Syllabus for JEE
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Mathematics
Physics
Chemistry
Syllabus for Main Examination
Mathematics
Physics
Chemistry
Mathematics
Algebra: Algebra of complex numbers, modulus and argument, triangle inequality, nth roots of unity. Theory of quadratic equations and quadratic expressions, relationship between the roots and coefficients, sign of a quadratic expression, greatest and least values of a quadratic expression. Arithmetic, geometric and harmonic progressions, sums of arithmetic, geometric and harmonic progressions, infinite geometric series, sums of the squares and cubes of the first n natural numbers. Permutations and combinations, Binomial theorem for a positive integral index. Determinants of order two and three, solutions of simultaneous linear equations in two and three variables.
Trigonometry: Trigonometric functions and their graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations, relations between the sides and angles of a triangle, properties of a triangle, solutions of triangles, heights and distances, trigonometric functions. Analytical geometry of two dimensions:Equation of a straight line in various forms, angle between two lines, distance of a point from a line, lines through the point of intersection of two given lines, concurrency of lines. Equation of a circle in various forms, equations of tangent and normal, intersection of a circle with a straight line, equation of a circle through the points of intersection of two circles and that of a circle and a straight line. Equation of a parabola in the standard forms, focus, directrix, parametric equations, equations of tangent and normal.
Calculus: Into, onto and one-to-one functions. Sum, difference, product and quotient of two functions, composite function; absolute value, greatest integer, polynomial, rational, trigonometric, exponential and logarithmic functions, even and odd functions, inverse of a function. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, continuity of composite function. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, derivative of composite and implicit functions, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions. Geometrical interpretation of derivative, tangents and normals, monotonicity, maximum and minimum values of a function. Derivatives up to order three.
Integration: As the inverse process of differentiation, integration by parts, integration by the methods of substitution and partial fractions. Properties of definite integrals.
Vectors: Addition of vectors, scalar product, cross product, scalar and vector triple products.
Units and dimensions; Kinematics in one and two dimensions; Circular motion; Relative motion.
Newton's laws of motion; Inertial and uniformly accelerated frames of reference; Spring force; Static and dynamic frictions; Kinetic and potential
energy; Work and Power; Linear Momentum; Conservation of linear momentum and energy; Linear and angular simple harmonic motions.
Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion of planets and satellites in circular orbits.
Systems of particles; Centre of mass and its motion; Elastic and inelastic collisions; Moment of inertia; Parallel and perpendicular axes theorems;
Moment of inertia of bodies having simple geometrical shapes, e.g., uniform ring, disc, thin rod and cylinder; Angular momentum; Torque;
Conservation of angular momentum.
Hooke's law. Young's modulus.
Buoyancy; Pressure in a fluid; Bernoulli's theorem.
Wave motion; Longitudinal and transverse waves; Superposition of waves; Progressive and stationary waves; Vibration of strings and air
columns; Resonance; Beats; Speed of sound; Doppler effect (in sound).
Thermal expansion of solids, liquids and gases; Elements of the Kinetic theory of gases; Ideal gas laws; Specific heats and their ratio; Isothermal
and adiabatic processes; First law of thermodynamics; Calorimetry; Latent heat; Equivalence of heat and work.
Heat conduction in one dimension; Elementary concepts of convection and radiation; Newton's law of cooling; Black body radiation: absorptive
and emissive powers; Kirchhoff's law.
Coulomb's law; Electric field and potential; Lines of force.
Capacitance; Dielectric constant; Parallel plate capacitor; Capacitors in series and parallel; Energy stored in a capacitor.
Electric current: Ohm's law; Series and parallel arrangements of resistances and cells; Kirchhoff's laws and applications to networks; Charging
and discharging of capacitor; Heating effect of current.
Ampere's law and Biot-Savart law; Force on a moving charge and on a current-carrying wire in a magnetic field.
Magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop; Moving coil galvanometer, voltmeter and ammeter.
Electromagnetic induction: Faraday's law; Lenz's law; Self and mutual inductance; Growth and decay of current in an L-R circuit.
Rectilinear propagation of light; Reflection and refraction at plane and curved surfaces; Total internal reflection; Deviation and dispersion of
light by a prism; Thin lenses; Combinations of mirrors and thin lenses;
Magnification; Microscope and telescope.
Wave nature of light: interference, Young's double slit experiment; fringe width.
Alpha, beta and gamma radiations; Law of radioactive decay; Decay constant; Half-life and mean life;
Bohr's theory of hydrogen like atoms; Characteristic and continuous X-rays.
The concept of atoms and molecules; laws of chemical combination; mole concept; chemical formulae, balanced chemical equations,
concentration in terms of mole fraction, molarity, molality and normality.
Gaseous, liquid and solid states; absolute scale of temperature, ideal gas equation; kinetic theory of gases, average, root mean square and most
probable velocities and their relation with temperature; law of partial pressures; vapour pressure; surface tension and viscosity; classification of
solids, crystalline state; seven crystal systems (only cell parameters a, b, c,
, 
, and
close packed structure of solids - only cubic).
Atomic structure: Rutherford model, Bohr model, quantum numbers, electronic configuration of elements (upto atomic number 36), Aufbau
principle, Pauli's exclusion principle, and Hund's rule.
Periodicity of properties of elements: classification of elements into s, p, and d block; periodicity in properties with respect to atomic and ionic
radii, ionisation energy, electron affinity, electronegativity, oxidation state, metallic and non-metallic character and trends in reactivity.
Bonding and molecular structure: Lewis structures; orbital overlap and covalent bond; hybridisation involving s and p and d orbitals only;
co-ordinate covalent bond, ionic bond, hydrogen bond; molecular shapes; linear, angular, planar, pyramidal, tetrahedral, and octahedral.
Energetics: Ist law of thermodynamics; Internal energy; enthalpy; Hess's law; heat of reaction, fusion, and vaporisation.
Chemical equilibrium: chemical equilibria; law of mass action, reaction quotient; equilibrium constant; dependence on concentration; temperature
and pressure, solubility product, common ion effect.
Electrochemistry: Electrochemical cells and cell reactions; standard electrode potential and electrochemical series; emf of a galvanic cell.
Chemical kinetics: Rates of chemical reactions; order of reaction; rate constant; effect of concentration and temperature (excluding Arrhenius
equation).
Isolation/preparation and properties of the following non-metals: Nitrogen, phosphorous, oxygen, sulphur, fluorine, chlorine, bromine and
iodine. Properties of allotropes of carbon (graphite and diamond only); preparation and properties of zone.
Preparation and properties of the following compounds: Oxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium,
potassium, magnesium and calcium, alumina, aluminium chloride and alums, hydrogen peroxide; carbon: oxides and carbides; nitrogen; oxides;
oxyacids and ammonia; phosphorous: oxides and oxyacids (meta- nd orthophosphoric acids); Boron: diborane; silicon: silicates; sulphur:
oxides, sulphurous and sulphuric acids, sodium thiosulphate and hydrogen sulphide; halogens: hydrohalic acids, oxyacids of chlorine,
bleaching powder.
Preparation and properties of the following compounds: Ferrous sulphate, ferric chloride, Mohr's salt, ferric oxide, copper sulphate, oxide and
sulphate of zinc.
Principles of qualitative analysis: Group I to V excluding interfering radicals.
Ores and minerals: Commonly occurring ores of iron, copper, lead, magnesium and aluminium.
Extractive metallurgy (Chemical principles and reactions only; industrial details excluded): Carbon reduction method (iron), self reduction method
(copper and lead), electrolytic reduction method (magnesium and aluminium).
Concepts of hybridisation of carbon, sigma and pi-bonds. Resonance.
Homologous series, structural and geometrical isomerism, optical isomerism of compounds containing one asymmetric centre only. IUPAC
nomenclature of simple organic compounds (hydrocarbons and mono functional compounds only).
Inductive and resonance effects on acidity and basicity of acids and bases respectively.
Polarity and inductive effects in alkyl halides. Reactive intermediates produced during homolytic and heterolytic bond cleavage. Formation,
structure and stability of Alkyl carbocations and free radicals.
Physical properties of alkanes (mp, bp and density), combustion and halogenation of alkanes. Preparation of alkanes by Wurtz coupling and
decarboxylation reaction.
Structure and physical properties of alkenes and alkynes (bp, density, dipole moment), acidity of alkynes. Preparation of alkenes and alkynes by
elimination reaction. Electrophilic addition reaction of alkenes with Br2 HBr, HOCl. Reactions of alkynes: Metal acetylides.
Benzene: structure and aromaticity. Electrophilic substitution reactions; bromination, nitration, sulfonation (orientation excluded). Phenols:
acidity, electrophilic reaction (halogenation, nitration and sulphonation).
Characteristic reactions of the followings: Alcohol (esterification, dehydration and oxidation). Reaction of alcohols with sodium, phosphorous
halides, ZnCl2/Conc. HCl. Alkyl halides (nucleophilic substitution reactions). Aldehydes and ketones (oxidation, reduction, oxime and hydrazone
formation). Carboxylic acids (formation of esters, acid chlorides and amides).
Mathematics
Algebra: Algebra of complex numbers, modulus and argument, triangle inequality, nth roots of unity.
Theory of quadratic equations and quadratic expressions, relationship between the roots and coefficients, sign of a quadratic expression,
greatest and least values of a quadratic expression.
Arithmetic, geometric and harmonic progressions, sums of arithmetic, geometric and harmonic progressions, infinite geometric series, sums of
the squares and cubes of the first n natural numbers.
Mathematical induction. Permutations and combinations, Binomial theorem for a positive integral index.
Determinants of order two and three, solutions of simultaneous linear equations in two and three variables.
Trigonometry: Trigonometric functions and their graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles,
general solution of trigonometric equations, relations between the sides and angles of a triangle, properties of a triangle, solutions of triangles,
heights and distances, trigonometric functions.
Analytical geometry of two dimensions:Equation of a straight line in various forms, angle between two lines, distance of a point from a line, lines
through the point of intersection of two given lines, concurrency of lines.
Equation of a circle in various forms, equations of tangent and normal, intersection of a circle with a straight line, equation of a circle through the
points of intersection of two circles and that of a circle and a straight line.
Equations of the conic sections in the standard form, focus, directrix, eccentricity of the conic sections, parametric equations, equations of
tangent and normal.
Calculus: Into, onto and one-to-one functions. Sum, difference, product and quotient of two functions, composite function; absolute value,
greatest integer, polynomial, rational, trigonometric, exponential and logarithmic functions, even and odd functions, inverse of a function.
Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, continuity of composite
function. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, derivative of composite and implicit
functions, derivatives of polynomial, rational, trigonometric, inverse
trigonometric, exponential and logarithmic functions.
Geometrical interpretation of derivative, tangents and normals, monotonicity, maximum and minimum values of a function.
Derivatives up to order three.
Integration: As the inverse process of differentiation, integration by parts, integration by the methods of substitution and partial fractions.
Definite integral and its application for the determination of areas. Properties of definite integrals.
Differential equations: Formation of differential equations. First order equation, variable separable method and homogeneous equations.
Probability: Addition and multiplication laws, conditional probabilities.
Vectors: Addition of vectors, scalar product, cross product, scalar and vector triple products, applications in geometry.
Units and dimensions. Displacement, velocity and acceleration. Kinematics in one and two dimensions. Projectiles, circular motion. Concept of
relative motion.
Newton's laws of motion, concepts of inertial and uniformly accelerated frames. Force; spring force, frictional force and gravitational force. Work,
energy and power. Momentum. Conservation of momentum and energy. Linear and angular simple
harmonic motions.
Universal law of gravitation; gravitational potential and field; acceleration due to gravity; motion of planets and satellites in circular orbits;
Kepler's laws.
Systems of particles; centre of mass and its motion. Elastic and inelastic collisions. Rigid bodies: moment of inertia; parallel and perpendicular
axes theorems; moment of inertia of simple geometrical shapes, e.g., uniform ring, disc, thin rod, and cylinder. Angular momentum and torque;
equilibrium of rigid bodies; conservation of angular momentum.
Hooke's law; Young's modulus; shear and bulk moduli. Principle of buoyancy; pressure in a fluid; streamlined flow; Bernoulli's theorem.
Wave motion: concepts of amplitude, frequency and phase; longitudinal and transverse waves; superposition of waves; progressive and
stationary waves; vibration of strings and air columns; resonance; beats. Velocity of sound; echo; Doppler
effect.
Thermal expansion of solids, liquids and gases. Ideal gas laws; absolute temperature. Specific heats and their ratio. Isothermal and adiabatic
processes. First law of thermodynamics. Calorimetry; latent heat; equivalence of heat and work. Heat conduction in one dimension; convection
and elementary concepts of radiation; Stefan's law of radiation; Wien's displacement law; Newton's law of cooling.
Elements of the kinetic theory of gases. Pressure and temperature of an ideal gas.
Coulomb's law; electric field and electric potential; lines of force; capacitance; dielectric constant; parallel plate capacitor; capacitors in series
and parallel; energy stored in a capacitor; charging and discharging of a capacitor.
Electric current; Ohm's law; series and parallel arrangements of resistances and cells. Kirchhoff's laws and their application to networks. Heating
effect of a current.
Biot-Savart law; force on a moving charge and on a current-carrying wire in a magnetic field. Magnetic moment of a current loop; effect of a
uniform magnetic field on a current loop; moving coil galvanometer, voltmeter and ammeter.
Electromagnetic induction; Faraday's law; Lenz's law; definitions of self and mutual inductance. Growth and decay of current in an L-R circuit;
L-C oscillation.
Rectilinear propagation of light; reflection and refraction at plane and curved surfaces; total internal reflection and critical angle. Deviation and
dispersion of light by a prism. Thin lenses; spherical aberration; combinations of mirrors and lenses; magnification; microscope and telescope.
Wave nature of light; interference; Young's double slit experiment; fringe width; elementary concepts of diffraction by a single slit.
Alpha, beta and gamma radiations; law of radioactive decay; decay constant; half-life and mean life. Photoelectric effect. De Broglie wavelength.
Bohr's theory of hydrogen like atoms. Production of characteristic and continuous X-rays; properties of X-rays. Atomic nucleus; binding energy
and its calculation. Fission and fusion processes; energy calculations in these processes.
Elenentary concepts of metals, insulators and semiconductors. Intrinsic and extrinsic semiconductors; p-n junction as a rectifier; transistors:
quantitative application as amplifier (in common emitter mode) and oscillator.
The concept of atoms and molecules: laws of chemical combination; mole concept; chemical formulae; balanced chemical equations
concentration in terms of mole fraction, molarity, molality and normality, calculations involving common oxidation-reduction, neutralisation, and
displacement reactions.
Gaseous, liquid and solid states: ideal gas equation, deviation from ideality (compression factor, Z); van der Waal's equation; diffusion of gases,
kinetic theory of gases; average, root mean square and most probable velocities and their relation with temperature, law of partial pressures;
vapour pressure, surface tension and viscosity, classification of solids; crystalline state, seven crystal systems (only cell parameters: a, b, c,
, , and
); packing fcc, bcc, hcp; nearest neighbours, simple ionic compounds, point defects.
Atomic structure: Rutherford model; spectrum of hydrogen atom; Bohr model; de-Broglie relations, uncertainty principle, quantum mechanical
model; electronic configuration of elements (upto atomic number 36); Aufbau principle, Pauli's exclusion principle, and Hund?s rule, shapes of s,
p, and d orbitals.
Periodicity of properties of elements: classification of elements into s, p, and d block; periodicity in properties with respect to atomic and ionic
radii, ionisation energy, electron affinity, electronegativity, oxidation state and metallic and non-metallic character.
Bonding and molecular structure: Lewis structures; orbital overlap and covalent bond; hybridisation involving s, p & d orbitals only; coordinate
covalent bond; ionic bond, hydrogen bond; orbital energy diagrams for diatomic species; polarity in molecules, dipole moment (qualitative
aspects only); VSEPR model and shapes of molecules (linear, angular, planar, pyramidal, tetrahedral, octahedral and square planar.
Energetics: First and second law of thermodynamics; Internal energy; enthalpy, work and heat; heats of reaction, fusion, and vaporisation,
Hess's law; pressure-volume work.
Chemical equilibrium: chemical equilibria including phase equilibria, law of mass action, reaction quotient, equilibrium constant; relation between
kp and
Kc; Le-Chatelier's principle and its applications; effect of concentration, temperature and pressure on equilibrium, solubility product,
significance of 
Go and
Go in chemical equilibrium, common ion effect, pH and buffer solutions; acids and bases (Bronsted and Lewis),
hydrolysis of salts.
Electrochemistry: Faraday's laws of electrolysis; Electrochemical cells and cell reactions; standard electrode potential and electrochemical series;
emf of a galvanic cell; Nernst equation and G.
Solutions, Raoult's law; molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing
point.
Chemical kinetics: Rates of chemical reactions; order of reaction; rate constant; effect of concentration and temperature; kinetics of first order
reactions, Arrhenius equation.
Surface Chemistry: elementary concepts in adsorption (excluding adsorption isotherms), colloids, emulsions, surfactants and micelles
(definitions and examples only).
Nuclear Chemistry: radioactivity, properties of ,
,
and -rays, kinetics of radioactive decay (decay series excluded); stability of nuclei with
respect to proton-neutron ratio.
Isolation/preparation and properties of the following non-metals: Silicon, nitrogen, phosphorous, oxygen, sulphur, fluorine, chlorine, bromine
and iodine. Properties of allotropes of carbon (graphite and diamond only), preparation and properties of ozone.
Preparation and properties of the following compounds: Oxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium,
potassium, magnesium and calcium; alumina, aluminium chloride and alums; hydrogen peroxide; Boron: diborane, boric acid and borax; Carbon;
oxides and carbides; Silicon: silicones, silicates and silicon carbides; Nitrogen: oxides and oxyacids, ammonia, phosphorous: oxides and oxyacids
(meta- and orthophosphoric acids); Sulphur: oxides, sulphurous and sulphuric acids, sodium thiosulphate and hydrogen sulphide; Halogens:
hydrohalic acids, oxyacids of chlorine; bleaching powder; Fertilizers: commercially available (common) NPK type; Tin and lead: Oxides and
chlorides.
Preparation and properties of XeF2,
XeF4 and
XeF6. Transition elements (only the first row, 3d series): Definition, Werner's approach to
coordination compounds, general characteristic properties [viz., variable oxidation states, colour excluding the details of electronic transition)],
calculation of spin-only magnetic moment, formation of complexes (stereochemistry excluded), nomenclature of simple coordination compounds,
valence bond approach to define geometries of coordination compounds of linear, tetrahedral, octahedral and square planar geometries.
Preparation and properties of the following compounds: Ferrous sulphate,, Potassium Permanganate, Potassium dichromate, ferric chloride,
Mohr?s salt, ferric oxide, copper sulphate; oxide and sulphate of zinc; silver oxide, silver nitrate, silver bromide, silver thiosulphate.
Principles of qualitative analysis: Group I to V excluding interfering radicals.
Ores and minerals: Commercially important (common) ores of iron, copper, lead, magnesium and aluminium, tin and silver.
Extractive metallurgy (Chemical principles and reactions only; industrial details excluded): Carbon reduction method (iron, tin); self reduction
method (copper and lead); electrolytic reduction method (magnesium and aluminium); cyanide process
(silver, gold).
Concepts of hybridisation of carbon, sigma and pi-bonds. Resonance.
Homologous series, structural and geometrical isomerism, optical isomerism of compounds containing one and two asymmetric centres only (R/S
and E/Z nomenclature excluded), Keto-enol tautomerism. IUPAC nomenclature of simple organic compounds; hydrocarbons, mono and
bifunctional compounds. Determination of empirical and molecular formula of
simple compounds (combustion method).
Inductive and resonance effects on acidity and basicity of acids and bases respectively. Hydrogen bonds and their effects on physical
properties of alcohols and carboxylic acids. Polarity and inductive effects in alkyl halides. Reactive intermediates produced during homolytic and
heterolytic bond cleavage. Formation, structure, stability and reactivity of alkyl carbocations
and free radicals.
Physical properties of alkanes (mp, bp and density), combustion and halogenation of alkanes. Preparation of alkanes by Wurtz coupling and
decarboxylation reaction. Conformation of ethane.
Structure and physical properties, of alkenes and alkynes (bp, density, dipole moment), acidity of alkynes. Preparation of alkenes and alkynes by
elimination reaction, Electrophilic addition reaction of alkenes with
Br2, HBr, HOCl, and acid catalyzed hydration (Stereochemistry of addition and
elimination excluded). Reaction of alkene with KMnO4 and Ozone.
Reactions of alkynes: Metal acetylides, reduction and hydration.
Benzene: structure and aromaticity, bromination, nitration, sulfonation. Friedel Crafts alkylation and acylation. Effect of o, m, p directing groups
in mono substituted benzenes.
Characteristic reactions of the following: Alcohol (esterification, dehydration and oxidation). Reaction of alcohols with sodium, phosphorous
halides, ZnCl2/Conc. HCl. Alkyl halides (nucleophilic substitution reactions, rearrangement of alkyl carbocations). Aldehydes and ketones
(oxidation, reduction, oxime and hydrazone formation, Aldol condensation, Perkin
reaction, Canizzaro reaction, haloform and Grignard reaction only). Carboxylic acids (formation of esters acid chlorides and amide). Phenol:
Acidity of phenols, halogenation, nitration, sulfonation and Riemer-Tiemann reaction. Amines: Basicity of aniline and aliphatic amine,
Preparation from nitro compounds, reaction with nitrous acid, formation and reactions of diazonium salts, and its coupling with phenols,
carbylamine reaction. Nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine
substitution).
Carbohydrates: classification - mono, di and polysaccharides (glucose, surcose and starch only); hydrolysis of sucrose.
Amino acids and Peptides: General structure and physical properties.
Properties and uses of some important polymers (natural Rubber, Cellulose, Nylon, teflon, PVC).
For admission to B. Arch.: Geometric construction of lines, curves, forms, rotation and development of surfaces, simple plans and elevations, lettering, visual logic, composition, space relation, colour concepts, aesthetic appreciation, basic knowledge of significant buildings, building elements and materials, memory drawing, sense of three dimensions, shading and colouring, proportion and scale.
For admission to B. Des.: Memory drawing, object drawings, quizzes to understand the aesthetic sensitivity, simple design project 2D and 3D, composition on 2D space, shading and colouring, proportion and scale.
Candidates are advised to bring geometry box sets, pencils, erasers and coloured pencils/crayons (pastel colours) for these aptitude tests during counselling.
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