fundamental relationships; traffic signs; signal design by Webster's method |
| Types of intersections; highway capacity |
Geomatics engineering
Geomatics engineering: Unit 01
Principles of surveying |
|---|
Errors and their adjustment |
|---|
Maps |
|---|
| Scale, coordinate system |
Distance and angle measurement |
|---|
| Levelling and trigonometric levelling |
Traversing and triangulation survey |
|---|
Total station |
|---|
Horizontal and vertical curves |
|---|
Photogrammetry and remote sensing |
|---|
| Scale, flying height |
Basics of remote sensing and GIS |
|---|
GATE Chemical Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
|---|
| Matrix algebra, systems of linear equations, eigen values and eigen vectors |
Calculus |
|---|
| Functions of single variable, limit, continuity, and differentiability, Taylor series, mean value theorems, evaluation of definite and improper integrals, partial derivatives, total derivative, maxima and minima, gradient, divergence and curl |
| Vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green's theorems |
Differential equations |
|---|
| First order equations (linear and nonlinear), higher order linear differential equations with constant coefficients, Cauchy's and Euler's equations, initial and boundary value problems, Laplace transforms |
| Solutions of one dimensional heat and wave equations and Laplace equation |
Complex variables |
|---|
| Complex number, polar form of complex number, triangle inequality |
Probability and Statistics |
|---|
| Definitions of probability and sampling theorems, conditional probability, mean, median, mode and standard deviation, random variables, Poisson, normal and binomial distributions, linear regression analysis |
Numerical methods |
|---|
| Numerical solutions of linear and non-linear algebraic equations |
| Integration by trapezoidal and Simpson's rule |
| Single and multi-step methods for numerical solution of differential equations |
Process calculations and thermodynamics
Process calculations and thermodynamics: Unit 01
Steady and unsteady state mass and energy balances including multiphase |
|---|
Multi-component |
|---|
Reacting and non-reacting systems |
|---|
Use of tie components |
|---|
Recycle, bypass, and purge calculations |
|---|
Gibb's phase rule and degree of freedom analysis |
|---|
First and second laws of thermodynamics |
|---|
Applications of first law to close and open systems |
|---|
Second law and entropy |
|---|
Thermodynamic properties of pure substances |
|---|
| Equation of state and residual properties |
Properties of mixtures |
|---|
| Partial molar properties, fugacity, excess properties and activity coefficients |
Phase equilibria |
|---|
| Predicting VLE of systems; chemical reaction equilibrium |
Fluid mechanics and mechanical operations
Fluid mechanics and mechanical operations: Unit 01
Fluid statics |
|---|
Surface tension |
|---|
Newtonian and non-Newtonian fluids |
|---|
Transport properties |
|---|
Shell-balances including differential form of Bernoulli equation and energy balance |
|---|
Equation of continuity |
|---|
Equation of motion |
|---|
Equation of mechanical energy |
|---|
Macroscopic friction factors |
|---|
Dimensional analysis and similitude |
|---|
Flow through pipeline systems |
|---|
Velocity profiles |
|---|
Flow meters |
|---|
Pumps and compressors |
|---|
Elementary boundary layer theory |
|---|
Flow past immersed bodies including packed and fluidized beds |
|---|
Turbulent flow |
|---|
| Fluctuating velocity, universal velocity profile and pressure drop |
Particle size and shape |
|---|
Particle size distribution |
|---|
Size reduction and classification of solid particles |
|---|
Free and hindered settling |
|---|
Centrifuge and cyclones |
|---|
Thickening and classification |
|---|
Filtration |
|---|
Agitation and mixing |
|---|
Conveying of solids |
|---|
Heat transfer
Heat transfer: Unit 01
Equation of energy |
|---|
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, and single and multiple effect evaporators |
|---|
Mass transfer
Mass transfer: Unit 01
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 and NTU concepts |
|---|
Design and operation of equipment for distillation |
|---|
Absorption |
|---|
Leaching |
|---|
Liquid-liquid extraction |
|---|
Drying |
|---|
Humidification |
|---|
Dehumidification and adsorption |
|---|
Membrane separations (micro-filtration, ultra-filtration, nano-filtration and reverse osmosis) |
|---|
Chemical reaction engineering
Chemical reaction engineering: Unit 01
Theories of reaction rates |
|---|
Kinetics of homogeneous reactions |
|---|
Interpretation of kinetic data |
|---|
Single and multiple reactions in ideal reactors |
|---|
Kinetics of enzyme reactions (Michaelis-Menten and Monod models) |
|---|
Non-ideal reactors |
|---|
Residence time distribution |
|---|
Single parameter model |
|---|
Non-isothermal reactors |
|---|
Kinetics of heterogeneous catalytic reactions |
|---|
Diffusion effects in catalysis |
|---|
Rate and performance equations for catalyst deactivation |
|---|
Instrumentation and process control
Instrumentation and process control: Unit 01
Measurement of process variables |
|---|
Sensors and transducers |
|---|
P and ID equipment symbols |
|---|
Process modeling and linearization |
|---|
Transfer functions and dynamic responses of various systems |
|---|
Systems with inverse response |
|---|
Process reaction curve |
|---|
Controller modes (P, PI, and PID) |
|---|
Control valves |
|---|
Transducer dynamics |
|---|
Analysis of closed loop systems including stability |
|---|
Frequency response |
|---|
Controller tuning |
|---|
Cascade and feed forward control |
|---|
Plant design and economics
Plant design and economics: Unit 01
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 equipments such as heat exchangers and multistage contactors |
|---|
Chemical technology
Chemical technology: Unit 01
Inorganic chemical industries (sulphuric acid, phosphoric acid, chlor-alkali industry) |
|---|
Fertilizers (ammonia, urea, SSP and TSP) |
|---|
Natural products industries (pulp and paper, sugar, oil, and fats) |
|---|
Petroleum refining and petrochemicals |
|---|
Polymerization industries (polyethylene, polypropylene, PVC and polyester synthetic fibers) |
|---|
GATE Computer Science and Information Technology Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Discrete mathematics |
|---|
| Propositional and first order logic |
| Sets, relations, functions, partial orders and lattices |
| Monoids, groups |
| Graphs: Connectivity, matching, colouring |
| 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 and Statistics |
|---|
| 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
Computer science and information technology: Unit 01
Digital logic |
|---|
| Boolean algebra |
| Combinational and sequential circuits |
| Minimization |
| Number representations and computer arithmetic (fixed and floating point) |
Computer organization and architecture |
|---|
| Machine instructions and addressing modes |
| ALU, data‐path and control unit |
| Instruction pipelining, pipeline hazards |
| Memory hierarchy: Cache, main memory and secondary storage; I/O interface (interrupt and DMA mode) |
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: Greedy, dynamic programming and divide‐and‐conquer |
| Graph traversals, minimum spanning trees, shortest paths |
Theory of computation |
|---|
| Regular expressions and finite automata |
| Context-free grammars and push-down automata |
| Regular and contex-free languages, pumping lemma |
| Turing machines and undecidability |
Compiler design |
|---|
| Lexical analysis, parsing, syntax-directed translation |
| Runtime environments |
| Intermediate code generation |
| Local optimisation, data flow analyses: Constant propagation, liveness analysis, common subexpression elimination |
Operating system |
|---|
| System calls, processes, threads, inter‐process communication, concurrency and synchronization |
| Deadlock |
| CPU and I/O scheduling |
| Memory management and virtual memory |
| File systems |
Databases |
|---|
| ER‐model |
| Relational model: Relational algebra, tuple calculus, SQL |
| Integrity constraints, normal forms |
| File organization, indexing (e.g., B and B+ trees) |
| Transactions and concurrency control |
Computer networks |
|---|
| Concept of layering: OSI and TCP/IP protocol stacks; basics of packet, circuit and virtual circuit-switching; data link layer: Framing, error detection, medium access control, ethernet bridging |
| Routing protocols: Shortest path, flooding, distance vector and link state routing; fragmentation and IP addressing, IPv4, CIDR notation, basics of IP support protocols (ARP, DHCP, ICMP), network address translation (NAT) |
| Transport layer: Flow control and congestion control, UDP, TCP, sockets; application layer protocols: DNS, SMTP, HTTP, FTP, Email |
GATE Chemistry Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Physical chemistry
Physical chemistry: Unit 01
Structure |
|---|
| 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 |
Equilibrium |
|---|
| Laws of thermodynamics |
| Standard states |
| Thermochemistry |
| Thermodynamic functions and their relationships: Gibbs-Helmholtz and Maxwell relations, Gibbs-Duhem equation, Van't Hoff equation |
| Criteria of spontaneity and equilibrium |
| Absolute entropy |
| Partial molar quantities |
| Thermodynamics of mixing |
| Chemical potential |
| Fugacity, activity and activity coefficients |
| Ideal and Non-ideal solutions, 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 |
Kinetics |
|---|
| Elementary, parallel, opposing and consecutive reactions |
| Steady state approximation |
| Mechanisms of complex reactions |
| Unimolecular reactions |
| Potential energy surfaces and classical trajectories, concept of Saddle points, transition state theory: Eyring equation, thermodynamic aspects |
| Kinetics of polymerization |
| Catalysis concepts and enzyme catalysis |
| Kinetic isotope effects |
| Fast reaction kinetics: Relaxation and flow methods |
| Diffusion controlled reactions |
| Kinetics of photochemical and photophysical processes |
Surfaces and interfaces |
|---|
| Physisorption and Chemisorption |
| Langmuir, Freundlich and Brunauer-Emmett-Teller (BET) isotherms |
| Surface catalysis: Langmuir-Hinshelwood mechanism |
| Surface tension, viscosity |
| Self-assembly |
| Physical chemistry of colloids, micelles and macromolecules |
Inorganic chemistry
Inorganic chemistry: Unit 01
Main group elements |
|---|
| Hydrides, halides, oxides, oxoacids, nitrides, sulfides-shapes and reactivity |
| Structure and bonding of boranes, carboranes, silicones, silicates, boron nitride, borazines and phosphazenes |
| Allotropes of carbon, 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) |
Transition elements |
|---|
| Coordination chemistry-structure and isomerism, theories of bonding (VBT, CFT, and MOT) |
| Energy level diagrams in various crystal fields, CFSE, applications of CFT, Jahn-Teller distortion |
| Electronic spectra of transition metal complexes: Spectroscopic term symbols, selection rules, Orgel and Tanabe-Sugano diagrams, nephelauxetic effect and Racah parameter, charge-transfer spectra |
| Magnetic properties of transition metal complexes |
| Ray-Dutt and Bailar twists, reaction mechanisms: Kinetic and thermodynamic stability, substitution and redox reactions |
| Metal-metal multiple bond |
Lanthanides and actinides |
|---|
| Recovery |
| Periodic properties, spectra and magnetic properties |
Organometallics |
|---|
| 18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metal-carbene complexes and 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 |
|---|
| Detection of radioactivity, decay processes, half-life of radioactive elements, fission and fusion processes |
Bioinorganic chemistry |
|---|
| Ion (Na+ and K+ ) transport, oxygen binding, transport and utilization, electron transfer reactions, nitrogen fixation, metalloenzymes containing magnesium, molybdenum, iron, cobalt, copper and zinc |
Solids |
|---|
| Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg's law, ionic crystals, structures of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors |
Instrumental methods of analysis |
|---|
| UV-visible, fluorescence and FTIR spectrophotometry, NMR and ESR spectroscopy, mass spectrometry, atomic absorption spectroscopy, 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
Organic chemistry: Unit 01
Stereochemistry |
|---|
| 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 |
Reaction mechanisms |
|---|
| Basic mechanistic concepts-kinetic versus thermodynamic control, Hammond's postulate and Curtin-Hammett principle |
| Methods of determining reaction mechanisms through kinetics, identification of products, intermediates and isotopic labelling |
| Linear free-energy 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 synthesis |
|---|
| Synthesis, reactions, mechanisms and selectivity involving the following classes of compounds-alkenes, alkynes, arenes, alcohols, phenols, aldehydes, ketones, carboxylic acids, esters, nitriles, halides, nitro compounds, amines and amides |
| Uses of Mg, Li, Cu, B, Zn, P, S, Sn and Si based reagents in organic synthesis |
| Carbon-carbon bond formation through coupling reactions-Heck, Suzuki, Stille, Sonogoshira, Negishi, Kumada, Hiyama, Tsuji-Trost, olefin metathesis and McMurry |
| Concepts of multistep synthesis-retrosynthetic analysis, strategic disconnections, synthons and synthetic equivalents |
| Atom economy and green chemistry, umpolung reactivity-formyl and acyl anion equivalents |
| Selectivity in organic synthesis-chemo-, regio- and stereoselectivity |
| Protection and deprotection of functional groups |
| Concepts of asymmetric synthesis-resolution (including enzymatic), 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) |
Pericyclic reactions and photochemistry |
|---|
| 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 |
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, chemical structure determination of peptides and proteins |
| Structural features of proteins, nucleic acids, lipids, steroids, terpenoids, carotenoids, and alkaloids |
Experimental techniques in organic chemistry |
|---|
| Optical rotation (polarimetry) |
| Applications of various chromatographic techniques such as thin-layer, column, HPLC and GC |
| Applications of UV-visible, IR, NMR and mass spectrometry in the structural determination of organic molecules |
GATE Electronics and Communication Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
|---|
| Vector space, basis, linear dependence and independence, matrix algebra, eigenvalues and eigenvectors, rank, solution of linear equations-existence and uniqueness |
Calculus |
|---|
| Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series |
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, divergence and curl, Gauss's, Green's and Stokes' theorems |
Complex analysis |
|---|
| Analytic functions, Cauchy's integral theorem, Cauchy's integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem |
Probability and Statistics |
|---|
| Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability |
Networks, signals, and systems
Networks, signals, and systems: Unit 01
Circuit analysis |
|---|
| Node and mesh analysis, superposition, Thevenin's theorem, Norton's theorem, reciprocity |
| Sinusoidal steady state analysis: Phasors, complex power, maximum power transfer |
| Time and frequency domain analysis of linear circuits: RL, RC and RLC circuits, solution of network equations using Laplace transform |
| Linear 2-port network parameters, Wye-delta transformation |
Continuous-time signals |
|---|
| Fourier series and Fourier transform, sampling theorem and applications |
Discrete-time signals |
|---|
| DTFT, DFT, z-transform, discrete-time processing of continuous-time signals |
| LTI systems: Definition and properties, causality, stability, impulse response, convolution, poles and zeroes, frequency response, group delay, phase delay |
Electronic devices
Electronic devices: Unit 01
Energy bands in intrinsic and extrinsic semiconductors |
|---|
Equilibrium carrier concentration |
|---|
Direct and indirect band-gap semiconductors |
|---|
Carrier transport |
|---|
| Diffusion current, drift current, mobility and resistivity, generation and recombination of carriers, Poisson and continuity equations |
P-N junction |
|---|
Zener diode |
|---|
BJT |
|---|
MOS capacitor |
|---|
MOSFET |
|---|
LED |
|---|
Photo diode and solar cell |
|---|
Analog circuits
Analog circuits: Unit 01
Diode circuits |
|---|
| Clipping, clamping and rectifiers |
BJT and MOSFET amplifiers |
|---|
| Biasing, ac coupling, small signal analysis, frequency response |
| Current mirrors and differential amplifiers |
OP-AMP Circuits |
|---|
| Amplifiers, summers, differentiators, integrators, active filters, Schmitt triggers and oscillators |
Digital circuits
Digital circuits: Unit 01
Number representations |
|---|
| Binary, integer and floating-point-numbers |
Combinatorial circuits |
|---|
| Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders |
Sequential circuits |
|---|
| Latches and flip-flops, counters, shift-registers, finite state machines, propagation delay, setup and hold time, critical path delay |
Data converters |
|---|
| Sample and hold circuits, ADCs and DACs |
Semiconductor memories |
|---|
| ROM, SRAM, DRAM |
Computer organization |
|---|
| Machine instructions and addressing modes, ALU, data-path and control unit, instruction pipelining |
Control systems
Control systems: Unit 01
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 |
|---|
Communications
Communications: Unit 01
Random processes |
|---|
| Autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems |
Analog communications |
|---|
| Amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers |
Information theory |
|---|
| Entropy, mutual information and channel capacity theorem |
Digital communications |
|---|
| PCM, DPCM, digital modulation schemes (ASK, PSK, FSK, QAM), bandwidth, inter-symbol interference, MAP, ML detection, matched filter receiver, SNR and BER |
Fundamentals of error correction |
|---|
Hamming codes |
|---|
CRC |
|---|
Electromagnetics
Electromagnetics: Unit 01
Maxwell's equations |
|---|
| Differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector |
Plane waves and properties |
|---|
| Reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth |
Transmission lines |
|---|
| Equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart |
Rectangular and circular waveguides |
|---|
Light propagation in optical fibers |
|---|
Dipole and monopole antennas |
|---|
Linear antenna arrays |
|---|
GATE Electrical Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
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, Stokes's theorem, Gauss's theorem, divergence theorem, Green's theorem |
Differential equations |
|---|
| First order equations (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchy's equation, Euler's equation, Initial and boundary value problems |
| Partial differential equations, method of separation of variables |
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, median, mode, standard deviation, random variables, discrete and continuous distributions, Poisson distribution, normal distribution, binomial distribution, correlation analysis, regression analysis |
Electric circuits
Electric circuits: Unit 01
Network elements |
|---|
| Ideal voltage and current sources, dependent sources, R, L, C, M elements |
Network solution methods |
|---|
| KCL, KVL, node and mesh analysis |
Network theorems |
|---|
| Thevenin's, Norton's, superposition and maximum power transfer theorem; transient response of dc and ac networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation |
| Complex power and power factor in ac circuits |
Electromagnetic fields
Electromagnetic fields: 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 |
|---|
Signals and systems
Signals and systems: Unit 01
Representation of continuous and discrete time signals |
|---|
Shifting and scaling properties |
|---|
Linear time invariant and causal systems |
|---|
Fourier series representation of continuous and discrete time periodic signals |
|---|
Sampling theorem |
|---|
Applications of Fourier transform for continuous and discrete time signals |
|---|
Laplace transform and Z transform |
|---|
Electrical machines
Electrical machines: Unit 01
Single phase transformer |
|---|
| Equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency |
Three-phase transformers |
|---|
| Connections, vector groups, parallel operation |
Auto-transformer |
|---|
Electromechanical energy conversion principles |
|---|
DC machines |
|---|
| Separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of dc motors |
Three-phase induction machines |
|---|
| Principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control |
Operating principle of single-phase induction motors |
|---|
Synchronous machines |
|---|
| Cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors |
Types of losses and efficiency calculations of electric machines |
|---|
Power systems
Power systems: Unit 01
Basic concepts of electrical power generation |
|---|
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 |
|---|
Directional and distance protection |
|---|
Circuit breakers |
|---|
System stability concepts |
|---|
Equal area criterion |
|---|
Economic load dispatch (with and without considering transmission losses) |
|---|
Control systems
Control systems: Unit 01
Mathematical modeling and representation of systems |
|---|
Feedback principle |
|---|
Transfer function |
|---|
Block diagrams and signal flow graphs |
|---|
Transient and steady‐state analysis of linear time invariant systems |
|---|
Stability analysis using Routh-Hurwitz and Nyquist criteria |
|---|
Bode plots |
|---|
Root loci |
|---|
Lag |
|---|
Lead and lead‐lag compensators |
|---|
P, PI and PID controllers |
|---|
State space model |
|---|
Solution of state equations of LTI systems |
|---|
R.M.S. value |
|---|
Average value calculation for any general periodic waveform |
|---|
Electrical and electronic measurements
Electrical and electronic measurements: Unit 01
Bridges and potentiometers |
|---|
Measurement of voltage |
|---|
Current |
|---|
Power |
|---|
Energy and power factor |
|---|
Instrument transformers |
|---|
Digital voltmeters and multimeters |
|---|
Phase |
|---|
Time and frequency measurement |
|---|
Oscilloscopes |
|---|
Error analysis |
|---|
Analog and digital electronics
Analog and digital electronics: Unit 01
Simple diode circuits |
|---|
| Clipping, clamping, rectifiers |
Amplifiers |
|---|
| Biasing, equivalent circuit and frequency response |
Oscillators and feedback amplifiers |
|---|
Operational amplifiers |
|---|
| characteristics and applications |
Single stage active filters |
|---|
Sallen Key |
|---|
Butterworth |
|---|
VCOs and timers |
|---|
Combinatorial and sequential logic circuits |
|---|
Multiplexers |
|---|
Demultiplexers |
|---|
Schmitt triggers |
|---|
Sample and hold circuits |
|---|
A/D and D/A converters |
|---|
Power electronics
Power electronics: Unit 01
Static V-I characteristics and firing/ gating circuits for thyristor |
|---|
MOSFET |
|---|
IGBT |
|---|
DC to DC conversion |
|---|
| Buck, boost, and buck-boost converters |
Single and three-phase configuration of uncontrolled rectifiers |
|---|
Voltage and current commutated thyristor based converters |
|---|
Bidirectional AC to DC voltage source converters |
|---|
Magnitude and phase of line current harmonics for uncontrolled and thyristor based converters |
|---|
Power factor and distortion factor of AC to DC converters |
|---|
Single-phase and three-phase voltage and current source inverters |
|---|
Sinusoidal pulse width modulation |
|---|
GATE Geology and Geophysics Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Common section
Common section: Unit 01
Earth and planetary system |
|---|
| Terrestrial planets and moons of the solar system; size, shape, internal structure and composition of the earth; concept of isostasy; elements of seismology-body and surface waves, propagation of body waves in the earth’s interior |
| Heat flow within the earth; gravitational field of the Earth; geomagnetism and paleomagnetism; continental drift; plate tectonics-relationship with earthquakes, volcanism and mountain building; continental and oceanic crust |
| Composition, structure, and thickness |
Weathering and soil formation |
|---|
Landforms created by river, wind, glacier, ocean, and volcanoes |
|---|
Basic structural geology |
|---|
| Stress, strain and material response; brittle and ductile deformation; nomenclature and classification of folds and faults |
Crystallography |
|---|
| Basic crystal symmetry and concept of point groups |
| Mineralogy-silicate crystal structure and determinative mineralogy of common rock forming minerals |
Petrology of common igneous, sedimentary and metamorphic rocks |
|---|
Geological time scale |
|---|
Geochronology and absolute time |
|---|
Stratigraphic principles |
|---|
Major stratigraphic divisions of India |
|---|
Mineral, coal, and petroleum resources of India |
|---|
Introduction to remote sensing |
|---|
Engineering properties of rocks and soils |
|---|
Elements of hydrogeology |
|---|
Principles and applications of gravity, magnetic, electrical, electromagnetic, seismic, and radiometric methods of prospecting for oil, mineral, and ground water |
|---|
Introductory well logging |
|---|
Geology
Geology: Unit 01
Geomorphology |
|---|
| Geomorphic processes and agents; development and evolution of landforms in continental, and oceanic settings; tectonic geomorphology |
Structural geology |
|---|
| Forces and mechanism of rock deformation; primary and secondary structures; geometry and genesis of planar, and linear structures (bedding, cleavage, schistosity, lineation); folds, faults, joints, and unconformities; stereographic projection; shear zones |
| Thrusts and superposed folding; basement-cover relationship |
| Interpretation of geological maps |
Crystallography and mineralogy |
|---|
| Elements of crystal symmetry, form and twinning; crystallographic projection; crystal chemistry; classification of minerals, physical and optical properties of rock-forming minerals |
Geochemistry |
|---|
| Cosmic abundance of elements; meteorites; geochemical evolution of the earth; geochemical cycles; distribution of major, minor, and trace elements in crust and mantle; elements of high temperature and low temperature geochemical thermodynamics |
| Isotopic evolution of the crust and the mantle, mantle reservoirs; geochemistry of water and water-rock interaction |
Igneous petrology |
|---|
| Classification, forms, textures, and genesis of common igneous rocks; magmatic differentiation; binary and ternary phase diagrams; major and trace elements as monitors of partial melting and magma evolutionary processes |
| Mantle plumes, hotspots, and large igneous provinces |
Sedimentology |
|---|
| Texture, structure, and sedimentary processes; petrology of common sedimentary rocks; sedimentary facies and environments, cyclicities in sedimentary succession; provencance and basin analysis |
| Important sedimentary basins of India |
Metamorphic petrology |
|---|
| 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 |
Paleobiology |
|---|
| Diversity of life through time, mass extinctions-causes and effects; taphonomy-processes of fossilization |
| Taxonomy |
| Morphology and functional morphology of invertebrates (bivalves, brachiopods, gastropods, echinoids, ammonites); microfossils (foraminifera, ostracoda, conodonts, bryozoa); vertebrate paleonology (equus, probicidea, human) |
| Paleobotany (plant, spores, pollens) |
| Basic concepts of ecology/ paleoecology; classification-ecological and taxonomic schemes (diversity and richness) |
| Fossils and paleoenvironments |
Stratigraphy |
|---|
| Principles of stratigraphy and concepts of correlation; lithostratigraphy, biostratigraphy, and chronostratigraphy |
| Principles of sequence stratigraphy and applications |
| Stratigraphy of peninsular and extra-peninsular India |
| Boundary problems in Indian stratigraphy |
Resource geology |
|---|
| Ore-mineralogy; ore forming processes vis-à-vis ore-rock association (magmatic, hydrothermal, sedimentary, supergene and 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 |
Global tectonics |
|---|
| Plate motions, driving mechanisms, plate boundaries, supercontinent cycles |
Applied geology |
|---|
| 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 |
Natural hazards (landslide, volcanic, seismogenic, coastal) and mitigation |
|---|
Principles of climate change Hydrogeology |
|---|
| Groundwater flow and exploration, well hydraulics and water quality |
Basic principles of remote sensing |
|---|
| Energy sources and radiation principles, atmospheric absorption, interaction of energy with earth's surface, aerial-photo interpretation, multispectral remote sensing in visible, infrared, thermal IR and microwave regions |
| Digital processing of satellite images |
| GIS-basic concepts, raster and vector mode operations |
Geophysics
Geophysics: Unit 01
Solid-earth geophysics |
|---|
| The earth as a planet; different motions of the earth; gravity field of the earth, Clairaut's theorem, size and shape of earth; geomagnetic field, paleomagnetism; geothermics and heat flow; seismology and interior of the earth; variation of density |
| Velocity, pressure, temperature, electrical and magnetic properties of the earth |
Geodesy |
|---|
| Gravitational field of the earth; geoid; ellipsoid; geodetic reference systems; datum; Everest (1830) and WGS 84 (1984) systems; GPS and DGPS; levelling and surveying |
Earthquake Seismology |
|---|
| Elements of elasticity theory-stress and strain tensors, generalized Hooke's law; body and surface waves; rotational, dilatational, irrotational, and 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 |
Potential and time varying fields |
|---|
| Scalar and vector potential fields; Laplace, Maxwell, and Helmholtz equations for solution of different types of boundary value problems in Cartesian, cylindrical and spherical polar coordinates; Green's theorem; image theory |
| Integral equations in potential and time-varying field theory |
Gravity methods |
|---|
| Absolute and relative gravity measurements; gravimeters; land, airborne, shipborne, and bore-hole gravity surveys; tensorial gravity sensors and surveys; various corrections for gravity data reduction-free air, Bouguer, and isostatic anomalies |
| Density estimates of rocks; regional and residual gravity separation; principle of equivalent stratum; data enhancement techniques, upward and downward continuation; derivative maps, wavelength filtering; preparation and analysis of gravity maps |
| Gravity anomalies and their interpretation-anomalies due to geometrical and irregular shaped bodies, depth rules, calculation of mass |
Magnetic methods |
|---|
| Elements of Earth's magnetic field, units of measurement, magnetic susceptibility of rocks and measurements, magnetometers, and magnetic gradiometers, land, airborne and marine magnetic, and magnetic gradiometer surveys |
| Various corrections applied to magnetic data, IGRF, reduction to Pole transformation, Poisson's relation of gravity, and magnetic potential field, preparation of magnetic maps, upward and downward continuation |
| Magnetic anomalies due to geometrical and irregular shaped bodies; image processing concepts in processing of magnetic anomaly maps; depth rules; interpretation of processed magnetic anomaly data; derivative |
| Analytic signal and Euler depth solutions |
| Applications of gravity and magnetic methods for mineral, and oil exploration |
Electrical methods |
|---|
| Conduction of electricity through rocks, electrical conductivities of metals, non-metals, rock forming minerals and different rocks, concepts of 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 |
Electromagnetic methods |
|---|
| 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 |
Seismic methods |
|---|
| Elastic properties of earth materials; reflection, refraction, and CDP surveys; land and marine seismic sources, generation, and propagation of elastic waves, velocity-depth models, geophones, hydrophones, digital recording systems, digital formats |
| Field layouts, seismic noise, and noise profile analysis, optimum geophone grouping, noise cancellation by shot and geophone arrays, 2D, 3D, and 4D seismic data acquisition, processing and interpretation; CDP stacking charts, binning, filtering |
| Static and dynamic corrections, digital seismic data processing, seismic deconvolution and migration methods, attribute analysis, bright and dim spots, seismic stratigraphy, high resolution seismics, VSP, AVO, multi |
| Component seismics and seismic interferometry |
| Reservoir geophysics-rock physics and petrophysics |
| Geophysical survey design |
Geophysical signal processing |
|---|
| Sampling theorem, Nyquist frequency, aliasing, Fourier series, periodic waveform, Fourier and Hilbert transform, Z-transform and wavelet transform; power spectrum, delta function, auto correlation, cross correlation, convolution, deconvolution |
| Principles of digital filters, windows, poles, and zeros |
Geophysical well logging |
|---|
| Principles and techniques of geophysical well-logging, SP, resistivity, induction, gamma ray, neutron, density, sonic, temperature, dip meter, caliper, nuclear magnetic resonance-longitudinal and transverse relaxation, CPMG sequence |
| Porosity characterization, cement bond logging, micro-logs |
| Pulsed neutron devices and spectroscopy; multi-array and triaxial induction devices; quantitative evaluation of formations from well logs; logging while drilling; high angle and horizontal wells; clay quantification; lithology and porosity estimation |
| Saturation and permeability estimation; application of bore hole geophysics in ground water, mineral, and oil exploration |
Radioactive methods |
|---|
| Prospecting and assaying of mineral (radioactive and non-radioactive) deposits, half-life, decay constant, radioactive equilibrium, GM counter, scintillation detector, semiconductor devices, application of radiometric for exploration |
| Assaying and radioactive waste disposal |
Geophysical Inversion |
|---|
| Basic concepts of forward and inverse problems, ill-posedness of inverse problems, condition number, non-uniqueness and stability of solutions; L1, L2, and Lp norms, overdetermined, underdetermined, and mixed determined inverse problems |
| Quasi-linear and non-linear methods including Tikhonov's regularization method, singular value decomposition, Backus-Gilbert method, simulated annealing, genetic algorithms, swarm intelligence, machine learning, and artificial neural networks |
| Statistics of misfit and likelihood, Bayesian construction of posterior probabilities, sparsity promoting L1 optimization |
| Ambiguity and uncertainty in geophysical interpretation |
GATE Instrumentation Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
|---|
| Matrix algebra, systems of linear equations, consistency and rank, eigen values and eigen vectors |
Calculus |
|---|
| Mean value theorems, theorems of integral calculus, partial derivatives, maxima and minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes, Gauss and Green's theorems |
Differential equations |
|---|
| First order equation (linear and nonlinear), second order linear differential equations with constant coefficients, method of variation of parameters, Cauchy's and Euler's equations, initial and boundary value problems |
| Solution of partial differential equations: variable separable method |
Analysis of complex variables |
|---|
| Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent's series, residue theorem, solution of integrals |
Probability and Statistics |
|---|
| Sampling theorems, conditional probability, mean, median, mode, standard deviation and variance; random variables: Discrete and continuous distributions: Normal, Poisson and binomial distributions |
Numerical methods |
|---|
| Matrix inversion, solutions of non-linear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis |
Instrumentation engineering
Instrumentation engineering: Unit 01
Electricity and magnetism |
|---|
| Coulomb's law, electric field intensity, electric flux density, Gauss's law, divergence, electric field and potential due to point, line, plane and spherical charge distributions, effect of dielectric medium, capacitance of simple configurations |
| Biot‐Savart's law, Ampere's law, Curl, Faraday's law, Lorentz force, inductance, magnetomotive force, reluctance, magnetic circuits, self and mutual inductance of simple configurations |
Electrical circuits and machines |
|---|
| Voltage and current sources: Independent, dependent, ideal and practical; V-I relationships of resistor, inductor, mutual inductance and capacitor; transient analysis of RLC circuits with DC excitation |
| 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 |
Signals and systems |
|---|
| Periodic, aperiodic and impulse signals; Laplace, Fourier and z-transforms; transfer function, frequency response of first and second order linear time invariant systems, impulse response of systems; convolution, correlation |
| Discrete time system: Impulse response, frequency response, pulse transfer function; DFT and FFT; basics of IIR and FIR filters |
Control systems |
|---|
| Feedback principles, signal flow graphs, transient response, steady-state-errors, Bode plot, phase and gain margins, Routh and Nyquist criteria, root loci, design of lead, lag and lead-lag compensators, state-space representation of systems |
| Time-delay systems; mechanical, hydraulic and pneumatic system components, synchro pair, servo and stepper motors, servo valves; on-off, P, PI, PID, cascade, feedforward, and ratio controllers, tuning of PID controllers and sizing of control valves |
Analog electronics |
|---|
| Characteristics and applications of diode, Zener diode, BJT and MOSFET; small signal analysis of transistor circuits, feedback amplifiers |
| Characteristics of ideal and practical operational amplifiers; applications of 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 |
Digital electronics |
|---|
| Combinational logic circuits, minimization of boolean functions |
| IC families: TTL and CMOS |
| Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flipflops, shift registers, timers and counters; sample-and-hold circuit, multiplexer |
| Analog-to-digital (successive approximation, integrating, flash and sigma-delta) and digital-to-analog converters (weighted R, R-2R ladder and current steering logic) |
| Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/ settling time); basics of number systems, embedded Systems: Microprocessor and microcontroller applications, memory and input-output interfacing |
| Basics of data acquisition systems, basics of distributed control systems (DCS) and programmable logic controllers (PLC) |
Measurements |
|---|
| SI units, standards (R,L,C, voltage, current and frequency), systematic and random errors in measurement, expression of uncertainty - accuracy and precision, propagation of errors, linear and weighted regression |
| Bridges: Wheatstone, Kelvin, Megohm, Maxwell, Anderson, Schering and Wien for measurement of R, L, C and frequency, Q-meter |
| Measurement of voltage, current and power in single and three phase circuits; AC and DC current probes; true RMS meters, voltage and current scaling, instrument transformers, timer/counter, time, phase and frequency measurements, digital voltmeter |
| Digital multimeter; oscilloscope, shielding and grounding |
Sensors and industrial instrumentation |
|---|
| Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal conditioning circuits; transducers for industrial instrumentation: Displacement (linear and angular), velocity, acceleration, force, torque, vibration, shock |
| Pressure (including low pressure), flow (variable head, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters) temperature (thermocouple, bolometer, RTD (3/4 wire), thermistor, pyrometer and semiconductor); liquid level, Ph |
| Conductivity and viscosity measurement |
| 4-20 mA two-wire transmitter |
Communication and optical instrumentation |
|---|
| Amplitude- and frequency modulation and demodulation; Shannon's sampling theorem, pulse code modulation; frequency and time division multiplexing, amplitude-, phase-, frequency-, quadrature amplitude, pulse shift keying for digital modulation |
| Optical sources and detectors: LED, laser, photo-diode, light dependent resistor, square law detectors and their characteristics; interferometer: Applications in metrology; basics of fiber optic sensing |
| UV-VIS spectro photometers, mass spectrometer |
GATE Mathematics Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Mathematics
Mathematics: Unit 01
Calculus |
|---|
| Functions of two or more variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; double and triple integrals and their applications to area |
| Volume and surface area; vector calculus: Gradient, divergence, and curl, line integrals and surface integrals, Green's theorem, Stokes' theorem, and Gauss divergence theorem |
Linear algebra |
|---|
| Finite dimensional vector spaces over real or complex fields; linear transformations and their matrix representations, rank and nullity; systems of linear equations, characteristic polynomial, eigen values and eigen vectors, diagonalization |
| Minimal polynomial, Cayley-Hamilton theorem, finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, symmetric, skew-symmetric, Hermitian, skew-Hermitian, normal, orthogonal and unitary matrices |
| Diagonalization by a unitary matrix, Jordan canonical form; bilinear and quadratic forms |
Real analysis |
|---|
| Metric spaces, connectedness, compactness, completeness; sequences and series of functions, uniform convergence, Ascoli-Arzela theorem; weier strass approximation theorem; contraction mapping principle, power series |
| Differentiation of functions of several variables, inverse and Implicit function theorems; Lebesgue measure on the real line, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem |
Complex analysis |
|---|
| Functions of a complex variable: Continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy's integral theorem and formula; Liouville's theorem, maximum modulus principle, Morera's theorem; zeros and singularities |
| Power series, radius of convergence, Taylor's series and Laurent's series; residue theorem and applications for evaluating real integrals; Rouche's theorem, argument principle, Schwarz lemma; conformal mappings, Mobius transformations |
Ordinary differential equations |
|---|
| First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients |
| Second order linear ordinary differential equations with variable coefficients; Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method) |
| Legendre and Bessel functions and their orthogonal properties; systems of linear first order ordinary differential equations, Sturm's oscillation and separation theorems, Sturm-Liouville eigen value problems |
| Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, linearized stability, Lyapunov functions |
Algebra |
|---|
| Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, group action, Sylow's theorems and their applications; rings, ideals, prime and maximal ideals, quotient rings |
| Unique factorization domains, principle ideal domains, euclidean domains, polynomial rings, Eisenstein's irreducibility criterion; fields, finite fields, field extensions, algebraic extensions, algebraically closed fields |
Functional analysis |
|---|
| Normed linear spaces, banach spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem, Riesz representation theorem |
| Spectral theorem for compact self-adjoint operators |
Numerical analysis |
|---|
| Systems of linear equations: Direct methods (Gaussian elimination, LU decomposition, Cholesky factorization), iterative methods (Gauss-Seidel and Jacobi) and their convergence for diagonally dominant coefficient matrices |
| Numerical solutions of nonlinear equations: Bisection method, secant method, Newton-Raphson method, fixed point iteration; interpolation: Lagrange and Newton forms of interpolating polynomial, error in polynomial interpolation of a function |
| Numerical differentiation and error, numerical integration: Trapezoidal and Simpson rules, Newton-Cotes integration formulas, composite rules, mathematical errors involved in numerical integration formulae |
| Numerical solution of initial value problems for ordinary differential equations: Methods of Euler, Runge-Kutta method of order 2 |
Partial differential equations |
|---|
| Method of characteristics for first order linear and quasilinear partial differential equations; second order partial differential equations in two independent variables: Classification and canonical forms |
| Second order partial differential equations in two independent variables: Method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable |
| Wave equation: Cauchy problem and D' Alembert formula, domains of dependence and influence, non-homogeneous wave equation; heat equation: Cauchy problem; Laplace and Fourier transform methods |
Topology |
|---|
| Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, quotient topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn's Lemma |
Linear programming |
|---|
| Linear programming models, convex sets, extreme points; basic feasible solution, graphical method, simplex method, two phase methods, revised simplex method ; infeasible and unbounded linear programming models, alternate optima; duality theory |
| Weak duality and strong duality; balanced and unbalanced transportation problems, initial basic feasible solution of balanced transportation problems (least cost method, north-west corner rule, Vogel’s approximation method); optimal solution |
| Modified distribution method; solving assignment problems, hungarian method |
GATE Mechanical Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
|---|
| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
|---|
| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
|---|
| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
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, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative |
| Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence, and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes, and Green's theorems |
Differential equations |
|---|
| First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace's equations |
Complex variables |
|---|
| Analytic functions; Cauchy-Riemann equations; Cauchy's integral theorem and integral formula; Taylor and Laurent series |
Probability and Statistics |
|---|
| Definitions of probability, sampling theorems, conditional probability; mean, median, mode, and standard deviation; random variables, binomial, Poisson, and normal distributions |
Numerical methods |
|---|
| Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson's rules; single and multi-step methods for differential equations |
Applied mechanics and design
Applied mechanics and design: Unit 01
Engineering mechanics |
|---|
| Free-body diagrams and equilibrium; friction and its applications including rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc; trusses and frames; virtual work; kinematics and dynamics of rigid bodies in plane motion |
| Impulse and momentum (linear and angular), and energy formulations; Lagrange's equation |
Mechanics of materials |
|---|
| Stress and strain, elastic constants, Poisson's ratio; Mohr's circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; concept of shear centre; deflection of beams |
| Torsion of circular shafts; Euler's theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength |
Theory of machines |
|---|
| Displacement, velocity, and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope |
Vibrations |
|---|
| Free and forced vibration of single degree of freedom systems, effect of damping; vibration isolation; resonance; critical speeds of shafts |
Machine design |
|---|
| Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings |
| Brakes and clutches, springs |
Fluid mechanics and thermal sciences
Fluid mechanics and thermal sciences: Unit 01
Fluid mechanics |
|---|
| Fluid properties; fluid statics, forces on submerged bodies, stability of floating bodies; control-volume analysis of mass, momentum, and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli's equation |
| Dimensional analysis; viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends, and fittings; basics of compressible fluid flow |
Heat-transfer |
|---|
| Modes of heat transfer; one dimensional heat conduction, resistance concept and electrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system, Heisler's charts; thermal boundary layer |
| Dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer |
| Stefan-Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis |
Thermodynamics |
|---|
| Thermodynamic systems and processes; properties of pure substances, behaviour of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in various processes; second law of thermodynamics |
| thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations |
Applications |
|---|
| Power engineering: Air and gas compressors; vapour and gas power cycles, concepts of regeneration and reheat |
| IC engines: Air-standard Otto, diesel, and dual cycles |
| Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes |
| Turbomachinery: Impulse and reaction principles, velocity diagrams, pelton-wheel, Francis and Kaplan turbines; steam and gas turbines |
Materials, manufacturing and industrial engineering
Materials, manufacturing and industrial engineering: Unit 01
Engineering materials |
|---|
| Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials |
Casting, forming, and joining processes |
|---|
| Different types of castings, design of patterns, moulds and cores; solidification and cooling; riser and gating design |
| Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy |
| Principles of welding, brazing, soldering, and adhesive bonding |
Machining and machine tool operations |
|---|
| Mechanics of machining; basic machine tools; single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, jigs, and fixtures |
| Abrasive machining processes; NC/ CNC machines and CNC programming |
Metrology and inspection |
|---|
| Limits, fits, and tolerances; linear and angular measurements; comparators; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly; concepts of coordinate-measuring machine (CMM) |
Computer integrated manufacturing |
|---|
| Basic concepts of CAD/ CAM and their integration tools; additive manufacturing |
Production planning and control |
|---|
| Forecasting models, aggregate production planning, scheduling, materials requirement planning; lean manufacturing |
Inventory control |
|---|
| Deterministic models; safety stock inventory control systems |
Operations research |
|---|
| Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM |
GATE Metallurgical Engineering Syllabus
General aptitude
General aptitude: Unit 01
Verbal aptitude |
|---|
| Basic English grammar: Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech |
| Basic vocabulary: Words, idioms, and phrases in context |
| Reading and comprehension |
| Narrative sequencing |
Quantitative aptitude |
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| Data interpretation: Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables |
| Numerical computation and estimation: Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series |
| Mensuration and geometry |
| Elementary statistics and probability |
Analytical aptitude |
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| Logic: Deduction and induction |
| Analogy |
| Numerical relations and reasoning |
Spatial aptitude |
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| Transformation of shapes: Translation, rotation, scaling, mirroring, assembling, and grouping, paper folding, cutting, and patterns in 2 and 3 dimensions |
Engineering mathematics
Engineering mathematics: Unit 01
Linear algebra |
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| Matrices and determinants; systems of linear equations; eigen values and eigen vectors |
Calculus |
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| Limit, continuity, and differentiability; partial derivatives; maxima and minima; sequences and series; test for convergence; Fourier series |
Vector calculus |
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| Gradient; divergence and curl; line; surface and volume integrals; Stokes, Gauss, and Green's theorems |
Differential equations |
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| Linear and non-linear first order ODEs; higher order linear ODEs with constant coefficients; Cauchy's and Euler's equations; Laplace transforms; PDEs-Laplace, one dimensional heat, and wave equations |
Probability and Statistics |
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| Definitions of probability and sampling theorems, conditional probability, mean, median, mode, and standard deviation; random variables; Poisson, normal, and binomial distributions; analysis of experimental data; linear least squares method |
Numerical methods |
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| Solutions of linear and non-linear (bisection, secant, Newton-Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations |
Metallurgical thermodynamics
Metallurgical thermodynamics: Unit 01
Laws of thermodynamics |
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| First law-energy conservation, second law-entropy; enthalpy, Gibbs and Helmholtz free energy; Maxwell's relations; chemical potential; applications to metallurgical systems, solutions, ideal and regular solutions; Gibbs phase rule, phase equilibrium |
| Binary phase diagram and lever rule, free-energy vs. composition diagrams; equilibrium constant, activity, Ellingham, and phase stability diagrams; thermodynamics of point defects, surfaces and interfaces, adsorption and segregation phenomena |
Electrochemistry |
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| Single electrode potential, electrochemical cells, Nernst equation, potential-pH diagrams |
Transport phenomena and rate processes
Transport phenomena and rate processes: Unit 01
Momentum transfer |
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| Concept of viscosity, shell balances, Bernoulli's equation, mechanical energy balance equation, flow past plane surfaces and through pipes |
Heat transfer |
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| Conduction, Fourier's law, 1-D steady state conduction |
Convection |
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| Heat transfer coefficient relations for forced convection |
Radiation |
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| Black body radiation, Stefan-Boltzmann law, Kirchhoff's law |
Mass transfer |
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| Diffusion and Fick's laws, mass transfer coefficients |
Dimensional analysis |
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| Buckingham Pi theorem, significance of dimensionless numbers |
Basic laws of chemical kinetics |
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| First order reactions, reaction rate |