TJEE Syllabus 2025: Detailed Topics for Physics, Chemistry, Mathematics & Biology

Module

Topics

MODULE 1

- Physics: Scope, excitement, and laws of physics; relationship between physics, technology, and society.

- Measurement necessity: Systems of units; SI units; basic and derived units.

- Precision and accuracy in measurement; Significant figures; Types of errors in measurement.

- Dimensional analysis and its applications.

- Motion: Frame of reference (inertial and non-inertial); Motion in a straight line; Position-time graph, velocity, and speed.

- Uniform and non-uniform motion; velocity-time and position-time graphs for uniformly accelerated motion; differentiation and integration in motion description.

- Scalars and Vectors: Position and displacement vectors; vector addition and subtraction; Unit vectors; Zero vectors.

- Vector operations: Scalar and vector products, relative velocity.

- Motion in a plane; Projectile motion; Uniform circular motion.

MODULE 2

- Force and inertia, Newton’s laws of motion; Impulse; Law of conservation of momentum.

- Free body diagrams; Problems on static and kinetic friction, rolling friction.

- Dynamics of circular motion; Centripetal force; Examples like vehicle motion on circular and banked roads.

- Work-energy: Work done by constant and variable forces; Kinetic and potential energies; Work-energy theorem; Power.

- Conservation of mechanical energy; Elastic and inelastic collisions in one and two dimensions.

- Centre of mass: Two-particle systems, rigid bodies, and momentum conservation.

- Rotational motion: Moment of inertia, torque, angular momentum; Conservation of angular momentum.

- Equilibrium of rigid bodies; Equations of rotational motion.

MODULE 3

- Kepler’s laws of planetary motion; Universal law of gravitation.

- Acceleration due to gravity and its variations; Gravitational potential energy, escape speed.

- Orbital velocity, time period, and mechanical energy of satellites; Geostationary satellites.

- Elasticity: Stress-strain relationship, Hooke’s law, Young's modulus, Bulk modulus, Poisson's ratio.

- Fluid mechanics: Pressure due to fluid columns, Pascal’s law, applications (hydraulic lift, brakes), Viscosity, Reynolds number, Streamline and turbulent flow.

- Surface tension and cohesive/adhesive forces; Capillarity, Bernoulli’s theorem.

MODULE 4

- Heat and temperature: Thermal expansion, specific heat capacity, calorimetry, latent heat.

- Heat transfer: Conduction, convection, and radiation; Blackbody radiation, Kirchhoff’s law, Stefan-Boltzmann law.

- Laws of thermodynamics: First and second laws, thermodynamic processes, heat engines, Carnot engine efficiency.

- Ideal gas laws; Kinetic theory of gases; Mean free path; Avogadro’s number.

MODULE 5

- Periodic motion: Period, frequency, displacement, simple harmonic motion (SHM), and energy in SHM.

- Free, forced, and damped oscillations; Resonance.

- Wave motion: Longitudinal and transverse waves, principle of superposition, standing waves, beats, Doppler effect.

MODULE 6

- Electrostatics: Conservation of charge, Coulomb’s law, Electric field, Electric dipole, Potential energy.

- Electric flux; Gauss’s law applications.

- Capacitors and capacitance: Series and parallel combinations; Van de Graaff generator.

MODULE 7

- Electric current: Drift velocity, Ohm’s law, Resistance, Electrical energy and power, Combination of resistors.

- Kirchhoff’s laws, Wheatstone Bridge, Potentiometer.

- Magnetic fields: Biot-Savart’s law, Ampere’s law, Forces on current-carrying conductors, Galvanometer.

MODULE 8

- Magnetic dipole: Current loops, Earth’s magnetic field, magnetic substances (paramagnetic, diamagnetic, ferromagnetic).

- Electromagnetic induction: Faraday’s law, Lenz’s law, Eddy currents, Self and mutual inductance.

- Alternating current: Reactance, impedance, power factor, AC generator, transformer.

MODULE 9

- Reflection and refraction of light; Mirrors, lenses, prism, and optical instruments (microscopes, telescopes).

- Wave optics: Interference, diffraction, polarization.

MODULE 10

- Photoelectric effect, de Broglie waves, Rutherford and Bohr models.

- Nuclear physics: Radioactivity, fission, fusion, binding energy.

- Semiconductors: Diodes, transistors, and logic gates.

- Electromagnetic waves: Propagation, modulation, and communication systems.

Module

Topics

Module 1

Sets: Definitions and representations, including empty, finite, infinite, and equal sets. Subsets of real numbers (focus on intervals). Power set, universal set, and Venn diagrams. Set operations such as union, intersection, difference, and complement.

Relations & Functions: Ordered pairs, Cartesian products, and their applications. Different types of relations, functions as special relations, domain, co-domain, and range. Real-valued functions and their graphs.

Module 2

Sequences & Series: Arithmetic and geometric progressions (A.P. & G.P.), arithmetic mean (A.M.), and geometric mean (G.M.). Relations between A.M. and G.M., and sum of special series Σn, Σn², Σn³.

Complex Numbers: Representation of complex numbers (a + ib), polar form, conjugates, and operations. Argand diagrams and triangle inequality.

Quadratic Equations: Roots (rational, irrational, complex), relation between roots and coefficients, and formation of equations.

Permutations & Combinations: Permutations as arrangements, combinations as selections, and related problems.

Module 3

Binomial Theorem: Expansion for positive indices, general and middle terms, greatest term, and simple applications.

Matrices & Determinants: Algebra of matrices (order ≤ 3), types, properties, determinants, adjoint, inverse, and Cramer's rule for solving linear equations.

Module 4

Trigonometry: Ratios of associated angles, compound/multiple angles, inverse circular functions, and trigonometric equations.

Properties of Triangles: Sine, cosine, and tangent rules, semi-angle formulas, area, and circumradius of triangles.

Module 5

Straight Lines: Cartesian coordinates, slope, equations of lines, angle between lines, distance from a point, and equations of bisectors.

Conic Sections: Equations of circles, parabolas, ellipses, and hyperbolas, with tangents and other properties.

Module 6

Vectors: Concepts of vectors, vector operations (addition, scalar, and vector products), and their geometric interpretations.

3D Geometry: Direction cosines, projections, equations of lines and planes, angles between lines and planes, and distances.

Module 7

Continuity & Differentiability: Limits, continuity, derivatives of composite and inverse functions, exponential and logarithmic functions, second-order derivatives, Rolle’s Theorem, and Lagrange’s Theorem.

Module 8

Integral Calculus: Integration as the reverse of differentiation, techniques like substitution, partial fractions, and integration by parts. Definite integrals and their properties, as well as the fundamental theorem of calculus.

Differential Equations: Definitions, orders, degrees, and methods for solving different types of first-order differential equations.

Module 9

Applications of Derivatives: Rate of change, tangent and normal lines, maxima and minima, and simple applications.

Applications of Integrals: Finding areas under curves.

Module 10

Probability: Basic concepts, conditional probability, Bayes’ theorem, random variables, Bernoulli trials, and binomial distributions.

Statistics: Measures of dispersion (mean deviation, variance, standard deviation).

Mathematical Reasoning: Logical reasoning, statements, connecting words, truth tables, and validating statements.

Linear Inequalities: Solutions of linear inequalities (algebraic and graphical methods).

Linear Programming: Mathematical formulation, graphical solutions, and optimal feasible solutions.

Module

Topics

MODULE 1: Some Basic Concepts of Chemistry

General Introduction: Importance and scope of Chemistry; Historical approach to particulate nature of matter; Laws of chemical combination; Dalton’s atomic theory; Concept of elements, atoms, and molecules; Atomic and molecular masses; Mole concept and molar mass; Percentage composition; Empirical and molecular formula; Chemical reactions; Stoichiometry and calculations based on stoichiometry.

Structure of Atom: Discovery of electron, proton, and neutron; Atomic number; Isotopes and isobars; Rutherford’s model and its limitations; Bohr’s model and its limitations; Concept of shells and sub-shells; Dual nature of matter and light; de Broglie’s relationship; Heisenberg uncertainty principle; Concept of orbitals; Quantum numbers; Shapes of s, p, and d orbitals; Rules for filling electrons in orbitals - Aufbau principle, Pauli exclusion principle, and Hund’s rule; Electronic configuration of atoms; Stability of half-filled and filled orbitals.

Classification of Elements and Periodicity in Properties: Significance of classification; Brief history of the periodic table; Modern periodic law; Present form of periodic table; Periodic trends in properties - atomic radii, ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity, valence; Nomenclature of elements with atomic number > 100.

MODULE 2: Chemical Bonding and Molecular Structure

Valence Electrons and Chemical Bonds: Valence electrons; Ionic bond; Covalent bond; Born Haber Cycle; Lewis structure; Polar character of covalent bond; Valence bond theory; Resonance; Geometry of covalent molecules; VSEPR theory; Concept of hybridization; Shapes of simple molecules; Molecular orbital theory of homonuclear diatomic molecules; Hydrogen bond.

Chemical Thermodynamics: Concepts of system; Types of systems; Surroundings; Work; Heat; Energy; Extensive and intensive properties; State functions; First law of thermodynamics; Hess’s law; Enthalpy of various processes; Introduction of entropy; Gibbs energy change for spontaneous processes; Second and third laws of thermodynamics.

Chemical Kinetics: Rate of reaction; Factors affecting rates; Order and molecularity; Rate law; Integrated rate equations; Concept of collision theory; Activation energy; Arrhenius equation.

MODULE 3: States of Matter: Gases and Liquids

Three states of matter; Intermolecular interactions; Gas laws: Boyle’s, Charles’, Gay Lussac’s, Avogadro’s law; Ideal behaviour; Ideal gas equation; Liquefaction of gases; Kinetic energy; Molecular speeds; Liquid state: Vapour pressure, viscosity, surface tension (qualitative only).

Equilibrium: Equilibrium in physical and chemical processes; Dynamic nature; Law of mass action; Equilibrium constant; Factors affecting equilibrium - Le Chatelier’s principle; Ionic equilibrium; pH concepts; Buffer solutions; Solubility product; Common ion effect.

Solid State: Classification of solids; Unit cell in 2D and 3D lattices; Packing efficiency; Density calculations; Point defects; Electrical and magnetic properties; Band theory of metals, conductors, semiconductors, and insulators.

MODULE 4: Redox Reactions

Concept of oxidation and reduction; Redox reactions; Oxidation number; Balancing redox reactions.

Solutions: Types of solutions; Expression of concentration; Colligative properties; Raoult’s law; Osmotic pressure; Molecular mass determinations.

Electrochemistry: Redox reactions; Conductance; Kohlrausch’s Law; Electrolysis; Galvanic cells; Standard electrode potential; Nernst equation; Gibbs energy and EMF relationship.

Surface Chemistry: Adsorption; Catalysis; Colloidal state; Properties of colloids; Tyndall effect; Brownian movement; Coagulation; Emulsions; Nanomaterials.

MODULE 5: Hydrogen

Position of hydrogen in the periodic table; Occurrence; Isotopes; Properties and uses of hydrogen; Hydrides; Properties of water; Hydrogen peroxide.

p-Block Elements: General introduction; Group 13-17 elements; Properties and uses of boron, aluminium, carbon, nitrogen, phosphorus, oxygen, sulfur, and halogens.

MODULE 6: s-Block Elements (Alkali and Alkaline Earth Metals)

Group 1 and 2 elements: General introduction, properties, and uses; Important compounds.

General Principles and Processes of Isolation of Elements: Principles and methods of extraction; Occurrence and extraction of aluminium, copper, zinc, and iron.

d and f Block Elements: Introduction; Properties and characteristics; Transition metals; Lanthanoids and actinoids.

MODULE 7: Coordination Compounds

Introduction; Ligands; Coordination number; Color; Magnetic properties; IUPAC nomenclature; Isomerism; Importance of coordination compounds.

MODULE 8: Organic Chemistry

Some Basic Principles and Techniques: Introduction to qualitative and quantitative analysis; Classification and nomenclature of organic compounds; Electronic displacements; Types of organic reactions.

Hydrocarbons: Classification; Properties and reactions of alkanes, alkenes, alkynes, and aromatic hydrocarbons.

Haloalkanes and Haloarenes: Nomenclature; Properties and reactions; Environmental effects of halogen compounds.

MODULE 9: Alcohols, Phenols, and Ethers

Nomenclature; Methods of preparation; Properties and uses of alcohols, phenols, and ethers.

Aldehydes, Ketones, and Carboxylic Acids: Nomenclature; Properties; Uses.

MODULE 10: Environmental Chemistry

Environmental pollution; Chemical reactions in the atmosphere; Green chemistry; Pollution control strategies.

Organic Compounds Containing Nitrogen: Nitro compounds; Amines; Cyanides; Diazonium salts.

Polymers: Classification; Methods of polymerization; Important natural and synthetic polymers.

Biomolecules: Carbohydrates, proteins, lipids, vitamins, nucleic acids.

Chemistry in Everyday Life: Chemicals in medicines, food, and cleansing agents.