GATE XE Syllabus 2021 - Download PDF for XE Section-wise Syllabus

By Kajal Vats|Updated : October 13th, 2020

GATE XE Syllabus 2021: This year, the GATE Engineering Science (XE) syllabus has been revised by IIT Bombay. There is a total of 9 Sections in GATE XE out of which General Aptitude (GA) and Engineering Mathematics (XE-A) are compulsory sections. All the section includes important topics to be covered for Engineering Science exam preparation. Here we have shared the GATE Engineering Sciences (XE) syllabus for all sections.

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As you know, the GATE 2021 exam is scheduled for 5th, 6th, 7th, 12th, 13th, and 14th February 2021. Thus, with the help of the GATE XE syllabus 2021, none of the topics will be left untouched in your preparations. You can check the syllabus of each section (A-H) of GATE XE in this article. Download the GATE Engineering Science (XE) syllabus PDF also here.

GATE Engineering Sciences (XE) includes the following subjects and their codes:

  • Engineering Mathematics - XE-A
  • Fluid mechanics - XE-B
  • Material Science - XE-C
  • Solid mechanics - XE-D
  • Thermodynamics - XE-E
  • Polymer Science and Engineering - XE-F
  • Food technology - XE-G
  • Atmospheric and Oceanic Sciences - XE-H

Before proceeding to the syllabus let's have an overview of the XE exam pattern and the marking scheme.

Section Marks Distribution
General Aptitude5 questions of 1 mark each
5 questions of 2marks each
Section A – Engineering Mathematics (compulsory)7 questions of 1mark each
4 questions of 2 marks each
Sections B - H (Any 2)9 questions of 1 mark each
13 questions of 2 marks each

GATE XE Syllabus 2021 Section-wise

GATE XE Syllabus 2021 for General Aptitude - Download PDF

GATE XE Syllabus for Engineering Mathematics (XE-A)

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)
    • Eigenvalues and eigenvectors of matrices
    • Properties of eigenvalues and eigenvectors of symmetric matrices, diagonalization of matrices
    • Cayley-Hamilton Theorem.


  • 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 non-negative terms (ratio, root and integral tests)
    • Power series
    • Taylor's series
    • Fourier Series of functions of period 2π.

Vector Calculus

  • Gradient, divergence and curl
  • Line integrals and Green's theorem.

Complex variables

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

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
  • Eigenvalue problem for second-order equations with constant coefficients
  • Power series solutions for ordinary points.

Partial Differential Equations

  • Classification of second-order linear partial differential equations
  • Method of separation of variables: One-dimensional heat equation and two dimensional Laplace equation

Probability and Statistics

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

Numerical Methods

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

GATE XE Syllabus 2021 for Engineering Mathematics (XE-A): Download PDF

GATE XE Syllabus for Fluid Mechanics (XE-B)

Flow and Fluid Properties

  • Fluid Properties: Density, viscosity, surface tension, relationship between stress and strain-rate for Newtonian fluids.
  • 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.
  • Hydrostatics: Buoyancy, manometry, forces on submerged bodies and its stability.

Kinematics of Fluid Motion

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

Integral Analysis for a Control Volume

  • Reynolds Transport Theorem (RTT) for the conservation of mass
  • Linear and angular momentum.

Differential Analysis

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

Dimensional Analysis

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

Internal Flows

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

Bernoulli’s Equation and its Applications, Potential Flows

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

External Flows

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

GATE XE Syllabus 2021 for Fluid Mechanics (XE-B): Download PDF

GATE XE Syllabus for Materials Science (XE-C)

  • Classification and Structure of Materials
  • Thermodynamics, Kinetics, and Phase Transformations
  • Properties and Applications of Materials
  • Characterization and Measurements of Properties
  • Processing of Materials, Degradation of Materials

GATE XE Syllabus 2021 for Materials Science (XE-C): Download PDF

GATE XE Syllabus for Solid Mechanics (XE-D)

Mechanics of rigid bodies

  • Equivalent force systems; free-body diagrams
  • Equilibrium equations; analysis of determinate trusses and frames
  • Friction
  • principle of minimum potential energy
  • Particle kinematics and dynamics
  • Dynamics of rigid bodies under the planar motion
  • Law of conservation of energy
  • Law of conservation of momentum.

Mechanics of deformable bodies

  • Stresses and strains
  • Transformation of stresses and strains, principal stresses and strains
  • Mohr’s circle for plane stress and plane strain; generalized Hooke’s Law
  • Elastic constants; thermal stresses
  • Theories of failure
  • Axial force, shear force, and bending moment diagrams
  • Axial, shear, and bending stresses
  • Combined stresses
  • Deflection (for symmetric bending)
  • Torsion in circular shafts
  • Thin-walled pressure vessels
  • Energy methods (Castigliano’s Theorems)
  • Euler buckling


  • Free vibration of undamped single degree of freedom systems

GATE XE Syllabus 2021 for Solid Mechanics (XE-D): Download PDF

GATE XE Syllabus for Thermodynamics (XE-E)

Basic Concepts

  • Continuum and macroscopic approach
  • Thermodynamic systems (closed and open)
  • Thermodynamic properties and equilibrium
  • State of a system, state postulate for simple compressible substances, state diagrams, paths and processes on state diagrams
  • Concepts of heat and work, different modes of work
  • Zeroth law of thermodynamics
  • Concept of temperature.

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 and unsteady flow analysis.

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

Properties of Pure Substances

  • Thermodynamic properties of pure substances in solid, liquid, and vapor phases
  • P-v-T behavior 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.

Thermodynamic Relations

  • T-ds relations, Helmholtz and Gibbs functions, Gibbs relations
  • Maxwell relations, Joule-Thomson coefficient, coefficient of volume expansion
  • Adiabatic and isothermal compressibilities, Clapeyron, and Clapeyron-Clausius equations.

Thermodynamic Cycles

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

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

GATE XE Syllabus 2021 for Thermodynamics (XE-E): Download PDF

GATE XE Syllabus for Polymer Science & Engineering (XE-F)

  • Chemistry of high polymers
  • Polymer Characterization
  • Synthesis, manufacturing, and properties
  • Polymer blends and composites
  • Polymer Technology, Polymer rheology
  • Polymer processing, Polymer testing
  • Polymer Recycling and Waste management.

GATE XE Syllabus 2021 for Polymer Science & Engineering (XE-F): Download PDF

GATE XE Syllabus for Food Technology (XE-G)

  • Food Chemistry and Nutrition
  • Food Microbiology
  • Food Products Technology
  • Food Engineering

GATE XE Syllabus 2021 for Food Technology (XE-G): Download PDF

GATE XE Syllabus for Atmospheric & Oceanic Sciences (XE-H)

  • Atmospheric Science Vertical Structure and Composition of the Atmosphere
  • Blackbody Radiation and Radiation Balance
  • Modes of Heat Transfer in the Atmosphere
  • Ocean Sciences, Chemical Properties of Seawater
  • Major and Minor Elements, Ocean Acidification

GATE XE Syllabus 2021 for Atmospheric & Oceanic Sciences (XE-H): Download PDF

Candidates can opt for any two sections from Section B-H along with Engineering Mathematics and General Aptitude which are compulsory for all the XE Candidates. Check the Exam Pattern for GATE XE 2021 in detail in the following article:

GATE XE 2021 Exam Pattern

List of Best Books to Prepare for GATE XE 2021 Exam


The Most Comprehensive Exam Prep App.

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Kajal VatsKajal VatsMember since Apr 2020
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