GATE MN syllabus 2026

• Matrices and Determinants
• Inverse and Rank of matrix
• Systems of linear equations
• Eigen values and Eigen vectors. Cayley-Hamilton Theorem.

• Limit, continuity and differentiability
• Partial Derivatives
• Mean value theorems
• Indeterminate forms and L’ Hospital’s rule
• Maxima and minima
• Taylor’s theorem
• Sequences and series
• Test for convergence
• Fourier series.

• Gradient
• Divergence and Curl
• Line, surface and volume integrals
• Stokes, Gauss and Green’s theorems.

• Linear and non-linear first order ODEs
• Higher order linear ODEs with constant coefficients
• Cauchy’s and Euler’s equations.

• Measures of central tendency and dispersion
• hypothesis testing
• Binomial, Poisson, exponential and normal distributions
• Correlation and regression analysis.

• Solutions of linear algebra equations
• Interpolation
• Integration of trapezoidal and Simpson’s rule
• Single and multi-step methods for differential equations.

• Minerals, Rocks and their Origin, Classification, Ore Genesis
• Structural Geology.

• Methods of access to deposits
• Underground drives
• Drilling method and machines
• Explosives and energetics, blasting devices, blast design practices
• Rock-Tool Interaction applicable to mechanical cutting systems and their selection.

• Levels and levelling, theodolite, tacheometry, triangulation
• Contouring
• Errors and adjustments
• Correlation
• Underground surveying
• Curves
• Photogrammetry
• EDM, Total Station, GPS, Basics of GIS and remote sensing.

• Equivalent force systems
• Equations of equilibrium
• Two dimensional frames and trusses
• Free body diagrams
• Friction forces
• Particle kinematics and dynamics
• Beam analysis.

• Geo-technical properties of rocks
• Rock mass classification
• Instrumentation and in-situ stress measurement techniques
• Theories of rock failure
• Ground vibrations
• Stress distribution around mine openings
• Subsidence
• Slope stability

• Design of pillars
• Roof supporting systems
• Mine filling. Strata Control and Monitoring Plan.

• Surface mining: layout, development, loading, transportation and mechanization, continuous surface mining systems
• highwall mining
• Underground coal mining: bord and pillar systems, room and pillar mining, longwall mining, thick seam mining methods, Underground metal mining: open, supported and caved stoping methods, stope mechanization, ore handling systems.

• Generation and transmission of mechanical, hydraulic and pneumatic power
• Materials handling: wire ropes, hoists, conveyors, face and development machinery, hoisting systems, pumps
• comminution methods and machinery.

• Air, water and soil pollution: Standards of quality, causes and dispersion of contamination and control
• Noise pollution and control
• Land reclamation
• EIA.

• Underground atmosphere
• Heat load sources and thermal environment, air cooling
• Mechanics of airflow distribution, natural and mechanical ventilation
• Mine fans and usage
• Auxiliary ventilation
• Ventilation survey and planning
• Ventilation networks.

• Mine Gases, Methane drainage
• Underground hazards from fires, explosions, dust and inundation
• Rescue apparatus and practices
• Safety management plan
• Accident data analysis
• assessment
• Mine lighting
• Mine legislation
• Occupational health and safety.

• Mineral resource classification
• Discounted cash flow analysis
• Mine valuation
• Mineral taxation.

• Sampling methods, practices and interpretation
• Reserve estimation techniques: Basics of geostatistics and quality control
• Optimization of facility location
• Mine planning and its components, Determination of mine size and mine life
• Ultimate pit configuration and its determination, Optimum mill cut-off grade and its determination, Stope planning, Design of haul road, Selection of mining system vis-à-vis equipment system.

• Concepts of reliability
• Reliability of simple systems
• Maintainability and availability
• Linear programming, transportation and assignment problems
• Network analysis
• Inventory models
• Queuing theory
• Decision trees.

• Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech
• Basic vocabulary: words, idioms, and phrases in context. Reading and comprehension, Narrative sequence.

• Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables
• Numerical computation and estimation: ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series
• Mensuration and geometry
• Elementary statistics and probability.

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

• Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping
• paper folding, cutting, and patterns in 2 and 3 dimensions.