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    GATE Engineering Sciences Syllabus 2027 (Out): Subject & Topic Wise Weightage

    GATE Engineering Sciences Syllabus 2027 (Out): Subject & Topic Wise Weightage

    Kanak MukhijaUpdated on 23 Jul 2026, 10:49 AM IST

    GATE Engineering Sciences Syllabus 2027: IIT Madras has released the GATE 2027 Engineering Sciences (XE) syllabus on the official website. Candidates can check the detailed GATE XE syllabus 2027 to understand the topics prescribed for the examination. The syllabus comprises General Aptitude (GA), Engineering Mathematics, and a range of optional sections from which candidates can choose based on their specialization. The recently introduced Energy Science (XE-I) section continues to be part of the GATE 2027 syllabus. Aspirants are advised to refer to the latest syllabus and exam pattern while preparing for the GATE examination. The GATE 2027 examinations will be conducted on February 6, 7, 13, 14, 20, and 21, 2027, and the complete subject-wise syllabus is available on the official GATE website.
    Direct link for the GATE 2027 Engineering Science Syllabus

    This Story also Contains

    1. GATE Engineering Sciences Syllabus 2027
    2. GATE Exam Pattern 2027 for Engineering Sciences
    3. GATE Engineering Sciences 2027- Marking Scheme
    GATE Engineering Sciences Syllabus 2027 (Out): Subject & Topic Wise Weightage
    GATE Engineering Sciences Syllabus

    IIT Madras will conduct the GATE exam for admission to MTech programmes at several prestigious universities. Students must also follow the GATE exam pattern along with the syllabus.

    GATE Engineering Sciences Syllabus 2027

    IIT Madras has released the GATE XE syllabus on the official website, gate2027.iitg.ac.in. Engineering Sciences or XE paper consists of two compulsory sections- General Aptitude (GA) and Engineering Mathematics, along with two optional sections. Candidates can check the table below for the detailed syllabus of GATE Engineering Sciences 2025.

    GATE 2027 Engineering Science Syllabus for Engineering Mathematics (XE-A)

    Engineering Mathematics is compulsory and common for all Engineering Science (XE) sections. The GATE Engineering Mathematics syllabus consists of topics such as Linear Algebra, Calculus, Vector Calculus, Complex variables, Ordinary Differential Equations, Partial Differential Equations, Probability and Statistics, and Numerical Methods. Aspirants can check the detailed GATE XE syllabus for Engineering Mathematics here.

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    GATE Engineering Mathematics (XE-A) Syllabus

    TopicsSub-Topics
    GATE Engineering Mathematics Syllabus for Linear Algebra
    • Algebra of real matrices:
      • Determinant, inverse and rank of a matrix
      • System of linear equations (conditions for unique solution, no solution and infinite number of solutions)
      • Eigen values and eigen vectors of matrices
      • Properties of eigen values and eigen vectors of symmetric matrices, diagonalization of matrices
      • Cayley-Hamilton Theorem
    GATE Engineering Mathematics Syllabus for Calculus
    • Functions of Single Variable: Limit, indeterminate forms and L'Hospital's rule; Continuity and differentiability; Mean value theorems; Maxima and minima; Taylor's theorem; Fundamental theorem and mean value theorem of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes (rotation of a curve about an axis).
    • Functions of Two Variables: Limit, continuity and partial derivatives; Directional derivative; Total derivative; Maxima, minima and saddle points; Method of Lagrange multipliers; Double integrals and their applications.
    • Sequences and Series: Convergence of sequences and series; Tests of convergence of series with nonnegative terms (Cauchy Condensation Test, Ratio, Root and integral tests); Power series; Taylor's series.
    GATE Engineering Mathematics Syllabus for Vector Calculus
    • Gradient
    • Divergence and curl
    • Line integrals and Green's theorem
    GATE Engineering Mathematics Syllabus for Complex Variables
    • Complex numbers
    • Argand plane and polar representation of complex numbers
    • De Moivre’s theorem
    • Definition and examples of Analytic functions
    • Cauchy-Riemann equations
    GATE Engineering Mathematics Syllabus for Ordinary Differential Equations
    • First order equations(linear and nonlinear)
    • Second order linear differential equations with constant coefficients
    • Cauchy-Euler equation
    • Second order linear differential equations with variable coefficients
    • Wronskian
    • Method of variation of parameters
    • Eigen value problem for second order equations with constant coefficients
    • Power series solutions for ordinary points
    GATE Engineering Mathematics Syllabus for Partial Differential Equations
    • Classification of second order linear partial differential equations
    • Fourier series method.
    • Method of separation of variables
    • One dimensional heat equation and two dimensional Laplace equation
    GATE Engineering Mathematics Syllabus for Probability and Statistics
    • Axioms of probability
    • Total probability theorem
    • Conditional probability
    • Bayes' Theorem
    • Mean
    • Variance and standard deviation of random variables
    • Binomial
    • Poisson and Normal distributions
    • Correlation and linear regression
    GATE Engineering Mathematics Syllabus for Numerical Methods
    • Solution of systems of linear equations using LU decomposition
    • Gauss elimination method
    • Lagrange and Newton's interpolations
    • Solution of polynomial and transcendental equations by Bisection method and Newton-Raphson method
    • Numerical integration by trapezoidal rule and Simpson's rule 1/3rd and 3/8th rules
    • Numerical solutions of first order differential equations by explicit Euler's method
    GATE 2027 Syllabus (All Subjects)
    Download the GATE 2027 subject-wise syllabus PDF and prepare with the latest topics, section-wise weightage, and exam pattern for your chosen discipline.
    Check Now

    GATE 2027 XE1: Fluid Mechanics

    Section

    Topics

    Classification of Flows

    Concept of a fluid, Viscous versus inviscid flows, Concept of viscosity, Newtonian versus non-Newtonian fluid, Incompressible versus compressible flows, Internal versus external flows, Steady versus unsteady flows, Laminar versus turbulent flows.


    Hydrostatics

    Buoyancy, Manometry, Forces on submerged bodies and their stability.


    Kinematics of Fluid MotionEulerian and Lagrangian descriptions of fluid motion, Concept of local, Convective and material derivatives, Streamline, Streakline, and Pathline.
    Integral Analysis for a Control VolumeReynolds Transport Theorem (RTT) for conservation of mass and linear momentum.
    Differential AnalysisDifferential equations of mass and momentum for incompressible flows, Euler equation, Bernoulli equation and its application for venturi meter, Pitot-static tube, and Orifice meter. Navier-Stokes equation and its exact solutions for Couette flow and Poiseuille flow. Concept of fluid rotation, Vorticity, Stream function, and Circulation.
    Dimensional AnalysisConcept of similarity, Buckingham Pi theorem and its applications. Dimensionless groups and their physical significance - Reynolds number, Froude number, and Mach number.
    Internal FlowsFully developed pipe flow - Friction factor, Darcy-Weisbach relation and Moody’s chart, Major and minor losses. Concept of flow development.
    Potential FlowsVelocity potential function, Uniform flow, Source, Sink, and Vortex.
    External Flows
    Concept of Prandtl boundary layer, Boundary layer thickness, Displacement thickness and momentum thickness. Qualitative idea of boundary layer separation, Streamlined and bluff bodies, Drag and lift forces.
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    GATE 2027 XE2: Materials Science

    Section

    Topics

    Classification and Structure of Materials
    Classification of MaterialsMetals, ceramics, polymers and composites.
    Fundamentals of crystallographyDefinitions of crystal, lattice and motif: Crystal=Lattice+Motif. Distinction between atoms and lattice points; Symmetry operations: Translations (required symmetry of crystals/lattices); Symmetry based definitions of 7 crystal systems; Unit cells: primitive and non-primitive cells; Fourteen Bravais lattices and their classification into crystal systems; Miller and Miller-Bravais indices of crystallographic planes and directions.
    Close-packed crystal structures of elementsCubic close-packed (CCP), Hexagonal close-packed (HCP) and body-centred cubic (BCC) structures; Stacking sequence of planes; Tetrahedral and octahedral voids.
    Crystalline and other ordered structures of carbonDiamond and Graphite in terms of lattice and motif; Graphene and fullerene; Carbon nanotubes.
    Crystalline structure of compoundsNaCl, CsCl, ZnS (Zinc blend and Wurtzite), Perovskite, Spinels; Pauling’s rule for structure of ionic compounds.
    Structure of amorphous materialsCrystalline and glassy silica; Fused silica and soda-lime glass
    Solid solutionsInterstitial and substitutional; Hume-Rothery rules.
    Structure of polymersMonomers and polymers. Addition and condensation polymers. Bonding in polymers. CC chain. Degree of polymerization. Chain configuration vs. chain conformations. Atactic, isotactic and syndiotactic configurations. Crystalline, semi-crystalline and amorphous polymers. Copolymers: alternating, block and random. Examples of common polymers: Polyethylene (PE), Polypropylene (PP), Polyvinylchloride (PVC), Polyetraflouroethylene (PTFE), Polystyrene (PS). Crosslinking. Natural and vulcanised rubber
    Defects in Crystalline Materials:
    Zero-dimensional or point defectsVacancies, interstitials, substitutional atoms, Frenkel and Schottky defects; Equilibrium concentration of point defects.
    One-dimensional or line defectsDislocations: edge, screw and mixed. Burgers vector and Burgers circuit; Burgers vectors of stable dislocations in simple cubic, body-centred cubic and face-centred cubic lattices; Dislocations meeting at a node; Line energy of a dislocation. Dislocation motion: glide and climb.
    Two-dimensional or surface defectsFree surfaces, Grain boundaries, twin boundaries, stacking faults, phase boundary; Surface energy of a free surface in terms of a simple bond breaking model.
    Thermodynamics, Kinetics and Phase Transformations

    Extensive and intensive thermodynamic properties, laws of thermodynamics, phase equilibria, phase rule, phase diagrams - unary pressure-temperature diagrams, binary temperature-composition diagrams, construction of temperature composition diagrams from free energies, common tangent construction in free energy-composition diagrams, invariant reactions.

    Reaction kinetics, rate constants, order of reactions, Arrhenius law, Fick’s laws, Steady state and non-steady state solutions of diffusion equations, diffusion distance and diffusion time, applications of solutions of diffusion equations, atomistic mechanisms of diffusion, fast diffusion paths.

    Solidification of pure metals and alloys, homogeneous and heterogeneous nucleation, nucleation rate, growth, partitioning during binary solidification; diffusional solid-state phase transformations (precipitation and eutectoid), overall transformation kinetics (TTT and CCT), martensitic/displacive transformation; glass transition.
    Properties and Applications of Materials
    Mechanical properties
    elastic and plastic deformation; atomic bonding and elasticity; shear strength of perfect crystals; plastic deformation by slip and dislocation motion; Strengthening mechanisms: strain hardening, solid solution hardening, precipitation hardening, grain size refinement; Grifith theory of fracture; fatigue: cyclic loading, S-N curve, crack initiation and propagation; Creep in crystalline materials: stages and mechanisms of creep; Composites: particle and fibre reinforced composites; elastic modulus (rule of mixtures).
    Electronic Properties
    Drude model and classical description of electrical conductivity, Drawbacks of classical theory, Quantum mechanical description including concept of Fermi energy, Fermi surface and density of states. Band Theory to explain insulators, conductors, and semiconductors via allowed and forbidden energy bands, Effective mass concept, Intrinsic and extrinsic semiconductors, temperature dependence of conductivity, Carrier concentration and mobility, drift vs. diffusion current, Hall Effect for a simple metal or semiconductor. Dielectric behavior, piezo- and ferro-electric behavior.

    Magnetic Properties
    Origin of magnetism in materials, types of Magnetism: Diamagnetism, Paramagnetism, Ferromagnetism, Ferrimagnetism and Antiferromagnetism, Magnetic Domains & Hysteresis, Hard and soft magnetic materials.

    Thermal Properties
    Specific heat, Classical Dulong–Petit Law, Wiedemann-Franz Law, Thermal conductivity of metals and insulators (role of electrons and phonons), Einstein and Debye model, heat conduction, thermal diffusivity, thermal expansion, and thermoelectricity.
    Optical Properties
    Refractive index, absorption and transmission of electromagnetic radiation
    Characterization and Measurements of Properties

    X-ray diffraction: Bragg’s Law, structure factor, indexing of cubic diffraction patterns; spectroscopic techniques: UV-Vis, IR and Raman; band-gap measurement; Microscopy (optical, scanning and transmission electron microscopy): wavelength range, resolution, depth of field; Composition analysis using energy dispersive spectroscopy.

    Tensile test: engineering and true stress-strain curves, parameters, such as, yield stress, ultimate tensile stress, elongation, area under the curve; Hardness: Brinell, Rockwell and Vickers.

    Electrical conductivity, carrier mobility and concentrations. Thermal analysis techniques: thermogravimetry and calorimetry
    Processing of Materials
    Heat Treatment of steels
    TTT and CCT diagram: coarse and fine pearlite, martensite and bainite; Annealing, normalizing, quenching, tempering.
    Heat treatment of aluminium alloys
    Precipitation hardening: Solutionising, quenching and ageing. Hardness vs. aging time and its dependence on aging temperature.
    Silicon processing
    production of metallurgical and semiconductor grade, zone refining, single crystal growth, silicon oxidation, doping, photolithographic process
    Degradation of Materials

    Electrochemical basis of corrosion of metals: standard electrode potential, galvanic series, Nernst equation, polarization and passivation; forms of corrosion; corrosion prevention

    Polymer degradation: swelling and dissolution; bond rupture: radiation, chemical and thermal effects; weathering

    GATE 2027 XE3: Solid Mechanics

    Section

    Topics

    Mechanics of Rigid Bodies

    Equivalent forces and moments; equilibrium equations; analysis of determinate trusses and frames; sliding and sticking friction; the principle of minimum potential energy and its relation to stable equilibrium; particle kinematics and dynamics; dynamics of inter-connected and/or constrained rigid bodies under planar motion; systems that conserve energy and/or momentum.


    Mechanics of Deformable Bodies

    Definition of stress and strain; Transformation of stresses and strains; Principal Stresses; Mohr’s circle for plane stress and plane strain; Elastic Constants; Generalized Hooke’s Law; Thermal Stresses; Theories of Failure - von Mises, Tresca and maximum principal stress theories.


    Axial force, shear force, and bending moment diagrams; axial, shear, and bending stresses; combined stresses; deflection (for symmetric bending); systems with up to one degree of static indeterminacy (i.e., up to one support or internal force not determinable from static equilibrium alone); energy methods (Castigliano’s theorems); torsion of circular shaft; Euler Buckling; thin-walled pressure vessels.


    Vibrations
    Free and forced vibration of single-degree-of-freedom systems; effect of damping; base excitation.

    GATE 2027 XE4: Thermodynamics

    Section

    Topics

    Basic Concepts

    Continuum, microscopic and macroscopic approaches; Thermodynamic systems (closed and open); Thermodynamic properties, state and equilibrium; State postulate for simple compressible substances, paths and processes on property diagrams; Concepts of heat and work, different modes of work; Zeroth law of thermodynamics, concept of temperature.

    Properties of Pure Substances

    Thermodynamic properties of pure substances in solid, liquid and vapor phases; P-v-T behaviour of simple compressible substances, Concept of triple point and critical point; Ideal and real gases, ideal gas equation of state and van der Waals equation of state.

    First Law of Thermodynamics


    Concept of energy and various forms of energy; Internal energy, enthalpy; Specific heats; First law applied to elementary processes, closed systems and control volumes, steady flow energy equation applied to simple engineering devices.

    Second Law of Thermodynamics
    Limitations of the first law of thermodynamics, concepts of heat engines and heat pumps/refrigerators, thermal efficiency, coefficient of performance; Kelvin-Planck and Clausius statements and their equivalence; Reversible and irreversible processes; Carnot cycle and Carnot principles/theorems; Thermodynamic temperature scale.
    Entropy
    Clausius inequality and concept of entropy, causes of irreversibility; Entropy generation, the principle of increase of entropy, T-s diagrams; Isentropic process and isentropic efficiency; Second law analysis of system and control volume; Second law efficiency; Concept of third law of thermodynamics.
    Thermodynamic Relations
    T-ds relations, Helmholtz and Gibbs functions, Gibbs relations, Maxwell relations, Joule-Thomson coefficient and inversion curve; Coefficient of volume expansion, adiabatic and isothermal compressibilities; Clapeyron and Clapeyron-Clausius equations.
    Thermodynamic Cycles
    Carnot vapor cycle, ideal Rankine cycle; Simple vapor-compression refrigeration cycle; Air-standard cycles - Otto, Diesel, and Brayton cycles.
    Mixtures of Ideal Gases

    Dalton’s and Amagat’s laws, properties of ideal gas mixtures, air-water vapor mixtures and simple thermodynamic processes; Specific and relative humidities; Dew point, dry bulb and wet bulb temperatures, adiabatic saturation temperature, Simple psychrometric processes.

    GATE 2027: Polymer Science and Engineering

    Section

    Topics

    Polymer Chemistry

    Monomers; Degree of polymerization; Classification of polymers; Polymerization reactions: addition and condensation, their kinetics; Metallocene polymers and other newer methods of polymerization; Copolymerization; Monomer reactivity ratios and its significance; Kinetics; Different copolymers; Random, alternating, azeotropic copolymerization; Block and graft copolymers; Techniques for polymerization-bulk, solution, suspension, emulsion.

    Polymer Characterization

    Solubility and swelling; Concept of molecular weight distribution and its significance; Concept of average molecular weight; Determination of number average, weight average, viscosity average and Z-average molecular weights; Glass transition; Melting transition; Amorphous and crystalline states of polymers; Orientation in polymers and polymer crystallinity; Factors affecting crystallinity; Analysis of polymers using IR, XRD, thermal (DSC, DMTA, TGA); Microscopic (optical and electronic) techniques; GPC; Mooney viscosity; Morphology and microstructure (SEM,TEM, AFM).

    Synthesis, Manufacturing and Properties

    Commodity and general-purpose thermoplastics: PE, PP, PS, PVC; Polyesters; Acrylic; PU polymers; Engineering Plastics: Nylon, PC, PBT, Polyphenylene oxide, ABS, Fluoropolymers; Thermosetting polymers: Polyurethane, PF, MF, UF, Epoxy, Unsaturated polyester, Alkyds; Natural and synthetic rubbers: recovery of NR hydrocarbon from latex; SBR; Nitrile; CR; CSM; EPDM; IIR; BR; Silicone; TPE; Specialty plastics: PEK, PEEK, Polyphenylene sulfide, Polysulfone, Polyethersulfone, etc.; Bio-compostable polymers such as PCL, PLA, PBAT, PHA/PHB, natural and biodegradable polymers such as cellulose, starch, alginate.

    Polymer Blends and Composites
    Polymer blends and composites, their significance; Choice of polymers for blending, blend miscibility: miscible and immiscible blends; Thermodynamics; Phase morphology; Polymer alloys; Polymer eutectics; Plastic-plastic, rubber-plastic and rubber-rubber blends; FRP, particulate, long and short fibre reinforced composites; Polymer reinforcement, reinforcing fibres – natural and synthetic.
    Additives, Compounding and Formulations
    Polymer compounding-need and significance; Different compounding ingredients for rubber and plastics (crosslinkers, antioxidants, heat stabilizers, UV stabilizers, lubricants, processing aids, impact modifiers, flame retardant, antistatic agents. PVC stabilizers and plasticizers) and their function; Use of carbon black; Polymer mixing equipment; Vulcanization and kinetics.
    Polymer Rheology
    Spin coating; Electrospinning; Solution and melt spinning; Film casting; Compression molding; Transfer molding; Injection molding; Blow molding; Reaction injection molding; Filament winding; SMC; BMC; DMC; Extrusion; pultrusion; Calendaring; Rotational molding; Thermoforming; Powder coating; Rubber processing in two-roll mill, internal mixer, twin screw extruder.
    Polymer Processing
    Carnot vapor cycle, ideal Rankine cycle; Simple vapor-compression refrigeration cycle; Air-standard cycles - Otto, Diesel, and Brayton cycles.

    Polymer Testing

    Mechanical-static and dynamic, tensile, flexural, compressive, abrasion, endurance, fatigue, hardness, tear, resilience, impact, toughness; Conductivity-thermal and electrical, dielectric constant, dissipation factor, power factor, electric resistance, surface resistivity, volume resistivity, swelling, ageing resistance, environmental stress cracking resistance, limiting oxygen index; Heat deflection temperature – Vicat softening temperature, ductile to brittle transition, glass transition temperature, coefficient of thermal expansion, shrinkage, flammability, dielectric constant, dissipation factor, power factor; Optical Properties - Refractive Index, Luminous Transmittance and Haze, Melt flow index.
    Polymer Recycling, Waste Management and Sustainability
    Polymer waste and its impact on environment; Sources, identification and separation techniques; Recycling classification: mechanical and chemical recycling, recycling of thermoplastics, thermosets and rubbers, applications of recycled materials; Life cycle assessment of polymer products (case studies like PET bottles, packaging bags); Recycling, segregation and disposal strategies of biodegradable and bio-compostable polymers, microplastics.

    GATE Exam Pattern 2027 for Engineering Sciences

    Check the exam pattern for GATE Engineering Sciences paper from the table below. It is crucial to understand the exam pattern of GATE 2027 XE along with the syllabus.

    GATE Exam Pattern for XE (Engineering Sciences)

    ParticularsDetails

    Examination Mode

    Computer Based Test (Online)

    Duration

    3 Hours

    Section

    General Aptitude (GA)

    Candidate Selected Subject

    Type of Questions

    Multiple Choice Questions (MCQs)

    Multiple Select Questions (MSQs)

    Numerical Answer Type (NAT) Questions

    Total Marks

    100 Marks

    Marking Scheme

    All of the questions will be worth 1 or 2 marks

    GATE Negative Marking

    • MCQs - 1 mark for each correct answer; 1/3 mark will be deducted for every wrong answer.

    • MCQs - 2 marks for each correct answer; 2/3 marks will be deducted for every incorrect response.

    • No negative marking for MSQ & NAT.

    • No partial marking for MSQ type questions.

    Related links:

    GATE Engineering Sciences 2027- Marking Scheme

    Candidates must check the marking scheme when preparing for the GATE exam. It defines the allocation of marks for various question types. The following table shows the marking schemes for the 3 sections as per last year GATE XE Exam Pattern.

    GATE Engineering Science Marking scheme

    Subject

    Marks Allotted



    General Aptitude (GA)

    15

    Engineering Mathematics (XE A)

    15

    2 choice Subject Questions (B-H)

    70

    Total

    100

    Frequently Asked Questions (FAQs)

    Q: Is the GATE 2027 syllabus released?
    A:

    Yes. the GATE 2027 syllabus was released online. 

    Q: When should I start preparing for GATE 2027?
    A:

    Aspirants must start preparing at least a year before the GATE 2027 exam.

    Q: What are the subjects of engineering science?
    A:

    The GATE XE 2027 syllabus consists of nine subjects, General Aptitude, Engineering Mathematics (two compulsory), Fluid Mechanics, Materials Science, Solid Mechanics, Thermodynamics, Polymer Science and Engineering, Food Technology, Atmospheric and Oceanic Sciences.

    Q: Who will conduct GATE 2027?
    A:

    IIT Madras will conduct the GATE 2027 exam.

    Q: What is engineering sciences in GATE?
    A:

    Candidates can take GATE Engineering sciences paper for admission to related MTech degrees or apply for the GATE based PSU recuitment. 

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