An Analysis of the IIT-JEE

An Analysis of the IIT-JEE Part-1

The complexity of the IIT-JEE arises from the fact that the questionsare always unique in their context, and solving them often requires a combination of concepts from across different chapters. Nonetheless,some basic data analysis can be quite revealing and could give some important insights into how one should go about preparing for each subject. Such analyses form the basis of our understanding of the JEE.

The section-wise breakup of marks in the past years

PHYSICS

'Electrostatics and Current Electricity', and 'Electromagnetism'-each of these topics has contributed about 15%
Students should devote about 30% of their preparation time to the coverage of Electromagnetism and Electrostatics; because together they constitute almost one-third of the total marks and can be more scoring as the degree of difficulty when compared to Mechanics is relatively low.
'Optics' too contributes approximately 13% to the IIT-JEE test. Within Optics, it has been observed that problems on Physical optics are more frequent than that on Geometrical optics. Students should
take care to devote about 10% of time on Optics for robust preparation.

In the past four years, approximately 20% of the total marks pertain to Mechanics. Within Mechanics, the favorite topics seem to be 'Rigid Body Rotation' and 'Motion on a Plane'. Topics like 'Simple Harmonic
Motion' and 'Work and Energy', on the other hand, have been accorded relatively less priority for these years. Apparently, students have to be thoroughly prepared with Mechanics as it forms almost one-fifth of the whole JEE Screening paper. It is important for students to realize that Mechanics though important, takes relatively more time for preparation. Thus, they should restrict their preparation of Mechanics
to about 30% of the total time.

The next important topics are

'Modern Physics' and 'Thermal Physics', each commanding a share of about 12% of the total marks. These topics can be covered thoroughly in a relatively less time (10% of total time can be allocated
to each topic); therefore, a student should look at exhaustively preparing for these topics.

The last but not the least, 'Mechanical Waves' (sound) has accounted for approximately 12% of the total marks. Students can prepare for Wave Motion by restricting their total time spent on this
particular topic to about 10%.

CHEMISTRY

'Organic Chemistry' has the highest weightage with mean marks of 36%. Topics like 'Isomerism' and 'Name Reactions', and 'Stability of reaction intermediates' should be thoroughly covered. It is easier to remember the reactions and conversions involving aromatic compounds and a considerable percentage of questions from organic chemistry are based on this part. An understanding of directive influence of substituent groups, resonance and mechanism of reactions definitely helps in cracking the problems of organic chemistry.
'Physical Chemistry' is a close second with a mean weightage of 33%.

In fact, questions on physical chemistry are all numerical in nature. Problems on topics like 'Electrochemistry', 'Kinetics', and'Chemical and Ionic Equilibrium' are always asked either directly or along with some other topic. Students are advised to cover all the topics of physical chemistry. This is an area in which students can be sure of hundred percent score, provided they have a clear understanding of the concepts and a good practice of solving problems within recommended time.

'Inorganic Chemistry' and 'General Chemistry' account for 21% and 10% of the total marks. Inorganic Chemistry should be prepared by studying the group properties and periodicity. Lots of emphasis has
to be given to Exceptions. Questions are asked from these topics invariably. The properties of some important compounds are also asked in the form of reactions. Remembering the reactions involved in
qualitative analysis is of great advantage.

Questions asked in General Chemistry mostly include that from 'Stoichiometry' and 'Chemical Bonding'.

MATHEMATICS

'Calculus' accounts for about 30% of the total marks in JEE. Students can score a high percentage of marks by firmly grasping the fundamentals of Calculus. More emphasis should be given in preparing 'Functions', 'Increasing/Decreasing Functions', and 'Maxima/ Minima of Functions'.In Integral Calculus, students must practice problems on 'Definite Integral' with a proper understanding of the use of their properties for
evaluation.
In 'Area of Regions Bounded by Curves', students should take care to draw figures for obtaining the limits of the integrals to be evaluated.'Algebra' has a weightage of about 23% of the total marks. Students
should emphasize practicing only those topics that have been well understood by them. Since problems on Algebra are trickier, students must practice solving as many different types of problems as they can.

'Analytical Geometry' has a weightage of about 20% of the total marks. It is also a conceptual topic. Before solving a problem, students must draw figures of the given curves to understand the problem.
The topics of 'Vectors and 3-D Geometry' and 'Probability' have a weightage of approximately 6% each. These also have to bethoroughly prepared.

'Trigonometry' carries a weightage of about 9%. It has been observed that this weightage was as high as 17% and as low as 4%. Students, anyways,must be thorough with the topics of 'Inverse functions', 'Solutions
of Trigonometric Equations', and 'Solution of Triangles'. Theformulae and standard results of trigonometry must be learnt by heartin order to do well in the Mathematics paper.

Please note that the JEE is not about scoring 100% in a subject or theexamination. Your aim should be to attain an optimal score in eachsubject, depending on your strengths and weaknesses.

PHYSICS
'Electrostatics and Current Electricity', and 'Electromagnetism'- -------15%
'Optics'---------------------------------------------------------------13%
Mechanics------------------------------------------------------------20%
'Modern Physics' and 'Thermal Physics',------------------------------ 12%
'Mechanical Waves'---------------------------------------------------12%

CHEMISTRY
'Organic Chemistry'---------------------------------------------------36%.
'Physical Chemistry'---------------------------------------------------33%.
'Inorganic Chemistry'--------------------------------------------------21%
'General Chemistry'-('Stoichiometry' and 'Chemical Bonding'. )---------10%

MATHEMATICS
'Calculus'---------------------------------------------------------------30%
'Algebra'----------------------------------------------------------------23%
'Analytical Geometry'----------------------------------------------------20%
'Vectors and 3-D Geometry' and 'Probability'----------------------------18%
'Trigonometry'-----------------------------------------------------------9%



JEE Mathematics Syllabus
Algebra
JEE Syllabus
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.
Physical chemistry
JEE Chemistry Syllabus
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 nonmetals:
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, FriedelCrafts
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 nonuniform);
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 currentcarrying
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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