About Gate
GATE Exam: An Overview
The Graduate Aptitude Test in Engineering (GATE) is a national examination conducted jointly by the Indian Institute of Science (IISc) and the seven Indian Institutes of Technology (IITs) on behalf of the National Coordination Board (NCB)-GATE and the Department of Higher Education, Ministry of Education (MoE) in India.
The GATE Committee, made up of representatives from the administering institutes, is responsible for regulating the examination and declaring the results. The examination is held in eight zones across India, and each zone is managed by a Zonal GATE Office at an administrative institute (IIT or IISc).
The GATE exam tests the comprehensive understanding of candidates in various undergraduate (UG) and postgraduate (PG) subjects in engineering, technology, and architecture.
A valid GATE score is required for obtaining financial assistance during Master’s programs and direct Doctoral programs in engineering, technology, and architecture.
Some colleges and institutes also require a GATE qualification for admission without an MHRD scholarship/assistantship. The GATE scorecard is valid for three years from the date of announcement of the results.
Note: Passing the GATE examination does not automatically guarantee admission, scholarship, or employment. Admission to any institute is based solely on the institute’s educational qualifications criteria. Similarly, A GATE qualification does not ensure a job in a Public Sector Undertaking (PSU) as it is subject to the recruitment process of the specific PSU. No responsibility will be taken for admission, scholarship, or job.
Exam Pattern
Examination Mode – Computer-Based Test (Online)
Duration – 3 Hours
Sections – 2
General Aptitude (GA)
Candidate’s Course Subject
Number of Subjects (Papers) – 30
Types of Questions –
Multiple Choice Questions (MCQs)
Multiple Select Questions (MSQ)
Numerical Answer Type (NAT) Questions
Number of Questions
10 (GA) + 55 (subject) = 65 Questions
Total Marks – 100 Marks
Scoring Criteria – Each question will have a value of 1 or 2 marks
Negative Marking
Multiple Choice Questions (MCQ)
1-mark Question: ⅓ marks will be subtracted for a wrong answer.
2-mark Question: ⅔ marks will be subtracted for a wrong answer.
There is NO negative marking for
Multiple Select Questions (MSQ)
Numerical Answer Type (NAT)
GATE 2025 Syllabus
GATE 2025 Metallurgy Syllabus
Linear Algebra: Matrices and Determinants, Systems of linear equations, Eigen values and Eigen vectors.
Calculus: Limit, continuity and differentiability; Partial derivatives; Maxima and minima; Sequences and series; Test for convergence; Fourier series.
Vector Calculus: Gradient; Divergence and Curl; Line, Surface and volume integrals; Stokes, Gauss and Green’s theorems.
Differential Equations: Linear and non-linear first order ODEs; Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace transforms; PDEs –Laplace, one dimensional heat and wave equations
Probability and Statistics: Definitions of probability and sampling theorems, conditional probability, Mean, median, mode and standard deviation; Random variables; Poisson, normal and binomial distributions; Correlation and regression analysis
Numerical Methods: Solutions of linear and non-linear (Bisection, Secant, Newton-Raphson methods) algebraic equations; integration by trapezoidal and Simpson’s rule; single and multi-step methods for differential equations
Laws of Thermodynamics: First law – energy conservation, Second law – entropy; Enthalpy, Gibbs and Helmholtz free energy; Maxwell’s relations; Chemical potential; Applications to metallurgical systems, solutions, ideal and regular solutions; Gibbs phase rule, phase equilibria, binary phase diagram and lever rule, free-energy vs. composition diagrams; Equilibrium constant, Activity, Ellingham and phase stability diagrams; Thermodynamics of point defects, surfaces and interfaces, adsorption and segregation phenomena.
Electrochemistry: Single electrode potential, Electrochemical cells, Nernst equation, Potential-pH diagrams.
Momentum Transfer: Concept of viscosity, shell balances, Bernoulli’s equation, mechanical energy balance equation, flow past plane surfaces and through pipes.
Heat Transfer: Conduction, Fourier’s Law, 1-D steady-state conduction.
Convection: Heat transfer coefficient relations for forced convection.
Radiation: Black body radiation, Stefan-Boltzman Law, Kirchhoff’s Law.
Mass Transfer: Diffusion and Fick’s laws, Mass transfer coefficients.
Dimensional Analysis: Buckingham Pi theorem, Significance of dimensionless numbers.
Basic Laws of Chemical Kinetics: First-order reactions, reaction rate constant, Arrhenius relation, heterogeneous reactions, oxidation kinetics.
Electrochemical Kinetics: Polarisation.
Commination techniques, size classification, Flotation, Gravity and other methods of mineral beneficiation; Agglomeration: sintering, pelletizing and briquetting.
Material and Energy balances in metallurgical processes; Principles and processes for the extraction of non-ferrous metals – aluminium, copper, and titanium.
Iron and Steel Making: Material and heat balance in blast furnace; Structure and properties of slags and molten salts – basicity of slags – sulphide and phosphate capacity of slags; Production of metallurgical coke.
Other methods of iron making (COREX, MIDRE)
Primary Steel Making: Basic oxygen furnace, process dynamics, oxidation reactions, electric arc furnace.
Secondary Steel Making: Ladle process – deoxidation, argon stirring, desulphurization, inclusion shape control, principles of degassing methods; Basics of stainless steel manufacturing.
Continuous Casting: Fluid flow in the tundish and mould, heat transfer in the mould, segregation, inclusion control.
Ionic, covalent, metallic, and secondary bonding in materials, Crystal structure of solids – metals and alloys, ionic and covalent solids, and polymers.
X-ray Diffraction – Bragg’s law, optical metallography, principles of SEM imaging.
Crystal Imperfections: Point, line and surface defects; Coherent, semi-coherent and incoherent interfaces.
Diffusion in Solids: Diffusion equation, steady state and error function solutions; Examples homogenization and carburization; Kirkendall effect; Uphill diffusion; Atomic models for interstitial and substitutional diffusion; Pipe diffusion and grain boundary diffusion.
Phase Transformation: Driving force, Homogeneous and heterogeneous nucleation, growth Kinetics Solidification in isomorphous, eutectic and peritectic systems, cast structures and macro segregation, dendritic solidification and constitutional supercooling, coring and microsegregation.
Solid State Transformations: Precipitation, spinodal decomposition, ordering, massive transformation, discontinuous precipitation, eutectoid transformation, diffusionless transformations; Precipitate coarsening, Gibbs-Thomson effect.
Principles of heat treatment of steels, TTT and CCT diagrams; Surface hardening treatments; Recovery, recrystallization, and grain growth; Heat treatment of cast iron and aluminium alloys.
Electronic, magnetic and optical properties of materials.
Basic forms of corrosion and its prevention.
Strain tensor and stress tensor, Representation by Mohr’s circle, elasticity, stiffness and compliance tensor, yield criteria, Plastic deformation by slip and twinning.
Dislocation Theory: Edge, screw and mixed dislocations, source, and multiplication of dislocations, stress fields around dislocations; Partial dislocations, dislocation interactions and reactions.
Strengthening Mechanisms: Work/strain hardening, strengthening due to grain boundaries, solid solution, precipitation, and dispersion.
Fracture behaviour, Griffith theory, linear elastic fracture mechanics, fracture toughness, fractography, ductile to brittle transition.
Fatigue: Cyclic stress-strain behaviour – low and high cycle fatigue, crack growth. Mechanisms of high-temperature deformation and failure; creep and stress rupture, stress exponent and activation energy.
Metal Casting: Mould design involving feeding, gating and risering, casting practices, and casting defects.
Hot, Warm and Cold Working of Metals: Metal forming – fundamentals of metal forming processes of rolling, forging, extrusion, wire drawing and sheet metal forming, defects in forming.
Metal Joining: Principles of soldering, brazing and welding, welding metallurgy, defects in welded joints in steel and aluminium alloys.
Powder Metallurgy: production of powders, compaction and sintering.
Non-destructive Testing (NDT): Dye-penetrant, ultrasonic, radiography, eddy current, acoustic emission and magnetic particle inspection methods.
GATE 2025 Material Science (XE-C)
1: Linear Algebra Algebra of real matrices: Determinant, inverse and rank of a matrix; System of linear equations (conditions for a unique solution, no solution and an infinite number of solutions); Eigenvalues and eigenvectors of matrices; Properties of eigenvalues and eigenvectors of symmetric matrices, diagonalization of matrices; Cayley-Hamilton Theorem.
2: 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.
3: Vector Calculus Gradient, divergence, and curl; Line integrals and Green’s theorem.
4: Complex Variables: Complex numbers, Argand plane and polar representation of complex numbers; De Moivre’s theorem; Analytic functions; Cauchy-Riemann equations.
5: 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.
6: 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.
7: 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.
8: 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 Newton Raphson method; Numerical integration by trapezoidal rule and Simpson’s rule; Numerical solutions of first-order differential equations by explicit Euler’s method.
Metals, ceramics, polymers, and composites.
Nature of Bonding in Materials: Metallic, ionic, covalent and mixed bonding; structure of materials: Fundamentals of crystallography, symmetry operations, crystal systems, Bravais lattices, unit cells, primitive cells, crystallographic planes and directions; structures of metals, ceramics, polymers, amorphous materials and glasses.
Defects in Crystalline Materials: 0-D, 1-D and 2-D defects; vacancies, interstitials, solid solutions in metals and ceramics, Frenkel and Schottky defects; dislocations; grain boundaries, twins, stacking faults; surfaces and interfaces.
Extensive and intensive thermodynamic properties, laws of thermodynamics, phase equilibria, phase rule, phase diagrams (unary and binary), and basic electrochemistry.
Reaction kinetics, fundamentals of diffusion, Fick’s laws, their solutions, and applications.
Solidification of pure metals and alloys, nucleation and growth, diffusional solid-state phase transformations (precipitation and eutectoid), and martensitic transformation.
Mechanical properties of metals, ceramics, polymers, and composites at room temperature; stress-strain response (elastic, anelastic and plastic deformation).
Electronic Properties: free electron theory, Fermi energy, density of states, elements of band theory, semiconductors, Hall effect, dielectric behaviour, piezo- and ferroelectric behaviour.
Magnetic Properties: Origin of magnetism in materials, para-, dia-, Ferro- and ferri magnetism.
Thermal Properties: Specific heat, heat conduction, thermal diffusivity, thermal expansion, and thermoelectricity.
Optical Properties: Refractive index, absorption, and transmission of electromagnetic radiation. Examples of materials exhibiting the above properties, and their typical/common applications.
X-ray diffraction; spectroscopic techniques such as UV-Vis, IR and Raman; optical microscopy, electron microscopy, and composition analysis in electron microscopes. Tensile test, hardness measurement. Electrical conductivity, carrier mobility and concentrations. Thermal analysis techniques: thermogravimetry and calorimetry.
Heat treatment of ferrous and aluminium alloys; preparation of ceramic powders, sintering; thin film deposition: evaporation and sputtering techniques, and chemical vapour deposition, thin film growth phenomena.
Corrosion and its prevention; embrittlement of metals; polymer degradation.