Syllabus for the GATE exam and its preparation remains the same to apply for a job at a Public Sector Undertaking (PSU), as well as an admission for a post-graduate degree in engineering.

**General Aptitude**

**This section is common in all papers of GATE. It is divided into
two sections:**

**Verbal Ability **

- English grammar
- Sentence completion
- Verbal analogies
- Word groups
- Critical reasoning
- Verbal deduction

**Numerical Ability**

- Numerical computation
- Numerical estimation
- Numerical reasoning
- Data interpretation

**Aerospace Engineering**

This paper is split into two categories – core & special topics where 90% questions are asked from the former and 10% from the latter. Following are the topics:

**Engineering Mathematics**

**Core Topics**: Linear Algebra, Calculus and Differential Equations.**Special Topics**: Fourier series, Laplace Transforms, Numerical methods for linear and nonlinear algebraic equations, Numerical integration and differentiation.

**Flight Mechanics**:

**Core Topics**: Basics, Airplane performance & Static stability.**Special Topics**: Dynamic stability: Euler angles, Equations of motion, aerodynamic forces and moments, stability & control derivatives, decoupling of longitudinal and lateral-directional dynamics, longitudinal modes, lateral-directional modes.

**Space Dynamics**:

**Core Topics**: Central force motion, determination of trajectory and orbital period in simple cases**Special Topics**: Orbit transfer, in-plane and out-of-plane.

**Aerodynamics:**

**Core Topics**: Basic Fluid Mechanics, Airfoils and wings & Compressible Flows.**Special Topics**: Elementary ideas of viscous flows including boundary layers, Wind Tunnel Testing: Measurement and visualization techniques

**Structures:**

**a) Core Topics:** Strength
of Materials, Flight vehicle structures & Structural Dynamics.

**b) Special Topics**: Vibration of beams,
Theory of elasticity: Equilibrium and compatibility equations, Airy’s stress
function.

**Propulsion:**

**a) Core Topics**: Basics,
Thermodynamics of aircraft engines, Axial compressors, Axial turbines,
Centrifugal compressor & Rocket propulsion.

**b) Special Topics**: No Special Topics

**Statistics **

**Calculus:**Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals; Functions of two or three 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; 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; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Jordan canonical form, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt ortho normalization process, definite forms.

**Probability:**Classical, relative frequency and axiomatic definitions of probability, conditional probability, Bayes’ theorem, independent events; Random variables and probability distributions, moments and moment generating functions, quantiles; Standard discrete and continuous univariate distributions; Probability inequalities (Chebyshev, Markov, Jensen); Function of a random variable; Jointly distributed random variables, marginal and conditional distributions, product moments, joint moment generating functions, independence of random variables; Transformations of random variables, sampling distributions, distribution of order statistics and range; Characteristic functions; Modes of convergence; Weak and strong laws of large numbers; Central limit theorem for i.i.d. random variables with existence of higher order moments.

**Stochastic Processes:**Markov chains with finite and countable state space, classification of states, limiting behaviour of n-step transition probabilities, stationary distribution, Poisson and birth-and-death processes.

**Inference:**Unbiasedness, consistency, sufficiency, completeness, uniformly minimum variance unbiased estimation, method of moments and maximum likelihood estimations; Confidence intervals; Tests of hypotheses, most powerful and uniformly most powerful tests, likelihood ratio tests, large sample test, Sign test, Wilcoxon signed rank test, Mann-Whitney U test, test for independence and Chi-square test for goodness of fit.

**Regression Analysis:**Simple and multiple linear regression, polynomial regression, estimation, confidence intervals and testing for regression coefficients; Partial and multiple correlation coefficients. Multivariate Analysis: Basic properties of multivariate normal distribution; Multinomial distribution; Wishart distribution; Hotellings T2 and related tests; Principal component analysis; Discriminant analysis; Clustering.

**Design of Experiments:**One and two-way ANOVA, CRD, RBD, LSD, 22 and 23 Factorial experiments

**Agricultural Engineering**

**Engineering Mathematics:**Linear Algebra, Calculus, Vector Calculus, Differential Equations, Probability and Statistics & Numerical Methods.

**Farm Machinery:**Machine Design and Farm Machinery**Farm Power:**Sources of Power, Farm Power, Tractors and Powertillers**Soil and Water Conservation Engineering:**Fluid Mechanics, Soil Mechanics, Hydrology, Surveying and Leveling, Soil and Water Erosion & Watershed Management**Irrigation and Drainage Engineering:**Soil-Water-Plant Relationship, Irrigation Water Conveyance and Application Methods, Agricultural Drainage, Groundwater Hydrology & Wells and Pumps

**Agricultural Processing Engineering**: Drying, Size Reduction and Conveying, Processing and By-product Utilization & Storage Systems**Dairy and Food Engineering**: Heat and Mass Transfer & Preservation of Food.

**Architecture and Planning (AR):**Architecture and Design, Building Materials, Construction and Management, Building and Structures, Environmental Planning and Design, Urban Design, Urban Planning and Housing, Planning Techniques and Management, Services, Infrastructure and Transportation.

**Biotechnology (BT):**Engineering Mathematics, General Biotechnology (Biochemistry, Microbiology, Cell Biology, Molecular Biology and Genetics, Analytical Techniques, Immunology, Bioinformatics), Recombinant DNA Technology, Plant and Animal Biotechnology, Bioprocess Engineering and Process Biotechnology.

**Chemical Engineering (CH):**Engineering Mathematics, (Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods), Process Calculations and Thermodynamics, Fluid Mechanics and Mechanical Operations, Heat Transfer, Mass Transfer, Chemical Reaction Engineering, Instrumentation and Process Control, Plant Design and Economics & Chemical Technology.

**Chemistry (CY):****Physical Chemistry**: Structure, Equilibrium, Kinetics & Surfaces and Interfaces.

**Inorganic Chemistry**: Main Group Elements, Transition Elements, Lanthanides and Actinides, Organometallics, Radioactivity, Bioinorganic Chemistry, Solids & Instrumental Methods of Analysis.**Organic Chemistry**: Stereochemistry, Reaction Mechanisms, Organic Synthesis, Pericyclic Reactions and Photochemistry, Heterocyclic Compounds, Biomolecules & Spectroscopy.

**Civil Engineering (CE):**

**Engineering Mathematics**: Linear Algebra, Calculus, Ordinary Differential Equation (ODE), Partial Differential Equation (PDE), Probability and Statistics & Numerical Methods.

**Structural Engineering**: Engineering Mechanics, Solid Mechanics, Structural Analysis, Construction Materials and Management, Concrete Structures & Steel Structures.

**Geotechnical Engineering**: Soil Mechanics & Foundation Engineering.**Water Resources Engineering**: Fluid Mechanics, Hydraulics, Hydrology & Irrigation.**Environmental Engineering**: Water and Waste Water, Air Pollution, Municipal Solid Wastes & Noise Pollution.

**Transportation Engineering**: Transportation Infrastructure, Highway Pavements & Traffic Engineering.

**Geomatics Engineering**: Principles of surveying, Photogrammetry & Remote sensing.

**Computer Science and Information Technology (CS):**Engineering Mathematics (Discrete Mathematics, Linear Algebra, Calculus, Probability), Digital Logic, Computer Organization and Architecture, Programming and Data Structures, Algorithms, Theory of Computation, Compiler Design, Operating System, Databases & Computer Networks.**Ecology and Evolution (EY):**Ecology, Evolution, Mathematics and Quantitative Ecology & Behavioural Ecology.

**Electrical Engineering (EE):**Engineering Mathematics (Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, Transform Theory), Electric Circuits, Electromagnetic Fields, Signals and Systems, Electrical Machines, Power Systems, Control Systems, Electrical and Electronic Measurements, Analog and Digital Electronics & Power Electronics.

**Electronics and Communications (EC):**Engineering Mathematics, Networks, Signals and Systems, Electronic Devices, Analog Circuits, Digital Circuits, Control Systems, Communications & Electromagnetics.

**Geology and Geophysics (GG):**Earth and Planetary system, Weathering and soil formation, Introduction to remote sensing, Principles and applications of gravity.

a) Common Section:

**Geology**: Geomorphic processes and agents, Mechanism of rock deformation, Crystallography, Cosmic abundance of elements, Igneous rocks, Physico-chemical conditions of metamorphism, Morphology, Principles of Stratigraphy, Engineering properties of rocks and soils.

**Geophysics**: The earth as a planet, different motions of the earth, Scalar and vector potential fields, Absolute and relative gravity measurements, Elements of Earth’s magnetic field, Conduction of electricity through rocks, Basic concept of EM induction in the earth, Geophysical signal processing.

**Instrumentation Engineering:**Engineering Mathematics (Linear Algebra, Calculus, Differential equations, Analysis of complex variables, Probability and Statistics, Numerical Methods), Electrical Circuits, Signals and Systems, Control Systems, Analog Electronics, Digital Electronics, Measurements, Sensors and Industrial Instrumentation, Communication and Optical Instrumentation.

**Mathematics:**Linear Algebra, Complex Analysis, Real Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Partial Differential Equations, Topology, Probability and Statistics & Linear programming.**Mechanical Engineering (ME):**

**a) Engineering Mathematics**: Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics & Numerical Methods.

**b) Applied Mechanics and Design**: Engineering
Mechanics, Mechanics of Materials, Types of Machines, Vibrations & Machine
Design.

c) **Fluid Mechanics and Thermal Sciences**: Fluid Mechanics,
Heat-Transfer, Thermodynamics & Applications.

d) **Materials, Manufacturing and Industrial Engineering**: Engineering
Materials, Casting, Forming and Joining Processes, Machining and Machine Tool
Operations, Metrology and Inspection, Computer Integrated Manufacturing,
Production Planning and Control, Inventory Control & Operations Research.

**Metallurgical Engineering:**Engineering Mathematics (Linear Algebra, Calculus, Vector Calculus, Differential equations, Probability and Statistics, Numerical Methods), Thermodynamics and Rate Processes, Extractive Metallurgy, Physical Metallurgy, Mechanical Metallurgy & Manufacturing Processes.

**Mining Engineering:**

**Engineering Mathematics**: Linear Algebra, Calculus, Vector Calculus, Differential equations, Probability and Statistics & Numerical Methods.**Mine Development and Surveying**: Mine Development & Mine Surveying.**Geomechanics and Ground Control**: Engineering Mechanics, Geomechanics & Ground Control.

**Mining Methods and Machinery**: Mining Methods and Mining Machinery

**Surface Environment, Mine Ventilation, and Underground Hazards**: Surface Environment, Mine Ventilation and Subsurface Hazards.

**Mine Economics, Mine Planning, Systems Engineering**: Mine Economics, Mine Planning and Systems Engineering.

**Petroleum Engineering:**Linear Algebra, Calculus, Differential equations, Complex variables, Probability and Statistics, Numerical Methods, Petroleum Exploration, Oil and Gas Well Drilling Technology, Reservoir Engineering, Petroleum Production Operations, Offshore Drilling and Production Practices, Petroleum Formation Evaluation, Oil and Gas Well Testing, Health Safety and Environment in Petroleum Industry, Enhanced Oil Recovery Techniques, Latest trends in Petroleum Engineering.**Physics:**Mathematical Physics, Classical Mechanics, Electromagnetic Theory, Quantum Mechanics, Thermodynamics and Statistical Physics, Atomic and Molecular Physics, Solid State Physics & Electronics, Nuclear and Particle Physics

**Production & Industrial Engineering:**

**a) Engineering Mathematics**: Linear Algebra, Calculus, Differential equations, Complex variables,
Probability and Statistics & Numerical Methods.

**b) General Engineering**: Engineering Materials, Applied Mechanics, Theory of Machines and
Design, Thermal and Fluids Engineering.

**c) Manufacturing Processes
I**: Casting, Metal Forming, Joining of materials,
Powder processing, Polymers and Composites.

d) **Manufacturing Processes II**:
Machine Tools and Machining, Non-traditional Manufacturing & Computer
Integrated Manufacturing.

e) **Quality and Reliability**: Metrology
and Inspection, Quality management, Reliability and Maintenance.

f) **Industrial Engineering**: Product Design
and Development, Work System Design & Facility Design.

g) **Operations research and
Operations Management**: Operation Research, Engineering Economy and Costing,
Production control & Project management.

**19) Textile Engineering
and Fibre Science:** Engineering Mathematics (Linear Algebra, Calculus,
Vector Calculus, Differential Equations, Probability and Statistics, Numerical
Methods), Textile Fibers, Yarn manufacture, Yarn structure and Properties,
Fabric manufacture, Structure and Properties, Textile Testing & Chemical
processing.

**20)
Engineering Science: **

**a) ****Engineering Mathematics**: Linear Algebra, Calculus, Vector Calculus, Complex variables, Ordinary
Differential Equations, Partial Differential Equations, Probability and
Statistics & Numerical Methods.

b) **Fluid Mechanics**: Flow and Fluid
Properties, Kinematics, Integral analysis, Differential Analysis, Inviscid
flows, Dimensional analysis, Internal flows, Prandtl boundary layer equations.

c) **Materials Science**: Processing of
Materials, Characterization Techniques, Structure and Imperfections,
Thermodynamics and Kinetics, Properties of Materials (Mechanical Properties,
Electronic Properties, Magnetic Properties, Thermal Properties, Optical
Properties), Material types, Environmental Degradation, Elements of Quantum
Mechanics and Mathematics.

d) **Solid Mechanics**: Equivalent force
systems, Stresses and strains, Axial, shear and bending moment diagrams, Free
vibration of single degree of freedom systems.

e) **Thermodynamics**: Basic Concepts, First
Law of Thermodynamics, Second Law of Thermodynamics, Properties of Pure
Substances, Thermodynamic Relations, Thermodynamic Cycles, Ideal Gas Mixtures.

**f)** **Polymer Science and Engineering**:
Chemistry of high polymers, Polymer Characterization, Synthesis and properties,
Polymer blends and composites, Polymer Technology, Polymer rheology, Polymer
processing, Polymer testing.

**g) Food Technology**: Food Chemistry
and Nutrition, Food Microbiology, Food Products Technology & Food
Engineering.

**h) Atmospheric & Ocean Science: **Atmospheric
Science and Ocean Sciences.

**20) Syllabus
of Life Science (XL):
**

**a)**

**Chemistry**: Atomic Structure and Periodicity, Structure and Bonding, s, p and d Block Elements, Chemical Equilibria, Electrochemistry, Reaction Kinetics, Thermodynamics, Structure-Reactivity Correlations and Organic Reaction Mechanisms.

**b) Biochemistry**: Organization of life, Enzyme kinetics including its regulation and inhibition, Biochemical separation techniques, Cell structure and organelles, DNA replication & Immune system.

**c) Botany**: Plant
Systematics, Plant Anatomy, Morphogenesis & Development, Physiology and Biochemistry,
Genetics, Plant Breeding and Genetic Modification, Economic Botany, Plant
Pathology, Ecology and Environment.

**d) Microbiology**: Historical
Perspective, Methods in Microbiology, Microbial Taxonomy and Diversity,
Prokaryotic and Eukaryotic Cells: Structure and Function, Microbial Growth,
Control of Micro-organisms, Microbial Metabolism, Microbial Diseases and Host
Pathogen Interaction, Chemotherapy/Antibiotics, Microbial Genetics &
Microbial Ecology.

e) **Zoology**: Animal world, Evolution,
Genetics, Biochemistry and Molecular Biology, Cell Biology, Gene expression in
Eukaryotes, Animal Anatomy and Physiology, Parasitology and Immunology,
Development Biology, Ecology & Animal Behaviour.

f) **Food Technology**: Food Chemistry and
Nutrition, Food Microbiology, Food Products Technology & Food Engineering.