DTE Kerala LET 2022 Syllabus: Subject wise Syllabus, Important Topics

• 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
• Maclaurin's series, Taylor series, the radius of convergence 

• Partial derivatives and their 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, a 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 coordinates 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 the area - Parallel and perpendicular axis theorem – Centroid and Moment of Inertia of composite area. Polar Moment of Inertia – Radius of gyration - Mass moment of Inertia of the cylinder and a 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 coordinate system. 

The 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 a 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 subproblems
• Overview of the solution to the subproblems 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

For English, out of the 10 marks to be awarded, 5 marks will be for questions based on a given passage and the 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.

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 a stretched string.

Interference: Coherence, Interference in thin films and wedge-shaped films (Reflected System), Newtons 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 Dirac statistics. Distribution equation in the three cases. Fermi 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 photodiodes, phototransistors, thermal; detectors, Solar cells-I-V characteristic optic fiber-Principle of propagation-numerical aperture-optic communication system-Industrial, medical and technological applications of optical fibre. Fibre 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 & numericals.  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 

Fuels and Lubricants: Fuels - Calorific Value, HCV and LCV - Determination of calorific value of 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, Flashpoint, 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.