📚 LEARN & SOLVE ENGINE
The GATE MN Syllabus, Section by Section
Organised exactly like the official syllabus — six sections, each split into its sub-topics. Every live sub-topic opens an IIT-style module: the core principle, a complete formula matrix, the common traps, and a progressive 3-tier question suite (basic → medium → hard) with worked solutions revealed on submit.
79 sub-topics live · more added every week across all six sections.
📊
Exam Insights — Topic & Trend Analysis
NEWSee exactly what GATE MN has asked across 15 papers — topic distribution, year trends, question formats, conceptual gaps and a personalised prep plan.
1
Engineering Mathematics
6/6 liveThe mathematical toolkit underpinning every quantitative question on the paper.
- Linear Algebra· 3 QMatrices, rank, inverse, eigenvalues/vectors, Cayley–Hamilton, linear systemsFREE
- Calculus· 3 QLimits, continuity, partial derivatives, MVT, L'Hôpital, maxima/minima, Taylor, sequences & series, FourierFREE
- Vector Calculus· 3 QGradient, divergence, curl; line/surface/volume integrals; Stokes, Gauss & GreenFREE
- Differential Equations· 3 QFirst-order ODEs, higher-order linear, Cauchy–Euler equationsFREE
- Probability & Statistics· 3 QCentral tendency & dispersion, hypothesis testing, binomial/Poisson/exponential/normal, correlation & regressionFREE
- Numerical Methods· 3 QLinear systems, interpolation, trapezoidal & Simpson, single & multi-step ODE methodsFREE
2
Mining Geology, Mine Development and Surveying
14/14 liveThe deposit's geology, gaining access to it, and fixing everything accurately in space.
- Mining Geology: minerals & rocks· 3 QMineral properties; igneous, sedimentary & metamorphic rocks and their originFREE
- Classification & ore genesis· 3 QMagmatic, hydrothermal, sedimentary & placer ore-forming processesFREE
- Structural geology· 3 QFolds, faults, joints, dip & strike, unconformitiesFREE
- Methods of access to deposits· 3 QShaft/incline/adit, incline length L = H/sinθ, 1-in-n gradientFREE
- Underground drivages· 3 QAdvance = d·η_pull, rounds = L/a, muck = A·a·ρFREE
- Drilling methods & machines· 3 QPenetration rate, drilling time, specific drilling m/m³FREE
- Explosives, blasting devices & practices· 3 QPowder factor, bench geometry, charge per holeFREE
- Levelling, theodolite & tacheometry· 3 QHI method RL, stadia distance D = KS·cos²θFREE
- Triangulation, contouring, errors & adjustments· 3 QStandardisation, temperature, slope correctionsFREE
- Underground surveying & correlation· 3 QLength √(ΔN²+ΔE²), bearing, closing errorFREE
- Curves, photogrammetry & field astronomy· 3 QLatitude/departure, tangent length, arc lengthFREE
- EDM, Total Station & GPS· 3 QSlope reduction D = Scosα, V = SsinαFREE
- Rock–tool interaction & mechanical cutting· 3 QSpecific energy, pick forces, cutter selection for roadheaders & continuous minersFREE
- GIS & remote sensing basics· 3 QGeoreferencing, raster/vector, spectral bands, photogrammetry basicsFREE
3
Geomechanics and Ground Control
13/13 liveHow rock behaves under stress and how we keep openings stable.
- Engineering Mechanics· 3 QEquilibrium, 2-D trusses & frames, FBD, friction, beam analysis, particle kinematics & dynamicsFREE
- Geotechnical properties of rocks· 3 QPorosity n=Vv/V, void ratio e=n/(1−n), UCS≈22·Is(50)FREE
- Rock mass classification (RMR, Q)· 3 QRMR = Σ6 ratings + adjustment, Q = (RQD/Jn)(Jr/Ja)(Jw/SRF)FREE
- Stress distribution around openings· 3 Qσ_v = γH, Kirsch sidewall 3σ_v−σ_h, roof 3σ_h−σ_vFREE
- Theories of rock failure (Mohr–Coulomb)· 3 Qτ = c + σ tanφ, σ₁ = σ₃N_φ + 2c√N_φ, Mohr circleFREE
- Subsidence· 3 QS_max = a·m, critical width W = 2H tan(angle of draw)FREE
- Slope stability· 3 QFS = (cA + Wcosβ tanφ)/(Wsinβ); c=0 ⇒ tanφ/tanβFREE
- Design of supports in roadways & workings· 3 QSupport pressure p=γH_p, roof load p·A, bolts N=F·FS/capFREE
- Pillar design· 3 QTributary σ_p = σ_v(W+B)²/W², Obert–Duvall, FSFREE
- Rock bursts & coal bumps· 3 QStrain energy density u = σ²/(2E), total U = u·VFREE
- Ground vibrations· 3 QScaled distance SD=D/√W, PPV = k·SD^(−β)FREE
- In-situ stress measurement & instrumentation· 3 QHydrofracturing, overcoring, flat-jack; convergence & load monitoringFREE
- Mine filling & strata monitoring· 3 QHydraulic/paste fill, fill strength, strata-control & monitoring planFREE
4
Mining Methods and Machinery
11/11 liveExtracting the ore — the systems, layouts and machines that move rock.
- Surface mining: layout, development & mechanization· 3 QStripping ratio SR=waste/ore, BESR=(price−cost)/strip costFREE
- Continuous surface mining systems· 3 QBWE output = n·V_b·f·60, solid = loose/swell factorFREE
- Bord & pillar mining· 3 QExtraction e = 1 − W²/(W+B)² for square pillarsFREE
- Longwall mining· 3 QOutput/cycle = L·d·h·ρ, scaled to daily & annualFREE
- Thick-seam mining methods· 3 QRecovery = extracted/in-situ, LTCC h_eff = h_cut + h_top·RFREE
- Underground metal mining: stoping methods· 3 QDilution = waste/(ore+waste), diluted grade, mill tonnageFREE
- Generation & transmission of power· 3 QP = √3·V_L·I_L·cosφ, line loss 3I²RFREE
- Materials handling: haulage, conveyors & ropeways· 3 QBelt capacity Q_m = 3.6·A·v·ρ, lift power ṁgHFREE
- Rope haulage & gradients· 3 QT = W(sinθ + μcosθ), trip power T·vFREE
- Hoisting systems· 3 QStatic F = mg, accelerating m(g+a), P = Fv/ηFREE
- Pumps & comminution· 3 QPump P = ρgQH/η, Bond's law grinding energyFREE
5
Surface Environment, Mine Ventilation & Underground Hazards
19/19 liveKeeping the mine atmosphere and surroundings safe, breathable and legal.
- Air, water & soil pollution: standards & control· 3 QDecibel addition, +3 dB doubling rule, source combinationFREE
- Noise· 3 QPermissible T = 8/2^((L−90)/5), noise dose Σ(C/T)×100%FREE
- Land reclamation· 3 QVolume = area×depth, swell & truck loads, cut–fill balanceFREE
- Airway resistance & fan laws· 3 QAtkinson R, square law, series/parallel, fan lawsFREE
- Natural ventilation pressure (NVP)· 3 Qρ=P/RₐT, NVP=(ρ_d−ρ_u)gH, fan+NVP combination, shaft figureFREE
- Mechanical ventilation & mine fans· 3 QAir power P·Q, shaft power /η, operating point, P–Q curveFREE
- Auxiliary ventilation· 3 QDuct RQ², leakage η_d = Q_face/Q_fan, fan air powerFREE
- Mine gases & gas dilution· 3 Qppm↔%, dilution airflow Q=q/(C−B), explosive-range bar figureFREE
- Psychrometry & mine climate· 3 QRH, moisture content W=0.622·pv/(P−pv), psychrometric figureFREE
- Mine dust sampling & control· 3 Qgravimetric c=m/V, time-weighted average, sampler + exposure figuresFREE
- Mine fires & explosions· 3 QCH₄ 5–15% range, Graham's ratio, O₂ deficiency 0.265N₂−O₂FREE
- Mine inundation· 3 QHydrostatic p=ρgh, pump-out t=V/Q, power ρgQH/ηFREE
- Mine lighting· 3 QE=Φ/A lux, inverse-square E=I/d², lumen methodFREE
- Rescue apparatus, safety & occupational health· 3 QApparatus duration V/rate, accident frequency rate ×10⁶/man-hoursFREE
- Heat load, thermal environment & air cooling· 3 QStrata & auto-compression heat, cooling load, refrigeration & spot coolingFREE
- Ventilation networks, survey & planning· 3 QKirchhoff laws, Hardy–Cross mesh balancing, pressure surveyFREE
- Methane drainage· 3 QPre/post drainage, borehole capture, drainage efficiencyFREE
- Environmental impact assessment (EIA)· 3 QBaseline study, impact prediction, EMP, statutory clearancesFREE
- Mine legislation & accident analysis· 3 QMines Act & Regulations, frequency & severity rates, accident dataFREE
6
Mineral Economics, Mine Planning, Systems Engineering
16/16 liveValuing the deposit and planning the operation as an optimised system.
- Mineral resource & reserve classification· 3 QIn-situ T = A×t×ρ, recoverable reserve T×recoveryFREE
- Sampling & reserve estimation· 3 QLength-weighted grade Σ(g·l)/ΣlFREE
- Discounted cash flow & mine valuation· 3 QPV = FV/(1+i)ⁿ, NPV = −C₀ + Σ CF/(1+i)ᵗFREE
- Mineral taxation· 3 QRoyalty = rate×value, PAT = PBT×(1−tax)FREE
- Mine planning, layouts & facility location· 3 QCentre of gravity x*=Σw·x/Σw, y*=Σw·y/ΣwFREE
- Reliability of series & parallel systems· 3 QSeries ∏Rᵢ, parallel 1−∏(1−Rᵢ), mixed blocksFREE
- Cost-benefit analysis & work study· 3 QB/C = PV benefits/PV costs, standard time, shift outputFREE
- Queueing theory· 3 QM/M/1: ρ=λ/μ, L_s=λ/(μ−λ), W_qFREE
- Linear programming, transportation & assignment· 3 QGraphical LP, corner-point theorem, vertex optimumFREE
- Sampling, geostatistics & grade control· 3 QVariogram, ordinary kriging, nugget/sill/range, QA–QCFREE
- Mine size, life & optimum cut-off grade· 3 QTaylor's rule, optimum mill cut-off, NPV-driven mine lifeFREE
- Ultimate pit & stope planning· 3 QLerchs–Grossmann pit limits, stope layout & sequencingFREE
- Haul-road design & equipment selection· 3 QGrade/width/superelevation, truck–shovel match, fleet sizingFREE
- Network analysis (PERT/CPM)· 3 QCritical path, float, project crashing, PERT expected timeFREE
- Inventory models· 3 QEOQ, reorder point, safety stock, total costFREE
- Maintainability, availability & decision trees· 3 QMTBF/MTTR, availability A=MTBF/(MTBF+MTTR), EMV decision treesFREE