• Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
• Calculus: Functions of two variables, partial derivatives, maxima and minima, multiple integrals.
• Differential Equations: First order equations (linear and nonlinear), Cauchy’s and Euler’s equations.
• Probability & Statistics: Mean, median, mode, standard deviation, random variables, Poisson and Normal distributions.

• Engineering Mechanics: Free-body diagrams and equilibrium, trusses and frames, virtual work, impulse and momentum.
• Mechanics of Materials: Stress and strain, elastic constants, Poisson's ratio, Mohr’s circle, beam bending, torsion of circular shafts.
• Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms, cams, gears and gear trains, flywheels, and governors.
• Vibrations: Free and forced vibration of single degree of freedom systems, effect of damping, resonance.
• Machine Design: Design for static and dynamic loading, failure theories, fatigue strength, design of bolted, riveted, and welded joints.

• Fluid Properties: Surface tension, capillarity, viscosity.
• Fluid Statics: Manometry, buoyancy, forces on submerged bodies, stability of floating bodies.
• Fluid Dynamics: Bernoulli’s equation, control-volume analysis of mass, momentum and energy.
• Flow Measurement: Venturi meter, orifice meter, boundary layer theory, flow through pipes, head losses.

• Conduction: One-dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction.
• Convection: Free and forced convection, dimensionless numbers (Pr, Re, Nu), heat transfer correlations.
• Radiation: Stefan-Boltzmann law, Wien’s displacement law, black and grey surfaces, view factors.
• Heat Exchangers: LMTD and NTU methods.

• Basic Concepts: Thermodynamic systems and processes, properties of pure substances, behavior of ideal and real gases.
• Laws of Thermodynamics: Zeroth, First, and Second laws of thermodynamics, entropy, availability and irreversibility.
• Thermodynamic Cycles: Air-standard Otto, Diesel and Dual cycles.

• I.C. Engines: Air-standard cycles, combustion, performance parameters.
• Refrigeration & Air-conditioning: Vapour-compression refrigeration cycle, psychrometric chart and processes.
• Turbomachinery: Impulse and reaction principles, Pelton-wheel, Francis and Kaplan turbines, steam and gas turbines.

• Structure and Properties: Phase diagrams, heat treatment, stress-strain diagrams for engineering materials.
• Crystallography: Crystal structures (BCC, FCC, HCP), imperfections in solids.

• Casting, Forming, and Joining: Design of patterns, moulds and cores; solidification and cooling; hot and cold working processes; principles of welding, brazing, and soldering.
• Machining and Machine Tool Operations: Mechanics of machining; tool geometry and tool life; principles of non-traditional machining (EDM, ECM, USM).

Metrology and Inspection: Limits, fits and tolerances; linear and angular

• Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning.
• Inventory Control: Deterministic models, safety stock inventory control systems.
• Operations Research: Linear programming, simplex method, transportation, assignment, network flow models (PERT/CPM).

• Verbal Aptitude: Basic English grammar, narrative sequencing, reading comprehension.