[PDF] JEE Main & Advanced Exams Syllabus Free Download

• Sets and their representation
• Union, intersection and complement of sets and their algebraic properties
• Power set; Relation, Types of relations, equivalence relations, functions; One-one, into and onto functions, the composition of functions.

• 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,
• square root of a complex number,
• triangle inequality,
• Quadratic equations in real and complex number system and their solutions.
• Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

• Matrices,
• algebra of matrices,
• types of matrices,
• determinants and
• matrices of order two and three.
• Properties of determinants,
• evaluation of determinants,
• area of triangles using determinants.
• Ad joint and evaluation of inverse of a square matrix using determinants and elementary transformations,
• Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

Permutations and combinations

• Fundamental principle of counting,
• permutation as an arrangement and
• combination as selection,
• Meaning of P (n,r) and C (n,r),
• simple applications.

• Principle of Mathematical Induction and its simple applications

• Binomial theorem for a positive integral index,
• general term and middle term,
• properties of Binomial coefficients
• simple applications

• Arithmetic and Geometric progressions,
• insertion of arithmetic,
• geometric means between two given numbers
• relation between A.M. and G.M. sum upto n terms of special series: S n, S n2, Sn3
• Arithmetic – Geometric progression

• Real – valued functions,
• algebra of functions,
• polynomials,
• rational,
• trigonometric,
• logarithmic and exponential functions,
• inverse functions
• Graphs of simple functions
• Limits, continuity and differentiability
• Differentiation of the sum, difference, product and quotient of two functions
• Differentiation of trigonometric,
• inverse trigonometric,
• logarithmic,
• exponential,
• composite and implicit functions
• derivatives of order upto two
• Rolle’s and Lagrange’s Mean Value Theorems
• Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions,
• Maxima and minima of functions of one variable,
• tangents and normals

• Integral as an anti – derivative.
• Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.
• Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.

• Evaluation of simple integrals of the type Integral as limit of a sum.
• Fundamental Theorem of Calculus.
• Properties of definite integrals.
• Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

• Ordinary differential equations, their order and degree.
• Formation of differential equations.
• Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy/dx+p(x)y=q(x)

• Cartesian system of rectangular co-ordinates 10 in a plane,
• distance formula,
• section formula,
• locus and its equation,
• translation of axes,
• slope of a line,
• parallel and perpendicular lines,
• intercepts of a line on the coordinate axes.

• Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines.
• Skew lines, the shortest distance between them and its equation.
• Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

• Vectors and scalars,
• addition of vectors,
• components of a vector in two dimensions and three dimensional space,
• scalar and vector products, scalar and vector triple product.

Probability: Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

• Trigonometrical identities and equations
• Trigonometrical functions
• Inverse trigonometrical functions and their properties
• Heights and Distances

• Statements, logical operations and, or, implies, implied by, if and only if
• Understanding of tautology, contradiction, converse and contrapositive

• Physics, technology and society, S I units, Fundamental and derived units
• Least count, accuracy and precision of measuring instruments,
• Errors in measurement,
• Dimensions of Physical quantities, dimensional analysis and its applications

• 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, relations for uniformly accelerated motion.
• Scalars and Vectors, Vector addition and Subtraction, Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector
• Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion

• Force and Inertia,
• Newton’s First Law of motion; Momentum, Newton’s Second Law of motion; Impulse; Newton’s Third Law of motion.
• Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces.

• Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration.
• Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications.
• Rigid body rotation, equations of rotational motion.

• The universal law of gravitation.
• Acceleration due to gravity and its variation with altitude and depth.
• Kepler’s laws of planetary motion.
• Gravitational potential energy; gravitational potential.
• Escape velocity.
• Orbital velocity of a satellite. Geo-stationary satellites.

• Elastic behaviour, Stress-strain relationship, Hooke’s Law, Young’s modulus, bulk modulus, modulus of rigidity.
• Pressure due to a fluid column; Pascal’s law and its applications.
• Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, Reynolds number. Bernoulli’s principle and its applications.
• Surface energy and surface tension, angle of contact, application of surface tension – drops, bubbles and capillary rise.
• Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat.
• Heat transfer-conduction, convection and radiation, Newton’s law of cooling.

• Thermal equilibrium, zeroth law of thermodynamics, concept of temperature.
• Heat, work and internal energy.
• First law of thermodynamics.
• Second law of thermodynamics: reversible and irreversible processes.
• Carnot engine and its efficiency.

• Equation of state of a perfect gas, work done on compressing a gas.
• Kinetic theory of gases – assumptions, concept of pressure.
• Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of equipartition of energy, applications to specific heat capacities of gases; Mean free path, Avogadro’s number.

-Electric flux, Gauss’s law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field.

-Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor.

• Electric current, Drift velocity, Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance.
• Electric Cell and its Internal resistance, potential difference and emf of a cell, combination of cells in series and in parallel.
• Kirchhoff’s laws and their applications.
• Wheatstone bridge, Metre bridge.
• Potentiometer – principle and its applications.

• Biot – Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields. Cyclotron.
• Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter.
• Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances.
• Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.

• Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents.
• Self and mutual inductance.
• Alternating currents, peak and rms value of alternating current/ voltage; reactance and impedance; LCR series circuit, resonance; Quality factor, power in AC circuits, wattless current.
• AC generator and transformer.

• Electromagnetic waves and their characteristics. Transverse nature of electromagnetic waves.
• Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, Xrays, gamma rays).
• Applications of e.m. waves.

Wave optics

• wavefront and Huygens’ principle, Laws of reflection and refraction using Huygen’s principle. Interference, Young’s double slit experiment and expression for fringe width.
• Diffraction due to a single slit, width of central maximum.
• Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light; Brewster’s law, uses of plane polarized light and Polaroids.

• Dual nature of radiation.
• Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation; particle nature of light.
• Matter waves-wave nature of particle, de Broglie relation.
• Davisson-Germer experiment.

• Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum.
• Composition and size of nucleus, atomic masses, isotopes, isobars; isotones.
• Radioactivity-alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

• Semiconductors; semiconductor diode: I-V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED, photodiode, solar cell and Zener diode; Zener diode as a voltage regulator.
• Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR).
• Transistor as a switch.

• Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation,
• Need for modulation,
• Amplitude and Frequency Modulation,
• Bandwidth of signals,
• Bandwidth of Transmission medium,
• Basic Elements of a Communication System (Block Diagram only).

• 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

• Gaseous State: Measurable properties of gases
• Gas laws – Boyle’s law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure
• Concept of Absolute scale of temperature; Ideal gas equation
• Kinetic theory of gases (only postulates)
• Concept of average, root mean square and most probable velocities
• Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals equation

• Solid State: Classification of solids: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea)
• Bragg’s Law and its applications
• Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, imperfection in solids
• Electrical, magnetic and dielectric properties

• Thomson and Rutherford atomic models and their limitations
• Nature of electromagnetic radiation, photoelectric effect
• Spectrum of hydrogen atom, Bohr model of hydrogen atom – its postulates, derivation of the relations for energy of the electron and radii of the 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 atom, its important features, concept of atomic orbitals as one electron wave functions
• various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance
• shapes of s, p and d – orbitals, electron spin and spin quantum number
• Rules for filling electrons in orbitals – aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals.

• Covalent Bonding: Concept of electronegativity, Fajan’s rule, dipole moment
• Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple molecules
• Quantum mechanical approach to covalent bonding: Valence bond theory – Its important features, concept of hybridization involving s, p and d orbitals
• ResonanceMolecular Orbital Theory – Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, concept of bond order, bond length and bond energy.

• First law of thermodynamics – Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity
• Hess’s law of constant heat summation
• Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution
• Second law of thermodynamics
• Spontaneity of processes
• DS of the universe and DG of the system as criteria for spontaneity, Dgo (Standard Gibbs energy change) and equilibrium constant

• Different methods for expressing concentration of solution – molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoult’s Law – Ideal and non-ideal solutions, vapour pressure – composition, plots for ideal and non-ideal solutions
• Colligative properties of dilute solutions – relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure
• Determination of molecular mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor and its significance

• Equilibria involving physical processes: Solid -liquid, liquid – gas and solid – gas equilibria, Henry’s law, general characterics of equilibrium involving physical processes.
• Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of DG and DGo in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle.

• Electrochemical cells – Electrolytic and Galvanic cells, different types of electrodes, electrode potentials including standard electrode potential, half – cell and cell reactions, emf of a Galvanic cell and its measurement
• Nernst equation and its applications; Relationship between cell potential and Gibbs’ energy change
• Dry cell and lead accumulator; Fuel cells.

• Rate of a chemical reaction, factors affecting the rate of reactions: concentration, temperature, pressure and catalyst
• elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its units, differential and integral forms ofzero and first-order reactions, their characteristics and half-lives, effect of temperature on rate of reactions – Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

• Colloidal state- distinction among true solutions, colloids and suspensions, classification of colloids – lyophilic, lyophobic
• multi molecular, macromolecular and associated colloids (micelles), preparation and properties of colloids – Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation and flocculation
• Emulsions and their characteristics

• Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen
• Physical and chemical properties of water and heavy water
• Structure, preparation, reactions and uses of hydrogen peroxide
• Hydrogen as a fuel

General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group.

• Group – 13: Preparation, properties and uses of boron and aluminium; properties of boric acid, diborane, boron trifluoride, aluminium chloride and alums.
• Group – 14: Allotropes of carbon, tendency for catenation; Structure & properties of silicates, and zeolites.
• Group – 15: Properties and uses of nitrogen and phosphorus; Allotrophic forms of phosphorus; Preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of phosphorus.
• Group – 16: Preparation, properties, structures and uses of ozone; Allotropic forms of sulphur; Preparation, properties, structures and uses of sulphuric acid (including its industrial preparation); Structures of oxoacids of sulphur.
• Group – 17: Preparation, properties and uses of hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxoacids of halogens.
• Group –18: Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon.

• Introduction to co-ordination compounds, Werner’s theory
• ligands, co-ordination number, denticity, chelation; IUPAC nomenclature of mononuclear co-ordination compounds, isomerism
• Bonding-Valence bond approach and basic ideas of Crystal field theory, colour and magnetic properties; Importance of co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems).

• Environmental pollution – Atmospheric, water and soil.
• Atmospheric pollution – Tropospheric and Stratospheric
• Tropospheric pollutants – Gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention; Greenhouse effect and Global warming; Acid rain;
• Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention.
• Stratospheric pollution- Formation and breakdown of ozone, depletion of ozone layer – its mechanism and effects.
• Water Pollution – Major pollutants such as, pathogens, organic wastes and chemical pollutants; their harmful effects and prevention.
• Soil pollution – Major pollutants such as: Pesticides (insecticides,. herbicides and fungicides), their harmful effects and prevention. Strategies to control environmental pollution.

• Alcohols: Identification of primary, secondary and tertiary alcohols; mechanism of dehydration.
• Phenols: Acidic nature, electrophilic substitution reactions: halogenation, nitration and sulphonation, Reimer – Tiemann reaction.
• Ethers: Structure.
• Aldehyde and Ketones: Nature of carbonyl group
• Nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones
• Important reactions such as – Nucleophilic addition reactions (addition of HCN, NH3 and its derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen); acidity of r – hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction; Chemical tests to distinguish between aldehydes and Ketones.

• General methods of preparation, properties, reactions and uses.
• Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character.
• Diazonium Salts: Importance in synthetic organic chemistry.

• General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization
• Natural and synthetic rubber and vulcanization
• some important polymers with emphasis on their monomers and uses – polythene, nylon, polyester and bakelite.

• General introduction and importance of biomolecules.
• Carbohydrates – Classification: aldoses and ketoses; monosaccharides (glucose and fructose) and constituent monosaccharides of oligosacchorides (sucrose, lactose and maltose).
• Proteins – Elementary Idea of r – amino acids, peptide bond, polypeptides; Proteins: primary, secondary, tertiary and quaternary structure (qualitative idea only), denaturation of proteins, enzymes.
• Vitamins – Classification and functions.
• Nucleic Acids – Chemical constitution of DNA and RNA. Biological functions of nucleic acids.

• Chemistry involved in the preparation of the following: Inorganic compounds: Mohr’s salt, potash alum.
• Organic compounds: Acetanilide, pnitroacetanilide, aniline yellow, iodoform.