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Syllabus for General Aptitude (GA)
(COMMON TO ALL PAPERS)
Verbal Ability: English grammar, sentence completion, verbal analogies, word groups,
instructions, critical reasoning and verbal deduction.
Numerical Ability: Numerical computation, numerical estimation, numerical reasoning and data
XE-A (Compulsory for all XE candidates) Engineering Mathematics
Section 1: Linear Algebra
Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric,
skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors;
Diagonalisation of matrices; Cayley-Hamilton Theorem.
Section 2: Calculus
Functions of single variable: Limit, continuity and differentiability; Mean value theorems;
Indeterminate forms and L'Hospital's rule; Maxima and minima; Taylor's theorem;
Fundamental theorem and mean value-theorems of integral calculus; Evaluation of
definite and improper integrals; Applications of definite integrals to evaluate areas and
Functions of two variables: Limit, continuity and partial derivatives; Directional derivative;
Total derivative; Tangent plane and normal line; Maxima, minima and saddle points;
Method of Lagrange multipliers; Double and triple integrals, and their applications.
Sequence and series: Convergence of sequence and series; Tests for convergence;
Power series; Taylor's series; Fourier Series; Half range sine and cosine series.
Section 3: Vector Calculus
Gradient, divergence and curl; Line and surface integrals; Green's theorem, Stokes
theorem and Gauss divergence theorem (without proofs).
Section 3: Complex variables
Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy's integral theorem
and integral formula (without proof); Taylor's series and Laurent series; Residue theorem
(without proof) and its applications.
Section 4: Ordinary Differential Equations
First order equations (linear and nonlinear); Higher order linear differential equations with
constant coefficients; Second order linear differential equations with variable
coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series
solutions; Legendre polynomials, Bessel functions of the first kind and their properties.
Section 5: Partial Differential Equations
Classification of second order linear partial differential equations; Method of separation
of variables; Laplace equation; Solutions of one dimensional heat and wave equations.
Section 6: Probability and Statistics
Axioms of probability; Conditional probability; Bayes' Theorem; Discrete and continuous
random variables: Binomial, Poisson and normal distributions; Correlation and linear
Section 7: Numerical Methods
Solution of systems of linear equations using LU decomposition, Gauss elimination and
Gauss-Seidel methods; Lagrange and Newton's interpolations, Solution of polynomial and
transcendental equations by Newton-Raphson method; Numerical integration by
trapezoidal rule, Simpson's rule and Gaussian quadrature rule; Numerical solutions of first
order differential equations by Euler's method and 4th order Runge-Kutta method.
XE-B Fluid Mechanics
Section 1: Flow and Fluid Properties
viscosity, relationship between stress and strain-rate for Newtonian fluids, incompressible
and compressible flows, differences between laminar and turbulent flows. Hydrostatics:
Buoyancy, manometry, forces on submerged bodies.
Section 2: Kinematics
Eulerian and Lagrangian description of fluids motion, concept of local and convective
accelerations, steady and unsteady flows.
Section 3: Integral analysis
Control volume analysis for mass, momentum and energy.
Section 4: Differential Analysis
Differential equations of mass and momentum for incompressible flows: inviscid - Euler
equation and viscous flows - Navier-Stokes equations, concept of fluid rotation, vorticity,
stream function, Exact solutions of Navier-Stokes equation for Couette Flow and Poiseuille
Section 5: Inviscid flows
Bernoulli’s equation - assumptions and applications, potential function, Elementary plane
flows - uniform flow, source, sink and doublet and their superposition for potential flow
past simple geometries.
Section 6: Dimensional analysis
Concept of geometric, kinematic and dynamic similarity, some common non-dimensional
parameters and their physical significance: Reynolds number, Froude number and Mach
Section 7: Internal flows
Fully developed pipe flow, empirical relations for laminar and turbulent flows: friction
factor and Darcy-Weisbach relation.
Section 8: Prandtl boundary layer equations
Concept and assumptions, qualitative idea of boundary layer and separation,
streamlined and bluff bodies, drag and lift forces. Flow measurements: Basic ideas of flow
measurement using venturimeter, pitot-static tube and orifice plate.
XE-C Materials Science
Section 1: Processing of Materials:
Powder synthesis, sintering, chemical methods, crystal growth techniques, zone
refining, preparation of nanoparticles and thin films
Section 2: Characterisation Techniques:
X-ray diffraction, spectroscopic techniques like UV-vis, IR, Raman. Optical and
Section 3: Structure and Imperfections:
Crystal symmetry, point groups, space groups, indices of planes, close packing in
solids, bonding in materials, coordination and radius ratio concepts, point defects,
dislocations, grain boundaries, surface energy and equilibrium shapes of crystals
Section 4: Thermodynamics and Kinetics:
Phase rule, phase diagrams, solid solutions, invariant reactions, lever rule, basic
heat treatment of metals, solidification and phase transformations, Fick’s laws of
diffusion, mechanisms of diffusion, temperature dependence of diffusivity
Section 5: Properties of Materials:
Mechanical Properties: Stress-strain response of metallic, ceramic and polymer
materials, yield strength, tensile strength and modulus of elasticity, toughness,
plastic deformation, fatigue, creep and fracture
Electronic Properties:Free electron theory, Fermi energy, density of states, elements
of band theory, semiconductors, Hall effect, dielectric behaviour, piezo, ferro,
Magnetic Properties: Origin of magnetism in metallic and ceramic materials,
paramagnetism, diamagnetism, ferro and ferrimagnetism
Thermal Properties: Specific heat, thermal conductivity and thermal expansion,
Optical Properties: Refractive index, absorption and transmission of
electromagnetic radiation in solids, electrooptic and magnetoopticmaterials,
spontaneous and stimulated emission, gas and solid state lasers
Section 6: Material types
Concept of amorphous, single crystals and polycrystalline materials, crystallinity
and its effect on physical properties, metal, ceramic, polymers, classification of
polymers, polymerization, structure and properties, additives for polymer products,
processing and applications, effect of environment on materials, composites
Section 7: Environmental Degradation
Corrosion, oxidation and prevention
Section 8: Elements of Quantum Mechanics and Mathematics
Basics of quantum mechanics, quantum mechanical treatment of electrical,
optical and thermal properties of materials, analytical solid geometry,
differentiation and integration, differential equations, vectors and tensors, matrices,
Fourier series, complex analysis, probability and statistics
XE-D Solid Mechanics
Equivalent force systems; free-body diagrams; equilibrium equations; analysis of
determinate trusses and frames; friction; particle kinematics and dynamics;
dynamics of rigid bodies under planar motion; law of conservation of energy; law of
conservation of momentum.
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
Axial, shear 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 single degree of freedom systems.
Section 1: 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.
Section 2: 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.
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,
Joule-Thomson 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, air-standard Diesel cycle, air-standard Brayton cycle, vapor-compression
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,
XE-F Polymer Science and Engineering
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
techniques of polymerization, copolymerization, monomer reactivity ratios and its
significance, kinetics, different copolymers, random, alternating, azeotropic
copolymerization, block and graft copolymers, techniques for copolymerizationbulk,
solution, suspension, emulsion.
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, analysis of polymers using IR, XRD, thermal (DSC,
DMTA, TGA), microscopic (optical and electronic) techniques.
Section 3: Synthesis 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: 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.
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
Section 5: Polymer Technology
Polymer compounding-need and significance, different compounding ingredients
for rubber and plastics, cross-linking and vulcanization, vulcanization kinetics.
Section 6: Polymer rheology
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. Viscoelasticity-
creep and stress relaxations, mechanical models, control of rheological
characteristics through compounding, rubber curing in parallel plate viscometer,
ODR and MDR.
Section 7: Polymer processing
Compression molding, transfer molding, injection molding, blow molding, reaction
injection molding, extrusion, pultrusion, calendaring, rotational molding,
thermoforming, rubber processing in two-roll mill, internal mixer.
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
XE - G Food Technology
Section 1: Food Chemistry and Nutrition
Carbohydrates: structure and functional properties of mono-, oligo-, & polysaccharides
including starch, cellulose, pectic substances and dietary fibre,
gelatinization and retrogradation of starch. Proteins: classification and structure of
proteins in food, biochemical changes in post mortem and tenderization of
muscles. Lipids: classification and structure of lipids, rancidity, polymerization and
polymorphism. Pigments: carotenoids, chlorophylls, anthocyanins, tannins
and myoglobin. Food flavours: terpenes, esters, aldehydes, ketones and quinines.
Enzymes: specificity, simple and inhibition kinetics, coenzymes, enzymatic and nonenzymatic
browning. Nutrition: balanced diet, essential amino acids and essential
fatty acids, protein efficiency ratio, water soluble and fat soluble vitamins, role of
minerals in nutrition, co-factors, anti-nutrients, nutraceuticals, nutrient deficiency
diseases. Chemical and biochemical changes: changes occur in foods during
Section 2: Food Microbiology
Characteristics of microorganisms: morphology of bacteria, yeast, mold and
actinomycetes, spores and vegetative cells, gram-staining. Microbial growth:
growth and death kinetics, serial dilution technique. Food spoilage: spoilage
microorganisms in different food products including milk, fish, meat, egg, cereals
and their products. Toxins from microbes: pathogens and non-pathogens including
Staphylococcus, Salmonella, Shigella, Escherichia, Bacillus, Clostridium, and
Aspergillus genera. Fermented foods and beverages: curd, yoghurt, cheese, pickles,
soya-sauce, sauerkraut, idli, dosa, vinegar, alcoholic beverages and sausage.
Section 3: Food Products Technology
Processing principles: thermal processing, chilling, freezing, dehydration, addition of
preservatives and food additives, irradiation, fermentation, hurdle technology,
intermediate moisture foods. Food packaging and storage: packaging materials,
aseptic packaging, controlled and modified atmosphere storage. Cereal
processing and products: milling of rice, wheat, and maize, parboiling of paddy,
bread, biscuits, extruded products and ready to eat breakfast cereals. Oil
processing: expelling, solvent extraction, refining and hydrogenation. Fruits and
vegetables processing: extraction, clarification, concentration and packaging of
fruit juice, jam, jelly, marmalade, squash, candies, tomato sauce, ketchup, and
puree, potato chips, pickles. Plantation crops processing and products: tea, coffee,
cocoa, spice, extraction of essential oils and oleoresins from spices. Milk and milk
products processing: pasteurization and sterilization, cream, butter, ghee, icecream,
cheese and milk powder. Processing of animal products: drying, canning,
and freezing of fish and meat; production of egg powder. Waste utilization: pectin
from fruit wastes, uses of by-products from rice milling. Food standards and quality
maintenance: FPO, PFA, Agmark, ISI, HACCP, food plant sanitation and cleaning in
Section 4: Food Engineering
Mass and energy balance; Momentum transfer: Flow rate and pressure drop
relationships for Newtonian fluids flowing through pipe, Reynolds number. Heat
transfer: heat transfer by conduction, convection, radiation, heat exchangers. Mass
transfer: molecular diffusion and Fick’s law, conduction and convective mass
transfer, permeability through single and multilayer films. Mechanical operations:
size reduction of solids, high pressure homogenization, filtration, centrifugation,
settling, sieving, mixing & agitation of liquid. Thermal operations: thermal sterilization,
evaporation of liquid foods, hot air drying of solids, spray and freeze-drying, freezing
and crystallization. Mass transfer operations: psychrometry, humidification and
XE-H: Atmospheric & Ocean Science
Section A: Atmospheric Science
Fundamental of Meteorology, Thermal structure of the atmosphere and its
composition, Radiation Balance and Laws, Wind Belts, Monsoon, Climate.
Atmospheric Thermodynamics. Hydrostatic equilibrium and: Hydrostatic
equation, variation of pressure with height, geopotential, Tropical convection.
Atmospheric Electricity. Cloud Physics. Observation Techniques of the
Fundamental equations. Pressure, gravity, centripetal and Corolis forces,
continuity equation in Cartesian and isobaric coordinates, Scale analysis,
inertial flow, geostrophic and gradient winds, thermal wind, vorticity.
Atmospheric turbulence, baroclinic instabiltiy. Atmosphreric Waves.
Tropical meteorology: Trade wind inversion, ITCZ; monsoon trough tropical
cyclones, their structure and development theory; monsoon depressions;
Climate variability and forcings; Madden-Julian oscillation(MJO), ENSO, QBO
(quasi-biennial oscillation) and sunspot cycles. Primitive equations of
Numerical Weather Prediction. General Circulation and Climate Modelling.
Synoptic weather forecasting, prediction of weather elements such as rain,
maximum and minimum temperature and fog. Data Assimilation.
Section B: Ocean Sciences
Seawater Properties, T-S diagrams, Ocean Observations, Ocean Tide and
Waves and their properties. Coastal processes and Estuary Dynamics. coastal
zone management. Wind Driven Circulation: Ekman, Sverdrup, Stommel and
Munk theories, Inertial currents; geostrophic motion; barotropic and baroclinic
conditions; Oceanic eddies. Global conveyor belt circulation. Subtropical gyres;
Western boundary currents; equatorial current systems; Current System in the
Momentum equation, mass conservation, vorticity. Ocean and Wave Modeling,
Ocean State Forecasting. Data Assimilation. Ocean Turbulence.
Chemical Property of seawater, major and minor elements, their behavior and
chemical exchanges across interfaces and residence times in seawater, Element
chemistry in atypical conditions-estuaries, Biochemical cycling of nutrients,
trace metals and organic matter. Air-sea exchange of important biogenic
dissolved gases; carbon dioxide-carbonate system; alkalinity and control of pH;
biological pump. Marine Pollution. Primary and secondary production; factors
controlling phytoplankton and zooplankton abundance and diversity; nekton and