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 Aptitude | 5 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.

**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 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

**Vibrations**

- 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:

**List of Best Books to Prepare for GATE XE 2021 Exam**

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