GATE Engineering Sciences (XE) Syllabus 2024: PDF Download, List of Chapters and Topics

Vector Calculus

Divergence and curl; Gradient, Line integrals and Green's theorem.

Calculus

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;Functions of single variable: Limit, indeterminate forms and L'Hospital's rule; 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. Power series; Taylor's series; Fourier Series of functions of period 2π Sequences and series: Convergence of sequences and series; Tests of convergence of series with non-negative terms (ratio, root and integral tests).

Linear Algebra

Cayley- Hamilton Theorem; Algebra of real matrices: Determinant, inverse and rank of a matrix; Eigenvalues and eigenvectors of matrices; System of linear equations (conditions for unique solution, no solution and infinite number of solutions);  Properties of eigenvalues and eigenvectors of symmetric matrices, diagonalization of matrices.

Ordinary Differential Equations

First order equations (linear and nonlinear); Cauchy-Euler equation; Second order linear differential equations with constant coefficients; Second order linear differential equations with variable coefficients; Wronskian; Eigenvalue problem for second order equations with constant coefficients; Method of variation of parameters; Power series solutions for ordinary points.

Complex variables

Complex numbers, Argand plane and polar representation of complex numbers; Cauchy-Riemann equations; De Moivre’s theorem; Analytic functions.

Probability and Statistics

Mean, variance and standard deviation of random variables; Correlation and linear regression; Axioms of probability; Conditional probability; Bayes' Theorem; Binomial, Poisson and Normal distributions

Partial Differential Equations

One dimensional heat equation and two dimensional Laplace equation; Classification of second order linear partial differential equations; Method of separation of variables.

Numerical Methods

Solution of systems of linear equations using LU decomposition, Gauss elimination method; Lagrange and Newton's interpolations; Numerical integration by trapezoidal rule and Simpson's rule; Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical solutions of first order differential equations by explicit Euler's method.

SECTION 1: Flow and Fluid Properties

• Fluid Properties: Density, viscosity, surface tension, relationship between stress and strain-rate for Newtonian fluids. 
• Hydrostatics: Buoyancy, manometry, forces on submerged bodies and its stability
• Classification of Flows: Viscous versus inviscid flows, incompressible versus compressible flows, internal versus external flows, steady versus unsteady flows, laminar versus turbulent flows, 1- D, 2-D and 3-D flows, Newtonian versus non-Newtonian fluid flow.

SECTION 2: Kinematics of Fluid Motion

• Eulerian and Lagrangian descriptions of fluid motion. Concept of local, convective and material derivatives. Streamline, streakline, pathline and timeline. 

SECTION 3: Integral Analysis for a Control Volume

• Reynolds Transport Theorem (RTT) for conservation of mass, linear and angular momentum. 

SECTION 4: Differential Analysis 

• Inviscid flows - Euler equations and viscous flows - Navier-Stokes equations
• Differential equations of mass and momentum for incompressible flows
• Concept of fluid rotation, vorticity, stream function and circulation
• Exact solutions of Navier-Stokes equations for Couette flow and Poiseuille flow, thin film flow.

SECTION 5: Dimensional Analysis

• Concept of geometric, kinematic and dynamic similarity
• Non-dimensional parameters and their physical significance - Reynolds number, Froude number and Mach number
• Buckingham Pi theorem and its applications

SECTION 6: Internal Flows 

• Fully developed pipe flow
• Major and minor losses
• Empirical relations for laminar and turbulent flows: friction factor, Darcy-Weisbach relation and Moody’s chart

SECTION 7: Bernoulli’s Equation and its Applications, Potential Flows

• Bernoulli’s equation: Assumptions and applications. 
• Elementary potential flows: Velocity potential function
• Flow measurements - Venturi meter, Pitot-static tube and orifice meter
• Uniform flow, source, sink and vortex, and their superposition for flow past simple geometries.

SECTION 8: External Flows

• Prandtl boundary layer equations: Concept and assumptions
• Qualitative idea of boundary layer separation, streamlined and bluff bodies, and drag and lift forces
• Boundary layer characteristics: Boundary layer thickness, displacement thickness and momentum thickness

Section 1: Basic Concepts 

Continuum and macroscopic approach; thermodynamic systems (closed and open); thermodynamic properties and equilibrium; state of a system, concepts of heat and work, different modes of work; state postulate for simple compressible substances, state diagrams, paths and processes on state diagrams; zeroth law of thermodynamics; concept of temperature.

Section 2: First Law of Thermodynamics

Concept of energy and various forms of energy; first law applied to elementary processes, closed systems and control volumes, steady and unsteady flow analysis; internal energy, enthalpy; specific heats; 

Section 3: Second Law of Thermodynamics

Limitations of the first law of thermodynamics, concepts of heat engines and heat pumps/refrigerators, Kelvin-Planck and Clausius statements and their equivalence; reversible and irreversible processes; Carnot cycle and Carnot principles/theorems; thermodynamic temperature scale; Clausius inequality and concept of entropy; microscopic interpretation of entropy, the principle of increase of entropy, T-s diagrams; second law analysis of control volume; availability and irreversibility; third law of thermodynamics

Section 4: Properties of Pure Substances

Thermodynamic properties of pure substances in solid, liquid and vapor phases; P-v-T behaviour of simple compressible substances, phase rule, thermodynamic property tables and charts, ideal and real gases, ideal gas equation of state and van der Waals equation of state; law of corresponding states, compressibility factor and generalized compressibility chart.

Section 5: Thermodynamic Relations

T-ds relations, Helmholtz and Gibbs functions, Gibbs relations, Maxwell relations, JouleThomson coefficient, coefficient of volume expansion, adiabatic and isothermal compressibilities, Clapeyron and Clapeyron-Clausius equations

Section 6: Thermodynamic Cycles

Carnot vapor cycle, ideal Rankine cycle, Rankine reheat cycle, air-standard Otto cycle, airstandard Diesel cycle, air-standard Brayton cycle, vapor-compression refrigeration cycle. 

Section 7: Ideal Gas Mixtures

Dalton’s and Amagat’s laws, properties of ideal gas mixtures, air-water vapor mixtures and simple thermodynamic processes involving them; specific and relative humidities, dew point and wet bulb temperature, adiabatic saturation temperature, psychrometric chart.

Section 1: Chemistry of high polymers

Monomers, functionality, degree of polymerizations, classification of polymers, glass transition, melting transition, criteria for rubberiness, polymerization methods: 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. Concept of intermolecular order (morphology) – amorphous, crystalline, orientation states. Factor affecting crystallinity. Crystalline transition. Effect of morphology on polymer properties.

Section 2: Polymer Characterization

Solubility and swelling, concept of average molecular weight, determination of number average, weight average, viscosity average and Z-average molecular weights, polymer crystallinity, Concept of molecular weight distribution and its significance, analysis of polymers using IR, XRD, thermal (DSC, DMTA, TGA), microscopic (optical and electronic) techniques, Molecular wt. distribution: Broad and Narrow, GPC, mooney viscosity.

Section 3: Synthesis, manufacturing and properties

Commodity and general purpose thermoplastics: PE, PP, PS, PVC, Polyesters, Acrylic, PU polymers. Engineering Plastics: Nylon, PC, PBT, PSU, PPO, ABS, Fluoropolymers Thermosetting polymers: Polyurethane, PF, MF, UF, Epoxy, Unsaturated polyester, Alkyds. Biopolymers such as PLA, PHA/PHB. Natural and synthetic rubbers: Recovery of NR hydrocarbon from latex; SBR, Nitrile, CR, CSM, EPDM, IIR, BR, Silicone, TPE, Speciality plastics: PEK, PEEK, PPS, PSU, PES etc.

Section 4: Polymer blends and composites 

Difference between 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, base polymer for reinforcement (unsaturated polyester), ingredients / recipes for reinforced polymer composite. 

Section 5: Polymer Technology

Polymer compounding-need and significance, different compounding ingredients for rubber and plastics (Antioxidants, Light stabilizers, UV stabilizers, Lubricants, Processing aids, Impact modifiers, Flame retardant, antistatic agents. PVC stabilizers and Plasticizers) and their function, use of carbonblack, polymer mixing equipments, cross-linking and vulcanization, vulcanization kinetics. 

Section 6: Polymer rheology

Visco-elasticity-creep and stress relaxations, mechanical models, control of rheological characteristics through compounding, rubber curing in parallel plate viscometer, ODR and MDR.

Flow of Newtonian and non-Newtonian fluids, different flow equations, dependence of shear modulus on temperature, molecular/segmental deformations at different zones and transitions. Measurements of rheological parameters by capillary rotating, parallel plate, cone-plate rheometer. 

Section 7: Polymer processing

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.

Section 8: 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, Brittleness temperature, Glass transition temperature, Co-efficient of thermal expansion, Shrinkage, Flammability, dielectric constant, dissipation factor, power factor, Optical Properties - Refractive Index, Luminous Transmittance and Haze, Melt flow index 

Section 9: Polymer Recycling and Waste management 

Life cycle assessment of polymer products (case studies like PET bottles, packaging bags). Polymer waste, and its impact on environment, Sources, Identification and Separation techniques, recycling classification, recycling of thermoplastics, thermosets and rubbers, applications of recycled materials. 

Quantitative Aptitude

Data interpretation, 2- and 3-dimensional plots,Maps, Data graphs (bar graphs, pie charts, and other graphs representing data),  Mensuration and geometry, Numerical computation and estimation, Elementary statistics, Probability,Tables, Powers, Exponents and logarithms, Permutations and combinations, Series, Ratios, Percentages

Verbal Aptitude

Basic English grammar, Basic vocabulary, Words, Reading and comprehension, Prepositions, Idiomms, Conjunctions, Verb-noun agreement and other parts of speech, Narrative sequencing, Tenses, Articles, Adjectives, Phrases in context

Analytical Aptitude

Logic: deduction and induction, Numerical relations and reasoning, Analogy

Spatial Aptitude

Mirroring Assembling, Grouping, Paper folding, Cutting, Patterns in 2 and 3 dimensions, Rotation, Scaling, Transformation of shapes, Translation

Exam Mode

Online Mode (Computer Based Test)

Exam Duration

3 Hours (1 hour of grace time will be given for For PWD candidates )

Types of Question Asked

Multiple Choice Questions (MCQ), multiple select questions (MSQ), and numerical answer types

Sections

3 (Engineering Mathematics, General Aptitude, and Engineering Sciences) 

Total Marks 

100 Marks

Total Questions

65 questions( 10 questions of general Aptitude + 10 questions of engineering mathematics + 45 questions of textile engineering)