Syllabus for Module 1 JEE Main & Advanced

Physics

Module 1
Descriptions
1A. Physics and Measurement: Units of measurements, System of Units, SI Units, Fundamental and Derived Units, Least Count, Significant Figures, Errors in measurements, Dimensions of Physical quantities, dimensional analysis and its applications.
1B. Scalars and Vectors: Scalars and Vectors, Vector Addition and Subtraction, Scalar and Vector Products, Unit Vector, Resolution of a Vector.
2. Kinematics: The Frame of Reference, Motion in a Straight Line, Position-Time Graph, Speed and Velocity, Uniform and Non-Uniform Motion, Average Speed and Instantaneous Velocity, Uniformly Accelerated Motion, Velocity-Time, Position-Time Graphs, Equations for Uniformly Accelerated Motion, Relative Velocity.
3. Motion in a Plane: Projectile Motion.
4. Laws of Motion:

Force and Inertia, Newton’s First Law of Motion; Momentum, Newton’s Second Law of Motion, Impulses; Newton’s Third Law of Motion. Law of Conservation of Linear Momentum and its applications. Equilibrium of Concurrent Forces.

Static and Kinetic Friction, Laws of Friction, Rolling Friction.
5. Motion in a Plane: Uniform Circular Motion. Dynamics of Uniform Circular Motion: Centripetal Force and its applications — vehicle on a level circular road, vehicle on a banked road.
6. Work, Energy and Power:

Work done by a constant force and a variable force; Kinetic and Potential Energies, Work-Energy Theorem, Power.

Potential energy of a spring, Conservation of Mechanical Energy, Conservative and Non-conservative Forces; Motion in a Vertical Circle; Elastic and Inelastic Collisions in One and Two Dimensions.


Chemistry

Module 1
1. Some Basic Concepts of Chemistry: Matter and its nature, Dalton's atomic theory, Concept of atom, molecule, element, and compound. Physical quantities and their measurements in Chemistry, precision and accuracy, significant figures, S.I. Units, dimensional analysis. Laws of chemical combination; Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; Chemical equations and stoichiometry.
2. Structure of Atom: Thomson and Rutherford atomic models and their limitations; Nature of electromagnetic radiation, photoelectric effect; Spectrum of the hydrogen atom. Bohr model of hydrogen atom - its postulates, derivation of energy and radii of different orbits, limitations of Bohr's model. Dual nature of matter, de Broglie's relationship, Heisenberg uncertainty principle. Elementary ideas of quantum mechanics; quantum mechanical model of the atom and its important features. Atomic orbitals as one-electron wave functions; variation of Ψ and Ψ² with r for 1s and 2s orbitals; quantum numbers and their significance. Shapes of s, p, and d orbitals, electron spin and spin quantum number. Aufbau principle, Pauli's exclusion principle, Hund's rule, electronic configuration, and stability of half-filled and fully filled orbitals.
3. Classification of Elements and Periodicity in Properties: Modern periodic law and present form of the periodic table, s, p, d, and f block elements, periodic trends in atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valency, oxidation states, and chemical reactivity.
4. Chemical Bonding and Molecular Structure: Kossel-Lewis approach to chemical bonding; ionic and covalent bonds. Ionic Bonding: Formation and factors; lattice enthalpy. Covalent Bonding: Electronegativity, Fajan’s rule, dipole moment, VSEPR theory, shapes of molecules. Quantum mechanical approach – Valence bond theory, hybridization, resonance.

Molecular Orbital Theory: Features of MOT, LCAO, bonding and antibonding orbitals, sigma and pi bonds, MO configurations of homonuclear diatomic molecules, bond order, bond length and bond energy. Metallic bonding (elementary idea), hydrogen bonding and its applications.
5. States of Matter: Gases and Liquids: Gaseous State: Properties of gases, Gas laws (Boyle’s, Charles’s, Graham’s law, Avogadro’s, Dalton’s law), Ideal gas equation, kinetic theory (postulates), velocities, real gases, compressibility factor, van der Waals equation.

Liquid State: Vapour pressure, viscosity, surface tension and their temperature dependence (qualitative).
6. Chemical Thermodynamics: Fundamentals: System and surroundings, extensive and intensive properties, state functions, process types.

First Law of Thermodynamics: Work, heat, internal energy, enthalpy, heat capacity, Hess’s law, enthalpies of various processes (combustion, formation, atomization, etc.).

Second Law of Thermodynamics: Spontaneity, ΔS (entropy) of universe, ΔG (Gibbs free energy) of system, standard Gibbs energy (ΔG°) and equilibrium constant.

 

Mathematics

Module 1
Descriptions
1A. Basic Mathematics:

1B. Trigonometric Function: Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of a unit circle. Truth of the identity sin²x + cos²x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin(x ± y) and cos(x ± y) in terms of sinx, siny, cosx & cosy.

Trigonometric Diagram

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x, and tanx.
2. Sets: Sets and their representation: Union, intersection and complement of sets and their algebraic properties; Power set.
3. Relations and Functions: Relation, types of relations, equivalence relations, functions; one-one, into and onto functions, composition of functions.
4. Trigonometry:

Trigonometrical identities and equations, trigonometrical functions, inverse trigonometric functions, and their properties.
5. Mathematical Induction: Principle of Mathematical Induction and its simple applications.
6. Complex Numbers: Complex numbers as ordered pairs of reals, representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number.
7. Quadratic Equations: Quadratic equations in real and complex number system and their solutions. Relations between roots and coefficients, nature of roots, formation of quadratic equations with given roots.
8. Linear Inequalities: Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical solution of system of linear inequalities in two variables.