JEE Main and Advanced Complete Syllabus 2020

NTA conducts JEE Main in two sessions i.e. January and April. The national level examination will be conducted through online (computer-based) mode only. Aspirants can opt for one or all the 3 the paper of JEE Mains. The duration of the exam is 3 hours. A compensatory time of 1 hour is given to candidates with a 40% disability. If you wish to take both B. Arch and B. Planning, then the examination duration will be of 3 hours 30 minutes

## JEE Main Physics Syllabus

#### Section A :

Unit 1: Physics and Measurement |

Physics, technology and society, SI 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. |

Unit 2: Kinematics |

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. |

Unit 3: Laws of 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.Static and Kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion: Centripetal force and its applications. |

Unit 4: 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; Elastic and inelastic collisions in one and two dimensions. |

Unit 5: Rotational Motion |

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. |

Unit 6: Gravitation |

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. |

Unit 7: Properties of Solids and Liquids |

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. |

Unit 8: Thermodynamics |

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. |

Unit 9: Kinetic Theory of Gases |

Equation of state of a perfect gas, work done on compressing a gas. Kinetic theory of gases-assumptions, the 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. |

Unit 10: Oscillations and Waves |

Periodic motion – period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase; oscillations of a spring -restoring force and force constant; energy in S.H.M. – Kinetic and potential energies; Simple pendulum – derivation of expression for its time period; Free, forced and damped oscillations, resonance.Wave motion. Longitudinal and transverse waves, speed of a wave. Displacement relation for a progressive wave. Principle of superposition of waves, the reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect in sound |

Unit 11: Electrostatics |

Electric charges: Conservation of charge, Coulomb’s law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution.Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field.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, a combination of capacitors in series and in parallel, the capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor. |

Unit 12: Current Electricity |

Electric current, Drift velocity, Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and non-ohmic 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, a combination of cells in series and in parallel. Kirchhoffs laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer – principle and its applications. |

Unit 13: Magnetic Effects of Current and Magnetism |

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. The force between two parallel current-carrying conductors-definition of ampere, Torque experienced by a current loop in a 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. |

Unit 14: Electromagnetic Induction and Alternating Currents |

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, wattles current. AC generator and transformer. |

Unit 15: Electromagnetic Waves |

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

Unit 16: Optics |

Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifying powers.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, coherent sources and sustained interference of light. 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. |

Unit 17: Dual Nature of Matter and Radiation |

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. Davis son-Germer experiment. |

Unit 18: Atoms and Nuclei |

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. |

Unit 19: Electronic Devices |

Semiconductors; semiconductor diode: I-V characteristics in forward and reverse bias; diode as a rectifier; 1-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. |

Unit 20: Communication Systems |

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). |

For questions from experimental skills, the syllabus are:

#### Section B(20% weightage):

- Vernier callipers: its use to measure the internal and external diameter and depth of a vessel.
- Screw gauge: its use to determine thickness/diameter of thin sheet/wire.
- Simple Pendulum: dissipation of energy by plotting a graph between square of amplitude and time.
- Metre Scale: the mass of a given object by the principle of moments.
- Young’s modulus of elasticity of the material of a metallic wire.
- The surface tension of water by capillary rise and effect of detergents.
- The coefficient of Viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body.
- Plotting a cooling curve for the relationship between the temperature of a hot body and time.
- The speed of sound in air at room temperature using a resonance tube.
- The specific heat capacity of a given: Solid, and liquid by method of mixtures.
- The resistivity of the material of a given wire using meter bridge.
- The resistance of a given wire using Ohm’s law.
- Potentiometer: Comparison of emf of two primary cells and Determination of the internal resistance of a cell.
- Resistance and figure of merit of a galvanometer by half deflection method.
- The focal length of a Convex mirror, Concave mirror, and Convex lens using the parallax method.
- The plot of the angle of deviation vs angle of incidence for a triangular prism.
- Refractive index of a glass slab using a travelling microscope.
- Characteristic curves of a p-n junction diode in forward and reverse bias.
- Characteristic curves of a Zener diode and finding reverse breakdown voltage.
- Characteristic curves of a transistor and finding current gain and voltage gain.
- Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such items.
- Using the multimeter to: Identify base of a transistor, Distinguish between NPN and PNP type transistor, See the unidirectional flow of current in case of a diode and an LED. Check the correctness or otherwise of a given electronic component (diode, transistor or IC).

### JEE Main Chemistry Syllabus :

#### 1.Physical Chemistry

Unit 1 Some Basic Concepts of Chemistry |

Matter and its nature, Dalton’s the atomic theory, the concept of the 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. |

Unit 2 States of Matter |

Classification of matter into solid, liquid and gaseous states.Gaseous State: Measurable properties of gases; Gas laws – Boyle’s law, Charles’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial pressure.The concept of the Absolute scale of temperature; Ideal gas equation, Kinetic theory of gases (only postulates).The concept of average, root mean square and most probable velocities.Real gases, deviation from Ideal behaviour, compressibility factor, van der Waals equation, liquefaction of gases, critical constants.Liquid State: Properties of liquids – vapour pressure, viscosity and surface tension and effect of temperature on them (qualitative treatment only).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. |

Unit 3 Atomic Structure |

Discovery of subatomic particles (electron, proton, and neutron).Thomson and Rutherford atomic models and their limitations.Nature of electromagnetic radiation, photoelectric effect.The 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 relationship, Heisenberg uncertainty principle.Elementary ideas of quantum mechanics, the quantum mechanical model of an atom, its important features, the concept of atomic orbitals as one electron wave functions.Variation of Ψ1 and Ψ2 with r for 1s and 2s orbitals; 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 exclusion principle and Hund’s rule, electronic configuration of elements, the extra stability of half-filled and completely filled orbitals. |

Unit 4 Chemical Bonding and Molecular Structure |

Kossel – Lewis approach to chemical bond formation, the concept of ionic and covalent bonds.Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy.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, the concept of hybridization involving s, p, and d orbitals; Resonance.Molecular Orbital Theory: Its important features, LCAOs, types of molecular orbitals (bonding, antibonding), sigma and pi-bonds, molecular orbital electronic configurations of homonuclear diatomic molecules, the concept of bond order, bond length and bond energy. Elementary idea of metallic bonding, Hydrogen bonding, and its applications. |

Unit 5 Chemical Thermodynamics |

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes.First law of thermodynamics: Concept of work, heat internal energy, and enthalpy, heat capacity, molar heat capacityHess’s law of constant heat summation.Enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization, and solution.The second law of thermodynamics: Spontaneity of processes; Delta S of the universe and Delta G of the system as criteria for spontaneity, Delta Go (Standard Gibbs energy change) and equilibrium constant. |

Unit 6 Solutions |

Different methods for expressing the concentration of a solution: molality, molarity, mole fraction, percentage (by volume and mass both), the 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, Hoff factor, and its significance. |

Unit 7 Equilibrium |

Meaning of equilibrium, the concept of dynamic equilibrium.Equilibria involving physical processes: Solid – liquid, liquid – gas and solid – gas equilibria, Henry’s law, a general characteristic of equilibrium involving physical processes.Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, the significance of Delta G and Delta Go in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, the effect of the catalyst.Le Chatelier’s principle.Ionic equilibrium: Weak and strong electrolytes, ionization of electrolytes, various concepts of acids and bases (Arrhenius, Bronsted-Lowry and Lewis) and their ionization, acid-base equilibria (including multistage ionization) and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions. |

Unit 8 Redox Reactions and Electrochemistry |

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration.Kohlrausch’s law and its applications.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.Corrosion and its prevention. |

Unit 9 Chemical Kinetics |

The 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 of zero and first order reactions, their characteristics and half-lives, the effect of temperature on the rate of reactions.Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation). |

Unit 10 Surface Chemistry |

Adsorption: Physisorption and chemisorption and their characteristics, factors affecting the adsorption of gases on solids: Freundlich and Langmuir adsorption isotherms, adsorption from solutions.Catalysis: Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis, and its mechanism.Colloidal state: Distinction among true solutions, colloids, and suspensions, classification of colloids: lyophilic, lyophobic.Multimolecular, macromolecular and associated colloids (micelles), preparation and properties of colloids: Tyndall effect, Brownian movement, electrophoresis, dialysis, coagulation, and flocculation.Emulsions and their characteristics. |

The detailed list of all the concepts covered in JEE Main Chemistry Syllabus for Inorganic Chemistry is described below.

#### 2.Inorganic Chemistry

Unit 11 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 properties of elements atomic and ionic radii, ionization enthalpy.Electron gain enthalpy, valence, oxidation states and chemical reactivity. |

Unit 12 General Principles and Process of Isolation of Metals |

Modes of occurrence of elements in nature, minerals, ores.Steps involved in the extraction of metals: concentration, reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn, and Fe.Thermodynamic and electrochemical principles involved in the extraction of metals. |

Unit 13 Hydrogen |

The 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.Classification of hydrides: ionic, covalent and interstitial.Hydrogen as a fuel. |

Unit 14 S Block Elements (Alkali and Alkaline Earth Metals) |

Group 1 and Group 2 Elements: General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships.Preparation and properties of some important compounds: sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate.Industrial uses of lime, limestone, Plaster of Paris and cement.The biological significance of Na, K, Mg and Ca. |

Unit 15 P Block Elements |

Group 13 to Group 18 Elements: 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. Groupwise study of the p block elements.Group 13: Preparation, properties, and uses of boron and aluminium; Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium chloride, and alums.Group 14: Tendency for catenation; Structure, properties, and uses of allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites, and silicones.Group 15: Properties and uses of nitrogen and phosphorus; Allotropic forms of phosphorus; Preparation, properties, structure, and uses of ammonia, nitric acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of nitrogen and phosphorus.Group 16: Preparation, properties, structures and uses of dioxygen and ozone; Allotropic forms of sulfur; Preparation, properties, structures, and uses of sulfur dioxide, sulphuric acid (including its industrial preparation); Structures of oxoacids of sulfur.Group 17: Preparation, properties, and uses of chlorine and hydrochloric acid; Trends in the acidic nature of hydrogen halides; Structures of Interhalogen compounds and oxides and oxyacids of halogens.Group 18: Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon. |

Unit 16 D and F Block Elements |

Transition Elements: General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first-row transition elements: physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation.Preparation, properties, and uses of K2Cr2O7 and KMnO4.Inner Transition Elements: Lanthanides, Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction, and Actinoids: Electronic configuration and oxidation states. |

Unit 17 Coordination Compounds |

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

Unit 18 Environmental Chemistry |

Environmental pollution: Atmospheric, water, and soil.Atmospheric pollution: Tropospheric and stratospheric.Gaseous pollutants: Oxides of carbon, nitrogen, and sulfur, 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. |

The detailed list of all the concepts covered in JEE Main Chemistry Syllabus for Organic Chemistry is described below.

#### 3.Organic Chemistry

Unit 19 Purification and Characterisation of Organic Compounds |

Purification: Crystallization, sublimation, distillation, differential extraction, and chromatography principles and their applications.Qualitative analysis: Detection of nitrogen, sulfur, phosphorus, and halogens.Quantitative analysis (basic principles only): Estimation of carbon, hydrogen, nitrogen, halogens, sulfur, phosphorus.Calculations of empirical formula and molecular formulae; Numerical problems in organic quantitative analysis. |

Unit 20 Some Basic Principles of Organic Chemistry |

Tetravalency of carbon; Shapes of simple molecules – hybridization (s and p).Classification of organic compounds based on functional groups: -C = C- and those containing halogens, oxygen, nitrogen, and sulfur; Homologous series.Isomerism: structural and stereoisomerism.Nomenclature (Trivial and IUPAC): Covalent bond fission Homolytic and heterolytic: free radicals, carbocations, and carbanions; stability of carbocations and free radicals, electrophiles and nucleophiles.Electronic displacement in a covalent bond: Inductive effect, electromeric effect, resonance, and hyperconjugation.Common types of organic reactions: Substitution, addition, elimination, and rearrangement. |

Unit 21 Hydrocarbons |

Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.Alkanes: Conformations; Sawhorse and Newman projections (of ethane); Mechanism of halogenation of alkanes.Alkenes: Geometrical isomerism.Mechanism of electrophilic addition: addition of hydrogen, halogens, water, hydrogen halides (Markownikoff’s and peroxide effect); Ozonolysis, oxidation, and polymerization.Alkynes: Acidic character; Addition of hydrogen, halogens, water and hydrogen halides; Polymerization.Aromatic hydrocarbons: Nomenclature, benzene structure and aromaticity.Mechanism of electrophilic substitution: halogenation, nitration, Friedel Crafts alkylation and acylation, directive influence of the functional group in monosubstituted benzene. |

Unit 22 Organic Compounds Containing Halogens |

General methods of preparation, properties, and reactions.Nature of C-X bond.Mechanisms of substitution reactions.Uses, Environmental effects of chloroform, iodoform, freons, and DDT. |

Unit 23 Organic Compounds Containing Oxygen |

General methods of preparation, properties, reactions, and uses.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); the acidity of hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction.Chemical tests to distinguish between aldehydes and Ketones.Carboxylic Acids: Acidic strength and factors affecting it. |

Unit 24 Organic Compounds Containing Nitrogen |

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. |

Unit 25 Polymers |

General introduction and classification of polymers, general methods of polymerization addition and condensation, co-polymerization.Natural and synthetic rubber and vulcanization.Some important polymers with emphasis on their monomers and uses, polyethene, nylon, polyester, and bakelite. |

Unit 26 Biomolecules |

General introduction and importance of biomolecules.Carbohydrates: Classification: aldoses and ketoses; monosaccharides (glucose and fructose), constituent monosaccharides or oligosaccharides (sucrose, lactose, maltose) and polysaccharides (starch, cellulose, glycogen).Proteins: Elementary Idea of amino acids, peptide bond, polypeptides; Proteins: primary, secondary, tertiary and quaternary structure (qualitative idea only), denaturation of proteins, enzymes.Vitamins: Classification and functions.B Chemical constitution of DNA and RNA. Biological functions of nucleic acids. |

Unit 27 Chemistry in Everyday Life |

Chemicals in medicines: Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines their meaning and common examples.Chemicals in food: Preservatives, artificial sweetening agents common examples.Cleansing agents: Soaps and detergents, cleansing action. |

Unit 28 Principles Related to Practical Chemistry |

Detection of extra elements (N, S, halogens) in organic compounds.Detection of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl and amino groups in organic compounds.The chemistry involved in the preparation of the following: Inorganic compounds: Mohr’s salt, potash alum, and Organic compounds: Acetanilide, p-nitro acetanilide, aniline yellow, iodoform.The chemistry involved in the titrimetric exercises: Acids bases and the use of indicators, oxalic-acid vs KMnO4, Mohr’s salt vs KMnO4.Chemical principles involved in the qualitative salt analysis: Cations: Pb2+, Cu2+, AI3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+, and Anions: CO32-, S2-, SO42-, NO2-, NO3-, CI-, Br, I. (Insoluble salts excluded).Chemical principles involved in the following experiments: Enthalpy of solution of CuSO4, Enthalpy of neutralization of strong acid and strong base, Preparation of lyophilic and lyophobic sols, and Kinetic study of the reaction of iodide ion with hydrogen peroxide at room temperature. |

### JEE Main Maths Syllabus

Unit 1 Sets, Relations, and Functions |

Sets and their representation.Union, intersection, and complement of sets and their algebraic properties.Powerset.Relation, Types of relations, equivalence relations.Functions; one-one, into and onto functions, the composition of functions. |

Unit 2 Complex Numbers and Quadratic Equations |

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.The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots. |

Unit 3 Matrices and Determinants |

Matrices: Algebra of matrices, types of matrices, and matrices of order two and three.Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants.Adjoint 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. |

Unit 4 Permutations and Combinations |

The fundamental principle of counting.Permutation as an arrangement and combination as selection.The meaning of P (n,r) and C (n,r). Simple applications. |

Unit 5 Mathematical Induction |

The principle of Mathematical Induction and its simple applications. |

Unit 6 Binomial Theorem |

Binomial theorem for a positive integral index.General term and middle term.Properties of Binomial coefficients and simple applications. |

Unit 7 Sequence and Series |

Arithmetic and Geometric progressions, insertion of arithmetic.Geometric means between two given numbers.The relation between A.M. and G.M.Sum up to n terms of special series: Sn, Sn2, Sn3.Arithmetic Geometric progression. |

Unit 8 Limit, Continuity and Differentiability |

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 up to 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. |

Unit 9 Integral Calculus |

Integral as an antiderivative.Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.Integration by substitution, by parts, and by partial fractions.Integration using trigonometric identities.Integral as limit of a sum.Evaluation of simple integrals:Fundamental Theorem of Calculus.Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form. |

Unit 10 Differential Equations |

Ordinary differential equations, their order, and degree.Formation of differential equations.The solution of differential equations by the method of separation of variables.The solution of homogeneous and linear differential equations of the type: |

Unit 11 Coordinate Geometry |

Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines.Distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.Circles, conic sections: Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent.Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency. |

Unit 12 3D Geometry |

Coordinates of a point in space, the distance between two points.Section formula, direction ratios and direction cosines, the 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, the intersection of a line and a plane, coplanar lines. |

Unit 13 Vector Algebra |

Scalars and Vectors. Addition, subtraction, multiplication and division of vectors.Vector’s Components in 2D and 3D space.Scalar products and vector products, triple product. |

Unit 14 Statistics and Probability |

Measures of Dispersion: Calculation of mean, mode, median, variance, standard deviation, and mean deviation of ungrouped and grouped data.Probability: Probability of events, multiplication theorems, addition theorems, Baye’s theorem, Bernoulli trials, Binomial distribution and probability distribution. |

Unit 15 Trigonometry |

Identities of Trigonometry and Trigonometric equations.Functions of Trigonometry.Properties of Inverse trigonometric functions.Problems on Heights and Distances. |

Unit 16 Mathematical Reasoning |

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

### JEE Advanced Physics Syllabus

Unit 1: General Physics | |

Units and Dimensions | Units and dimensions, dimensional analysis.Least count and significant figures. |

Experimental Analysis | Methods of measurement and error analysis for physical quantities pertaining to the following experiments:Experiments based on using Vernier callipers and screw gauge (micrometre).Determination of g using the simple pendulum.Young’s modulus by Searle’s method.Specific heat of a liquid using calorimeter, the focal length of a concave mirror and a convex lens using the u-v method.The speed of sound using resonance column.Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box. |

Unit 2 Mechanics | |

Kinematics | Kinematics in one and two dimensions (Cartesian coordinates only), projectiles.Uniform Circular motion, relative velocity. |

Newton’s laws of motion | Newton’s laws of motion, Inertial and uniformly accelerated frames of reference.Static and dynamic friction, Kinetic and potential energy.Work and power.Conservation of linear momentum and mechanical energy. |

Systems of particles | Centre of mass and its motion; Impulse.Elastic and inelastic collisions. |

Gravitation | Laws of gravitation.Gravitational potential and field, acceleration due to gravity.The motion of planets and satellites in circular orbits and escape velocity. |

Inertia and Momentum | Rigid body, the moment of inertia, parallel and perpendicular axes theorems, the moment of inertia of uniform bodies with simple geometrical shapes.Angular momentum, Torque, Conservation of angular momentum.Dynamics of rigid bodies with a fixed axis of rotation.Rolling without slipping of rings, cylinders, and spheres; Equilibrium of rigid bodies.The collision of point masses with rigid bodies. |

Harmonic motions | Linear and angular simple harmonic motions.Hooke’s law, Young’s modulus. |

The pressure in a fluid | Pascal’s law; Buoyancy.Surface energy and surface tension, capillary rise, viscosity (Poiseuille’s equation excluded).Stoke’s law, terminal velocity, Streamline flow, the equation of continuity, Bernoulli’s theorem and its applications. |

Waves | Wave motion (plane waves only), longitudinal and transverse waves, superposition of waves.Progressive and stationary waves.The vibration of strings and air columns, Resonance, Beats.The speed of sound in gases; Doppler effect (in sound). |

Thermal Physics | Thermal expansion of solids, liquids, and gases, calorimetry, latent heat.Heat conduction in one dimension, elementary concepts of convection and radiation, Newton’s law of cooling; Ideal gas laws.Specific heats (Cv and Cp for monatomic and diatomic gases), Isothermal and adiabatic processes, the bulk modulus of gases.Equivalence of heat and work, First law of thermodynamics and its applications (only for ideal gases).Blackbody radiation, absorptive and emissive powers, Kirchhoff’s law.Wien’s displacement law, Stefan’s law. |

Unit 3 Electricity and magnetism | |

Electric Fields | Coulomb’s law; Electric field and potential.The electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field.Electric field lines; Flux of the electric field.Gauss’s law and its application in simple cases, such as, to find field due to the infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. |

Capacitance | Capacitance, Parallel plate capacitor with and without dielectrics.Capacitors in series and parallel, Energy stored in a capacitor. |

Electric current | Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells.Kirchhoff’s laws and simple applications.Heating effect of current. |

Magnetic Fields | Biot Savart’s law and Ampere’s law.Magnetic field near a current-carrying straight wire, along with the axis of a circular coil and inside a long straight solenoid.Force on a moving charge and on a current-carrying wire in a uniform magnetic field.The magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop.Moving coil galvanometer, voltmeter, ammeter and their conversions. |

Electromagnetic Induction | Electromagnetic induction, Faraday’s law, Lenz’s law.Self and mutual inductance.RC, LR and LC circuits with D.C. and A.C. sources. |

Unit 4 Optics | |

Reflection and Refraction | Rectilinear propagation of light.Reflection and refraction at plane and spherical surfaces, total internal reflection.Deviation and dispersion of light by a prism.Thin lenses, Combinations of mirrors and thin lenses; Magnification. |

Wave nature of light | Huygen’s principle.Interference limited to Young’s double-slit experiment. |

Unit 5 Modern Physics | |

Atoms and Nuclei | Atomic nucleus; Alpha, beta and gamma radiations; Law of radioactive decay.Decay constant; Half-life and mean life; Binding energy and its calculation; Fission and fusion processes; Energy calculation in these processes.Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays.Moseley’s law; de Broglie wavelength of matter waves. |

### JEE Advanced Chemistry Syllabus

#### 1. Physical Chemistry

Unit 1 General topics |

The concept of atoms and molecules, Mole concept, Dalton’s atomic theory.Balanced chemical equations, Chemical formulas, Calculations on mole concept involving common oxidation and reduction.Neutralization and displacement reactions.Concentration in terms of mole fraction, molality, molarity, and normality. |

Unit 2 Liquid and Gaseous States |

The absolute scale of temperature, ideal gas equation, Deviation from ideality, van der Waals equation.Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature.Law of partial pressures, Vapour pressure and Diffusion of gases. |

Unit 3 Atomic Structure and Chemical Bonding |

Bohr model, the spectrum of a hydrogen atom, quantum numbers, Wave-particle duality, de Broglie hypothesis and Uncertainty principle.Qualitative quantum mechanical picture of the hydrogen atom, shapes of s, p and d orbitals, Electronic configurations of elements (up to atomic number 36), Aufbau principle, Pauli exclusion principle and Hund’s rule.Orbital overlap and the covalent bond; Hybridization involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond.Polarity in molecules, dipole moment (qualitative aspects only), VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral). |

Unit 4 Energetics |

First law of Thermodynamics, Internal energy, work, and heat.Pressure-Volume work, Enthalpy, Hess’s law; Heat of reaction, fusion, and vaporization.The second law of Thermodynamics, Entropy, Free energy, and criterion of spontaneity. |

Unit 5 Chemical Equilibrium |

Law of mass action, Equilibrium constant, and Le Chatelier’s principle (effect of concentration, temperature and pressure).The significance of Delta G and Delta G0 in chemical equilibrium, Solubility product, common ion effect, pH, and buffer solutions.Acids and bases (Bronsted and Lewis concepts) and Hydrolysis of salts. |

Unit 6 Electrochemistry |

Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to Delta G.Electrochemical series, emf of galvanic cells, Faraday’s laws of electrolysis.Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law, and Concentration cells. |

Unit 7 Chemical Kinetics |

Rates of chemical reactions, Order of reactions, and Rate constant.First order reactions, Temperature dependence of rate constant (Arrhenius equation). |

Unit 8 Solid State |

Classification of solids, crystalline state, and seven crystal systems (cell parameters a, b, c, Alpha, Beta, Gamma).Close-packed structure of solids (cubic), packing in fcc, bcc and hcp lattices.Nearest neighbours, ionic radii, simple ionic compounds, point defects. |

Unit 9 Solutions |

Raoult’s law, Molecular weight determination from lowering of vapour pressure, the elevation of boiling point and depression of freezing point.Surface chemistry: Elementary concepts of adsorption (excluding adsorption isotherms).Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants, and micelles (only definitions and examples). |

Unit 10 Nuclear chemistry |

Radioactivity: isotopes and isobars, Properties of Alpha, Beta, and Gamma rays.Kinetics of radioactive decay (decay series excluded), carbon dating.Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions. |

#### 2.Inorganic Chemistry

Unit 1 Isolation/preparation and properties of the non-metals |

Boron, silicon, nitrogen, phosphorus, oxygen, sulphur, and halogens.Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur. |

Unit 2 Preparation and properties of the compounds |

Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium.Boron: diborane, boric acid, borax, and Aluminium: alumina, aluminium chloride and alums.Carbon: oxides and oxyacid (carbonic acid), and Silicon: silicones, silicates and silicon carbide.Nitrogen: oxides, oxyacids and ammonia, and Phosphorus: oxides, oxyacids (phosphorus acid phosphoric acid) and phosphine.Oxygen: ozone and hydrogen peroxide, and Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate.Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides. |

Unit 3 Transition elements (3d series) |

Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment.Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral). |

Unit 4 Preparation and properties of the following compounds |

Oxides and chlorides of tin, and lead.Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+.Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate. |

Unit 5 Ores and minerals |

Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminum, zinc, and silver.Extractive metallurgy: Chemical principles, and reactions only (industrial details excluded). |

Unit 6 Reduction Methods |

Carbon reduction method (iron and tin), Self-reduction method (copper and lead), Electrolytic reduction method (magnesium and aluminium), Cyanide process (silver and gold).Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide. |

#### 3.Organic Chemistry

Unit 1 Basic Concepts |

Hybridization of carbon; _ and _-bonds; Shapes of simple organic molecules, Structural and geometrical isomerism, Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded).IUPAC nomenclature of simple organic compounds (only hydrocarbons, monofunctional, and bifunctional compounds), Conformations of ethane and butane (Newman projections), Resonance and hyperconjugation.Keto-enol tautomerism, Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids.Inductive and resonance effects on acidity and basicity of organic acids and bases, Polarity and inductive effects in alkyl halides.Reactive intermediates produced during homolytic and heterolytic bond cleavage, Formation, structure and stability of carbocations, carbanions and free radicals. |

Unit 2 Preparation, properties, and reactions of Alkenes and Alkynes |

Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes.Acid-catalyzed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination), Reactions of alkenes with KMnO4 and ozone.Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions.Electrophilic addition reactions of alkenes with X2, HX, HOX, and H2O (X=halogen), Addition reactions of alkynes, and Metal acetylides. |

Unit 3 Properties, Preparation, and reactions of Alkanes |

Homologous series, physical properties of alkanes (melting points, boiling points and density).Combustion and halogenation of alkanes.Preparation of alkanes by Wurtz reaction and decarboxylation reactions. |

Unit 4 Reactions of Phenol and Benzene |

Structure and aromaticity, Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation, Effect of o-, m- and p-directing groups in monosubstituted benzenes.Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tiemann reaction, and Kolbe reaction. |

Unit 5 Characteristic Reactions |

Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions.Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and Ketones.Ethers: Preparation by Williamson’s Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition).Carboxylic acids: formation of esters, acid chlorides, and amides, ester hydrolysis.Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, the azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction.Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution). |

Unit 6 Carbohydrates |

Classification, mono- and disaccharides (glucose and sucrose), Oxidation, reduction, glycoside formation and hydrolysis of sucrose.Amino acids and peptides: General structure (only primary structure for peptides) and physical properties.Properties and uses of some important polymers: Natural rubber, cellulose, nylon, Teflon, and PVC. |

Unit 7 Practical Organic Chemistry |

Detection of elements (N, S, halogens).Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro.Chemical methods of separation of mono-functional organic compounds from binary mixtures. |

### JEE Advanced Maths Syllabus

Unit 1 Algebra | |

Complex Numbers | Algebra of complex numbers, addition, multiplication, conjugation.Polar representation, properties of modulus and principal argument.Triangle inequality, cube roots of unity.Geometric interpretations. |

Quadratic Equations | Quadratic equations with real coefficients.Relations between roots and coefficients.Formation of quadratic equations with given roots.Symmetric functions of roots. |

Sequence and Series | Arithmetic, geometric, and harmonic progressions.Arithmetic, geometric, and harmonic means.Sums of finite arithmetic and geometric progressions, infinite geometric series.Sums of squares and cubes of the first n natural numbers. |

Logarithms | Logarithms and their properties. |

Permutation and Combination | Problems on permutations and combinations. |

Binomial Theorem | Binomial theorem for a positive integral index.Properties of binomial coefficients. |

Matrices and Determinants | Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix.Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three.Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties.Solutions of simultaneous linear equations in two or three variables. |

Probability | Addition and multiplication rules of probability, conditional probability.Bayes Theorem, independence of events.Computation of probability of events using permutations and combinations. |

Unit 2 Trigonometry | |

Trigonometric Functions | Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.Formulae involving multiple and submultiple angles.The general solution of trigonometric equations. |

Inverse Trigonometric Functions | Relations between sides and angles of a triangle, sine rule, cosine rule.Half-angle formula and the area of a triangle.Inverse trigonometric functions (principal value only). |

Unit 3 Vectors | |

Properties of Vectors | The addition of vectors, scalar multiplication.Dot and cross products.Scalar triple products and their geometrical interpretations. |

Unit 4 Differential Calculus | |

Functions | Real-valued functions of a real variable, into, onto and one-to-one functions.Sum, difference, product, and quotient of two functions.Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions. |

Limits and Continuity | Limit and continuity of a function.Limit and continuity of the sum, difference, product and quotient of two functions.L’Hospital rule of evaluation of limits of functions. |

Derivatives | The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.Rolle’s Theorem and Lagrange’s Mean Value Theorem. |

Unit 5 Integral calculus | |

Integration | Integration as the inverse process of differentiation.Indefinite integrals of standard functions, definite integrals, and their properties.Fundamental Theorem of Integral Calculus.Integration by parts, integration by the methods of substitution and partial fractions. |

Application of Integration | Application of definite integrals to the determination of areas involving simple curves. |

Differential Equations | Formation of ordinary differential equations.The solution of homogeneous differential equations, separation of variables method.Linear first-order differential equations. |

The syllabus is focused more on numerical and practical concepts. However, to develop the conceptual clarity don’t skip the theoretical portion of the concepts.Choose the correct book for the prepration of IIT-JEE.Avoid going through multiple books.

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