With just 2.5 Months it's high time that you know the ACTUAL JEE SYLLABUS, so here it is, extracted from the Official Website, http://jeeadv.iitkgp.ac.in/
Physics Syllabus
General: Units and dimensions, dimensional analysis;
least count, significant figures; Methods of measurement and error analysis for
physical quantities pertaining to the following experiments: Experiments based
on using Vernier calipers and screw gauge (micrometer), Determination of g
using simple pendulum, Young's modulus by Searle's method, Specific heat of a
liquid using calorimeter, focal length of a concave mirror and a convex lens
using u-v method, 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.
Mechanics: Kinematics in one and two dimensions
(Cartesian coordinates only), projectiles; Uniform Circular motion; Relative
velocity.
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.
Law of gravitation;
Gravitational potential and field; Acceleration due to gravity; Motion of
planets and satellites in circular orbits; Escape velocity.
Rigid body, moment of
inertia, parallel and perpendicular axes theorems, moment of inertia of uniform
bodies with simple geometrical shapes; Angular momentum; Torque; Conservation
of angular momentum; Dynamics of rigid bodies with fixed axis of rotation;
Rolling without slipping of rings, cylinders and spheres; Equilibrium of rigid
bodies; Collision of point masses with rigid bodies.
Linear and angular
simple harmonic motions.
Hooke's law, Young's
modulus.
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, equation of continuity, Bernoulli's theorem and its
applications.
Wave motion (plane
waves only), longitudinal and transverse waves, superposition of waves;
Progressive and stationary waves; Vibration of strings and air
columns;Resonance; Beats; 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 monoatomic and diatomic gases); Isothermal
and adiabatic processes, 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.
Electricity
and magnetism: Coulomb's law;
Electric field and potential; Electrical potential energy of a system of point
charges and of electrical dipoles in a uniform electrostatic field; Electric
field lines; Flux of electric field; Gauss's law and its application in simple
cases, such as, to find field due to infinitely long straight wire, uniformly
charged infinite plane sheet and uniformly charged thin spherical shell.
Capacitance; Parallel
plate capacitor with and without dielectrics; 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 simple applications; Heating effect of current.
Biot Savart's law and
Ampere's law; Magnetic field near a current-carrying straight wire, along 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.
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: Faraday's law, Lenz's law; Self and mutual inductance; RC, LR and LC
circuits with D.C. and A.C. sources.
Optics: 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.
Modern
physics: 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.
Mathematics Syllabus
Algebra: 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
with real coefficients, relations between roots and coefficients, formation of
quadratic equations with given roots, symmetric functions of roots.
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 and their
properties.
Permutations and combinations,
Binomial theorem for a positive integral index, properties of binomial
coefficients.
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, 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.
Addition and
multiplication rules of probability, conditional probability, Bayes Theorem,
independence of events, computation of probability of events using permutations
and combinations.
Trigonometry: Trigonometric functions, their periodicity and
graphs, addition and subtraction formulae, formulae involving multiple and
sub-multiple angles, general solution of trigonometric equations.
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).
Analytical
geometry:
Two
dimensions: Cartesian coordinates,
distance between two points, section formulae, shift of origin.
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, equation of
the bisector of the angle between two lines, concurrency of lines; Centroid,
orthocentre, incentre and circumcentre of a triangle.
Equation of a circle
in various forms, equations of tangent, normal and chord.
Parametric equations
of a circle, intersection of a circle with a straight line or a circle,
equation of a circle through the points of intersection of two circles and those
of a circle and a straight line.
Equations of a
parabola, ellipse and hyperbola in standard form, their foci, directrices and
eccentricity, parametric equations, equations of tangent and normal.
Locus Problems.
Three
dimensions: Direction cosines and
direction ratios, equation of a straight line in space, equation of a plane,
distance of a point from a plane.
Differential
calculus: 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.
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.
Even and odd
functions, inverse of a function, continuity of composite functions,
intermediate value property of continuous functions.
Derivative of a function, 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.
Integral
calculus: 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 definite integrals to the determination of areas involving simple curves.
Formation of ordinary
differential equations, solution of homogeneous differential equations,
separation of variables method, linear first order differential equations.
Vectors: Addition of vectors, scalar multiplication,
dot and cross products, scalar triple products and their geometrical
interpretations.
Chemistry Syllabus
Physical
chemistry
General
topics: Concept of atoms and
molecules; Dalton’s atomic theory; Mole concept; Chemical formulae; Balanced
chemical equations; Calculations (based on mole concept) involving common
oxidation-reduction, neutralisation, and displacement reactions; Concentration
in terms of mole fraction, molarity, molality and normality.
Gaseous
and liquid states: 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; Diffusion of gases.
Atomic
structure and chemical bonding: Bohr model, spectrum of hydrogen atom, quantum numbers;
Wave-particle duality, de Broglie hypothesis; Uncertainty principle;
Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d
orbitals; Electronic configurations of elements (up to atomic number 36);
Aufbau principle; Pauli’s exclusion principle and Hund’s rule; Orbital overlap
and covalent bond; Hybridisation 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).
Energetics: First law of thermodynamics; Internal energy,
work and heat, pressure-volume work; Enthalpy, Hess’s law; Heat of reaction,
fusion and vapourization; Second law of thermodynamics; Entropy; Free energy;
Criterion of spontaneity.
Chemical
equilibrium: Law
of mass action; Equilibrium constant, Le Chatelier’s principle (effect of
concentration, temperature and pressure); Significance of ΔG and ΔG° in
chemical equilibrium; Solubility product, common ion effect, pH and buffer
solutions; Acids and bases (Bronsted and Lewis concepts); Hydrolysis of
salts.
Electrochemistry: Electrochemical cells and cell reactions;
Standard electrode potentials; Nernst equation and its relation to ΔG;
Electrochemical series, emf of galvanic cells; Faraday’s laws of electrolysis;
Electrolytic conductance, specific, equivalent and molar conductivity,
Kohlrausch’s law; Concentration cells.
Chemical
kinetics: Rates of
chemical reactions; Order of reactions; Rate constant; First order reactions;
Temperature dependence of rate constant (Arrhenius equation).
Solid
state: Classification of
solids, crystalline state, seven crystal systems (cell parameters a, b, c, α,
β, γ), close packed structure of solids (cubic), packing in fcc, bcc and hcp
lattices; Nearest neighbours, ionic radii, simple ionic compounds, point
defects.
Solutions: Raoult’s law; Molecular weight
determination from lowering of vapour pressure, 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).
Nuclear
chemistry: Radioactivity:
isotopes and isobars; Properties of α, β and γ 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.
Inorganic
Chemistry
Isolation/preparation
and properties of the following non-metals: Boron, silicon, nitrogen,
phosphorus, oxygen, sulphur and halogens; Properties of allotropes of carbon
(only diamond and graphite), phosphorus and sulphur.
Preparation
and properties of the following compounds: Oxides, peroxides, hydroxides, carbonates, bicarbonates,
chlorides and sulphates of sodium, potassium, magnesium and calcium; Boron:
diborane, boric acid and borax; Aluminium: alumina, aluminium chloride and
alums; Carbon: oxides and oxyacid (carbonic acid); Silicon: silicones,
silicates and silicon carbide; Nitrogen: oxides, oxyacids and ammonia;
Phosphorus: oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine;
Oxygen: ozone and hydrogen peroxide; Sulphur: hydrogen sulphide, oxides,
sulphurous acid, sulphuric acid and sodium thiosulphate; Halogens: hydrohalic
acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.
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-transand ionisation isomerisms, hybridization and geometries of
mononuclear coordination compounds (linear, tetrahedral, square planar and
octahedral).
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.
Ores and minerals:
Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium,
aluminium, zinc and silver.
Extractive
metallurgy: Chemical principles
and reactions only (industrial details excluded); 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.
Organic
Chemistry
Concepts: Hybridisation of carbon; Sigma and pi-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, mono-functional and bi-functional
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.
Preparation,
properties 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.
Preparation,
properties and reactions of alkenes and alkynes: Physical properties of alkenes and alkynes
(boiling points, density and dipole moments); Acidity of alkynes; Acid
catalysed 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
(X=halogen) and H2O; Addition reactions of alkynes; Metal acetylides.
Reactions
of 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-Tieman reaction, Kolbe
reaction.
Characteristic
reactions of the following (including those mentioned above): 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, 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).
Carbohydrates: Classification; mono- and di-saccharides
(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.
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.
