DTE Kerala LET 2025 Syllabus: Check Section-wise Exam Syllabus Here

• Single Variable Calculus and Infinite series, Basic ideas of infinite series and convergence
• Geometric series, Harmonic series, Convergence tests, comparison, ratio, root tests
• Alternating series, Leibnitz Test, Absolute convergence
• Maclaurins series, Taylor series, radius of convergence 

• Partial derivatives and its applications
• Partial derivatives of functions of more than two variables
• Higher order partial derivatives, differentiability
• Differentials and local linearity
• Maxima and Minima of functions of two variables
• Extreme value theorem relative extrema

• Calculus of vector valued functions
• Introduction to vector valued functions, parametric curves in 3-space
• Limits and continuity, derivatives, tangent lines, derivative of dot and cross product
• Definite integrals of vector valued functions, unit tangent, acceleration and speed
• Normal and tangential components of acceleration
• Directional derivatives and gradients-tangent planes and normal vectors 

• Multiple integrals, Double integrals, Evaluation of double integrals
• Double integrals in nonrectangular coordinates reversing the order of integration
• Area calculated as a double integral
• Triple integrals (Cartesian co-ordinates only), volume calculated as a triple integral

• Topics in vector calculus
• Vector and scalar fields, Gradient fields
• conservative fields and potential functions
• Line integrals, work as a line integral
• Independence of path conservative vector field

• Topics in vector calculus
• Green's Theorem, surface integrals
• Divergence Theorem, Stokes’ Theorem

Statics: Fundamental concepts and laws of mechanics - Rigid body – Principle of transmissibility of forces. Coplanar force systems – Moment of force – Principle of moments. Resultant of force and couple system. Equilibrium of rigid body – Free body diagram – Conditions of equilibrium in two dimensions – Two force and three force members.

Types of supports – problems involving point loads and uniformly distributed loads only.  Force systems in space – Degree of freedom – Free body diagram – Equations of equilibrium – Simple resultant and Equilibrium problems.

Properties of planar surfaces - Centroid and second moment of area - Parallel and perpendicular axis theorem – Centroid and Moment of Inertia of composite area. Polar Moment of Inertia – Radious of gyration - Mass moment of Inertia of cylinder and thin disc. Product of Inertia – Principle Moment Of Inertia. Theorems of Pappus and Guldinus.

Friction – Characteristics of dry friction – Problems involving friction of ladder, wedges and connected bodies. Definition of work and virtual work – Principle of virtual work for a system of connection bodies – problems of determinate beams only.

Dynamics: Rectangular and Cylindrical co-ordinate system. 

Combined motion of rotation and translation – Concepts of instantaneous centre – Motion of connecting rod of piston and crank of reciprocating pump. 

Rectilinear translation – Newton’s second law – D’Alembert’s Principle – Application to connected bodies.

Mechanical vibrations – free and forced vibrations – degree of freedom. 

Simple and harmonic motion – Spring-mass model – Period – Stiffness – Frequency – Simple numerical problems of single degree of freedom. 

• Introduction to digital computer - Von Neumann  concept 
• A  simple model  of computer,  acquisition  of data, storage of data, processing of data, the output of processed  data
• Details of functional units of a computer
• Storage - primary storage and secondary storage

• Introduction to programming  languages, types  of  programming languages

• System software, Operating  systems

• Problem-Solving strategies, Problem analysis, formal definition of the problem
• Solution top-down design breaking a problem into sub-problems
• Overview of the solution to the sub-problems by writing step by step procedure (algorithm)
• Representation of procedure by the flowchart
• Implementation of algorithms, use of procedures to achieve modularity

• Introduction to Python

• Functions, calling functions, type conversion and coercion, the composition  of functions
• Mathematical  functions, user-defined  functions, parameters  and arguments

• Strings and lists - string traversal and comparison with examples
• Tuples and dictionaries - operations and examples 

• Files and exceptions - text files, directories
• Introduction to classes and objects - attributes, instances

• General introduction to Civil Engineering
• History of civil Engineering
• Relevance of civil Engineering in the overall infrastructural development of the country
• Types and classification of structures - buildings, towers, chimneys, bridges, dams, retaining walls, water tanks, silos, roads, railways, runways and pipelines
• Definition and types of buildings as per National Building Code of India
• Selection of site-Components of a building and their functions- setting out of a building

• Stones: Classification of stones-Qualities of good building stones-Quarrying-Dressing-TestsSpecifications-Uses of common building stones
• Bricks: Composition of good brick earth - Classification-Qualities of good bricks –Field and laboratory tests-specifications
• Tiles: Classification-Manufacture-properties-Tests-Specifications

• Cement: Basic Ingredients- Manufacturing process- Grades- Properties-Tests Specifications
• Aggregates: Fine and coarse aggregate- Properties - uses-Tests
• Cement Mortar: Types and preparation

• Stone Masonry: Types-Details of Ashlars, Random Rubble, Coarse Rubble and Dry Rubble Masonry
• Brick Masonry: Types - Bond-Introduction to all types of Bonds - English bond in detail  - Comparison of stone and brick masonry

• Timber: Properties-Uses-Classification-Seasoning-Defects-Preservation-Tests
• Hardboard and particle board –Manufacture and use
• Steel: structural steel and steel as reinforcement- Types- Properties-Uses - Market forms

• Floors and Flooring materials: Different types and selections of floors and floor coverings
• Roofs and roof coverings: Different types of roofs, Suitability, Types and selection of roofing materials

• Thermodynamics: Nature and scope of thermodynamics; the basic concept
• Laws of Thermodynamics, Discovery Significance and Applications
• Qualitative ideas on Entropy, Available Energy , Irreversibility, Principle of increase of Entropy& Carnot engine
• Limitations of Thermodynamics; Source of power; history of power production; power production in the future

• Thermal Engineering
• Historical development of steam engine ,steam turbines, gas turbines and hydraulic turbines
• Principle of turbomachinary; History of IC engines; two stroke and four stroke engines-working, applications
• Air compressors-types and uses
• Principles of Rocket propulsion, chemical rockets, Indian space programme

• Refrigeration and air conditioning
• History & Scope of refrigeration; applications of refrigeration
• Food preservation, refrigerated storage; applications in chemical and process industries; special applications; Air conditioning
• Principles & system; scope of air conditioning
• Psychometric properties of air; Human comfort standards

• Automobiles & Aeronautical Engineering
• Introduction to an Automobile; history of the automobile; Indian automobiles
• Types of automobiles; Major components and their functions
• Manufactures of motor vehicles in India
• Fundamentals of aerodynamics; drag force and lift force; jet engines types and applications

• Engineering and Materials
• Introduction and history of materials
• Basic crystallography; metals, alloys composites, ceramic, polymers; mechanical properties and testing of engineering materials

• Manufacturing Engineering: Methods of manufacturing; casting, forging, rolling extrusion; machining operations-turning, milling, drilling, grinding, shaping, planning
• Joining operations- soldering, brazing& welding
• Introduction to CNC machines; examples of typical products manufactured by above methods

Fundamental Concepts of Circuit Elements and Circuit variables: Electromotive force, potential and voltage. Resistors, Capacitors Inductors- terminal V-I relations. Electromagnetic Induction: Faraday’s laws, I Lenz’s law, statically and dynamically induced EMF, self and mutual inductance, coupling coefficient-energy stored in inductance. Real and Ideal independent voltage and current sources, V-I relations. Passive sign convention. 

Basic Circuit Laws: Kirchhoff's current and voltage laws, analysis of resistive circuits-mesh analysis super mesh analysis. Node analysis-super node analysis, star delta transformation.

Magnetic Circuits: Magneto motive force, flux, reluctance, permeability -comparison of electric and magnetic circuits, analysis of series magnetic circuits. Parallel magnetic circuits, magnetic circuits with air-gaps.

Alternating current fundamentals:-Generation of Alternating voltages-waveforms, Frequency, Period, RMS and average values, peak factor and form factor of periodic waveforms and composite waveforms.  Phasor Concepts, Complex representation (exponential, polar and rectangular forms) of sinusoidal voltages and currents phasor diagrams. Complex impedance - series and parallel impedances and admittances, Phasor analysis of RL, RC, RLC circuits.

Complex Power: Concept of Power factor: active, reactive and apparent power. 

Resonance in series and parallel circuits 

Energy, bandwidth and quality factor, variation of impedance and admittance in series and parallel resonant circuits.

Three phase systems: Star and delta connections, three-phase three wires and three- 2 phase four-wire systems. Analysis of balanced and unbalanced star and delta connected loads. Power in three-phase circuits. Active and Reactive power measurement by one, two, and three-wattmeter methods.

Evolution of electronics, the impact of electronics in industry and in society. Resistors Capacitors: Types, Specifications, Standard values, marking color coding Inductors and Transformers: Types, Specifications, and Principles of working. Electromechanical components: relays and contactors.

Diodes: Intrinsic and extrinsic semiconductors, PN junction diode, barrier potential, V-I characteristics, Effect of temperature. Equivalent circuit of a diode. Piece-wise linear model.

Specification parameters of diodes and numbering. 

Zener diode, Varactor diodes, characteristics, working principle of LED, photodiode, solar cell.

Bipolar Junction Transistors: Structure, typical doping, Principle of operation, concept of different configurations. Detailed study of input and output characteristics of common base and common emitter configuration, current gain, and comparison of three configurations. Concept of load line and operating point. Need for biasing and stabilization, voltage divider biasing, Transistor as amplifier, switch, RC coupled amplifier and frequency response. Specification parameters of transistors and type numbering

Junction Field Effect Transistors: Structure, principle of operation, characteristics, comparison with BJT. MOSFET: Structure, principle of operation of Enhancement type MOSFET, Current voltage characteristics, Depletion-type MOSFET. Principle of operation of Phototransistor, UJT, SCR

Diode circuits and power supplies: Series and parallel diode circuits, Clippers, Clampers, Voltage multipliers. Half-wave and full wave (including bridge) rectifiers, Derivation of  Vrms, Vdc, ripple factor, peak inverse voltage, rectification efficiency in each case, capacitor filter, working and design of a simple Zener voltage regulator. Block diagram description of a DC Power supply, Principle of SMPS.

Electronic Measurements and measuring Instruments. Generalized performance parameters of instruments: error, accuracy, sensitivity, precision and resolution. Principle and block diagram of analog and digital multimeter, Block diagram of CRO, Measurements using CRO, Lissajous patterns, Principle and block diagram of DSO, function generator. Testing of Electronic components.

For English, out of the 10 marks to be awarded, 5 marks will be for questions based on a given passage and remaining 5 marks for basic Grammar and General English of  plus 2 standards.

Vocabulary Building , The concept of Word Formation,  Root words from foreign languages and their use in English,  Acquaintance with prefixes and suffixes from foreign languages in English to form derivatives. Synonyms, antonyms, and standard abbreviations. Basic Writing Skills,  Sentence Structures,  Use of phrases and clauses in sentences,  Importance of proper punctuation, Creating coherence, Organizing principles of paragraphs in documents,  Techniques for writing precisely  Identifying common errors in writing,  Subject-verb agreement,  Noun-pronoun agreement, Misplaced modifiers, Articles Prepositions, Redundancies, Clichés, Nature and Style of sensible writing, Describing , Defining, Classifying,  Providing examples or evidence, Writing introduction and conclusion.

• Single Variable Calculus and Infinite series, Basic ideas of infinite series and convergence
• Geometric series, Harmonic series, Convergence tests, comparison, ratio, root tests
• Alternating series, Leibnitz Test, Absolute convergence
• Maclaurins series, Taylor series, radius of convergence 

• Partial derivatives and its applications
• Partial derivatives of functions of more than two variables
• Higher order partial derivatives, differentiability
• Differentials and local linearity
• Maxima and Minima of functions of two variables
• Extreme value theorem relative extrema

• Calculus of vector valued functions
• Introduction to vector valued functions, parametric curves in 3-space
• Limits and continuity, derivatives, tangent lines, derivative of dot and cross product
• Definite integrals of vector valued functions, unit tangent, acceleration and speed
• Normal and tangential components of acceleration
• Directional derivatives and gradients-tangent planes and normal vectors 

• Multiple integrals, Double integrals, Evaluation of double integrals
• Double integrals in nonrectangular coordinates reversing the order of integration
• Area calculated as a double integral
• Triple integrals (Cartesian co-ordinates only), volume calculated as a triple integral

• Topics in vector calculus
• Vector and scalar fields, Gradient fields
• conservative fields and potential functions
• Line integrals, work as a line integral
• Independence of path conservative vector field

• Topics in vector calculus
• Green's Theorem, surface integrals
• Divergence Theorem, Stokes’ Theorem

Harmonic Oscillations: Differential equation of damped harmonic oscillation, forced harmonic oscillation and their solutions -Resonance, Qfactor, Sharpness of resonance-LCR circuit as an electrical analogue of mechanical Oscillator. 

Waves: One-dimensional waves-Differential equation& its solution. Transverse vibration of stretched string.

Interference: Coherence, Interference in thin films and wedge-shaped films (Reflected System), Newton's rings-measurement of wavelength and refractive index of liquid interference filters. Antireflection coating. 

Diffraction Fresnel and Fraunhofer diffraction. Fraunhofer diffraction at single slit. Plane transmission grating. Grating equation-measurement of wavelength, Rayleigh’s criterion for resolution of grating-Resolving power and dispersive power of grating.

Polarization of Light: Types of polarized light.Double refraction. Nicol Prism. Quarter wave plate and half-wave plate, production and detection of circularly and elliptically polarized light. Induced birefringence-Kerr Cell-Polaroid & applications. 

Superconductivity: Superconducting phenomena. Meissen effect. Type-I and Type II superconductors. BCS theory. High-temperature super conductors-Application of superconductors.

Quantum Mechanics: Uncertainty principle and its applications-formulation of Time-dependent and Time-dependent Schrodinger equations-physical meaning of wave function-Energy and momentum Operators-Eigen values functions-One dimensional infinite square well potential. Quantum mechanical Tunneling. 

Statistical Mechanics: Microstates and Microstates. Phase space.Basic postulates of MaxwellBoltzmann. Boltzmann, Bose-Einstein and Femi Diarc statistics. Distribution equation in the three cases. Femi Level and its significance.

Acoustics: Intensity of sound-Loudness-Absorption coefficient-Reverberation and reverberation time-Significance of reverberation time-Sabine’s formula-Factors affecting acoustics of a building. 

Ultrasonic’s: Production of Ultrasonic waves- Magnetostriction effect and Piezoelectric effect- Magnetostrictionj oscillator and Piezoelectric oscillator-Detection of ultrasonic’s-Thermal and piezoelectric methods-Applications of ultrasonics - -NDT and medical.

Laser: properties of lasers, absorption, spontaneous and stimulated emissions, population inversion, Einstein’s coefficients, Working principle of laser, Optical resonant cavity. Ruby Laser, Helium-Neon Laser, Semiconductor  Laser, Application of Laser, holography (recording and reconstruction).

Photonics: Basics of solid state lighting-LED-Photo detectors-photo voltaic cell, junction & avalanche photo diodes, photo transistors, thermal; detectors, Solar cells-I-V characteristicsOptic fiber-Principle of propagation-numerical aperture-optic communication system-Industrial, medical and technological applications of optical fiber. Fiber optic sensors-Basics of Intensity modulated and phase modulated sensors.

Spectroscopy: Introduction, Beer Lamberts Law.

UV-visible spectroscopy - Principle, Instrumentation and application.

IR spectroscopy- Principle and application. 

HNMR spectroscopy-Principle, chemical shift-spin-spin splitting and application including MRI, Spectral Problems.

Electrochemistry: Different types of electrodes, SHE, Calomel electrodes, Glass electrode Electrochemical series and its applications. 

Nernst equation - Derivation, application & numerical.  Potentiometric titration - Acid-base and redox titration Lithium ion cell and Fuel cell.

Instrumental Methods: Thermal analysis - Principle, instrumentation and applications of TGA and DTA

Chromatographic methods - Basic principles, column, TLC. Instrumentation and principles of GC and HPLC. 

Conductivity - Measurement of conductivity 

Chemistry of Engineering Materials: Copolymers - BS, ABS -Structure and Properties. 

Conducting Polymers - Polyaniline, Polypyrrole - Preparation, Structure and Properties.

OLED – An introduction 

Advanced Polymers – Kevlar, Polybutadiene rubber and silicone rubber: Preparation, Structure and Properties. 

Nanomaterials – Definition, Classification, chemical methods preparation- hydrolysis and reduction 

Properties and Applications - Carbon Nano Tubes and fullerenes.  

Fuels and Lubricants: Fuels - Calorific Value, HCV and LCV - Determination of calorific value of a solid and liquid fuel by Bomb calorimeter - Dulong’s formula and Numerical.  Liquid fuel - Petrol and Diesel - Octane number & Cetane number 

Biodiesel - Natural gas. 

Lubricant - Introduction, solid, semisolid and liquid lubricants. 

Properties of lubricants - Viscosity Index, Flash point, Fire point, Cloud point, Pour point and Aniline point.

Water Technology: Types of hardness, Units of hardness, Estimation of Hardness – EDTA method. 

Water softening methods - Ion exchange process - Principle. Polymer ion exchange.  Reverse Osmosis - Disinfection method by chlorination and UV  Dissolved oxygen, BOD and COD. 

Sewage water Treatment - Trickling Filter and UASB process.