BITSAT Syllabus 
I: Physics  II: Chemistry  III: (a) English Proficiency and (b) Logical Reasoning  IV: Mathematics 


Part I: Physics 
1. Units & Measurement 

1.1 
Units (Different systems
of units, SI units, fundamental and derived units) 
1.2 
Dimensional Analysis 
1.3 
Precision and
significant figures 
1.4 
Fundamental
measurements in Physics (Vernier calipers, screw gauge, Physical balance etc) 
2.
Kinematics 

2.1 
Properties of vectors 
2.2 
Position, velocity and acceleration vectors 
2.3 
Motion with constant acceleration 
2.4 
Projectile motion 
2.5 
Uniform circular motion 
2.6 
Relative motion 
3. 

3.1 

3.2 
Motion on an inclined plane 
3.3 
Motion of blocks with pulley systems 
3.4 
Circular motion – centripetal force 
3.5 
Inertial and noninertial frames 
4. Impulse and Momentum 

4.1 
Definition of impulse and momentum 
4.2 
Conservation of momentum 
4.3 
Collisions 
4.4 
Momentum of a system of
particles 
4.5 
Center of mass 
5. Work
and Energy 

5.1 
Work done by a force 
5.2 
Kinetic energy and
workenergy theorem 
5.3 
Power 
5.4 
Conservative forces and
potential energy 
5.5 
Conservation of
mechanical energy 
6. Rotational Motion 

6.1 
Description
of rotation (angular displacement, angular velocity and angular acceleration) 
6.2 
Rotational motion with
constant angular acceleration 
6.3 
Moment of inertia,
Parallel and perpendicular axes theorems, rotational kinetic energy 
6.4 
Torque and angular
momentum 
6.5 
Conservation of angular
momentum 
6.6 
Rolling motion 
7. Gravitation 

7.1 

7.2 
Gravitational potential
energy, Escape velocity 
7.3 
Motion of planets –
Kepler’s laws, satellite motion 
8. Mechanics of
Solids and Fluids 

8.1 
Elasticity 
8.2 
Pressure, density and
Archimedes’ principle 
8.3 
Viscosity and Surface
Tension 
8.4 
Bernoulli’s theorem 
9. Oscillations 

9.1 
Kinematics of simple
harmonic motion 
9.2 
Spring mass system,
simple and compound pendulum 
9.3 
Forced & damped
oscillations, resonance 
10. Waves 

10.1 
Progressive sinusoidal
waves 
10.2 
Standing waves in
strings and pipes 
10.3 
Superposition of waves,
beats 
10.4 
Doppler Effect 
11. Heat and
Thermodynamics 

11.1 
Kinetic theory of gases 
11.2 
Thermal equilibrium and
temperature 
11.3 
Specific heat 
11.4 
Work, heat and first law
of thermodynamics 
11.5 
2^{nd} law of thermodynamics, Carnot engine –
Efficiency and Coefficient of performance 
12. Electrostatics 

12.1 
Coulomb’s law 
12.2 
Electric field (discrete and continuous charge
distributions) 
12.3 
Electrostatic potential
and Electrostatic potential energy 
12.4 
Gauss’ law and its
applications 
12.5 
Electric dipole 
12.6 
Capacitance
and dielectrics (parallel plate capacitor, capacitors in series and parallel) 
13. Current
Electricity 

13.1 
Ohm’s
law, Joule heating 
13.2 
D.C
circuits – Resistors and cells in series and parallel, Kirchoff’s laws, potentiometer and Wheatstone bridge, 
13.3 
Electrical
Resistance (Resistivity, origin and temperature dependence of resistivity). 
14. Magnetic Effect
of Current 

14.1 
BiotSavart’s
law and its applications 
14.2 
Ampere’s
law and its applications 
14.3 
Lorentz
force, force on current carrying conductors in a magnetic field 
14.4 
Magnetic moment of a
current loop, torque on a current loop, Galvanometer and its conversion to
voltmeter and ammeter 
15. Electromagnetic
Induction 

15.1 
Faraday’s
law, Lenz’s law, eddy currents 
15.2 
Self
and mutual inductance 
15.3 
Transformers
and generators 
15.4 
Alternating
current (peak and rms value) 
15.5 
AC
circuits, LCR circuits 
16. Optics 

16.1 
Laws
of reflection and refraction 
16.2 
Lenses
and mirrors 
16.3 
Optical
instruments – telescope and microscope 
16.4 
Interference
– Huygen’s principle, Young’s double slit experiment 
16.5 
Interference
in thin films 
16.6 
Diffraction
due to a single slit 
16.7 
Electromagnetic
waves and their characteristics (only qualitative ideas), Electromagnetic
spectrum 
16.8 
Polarization
– states of polarization, Malus’ law, Brewster’s law 
17. Modern Physics 

17.1 
Dual
nature of light and matter – Photoelectric effect, De Broglie wavelength 
17.2 
Atomic
models – 
17.3 
Hydrogen
atom spectrum 
17.4 
Radioactivity 
17.5 
Nuclear
reactions : Fission and fusion, binding energy 
Part II: Chemistry 

1.
States of Matter 

1.1 
Measurement:
Physical quantities and SI units, Dimensional analysis, Precision,
Significant figures. 
1.2 
Chemical reactions: Laws of
chemical combination, 
1.3 
Gaseous
state: Gas Laws, Kinetic theory – Maxwell distribution of velocities,
Average, root mean square and most probable velocities and relation to
temperature, Diffusion; Deviation from ideal behaviour – Critical
temperature, Liquefaction of gases, van der Waals equation. 
1.4 
Liquid
state: Vapour pressure, surface tension, viscosity. 
1.5 
Solid
state: Classification; Space lattices & crystal systems; Unit cell –
Cubic & hexagonal systems; Close packing; 
2. Atomic Structure 

2.1 
Introduction:
Subatomic particles; 
2.2 
Quantum mechanics:
Waveparticle duality – de Broglie relation, Uncertainty principle; Hydrogen
atom: Quantum numbers and wavefunctions, atomic orbitals and their shapes (s,
p, and d), Spin quantum number. 
2.3 
Many
electron atoms: Pauli exclusion principle; Aufbau principle and the
electronic configuration of atoms, Hund’s rule. 
2.4 
Periodicity:
Periodic law and the modern periodic table; Types of elements: s, p, d, and f
blocks; Periodic trends: ionization energy, atomic and ionic radii, electron
affinity, electro negativity and valency. 
2.5 
Nucleus:
Natural and artificial radioactivity; Nuclear reactions. 
3.
Chemical Bonding &
Molecular Structure 

3.1 
Ionic
Bond: Lattice Energy and BornHaber cycle 
3.2 
Molecular
Structure: Lewis picture & resonance structures, VSEPR model &
molecular shapes 
3.3 
Covalent
Bond: Valence Bond Theory Orbital overlap, Directionality of bonds &
hybridistaion (s & p orbitals only), Resonance; Molecular orbital theory
Methodology, Orbital energy level diagram, Bond order, Magnetic properties
for homonuclear diatomic species. 
3.4 
Metallic
Bond: Qualitative description. 
3.5 
Intermolecular
Forces: Polarity; Dipole moments; Hydrogen Bond. 
4. Thermodynamics 

4.1 
Basic
Concepts: Systems and surroundings; State functions; Intensive &
Extensive Properties; Zeroth Law and Temperature 
4.2 
First
Law of Thermodynamics: Work, internal energy, heat, enthalpy, heat
capacities; Enthalpies of formation, phase transformation, ionization,
electron gain; Thermochemistry; Hess’s Law. Bond dissociation, combustion,
atomization, sublimation, dilution 
4.3 
Second
Law: Spontaneous and reversible processes; entropy; Gibbs free energy related
to spontaneity and nonmechanical work; Standard free energies of formation,
free energy change and chemical equilibrium; Third Law and Absolute
Entropies. 
5. Physical and Chemical Equilibria


5.1 
Concentration
Units: Mole Fraction, Molarity, and Molality 
5.2 
Solutions: Solubility of
solids and gases in liquids, Vapour Pressure, Raoult’s law, Relative lowering
of vapour pressure, depression in freezing point; elevation in boiling point;
osmotic pressure, determination of molecular mass. 
5.3 
Physical Equilibrium:
Equilibria involving physical changes (solidliquid, liquidgas, solidgas),
Adsorption, Physical and Chemical adsorption, Langmuir Isotherm. 
5.4 
Chemical
Equilibria: Equilibrium constants (K_{P}, K_{C}), LeChatelier’s
principle. 
5.5 
Ionic
Equilibria: Strong and Weak electrolytes, Acids and Bases (Arrhenius, Lewis,
Lowry and Bronsted) and their dissociation; Ionization of Water; pH; Buffer
solutions; Acidbase titrations; Hydrolysis; Solubility Product of Sparingly
Soluble Salts; Common Ion Effect. 
5.6 
Factors
Affecting Equilibria: Concentration, Temperature, Pressure, Catalysts,
Significance of DG and DG^{0} in Chemical Equilibria. 
6.
Electrochemistry


6.1 
Redox Reactions:
Oxidationreduction reactions (electron transfer concept); Oxidation number;
Balancing of redox reactions; Electrochemical cells and cell reactions;
Electrode potentials; Idea of heterogeneous equilibria on the surface of the
electrode; EMF of Galvanic cells; Nernst equation; Factors affecting the
electrode potential; Gibbs energy change and cell potential; Concentration
cells; Secondary cells; Fuel cells; Corrosion and its prevention. 
6.2 
Electrolytic Conduction:
Electrolytic Conductance; Specific, equivalent and molar conductivities;
Kolhrausch’s Law and its application, Faraday’s laws of electrolysis;
Coulometer; Electrode potential and electrolysis, Commercial production of
the chemicals, NaOH, Na, Al_{2},Cl_{2} , & F_{2} 
7. Chemical Kinetics


7.1 
Aspects
of Kinetics: Rate and Rate expression of a reaction; Rate constant; Order and
molecularity of the reaction; Integrated rate expressions and half life for
zero and first order reactions; Determination of rate constant and order of
reaction 
7.2 
Factor
Affecting the Rate of the Reactions: Concentration of the reactants, size of
particles; Temperature dependence of rate constant; Activation energy;
Catalysis, Surface catalysis, enzymes, zeolites; Factors affecting rate of
collisions between molecules; Effect of light. 
7.3 
Mechanism
of Reaction: Elementary reactions; Complex reactions; Reactions involving
two/three steps only; Photochemical reactions; Concept of fast reactions. 
7.4 
Radioactive
isotopes: Halflife period;
Radiochemical dating. 
8.
Hydrogen and sblock elements 

8.1 
Hydrogen:
Element: unique position in periodic table, occurrence, isotopes; Dihydrogen:
preparation, properties, reactions, and uses; Molecular, saline, interstitial
hydrides; Water: Properties; Structure and aggregation of water molecules;
Heavy water; Hydrogen peroxide; Hydrogen as a fuel. 
8.2 
sblock
elements: Abundance and occurrence;
Anomalous properties of the first elements in each group; diagonal
relationships. 
8.3 
Alkali
metals: Lithium, sodium and potassium: occurrence, extraction, reactivity,
and electrode potentials; Biological importance; Reactions with oxygen,
hydrogen, halogens and liquid ammonia; Basic nature of oxides and hydroxides;
Halides; Properties and uses of compounds such as NaCl, Na_{2}CO_{3},
NaHCO_{3}, NaOH, KCl, and KOH. 
8.4 
Alkaline
earth metals: Magnesium and calcium: Occurrence, extraction, reactivity and
electrode potentials; Reactions with nonmetals; Solubility and thermal
stability of oxo salts; Biological importance; Properties and uses of
important compounds such as CaO, Ca(OH)_{2}, plaster of Paris, MgSO_{4},
MgCl_{2}, CaCO_{3}, and CaSO_{4}; Lime and limestone,
cement. 
9.
p d and fblock elements 

9.1 
General:
Abundance, distribution, physical and chemical properties, isolation and uses
of elements; Trends in chemical reactivity of elements of a group;. 
9.2 
Group
13 elements: Boron; Properties and uses of borax, boric acid, boron hydrides
& halides. Reaction of aluminum with acids and alkalis; 
9.3 
Group
14 elements: Carbon: Uses, Allotropes (graphite, diamond, fullerenes),
oxides, halides and sulphides, carbides; Silicon: Silica, silicates,
silicone,.Zeolites. 
9.4 
Group
15 elements: Dinitrogen; Reactivity and uses of nitrogen and its compounds;
Industrial and biological nitrogen fixation; Ammonia: Haber’s process,
properties and reactions; Oxides of nitrogen and their structures; Ostwald’s
process of nitric acid production; Fertilizers – NPK type; Production of phosphorus;
Allotropes of phosphorus; Preparation, structure and properties of hydrides,
oxides, oxoacids and halides of phosphorus. 
9.5 
Group
16 elements: Isolation and chemical
reactivity of dioxygen; Acidic, basic and amphoteric oxides; Preparation,
structure and properties of ozone; Allotropes of sulphur; Production of
sulphur and sulphuric acid; Structure and properties of oxides, oxoacids,
hydrides and halides of sulphur. 
9.6 
Group
17 and group 18 elements: Structure and properties of hydrides, oxides,
oxoacids of chlorine; Inter halogen compounds; Bleaching Powder; Preparation,
structure and reactions of xenon fluorides, oxides, and oxoacids. 
9.7 
dblock
elements: General trends in the chemistry of first row transition elements;
Metallic character; Oxidation state; Ionic radii; Catalytic properties;
Magnetic properties; Interstitial compounds; Occurrence and extraction of
iron, copper, silver, zinc, and mercury; Alloy formation; Steel and some
important alloys; preparation and properties of CuSO_{4}, K_{2}Cr_{2}O_{7},
KMnO_{4}, Mercury halides; Silver nitrate and silver halides;
Photography. 
9.8 
fblock
elements: Lanthanides and actinides; Oxidation states and chemical reactivity
of lanthanide compounds; Lanthanide contraction; Comparison of actinides and
lanthanides. 
9.9 
Coordination
Compounds: Coordination number; Ligands; Werner’s coordination theory; IUPAC
nomenclature; Application and importance of coordination compounds (in
qualitative analysis, extraction of metals and biological systems e.g.
chlorophyll, vitamin B12, and hemoglobin); Bonding: Valencebond approach,
Crystal field theory (qualitative); Stability constants; Shapes, color and
magnetic properties; Isomerism including stereoisomerisms; Organometallic
compounds. 
10.
Principles of Organic Chemistry and Hydrocarbons 

10.1 
Classification: Based on functional groups, trivial and
IUPAC nomenclature. 
10.2 
Electronic
displacement in a covalent bond:
Inductive, resonance effects, and hyperconjugation; free radicals;
carbocations, carbanion, nucleophile and electrophile; types of reactions. 
10.3 
Alkanes
and cycloalkanes: Structural isomerism
and general properties. 
10.4 
Alkenes
and alkynes: General methods of preparation and reactions, physical
properties, electrophilic and free radical additions, acidic character of
alkynes and (1,2 and 1,4) addition to dienes. 
10.5 
Aromatic
hydrocarbons: Sources; Properties; Isomerism; Resonance delocalization;
polynuclear hydrocarbons; mechanism of electrophilic substitution reaction,
directive influence and effect of substituents on reactivity. 
10.6 
Haloalkanes
and haloarenes: Physical properties, chemical reactions. 
10.7 
Petroleum:
Composition and refining, uses of petrochemicals. 
11. Stereochemistry 

11.1 
Introduction:
Chiral molecules; Optical activity; Polarimetry; R,S and D,L configurations;
Fischer projections; Enantiomerism; Racemates; Diastereomerism and meso
structures. 
11.2 
Conformations:
Ethane, propane, nbutane and cyclohexane conformations; Newman and sawhorse
projections. 
11.3 
Geometrical
isomerism in alkenes 
12.
Organic Compounds with Functional Groups Containing Oxygen and
Nitrogen 

12.1 
General:
Electronic structure, important methods of preparation, important reactions
and physical properties of alcohols, phenols, ethers, aldehydes, ketones,
carboxylic acids, nitro compounds, amines, diazonium salts, cyanides and
isocyanides. 
12.2 
Specific:
Effect of substituents on alphacarbon on acid strength, comparative
reactivity of acid derivatives, basic character of amines and their
separation, importance of diazonium salts in synthetic organic chemistry 
13. Biological
, Industrial and Environmental chemistry 

13.1 
The Cell:
Concept of cell and energy cycle. 
13.2 
Carbohydrates: Classification; Monosaccharides;
Structures of pentoses and hexoses; Anomeric carbon; Mutarotation; Simple
chemical reactions of glucose, Disaccharides: reducing and nonreducing
sugars – sucrose, maltose and lactose; Polysaccharides: elementary idea of
structures of starch and cellulose. 
13.3 
Proteins:
Amino acids; Peptide bond; Polypeptides; Primary structure of proteins;
Simple idea of secondary , tertiary and quarternary structures of proteins;
Denaturation of proteins and enzymes. 
13.4 
Nucleic
Acids: Types of nucleic acids; Primary building blocks of nucleic acids
(chemical composition of DNA & RNA); Primary structure of DNA and its
double helix; Replication; Transcription and protein synthesis; Genetic code. 
13.5 
Lipids,
Hormones, Vitamins: Classification, structure, functions in biosystems. 
13.6 
Polymers:
Classification of polymers; General methods of polymerization; Molecular mass
of polymers; Biopolymers and biodegradable polymers; Free radical, cationic and
anionic addition polymerizations; Copolymerization: Natural rubber;
Vulcanization of rubber; Synthetic rubbers. Condensation polymers. 
13.7 
Pollution: Environmental pollutants; soil, water and
air pollution; Chemical reactions in atmosphere; Smog; Major atmospheric
pollutants; Acid rain; Ozone and its reactions; Depletion of ozone layer and
its effects; Industrial air pollution; Green house effect and global warming;
Green Chemistry. 
13.8 
Chemicals
in medicine, healthcare and food: Analgesics, Tranquilizers, antiseptics,
disinfectants, antimicrobials, antifertility drugs, antihistamines,
antibiotics, antacids; Cosmetics: Creams, perfumes, talcum powder,
deodorants; Preservatives, artificial sweetening agents, antioxidants, and
edible colours. 
13.9 
Other
Industrial Chemicals: Dyes: Classification with examples – Indigo, methyl
orange, aniline yellow, alizarin, malachite green; Advanced materials: Carbon
fibers, ceramics, micro alloys; Detergents; Insect repellents, pheromones,
sex attractants; Rocket Propellants. 
14.
Theoretical Principles of Experimental Chemistry 

14.1 
Volumetric Analysis: Principles; Standard solutions
of sodium carbonate and oxalic acid; Acidbase titrations; Redox reactions
involving KI, H_{2}SO_{4}, Na_{2}SO_{3,} Na_{2}S_{2}O_{3}and
H_{2}S; Potassium permanganate in acidic, basic and neutral media;
Titrations of oxalic acid, ferrous ammonium sulphate with KMnO_{4}, K_{2}
Cr_{2}O_{7}/Na_{2}S_{2}O_{3},
Cu(II)/Na_{2}S_{2}O_{3} 
14.2 
Qualitative
analysis of Inorganic Salts: Principles in the determination of the cations
Pb^{2+}, Cu^{2+}, As^{3+}, Mn^{2+}, Zn^{2+},
Co^{2+}, Ca^{2+}, Sr^{2+}, Ba^{2+}, Mg^{2+},
NH_{4}^{+}, Fe^{3+}, Ni^{2+} and the anions
CO_{3}^{2}, S^{2}, SO_{4}^{2}, SO_{3}^{2},
NO_{2}^{}, NO_{3}^{}, Cl^{}, Br^{},
I^{}, PO_{4}^{3}, CH_{3}COO^{}, C_{2}O_{4}^{2}. 
14.3 
Physical Chemistry Experiments: crystallization of
alum, copper sulphate, ferrous sulphate, double salt of alum and ferrous
sulphate, potassium ferric sulphate; Temperature vs. solubility; pH
measurements; Lyophilic and lyophobic sols; Dialysis; Role of emulsifying
agents in emulsification. Equilibrium
studies involving (i) ferric and
thiocyanate ions (ii) [Co(H_{2}O)_{6}]^{2+} and
chloride ions; Enthalpy determination for (i) strong acid vs. strong base
neutralization reaction (ii) hydrogen bonding interaction between acetone and
chloroform; Rates of the reaction between (i) sodium thiosulphate and
hydrochloric acid, (ii) potassium iodate and sodium sulphite (iii) iodide vs.
hydrogen peroxide, concentration and
temperature effects in these reactions; 
14.4 
Purification
Methods: Filtration, crystallization, sublimation, distillation, differential
extraction, and chromatography. Principles of melting point and boiling point
determination; principles of paper chromatographic separation – R_{f} values. 
14.5 
Qualitative Analysis of Organic Compounds: Detection
of nitrogen, sulphur, phosphorous and halogens; Detection of carbohydrates,
fats and proteins in foodstuff; Detection of alcoholic, phenolic, aldehydic,
ketonic, carboxylic, amino groups and unsaturation. 
14.6 
Quantitative Analysis of Organic Compounds: Basic
principles for the quantitative estimation of carbon, hydrogen, nitrogen,
halogen, sulphur and phosphorous; Molecular mass determination by silver salt
and chloroplatinate salt methods; Elementary idea of mass spectrometer for
accurate molecular mass determination; Calculations of empirical and molecular
formulae. 
14.7 
Principles of Organic Chemistry Experiments: Preparation of iodoform, acetanilide,
pnitro acetanilide, dibenzyl acetone, aniline yellow, betanaphthol;
Preparation of acetylene and study of its acidic character. 
Part III: (a) English Proficiency and (b) Logical Reasoning


(a) English Proficiency This
test is designed to assess the test takers’ general proficiency in the use of
English language as a means of
selfexpression in real life situations and specifically to test the test takers’
knowledge of basic grammar, their vocabulary, their ability to read fast and
comprehend, and also their ability to apply the elements of effective writing. 

1. Grammar 

1.1 
Agreement,
Time and Tense, Parallel construction, Relative pronouns 
1.2 
Determiners,
Prepositions, Modals, Adjectives 
1.3 
Voice,
Transformation 
1.4 
Question
tags, Phrasal verbs 
2.
Vocabulary 

2.1 
Synonyms, Antonyms, Odd
Word, One Word, Jumbled letters, Homophones, Spelling 
2.2 
Contextual
meaning. 
2.3 
Analogy 
3.
Reading Comprehension 

3.1 
Content/ideas 
3.2 
Vocabulary 
3.3 
Referents 
3.4 
Idioms/Phrases 
3.5 
Reconstruction
(rewording) 
4. Composition 

4.1 
Rearrangement 
4.2 
Paragraph
Unity 
4.3 
Linkers/Connectives 
(b) Logical
Reasoning The
test is given to the candidates to judge their power of reasoning spread in
verbal and nonverbal areas. The candidates should be able to think logically
so that they perceive the data accurately, understand the relationships
correctly, figure out the missing numbers or words, and to apply rules to new
and different contexts. These indicators are measured through performance on
such tasks as detecting missing links, following directions, classifying
words, establishing sequences, and completing analogies. 

5. Verbal Reasoning 

5.1 
Analogy Analogy
means correspondence. In the questions based on analogy, a particular
relationship is given and another similar relationship has to be identified
from the alternatives provided. 
5.2 
Classification Classification means to
assort the items of a given group on the basis of certain common quality they
possess and then spot the odd option out. 
5.3 
Series Completion Here series of numbers
or letters are given and one is asked to either complete the series or find
out the wrong part in the series. 
5.4 
Logical Deduction –
Reading Passage Here a brief passage is
given and based on the passage the candidate is required to identify the
correct or incorrect logical conclusions. 
5.5 
Chart
Logic Here
a chart or a table is given that is partially filled in and asks to complete
it in accordance with the information given either in the chart / table or in
the question. 
6. Nonverbal Reasoning 

6.1 
Pattern Perception Here a certain pattern
is given and generally a quarter is left blank. The candidate is required to
identify the correct quarter from the given four alternatives. 
6.2 
Figure Formation and
Analysis The candidate is
required to analyze and form a figure from various given parts. 
6.3 
Paper Cutting It involves the
analysis of a pattern that is formed when a folded piece of paper is cut into
a definite design. 
6.4 
Figure Matrix In this more than one
set of figures is given in the form of a matrix, all of them following the
same rule. The candidate is required to follow the rule and identify the
missing figure. 
6.5 
Rule Detection Here
a particular rule is given and it is required to select from the given sets
of figures, a set of figures, which obeys the rule and forms the correct
series. 


Part IV: Mathematics


1. Algebra 

1.1 
Complex numbers,
addition, multiplication, conjugation, polar representation, properties of
modulus and principal argument, triangle inequality, roots of complex
numbers, geometric interpretations. 
1.2 
Theory of Quadratic equations, quadratic
equations in real and complex number system and their solutions, relation
between roots and coefficients, nature of roots, equations reducible to
quadratic equations. 
1.3 
Arithmetic,
geometric and harmonic progressions, arithmetic, geometric and harmonic
means, arithmeticogeometric series, sums
of finite arithmetic and geometric progressions, infinite geometric series,
sums of squares and cubes of the first n natural numbers. 
1.4 
Logarithms
and their properties. 
1.5 
Exponential
series. 
1.6 
Permutations
and combinations, Permutations as an arrangement and combination as
selection, simple applications. 
1.7 
Binomial
theorem for a positive integral index, properties of binomial coefficients. 
1.8 
Matrices
and determinants of order two or three, properties and evaluation of
determinants, addition and multiplication of matrices, adjoint and inverse of
matrices, Solutions of simultaneous linear equations in two or three
variables. 
1.9 
Sets,
Relations and Functions, algebra of sets applications, equivalence relations,
mappings, oneone, into and onto mappings, composition of mappings. 
1.10 
Mathematical
Induction 
1.11 
Linear
Inequalities, solution of linear inequalities in one and two variables. 
2. Trigonometry 

2.1 
Trigonometric
ratios, functions and identities. 
2.2 
Solution
of trigonometric equations. 
2.3 
Properties
of triangles and solutions of triangles 
2.4 
Inverse
trigonometric functions 
2.5 
Heights
and distances 
3. Twodimensional
Coordinate Geometry 

3.1 
Cartesian
coordinates, distance between two points, section formulae, shift of origin. 
3.2 
Straight
lines and pair of straight lines: Equation of straight lines 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, concurrent lines. 
3.3 
Circles
and family of circles : Equation of
circle in various form, equation of tangent, normal & chords, parametric equations of a
circle , intersection of a circle with a straight line or a circle, equation of
circle through point of intersection of two circles, conditions for two
intersecting circles to be orthogonal. 
3.4 
Conic sections : parabola, ellipse and hyperbola their eccentricity, directrices &
foci, parametric forms, equations of
tangent & normal, conditions for y=mx+c to be a tangent and point of tangency. 
4. Three dimensional
Coordinate Geometry 

4.1 
Direction cosines and direction ratios, equation of a straight line in
space and skew lines. 
4.2 
Angle between two lines whose direction ratios are given 
4.3 
Equation of a plane, distance of a point from a plane, condition for
coplanarity of three lines. 
5. Differential calculus 

5.1 
Domain and range of a real valued function, Limits and Continuity of the sum, difference, product and quotient
of two functions, Differentiability. 
5.2 
Derivative of different types of functions (polynomial, rational,
trigonometric, inverse trigonometric, exponential, logarithmic, implicit
functions), derivative of the sum, difference, product and quotient of two
functions, chain rule. 
5.3 
Geometric interpretation of derivative, Tangents and Normals. 
5.4 
Increasing and decreasing functions, Maxima and minima of a function. 
5.5 
Rolle’s Theorem, Mean Value Theorem and Intermediate Value Theorem. 
6. Integral calculus 

6.1 
Integration as the inverse process of differentiation, indefinite
integrals of standard functions. 
6.2 
Methods of integration: Integration by substitution, Integration by
parts, integration by partial fractions, and integration by trigonometric
identities. 
6.3 
Definite integrals and their properties, Fundamental Theorem of
Integral Calculus and its applications. 
6.4 
Application of definite integrals to the determination of areas of
regions bounded by simple curves. 
7. Ordinary Differential
Equations 

7.1 
Variables separable method. 
7.2 
Solution of homogeneous differential equations. 
7.3 
Linear first order differential equations 
8. Probability 

8.1 
Addition and multiplication rules of probability. 
8.2 
Conditional probability 
8.3 
Independent events 
8.4 
Discrete random variables and distributions 
9. Vectors 

9.1 
Addition of vectors, scalar multiplication. 
9.2 
Dot and cross products of two vectors. 
9.3 
Scalar
triple products and their geometrical interpretations. 
10. Statistics 

10.1 
Measures of
dispersion 
10.2 
Measures of
skewness and Central Tendency 
11.Linear Programming 

11.1 
Formulation
of linear Programming 
11.2 
Solution of
linear Programming, using graphical method. 