IIT JEE Entrance Syllabus
IIT Entrance Syllabus
AIEEE/IIT JEE
JEE Syllabus
Complete IIT JEE
Syllabus
JEE 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, 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, applications of 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, application of the 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,
variables separable method, linear first order differential equations.
Vectors
Addition of vectors,
scalar multiplication, scalar products, dot and cross products, scalar triple
products and their geometrical interpretations.
JEE Chemistry Syllabus
Physical chemistry
General topics: The 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; Quantum
mechanical picture of hydrogen atom (qualitative treatment), 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 DG and DGo 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; Electrode potentials; Nernst equation and its relation to
DG; Electrochemical series, emf of galvanic cells; Faraday's laws of
electrolysis; Electrolytic conductance, specific, equivalent and molar
conductance, 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, a,
b, g), 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 vapor 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 a, b and g 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; Fertilizers: commercially available (common) NPK type.
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).
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, sulphide and sulphite.
Organic Chemistry
Concepts: Hybridisation of carbon; Sigma and pi-bonds;
Shapes of molecules; Structural and geometrical isomerism; Optical isomerism of
compounds containing up to two asymmetric centers, (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 formula 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 and H2O (X=halogen); 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/conc.-HCl, conversion of
alcohols into aldehydes and ketones; 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.
JEE 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; Circular motion (uniform and
non-uniform); 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.
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 monatomic 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 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.
JEE Syllabus for Aptitude Test in B. Arch. &
B. Des.
Freehand drawing: This would comprise of simple drawing
depicting the total object in its right form and proportion, surface texture,
relative location and details of its component parts in appropriate scale.
Common domestic or day-to-day life usable objects like furniture, equipment,
etc., from memory.
Geometrical drawing: Exercises in geometrical drawing containing
lines, angles, triangles, quadrilaterals, polygons, circles etc. Study of plan
(top view), elevation (front or side views) of simple solid objects like
prisms, cones, cylinders, cubes, splayed surface holders etc.
Three-dimensional
perception: Understanding and
appreciation of three-dimensional forms with building elements, colour, volume
and orientation. Visualization through structuring objects in memory.
Imagination and
aesthetic sensitivity: Composition exercise
with given elements. Context mapping. Creativity check through innovative
uncommon test with familiar objects. Sense of colour grouping or application.
Architectural awareness: General interest and awareness of famous
architectural creations - both national and international, places and
personalities (architects, designers etc. ) in the related domain.
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