As you Asking for the Syllabus of the Metallurgy of the Graduate Trainee Examination of HAL Let me tell you that As per My knowledge the Graduate Trainee Examination of HAL has the Following Subjects

Numerical Aptitude.
Reasoning.
Mechanical Engineering.
Electronics.
Electrical.
Instrumentation.
Computer Science.
Information Technology.
Civil Engineering

the Syllabus of All these Subjects Are As Follow

Numerical Aptitude

Number Systems.
Rational Numbers.
Decimal & Fractions.
Computation of Whole Numbers.
Linear Equations.
Exponents & Powers.
Proportions.
Interest (Simple &Compound).
Square Roots.
Cube Roots.
Averages.
Percentages.
Tables & Graphs.
Ratio & Percentages.
Geometry.
Discount.
Areas.
Algebraic Expressions.
Fundamental Arithmetical Operations.

Reasoning Syllabus

Alphabet Series.
Analogy.
Non-Verbal Series.
Number Series.
Logic.
Problem Solving.
Figure Classification.
Arrangements.
Directions.
Clocks & Calendars.
Puzzle Test.
Similarities and Differences.
Number Ranking.
Coding-Decoding.
Blood Relations.
Embedded Figures.
Logical Sequence of Words.
Verbal and Figure Classification.
Arithmetical Computation.
Relationship Concepts.
Arithmetical Number Series.
Arithmetical Reasoning etc.

– Mechanical

Applied Mechanics and Design.
Engineering Mechanics.
Strength of Materials.
Theory of Machines.
Vibrations.
Design.
Fluid Mechanics and Thermal Sciences.
Heat-Transfer.
Thermodynamics.
Applications.
Manufacturing and Industrial Engineering.
Engineering Materials.
Metal Casting.
Forming.
Joining.
Machining and Machine Tool Operations.
Metrology and Inspection.
Computer Integrated Manufacturing.
Production Planning and Control.
Inventory Control.
Operations Research.

Electronics Topics

Networks.
Electronic Devices.
Analog Circuits.
Digital circuits.
Signals and Systems.
Control Systems.
Communications.
Electromagnetics.

Civil Topics

Reinforced Concrete Structures.
Concrete Technology.
Hydrology & Water Resources Engineering.
Civil Engineering Materials and Construction.
Steel Structures.
Hydraulic Structures.
PSC Structures.
Fluid Mechanics.
Solid Mechanics, Structural Analysis.
Surveying.
Transportation Engineering.
Soil Mechanics and Foundation Engineering.
Environmental Engineering.
Construction and Project Management.
Bridge Engineering.
Estimation, Costing, and Specifications.
Environmental Studies etc.

Instrumentation Engineering Syllabus

Basics of Circuits and Measurement Systems.
Signals, Systems, and Communications.
Analog Electronics.
Electrical and Electronic Measurements.
Transducers, Mechanical Measurement and Industrial Instrumentation.
Digital Electronics.
Control Systems and Process Control.
Analytical, Optical and Biomedical Instrumentation.

HalIndia Syllabus for Electrical Engineering

Network Theory.
Basic Electrical Engineering Concepts.
Utilization of Electrical Energy.
Power Electronics & Drives.
AC Fundamentals.
Measurement and measuring instruments.
Estimation and costing.
Magnetic Circuit.
Analog and Digital Electronics.
Power Systems.
Electrical Machines.
Basic Electronics etc.

Computer Science/ IT

Operating System.
Digital Logic.
Compiler Design.
Programming and Data Structures.
Computer Organization and Architecture.
Web Technologies.
Theory of Computation.
Computer Networks.
Algorithms.
Databases.
Information Systems and Software Engineering etc.