Engineering Mathematics

Year	Linear Algebra	Calculus & Differential Equations	Complex Analysis & Transforms	Probability & Statistics	Numerical Methods & Others	Approx. Total Marks
2018	Matrix Algebra, Eigenvalues (3m)	Limits, Continuity, Differentiation, ODEs (5m)	Complex Numbers, Laplace Transform (3m)	Probability Distributions (2m)	Numerical Methods (2m)	~15
2019	Linear Systems, Vector Spaces (4m)	Integral Calculus, Partial Derivatives, PDEs (4m)	Fourier Series & Transforms (3m)	Statistics & Probability (3m)	Numerical Integration & Root Finding (1m)	~15
2020	Eigenvalues, Orthogonal Matrices (3m)	Calculus of Several Variables, ODEs (5m)	Complex Integration, Laplace (3m)	Random Variables, Distributions (2m)	Numerical Solution of ODEs (2m)	~15
2021	Vector Spaces, Diagonalization (4m)	Multivariate Calculus, PDEs (4m)	Fourier Series, Z-transform (3m)	Probability & Statistics (3m)	Numerical Linear Algebra (1m)	~15
2022	Matrix Theory, Eigenvalue Problems (3m)	Differential Equations, Limits & Continuity (4m)	Complex Analysis, Laplace Transforms (3m)	Statistics & Probability (3m)	Numerical Methods (2m)	~15
2023	Linear Algebra, Eigenvalues (3m)	Calculus (limits, ODEs) (5m)	Fourier, Laplace & Z-Transforms (3m)	Probability, Statistics (2m)	Numerical Solutions & Interpolation (2m)	~15
2024*	Estimated similar linear algebra topics (3m)	Estimated Calculus & ODE topics (5m)	Estimated Transforms & Complex Analysis (3m)	Estimated Probability & Statistics (2m)	Estimated Numerical Methods (2m)	~15
2025*	Projected stable topics in Linear Algebra	Projected Calculus & ODEs	Projected Fourier, Laplace & Z-transforms	Projected Probability & Statistics	Projected Numerical Methods	~15

Key Topics by Section

Linear Algebra

• Matrices, Determinants, Systems of Linear Equations
• Eigenvalues & Eigenvectors
• Vector spaces and Diagonalization

Calculus & Differential Equations

• Limits, Continuity, Differentiation & Integration
• Ordinary Differential Equations (ODEs)
• Partial Differential Equations (PDEs)
• Multivariate Calculus

Complex Analysis & Transforms

• Complex Numbers and Functions
• Laplace Transform, Fourier Series & Transforms
• Z-transform (occasionally)

Probability & Statistics

• Probability Theory & Distributions
• Random Variables & Expectation
• Statistics Basics (mean, variance)

Numerical Methods & Others

• Numerical Integration, Differentiation
• Numerical solution of ODEs
• Interpolation & Root Finding

Applied Mechanics & Design

Year	Engineering Mechanics	Mechanics of Materials	Theory of Machines	Vibrations	Machine Design	Approx. Total Marks
2018	FBD, Equilibrium (2m), Friction (1m)	Stress-Strain, Mohr’s circle, Beams SFD/BMD (5m), Torsion (2m), Columns (2m)	Linkages (2m), Gears (1m), Balancing (2m)	Free vibration (2m), Damping (3m)	Fatigue, Springs, Bolted Joints (4m)	~26
2019	FBD & Virtual Work (3m), Friction (1m)	Beam Deflection (4m), Thin Cylinders (2m), Thermal Stress (3m)	Cams (3m), Flywheels (2m), Governors (2m), Gyroscope (2m)	Forced vibration (2m), Resonance (1m)	Failure Theories (3m), Welded Joints (3m)	~32
2020	Equilibrium & Trusses (2m), Simple Machines (2m)	Mohr’s Circle (2m), Beam Bending (2m), Torsion (1m)	Gear Trains (3m), Dynamic Analysis of Linkages (2m), Balancing (3m)	Free vibration (2m), Critical Speed (1m)	Bearings (2m), Clutches & Brakes (4m)	~25
2021	FBD & Equilibrium (2m), Virtual Work (1m), Friction (2m)	SFD/BMD (3m), Beam Deflection (3m), Columns (2m), Energy Methods (1m)	Linkage kinematics (2m), Flywheels (3m), Governors (2m), Cams (1m)	Damping & Resonance (3m), Vibration Isolation (1m)	Springs (3m), Fatigue (2m)	~32
2022	FBD & Friction (4m), Simple Machines (2m)	Beams & Columns (3m), Thin Cylinders (2m), Thermal Stresses (1m)	Gear Trains (3m), Balancing (3m), Gyroscope (2m)	Forced Vibration (3m), Critical Speed (3m)	Bolted Joints (2m), Welded Joints (1m)	~29
2023	FBD (1m), Trusses (1m), Friction (1m)	Mohr’s Circle (2m), Beam Bending & Shear (4m), Torsion (2m), Columns (2m)	Cams (3m), Linkages (3m), Balancing (2m), Governors (2m)	Free & Forced Vibrations (4m)	Failure Theories (2m), Springs & Bearings (3m)	~34
2024*	Estimated FBD & Equilibrium (3m), Friction (2m)	Estimated Beam Deflection (4m), Torsion (2m), Columns (2m)	Estimated Linkage Kinematics (3m), Cams (2m), Gear Trains (3m)	Estimated Vibrations (4m)	Estimated Machine Design (5m)	~24
2025*	Projected similar topics to 2023-24	Projected similar distribution	Projected similar distribution	Projected similar distribution	Projected similar distribution	~27-32

Notes:

• Marks indicate approximate allocation in each year.
• *2024 and 2025 data are estimates based on previous years.
• This reflects question trends, not exact marks from official papers.
• Vibrations often combined with Theory of Machines in official sections.

Quick Insights:

• Engineering Mechanics: Regularly 2–4 marks, with emphasis on FBD, equilibrium, friction.
• Mechanics of Materials: Most stable and heavy, focused on beams, torsion, columns.
• Theory of Machines: Linkages, cams, balancing, governors appear every year.
• Vibrations: Increasing in recent years, mainly free/forced vibrations & damping.
• Machine Design: Failure theories, joints, springs, bearings consistently tested.

Fluid Mechanics & Thermal Sciences

Year	Fluid Mechanics	Thermodynamics & Thermal Sciences	Heat Transfer	IC Engines & Compressors	Approx. Total Marks
2018	Fluid Statics, Bernoulli, Laminar/Turbulent Flow	First Law, Second Law, Entropy, Carnot Cycle	Conduction (1D), Convection (forced/natural)	Air Compressor, SI/CI Engines	~28
2019	Control Volume Analysis, Boundary Layer, Dimensional Analysis	Air Standard Cycles, Thermodynamic Relations, Entropy, Psychrometry	Radiation basics, Heat Exchangers	IC Engines, Compressors, Nozzle Flow	~30
2020	Pipe Flow, Head Loss, Flow Measurement, Pumps	Properties of Pure Substances, Gas Mixtures, Exergy Analysis	Extended Surfaces, Transient Heat Conduction	Gas Turbines, IC Engines, Compressors	~27
2021	Inviscid Flow, Flow around Bodies, Turbomachinery	Second Law Applications, Vapor Power Cycle, Refrigeration Cycles	Combined Modes, Heat Exchangers, Lumped Capacitance Method	IC Engines, Nozzle & Diffuser Analysis	~29
2022	Flow in Pipes & Channels, Pumps, Compressible Flow	Entropy Generation, Gas Mixtures, Psychrometrics, Combustion	Radiation, Convection, Heat Transfer in Extended Surfaces	IC Engines, Compressors, Gas Turbines	~28
2023	Boundary Layer, Flow Measurement, Pumps, Compressible Flow	Air Standard Cycles, Entropy, Refrigeration Cycles, Gas Mixtures	Conduction, Convection, Heat Exchanger Analysis	IC Engines, Compressors, Turbomachinery	~31
2024*	Estimated similar to 2023 topics	Estimated similar core thermodynamics & cycles	Estimated combined heat transfer topics	Estimated IC Engines and compressors	~28
2025*	Projected stable topics (fluids + turbomachinery)	Projected stable thermodynamics + refrigeration + psychrometrics	Projected stable heat transfer + radiation	Projected stable IC Engines & compressors	~30

Key Topics by Section

Fluid Mechanics

• Fluid properties & statics
• Control volume analysis & momentum equations
• Laminar/turbulent flow, Reynolds number
• Flow in pipes & channels, pump & turbine performance
• Compressible flow fundamentals & shock waves
• Boundary layer theory & flow measurement

Thermodynamics & Thermal Sciences

• Laws of thermodynamics, entropy, and exergy
• Air standard cycles (Otto, Diesel, Dual cycles)
• Vapor power cycles & refrigeration cycles
• Psychrometry & gas mixtures
• Combustion basics

Heat Transfer

• Conduction (steady & transient)
• Convection (forced & natural)
• Radiation fundamentals
• Heat exchangers & extended surfaces

IC Engines & Compressors

• Engine cycles and performance parameters
• Air compressors (reciprocating, rotary)
• Gas turbines and nozzles
• Refrigeration & vapor compression cycles

Manufacturing & Industrial Engineering (MIE)

Year	Manufacturing Processes	Production Planning & Control	Operations Research & Inventory	Quality Control & Reliability	Approx. Total Marks
2018	Casting, Welding, Machining	Forecasting, Scheduling	Linear Programming, Queuing Theory	Statistical Quality Control, Reliability Basics	~20
2019	Forming, Machining, Welding	Inventory Control, MRP	Transportation Problem, PERT/CPM	Control Charts, Acceptance Sampling	~22
2020	Casting, Machining, Forming	Aggregate Planning, Capacity Planning	Network Models, Game Theory	Reliability, Design of Experiments	~18
2021	Machining, Welding, CNC	Scheduling, Production Control	Linear Programming, Queuing Theory	Process Capability, SPC, ISO Standards	~21
2022	Casting, Forming, Additive Manufacturing	Inventory Management, MRP	Transportation Problem, PERT/CPM	Quality Control Charts, Reliability	~20
2023	Welding, Machining, Metal Forming	Forecasting, Aggregate Planning	Network Models, Inventory Models	SPC, Acceptance Sampling	~23
2024*	Estimated combination of 2023 topics	Estimated Production Planning & Control	Estimated OR models	Estimated Quality Control & Reliability	~21
2025*	Projected stable topics	Projected steady focus areas	Projected steady OR & Inventory focus	Projected Quality & Reliability topics	~22

Key Topics by Section

Manufacturing Processes

• Casting, Welding, Machining
• Metal Forming (forging, rolling, extrusion)
• Additive Manufacturing & CNC machining
• Tool design and metallurgy basics

Production Planning & Control

• Forecasting methods
• Material Requirements Planning (MRP)
• Scheduling techniques and aggregate planning
• Inventory management & control

Operations Research & Inventory

• Linear programming
• Transportation & assignment problems
• Network models (PERT/CPM)
• Queuing theory & game theory basics

Quality Control & Reliability

Reliability engineering fundamentals

Statistical Process Control (SPC) charts

Acceptance sampling

Process capability analysis

General Aptitude

Year	Verbal Ability	Numerical Ability	Approx. Total Marks
2018	Grammar (5m), Sentence Completion (3m), Verbal Reasoning (2m)	Data Interpretation, Number Series (3m)	~10
2019	Verbal Reasoning, Grammar, Analogies (5m), Reading Comprehension (2m)	Data Interpretation, Arithmetic (3m)	~10
2020	Sentence Completion, Synonyms/Antonyms, Verbal Reasoning (6m)	Data Interpretation, Number Systems (2m)	~10
2021	Grammar, Logical Reasoning, Sentence Correction (5m)	Percentages, Ratio & Proportion, Data Interpretation (3m)	~10
2022	Reading Comprehension, Sentence Completion, Synonyms (5m)	Simple Interest, Time & Work, Data Interpretation (3m)	~10
2023	Verbal Reasoning, Grammar, Sentence Completion (5m)	Number Series, Data Interpretation, Profit & Loss (3m)	~10
2024*	Estimated similar Verbal Ability topics	Estimated similar Numerical Ability topics	~10
2025*	Projected similar Verbal Ability topics	Projected similar Numerical Ability topics	~10

Key Topics by Section

Verbal Ability

• Grammar & Sentence Correction
• Sentence Completion
• Synonyms & Antonyms
• Verbal Reasoning & Analogies
• Reading Comprehension

Numerical Ability

• Data Interpretation (graphs, charts)
• Number Systems & Series
• Percentages, Ratio & Proportion
• Time & Work, Simple Interest
• Profit & Loss

Overview

1. Engineering Mathematics

• Consistent Core: Linear Algebra (matrices, eigenvalues), Calculus (limits, derivatives, ODE/PDE), Complex Analysis (Fourier, Laplace transforms), Probability & Statistics, and Numerical Methods.
• Emphasis: Strong foundation in solving linear systems, differential equations, and transform techniques.

2. Applied Mechanics & Design

• Core Focus: Free Body Diagrams (FBD), Static Equilibrium, Friction, Beam bending & torsion, columns, stress-strain relationships.
• Theory of Machines: Linkages, cams, governors, gear trains, balancing.
• Vibrations: Free & forced vibrations with damping and resonance.
• Machine Design: Fatigue, springs, bolted & welded joints, failure theories, clutches, bearings.

3. Fluid Mechanics & Thermal Sciences

• Fluid Mechanics: Fluid statics, Bernoulli equation, pipe flow, pumps, turbines, compressible flow, boundary layers.
• Thermodynamics: First and Second Laws, entropy, air standard cycles (Otto, Diesel), vapor power cycles, refrigeration.
• Heat Transfer: Conduction, convection, radiation, heat exchangers.
• IC Engines & Compressors: Engine cycles, performance, compressors, gas turbines, nozzles.

4. Manufacturing & Industrial Engineering

• Manufacturing Processes: Casting, welding, machining, forming, additive manufacturing.
• Production Planning & Control: Forecasting, inventory management, scheduling, MRP.
• Operations Research: Linear programming, transportation problems, network models (PERT/CPM), queuing.
• Quality Control & Reliability: SPC charts, acceptance sampling, reliability fundamentals.

5. General Aptitude

• Verbal Ability: Grammar, sentence completion, verbal reasoning, reading comprehension.
• Numerical Ability: Data interpretation, number series, percentages, ratio & proportion, time & work, profit & loss.

Key Takeaways:

• Strong Fundamentals: Across all subjects, fundamentals and basic principles are tested repeatedly.
• Balanced Coverage: Each year covers both theory and application-oriented questions.
• Mathematics & GA: Engineering Mathematics and General Aptitude have stable, predictable weightage and topics.
• Interdisciplinary Overlaps: Some topics like vibrations overlap with theory of machines; thermodynamics with thermal sciences, etc.
• Consistent Practice: Repeated practice on FBD, beam problems, thermodynamics cycles, OR problems, and language skills will ensure readiness.