#### Chemistry

#### UNIT 1: Atomic Structure, States of Matter & Thermo dynamics

**Some basic concepts in chemistry:** Matter and its nature, Dalton’s
atomic theory; Concept of atom, molecule, element and compound; Physical quantities
and their measurements in Chemistry, precision and accuracy, significant figures,
S.I. Units, dimensional analysis; Laws of chemical combination; Atomic and molecular
masses, mole concept, molar mass, percentage composition, empirical and molecular
formulae; Chemical equations and stoichiometry.

**States of matter:** Classification of matter into solid, liquid and
gaseous states.

**Gaseous State:** Measurable properties of gases; Gas laws - Boyle’s
law, Charle’s law, Graham’s law of diffusion, Avogadro’s law, Dalton’s law of partial
pressure; Concept of Absolute scale of temperature; Ideal gas equation; Kinetic
theory of gases; Concept of average, root mean square and most probable velocities;
Real gases, deviation from Ideal behaviour, compressibility factor and van der Waals
equation.

**Liquid State:** Properties of liquids - vapour pressure, viscosity
and surface tension and effect of temperature on them.

**Solid State:** Classification of solids: molecular, ionic, covalent
and metallic solids, amorphous and crystalline solids; Bragg’s Law and its applications;
Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations
involving unit cell parameters, imperfection in solids; Electrical, magnetic and
dielectric properties.

**Atomic structure:** Thomson and Rutherford atomic models and their
limitations; Nature of electromagnetic radiation, photoelectric effect; Spectrum
of hydrogen atom, Bohr model of hydrogen atom - its postulates, derivation of the
relations for energy of the electron and radii of the different orbits, limitations
of Bohr’s model; Dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty
principle. Elementary ideas of quantum mechanics, quantum mechanical model of atom,
its important features, concept of atomic orbitals as one electron wave functions;
Variation of ¥ and ¥2 , with r for 1s and 2s orbitals; various quantum numbers (principal,
angular momentum and magnetic quantum numbers) and their significance; shapes of
s, p and d - orbitals, electron spin and spin quantum number; Rules for filling
electrons in orbitals – aufbau principle, Pauli’s exclusion principle and Hund’s
rule, electronic configuration of elements, extra stability of half- filled and
completely filled orbitals.

**Chemical bonding and molecular structure:** Kossel - Lewis approach
to chemical bond formation, concept of ionic and covalent bonds. Ionic Bonding:
Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation
of lattice enthalpy.

**Covalent Bonding:** Concept of electronegativity, Fajan’s rule, dipole
moment; Valence Shell Electron Pair Repulsion (VSEPR) theory and shapes of simple
molecules.

**Quantum mechanical approach to covalent bonding:** Valence bond theory
- Its important features, concept of hybridization involving s, p and d orbitals;
Resonance.

**Molecular Orbital Theory:** Its important features, LCAOs, types
of molecular orbitals(bonding, antibonding), sigma and pi-bonds, molecular orbital
electronic configurations of homonuclear diatomic molecules, concept of bond order,
bond length and bond energy. Elementary idea of metallic bonding. Hydrogen bonding
and its applications.

**Chemical thermodynamics: **Fundamentals of thermo dynamics: System
and surroundings, extensive and intensive properties, state functions, types of
processes.

**First law of thermodynamics: **Concept of work, heat internal energy
and enthalpy, heatcapacity, molar heat capacity; Hess’s law of constant heat summation;
Enthalpies of bond dissociation, combustion, formation, atomization, sublimation,
phase transition, hydration, ionization and solution.

**Second law of thermodynamics:** Spontaneity of processes; the system
as criteria for spontaneity 0 (zero) (Standard Gibbs energy change) and equilibrium
constant.

#### UNIT 2: Solutions, Chemical Kinetics & Surface Chemistry

**Solutions:** Different methods for expressing concentration of solution
- molality, molarity, mole fraction, percentage (by volume and mass both), vapour
pressure of solutions and Raoult’s Law – Ideal and non-ideal solutions, vapour pressure
- composition, plots for ideal and non-ideal solutions; Colligative properties of
dilute solutions - relative lowering of vapour pressure, depression of freezing
point, elevation of boiling point and osmotic pressure; Determination of molecular
mass using colligative properties; Abnormal value of molar mass, van’t Hoff factor
and its significance.

**Equilibrium:** Meaning of equilibrium, concept of dynamic equilibrium.

**Equilibria involving physical processes:** Solid -liquid, liquid
- gas and solid – gas equilibria, Henry’s law, general characteristics of equilibrium
involving physical processes.

**Equilibria involving chemical processes:** Law of chemical equilibrium,
equilibrium constants (Kp and Kc) and their Go in chemical equilibria, factors affecting
equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s
principle.

**Ionic equilibrium:** Weak and strong electrolytes, ionization of
electrolytes, various concepts of acids and bases (Arrhenius, Brnsted - Lowry and
Lewis) and their ionization, acid – base equilibria (including multistage ionization)
and ionization constants, ionization of water, pH scale, common ion effect, hydrolysis
of salts and pH of their solutions, solubility of sparingly soluble salts and solubility
products, buffer solutions.

**Redox reactions and electrochemistry:** Electronic concepts of oxidation
and reduction, redox reactions, oxidation number, rules for assigning oxidation
number, balancing of redox reactions. Electrolytic and metallic conduction, conductance
in electrolytic solutions, specific and molar conductivities and their variation
with concentration: Kohlrausch’s law and its applications.

**Electrochemical cells** - Electrolytic and Galvanic cells, different
types of electrodes, electrode potentials including standard electrode potential,
half - cell and cell reactions, emf of a Galvanic cell and its measurement; Nernst
equation and its applications; Relationship between cell potential and Gibbs’ energy
change; Dry cell and lead accumulator; Fuel cells.

**Chemical kinetics:** Rate of a chemical reaction, factors affecting
the rate of reactions: concentration, temperature, pressure and catalyst; elementary
and complex reactions, order and molecularity of reactions, rate law, rate constant
and its units, differential and integral forms of zero and first order reactions,
their characteristics and half - lives, effect of temperature on rate of reactions
– Arrhenius theory, activation energy and its calculation, collision theory of bimolecular
gaseous reactions (no derivation).

**Surface chemistry:** Adsorption- Physisorption and chemisorption
and their characteristics, factors affecting adsorption of gases on solids - Freundlich
and Langmuir adsorption isotherms, adsorption from solutions. Colloidal state -
distinction among true solutions, colloids and suspensions, classification of colloids-lyophilic,
lyophobic; multi molecular, macromolecular and associated colloids (micelles), preparation
and properties of colloids - Tyndall effect, Brownian movement, electrophoresis,
dialysis, coagulation and ﬂocculation; Emulsions and their characteristics.

#### UNIT 3: Hydrogen & s - Block Element

**Classiﬁcation of elements and periodicity in properties:** Modern
periodic law and present form of the periodic table, s, p, d and f block elements,
periodic trends in properties of elements atomic and ionic radii, ionization enthalpy,
electron gain enthalpy, valence, oxidation states and chemical reactivity.

**General principles and processes of isolation of metals:** Modes
of occurrence of elements in nature, minerals, ores; Steps involved in the extraction
of metals - concentration, reduction (chemical and electrolytic methods) and refining
with special reference to the extraction of Al, Cu, Zn & Fe; Thermodynamics and
electrochemical principles involved in the extraction of metals.

**Hydrogen**: Position of hydrogen in periodic table, isotopes, preparation
& uses of hydrogen; Physical & Chemical properties of water & Heavy Water; Structure,
preparation, reactions & uses of hydrogen peroxide; Hydrogen as a fuel.

**s - Block elements (alkali and alkaline earth metals) Group - 1 and 2 Elements:**
General introduction, electronic configuration and general trends in physical and
chemical properties of elements, anomalous properties of the first element of each
group, diagonal relationships. Preparation and properties of some important compounds
- sodium carbonate and sodium hydroxide; Industrial uses of lime, limestone, Plaster
of Paris and cement; Biological significance of Na, K, Mg and Ca.

#### UNIT 4: p, d & f block Elements and Environmental Chemistry

**p - Block elements**

**Group – 13 to Group – 18 Elements:** General Introduction: Electronic
configuration and general trends in physical and chemical properties of elements
across the periods and down the groups; unique behaviour of the first element in
each group. GroupWise study of the p – block elements.

**Group – 13:** Preparation, properties and uses of boron and aluminium;
properties of boric acid, diborane, boron tri- ﬂuoride, aluminium chloride and alums.

**Group – 14:** Allotropes of carbon, tendency for catenation; Structure
& properties of silicates, and zeolites.

**Group – 15:** Properties & uses of nitrogen and phosphorus; Allotrophic
forms of phosphorus; Preparation, properties, structures and uses of ammonia, nitric
acid, phosphine and phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids
of phosphorus.

**Group – 16:** Preparation, properties, structures & uses of ozone;
Allotropic forms of sulphur; Preparations, properties, structures & uses of sulphuric
acid (including its industrial preparation); Structures of oxoacids of sulphur.

**Group - 17:** Preparation, properties and uses of hydrochloric acid;
Trends in the acidic nature of hydrogen halides; Structures of interhalogen compounds
and oxides & oxoacids of halogens.

**Group – 18:** Occurrence and uses of noble gases; Structures of ﬂuorides
and oxides of xenon.

**d – and f – Block elements:** Transition Elements: General introduction,
electronic configuration, occurrence and characteristics, general trends in properties
of the first row transition elements - physical properties, ionization enthalpy,
oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties,
complex formation, interstitial compounds, alloy formation; Preparation, properties
and uses of K_{2} Cr_{2} O_{7} and KMnO_{4} .

**Inner Transition Elements:** Lanthanoids - Electronic configuration,
oxidation states and lanthanoid contraction. Actinoids - Electronic configuration
and oxidation states.

**Co-ordinating compounds:** Introduction to Co-ordination compounds,
Werner’s theory; ligands, co-ordination number, denticity, chelation; IUPAC nomenclature
of mononuclear co- ordination compounds, isomerism; Bonding-Valence bond approach
and basic ideas of Crystal field theory, colour and magnetic properties; Importance
of co-ordination compounds.

**Environmental chemistry:** Environmental pollution- Atmospheric,
water and soil.

**Tropospheric pollutants – Gaseous pollutants:** Oxides of carbon,
nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention;
Green house effect and Global warming; Acid rain; Particulate pollutants: Smoke,
dust, smog, fumes, mist; their sources, harmful effects and prevention.

**Stratospheric pollution:** Formation and breakdown of ozone, depletion
of ozone layer -its mechanism and effects. Water Pollution - Major pollutants such
as, pathogens, organic wastes and chemical pollutants; their harmful effects and
prevention. Soil pollution - Major pollutants such as: Pesticides (insecticides,.
Herbicides and fungicides), their harmful effects and prevention. Strategies to
control environmental pollution.

#### UNIT 5: Basic Concepts of Organic Chemistry

**Puriﬁcation and characterisation of organic compounds: Puriﬁcation:**
Crystallization, sublimation, distillation, differential extraction and chromatography
- principles and their applications.

**Qualitative analysis:** Detection of nitrogen, sulphur, phosphorus
and halogens.

**Quantitative analysis:** Estimation of carbon, hydrogen, nitrogen,halogens,
sulphur, phosphorus. Calculations of empirical formulae and molecular formulae;
Numerical problems in organic quantitative analysis.

**Some basic principles of organic chemistry:** Tetravalency of carbon;
Shapes of simple molecules - hybridization (s and p); Classification of organic
compounds based on functional groups: - C = C - , - C H C – and those containing
halogens, oxygen, nitrogen and sulphur; Homologous series; Isomerism - structural
and stereoisomerism.

**Nomenclature (Trivial and IUPAC) Covalent bond ﬁssion:** Homolytic
and heterolytic: free radicals, carbocations and carbanions; stability of carbocations
and free radicals, electrophiles and nucleophiles.

**Electronic displacement in a covalent bond** - Inductive effect,
electromeric effect, resonance and hyperconjugation. Hydrocarbons: Classification,
isomerism, IUPAC nomenclature, general methods of preparation, properties & reactions.

**Alkanes** - Conformations: Sawhorse and Newman projections (of ethane);
Mechanism of halogenations of Alkanes.

**Alkenes** - Geometrical isomerism; Mechanism of electrophilic addition:
addition of hydrogen, halogens, water, hydrogen halides (Markownikoff’s and peroxide
effect); Ozonolysis and polymerization.

**Alkynes** - Acidic character; Addition of hydrogen, halogens, water
and hydrogen halides; Polymerization.

**Aromatic hydrocarbons** - Nomenclature, benzene - structure and aromaticity;
Mechanism of electrophilic substitution: halogenations, nitration, Friedel – Craft’s
alkylation and acylation, directive inﬂuence of functional group in mono- substituted
benzene.

**Organic compounds containing halogens:** General methods of preparation,
properties and reactions; Nature of C-X bond; Mechanisms of substitution reactions.
Uses; Environmental effects of chloroform & iodoform.

#### UNIT 6: Oxygen, Nitrogen, Polymers & Bio molecules

**Organic compounds containing oxygen:** General methods of preparation,
properties, reactions and uses.

**Alcohols:** Identification of primary, secondary and tertiary alcohols;
mechanism of dehydration.

**Phenols:** Acidic nature, electrophilic substitution reactions: halogenations,
nitration and sulphonation, Reimer - Tiemann reaction.

**Ethers:** Structure.

**Aldehyde and Ketones:** Nature of carbonyl group; Nucleophilic addition
to >C=O group, relative reactivities of aldehydes and ketones; Important reactions
such as – Nucleophilic addition reactions (addition of HCN, NH_{3} and its
derivatives), Grignard reagent; oxidation; reduction (Wolff Kishner and Clemmensen);
acidity of - hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction;
Chemical tests to distinguish between aldehydes and Ketones.

**Carboxylic acids:** Acidic strength and factors affecting it.

**Organic compounds containing nitrogen:** General methods of preparation,
properties, reactions and uses.

**Amines:** Nomenclature, classification, structure, basic character
and identification of primary, secondary and tertiary amines and their basic character.

**Diazonium Salts:** Importance in synthetic organic chemistry.

**Polymers:** General introduction and classification of polymers,
general methods of polymerization-addition and condensation, copolymerization; Natural
and synthetic rubber and vulcanization; some important polymers with emphasis on
their monomers and uses - polythene, nylon, polyester and bakelite.

**Biomolecules:** General introduction and importance of biomolecules.

**Carbohydrates:** Classification: aldoses and ketoses; monosaccharides
(glucose and fructose) and constituent monosaccharides of oligosacchorides (sucrose,
lactose and maltose).

**Proteins:** Elementary Idea of - amino acids, peptide bond, polypeptides;
Proteins: primary, secondary, tertiary and quaternary structure (qualitative idea
only), denaturation of proteins, enzymes.

**Vitamins:** Classification and functions.

**Nucleic acids:** Chemical constitution of DNA and RNA. Biological
functions of nucleicacids.

**Chemistry in everyday life:** Chemicals in medicines– Analgesics,
tranquilisers, antiseptics, disinfectants, antimicrobials, antifertility drugs,
antibiotics, antacids antihistamines-their meaning & common example.

**Chemicals in food** - Preservatives, artificial sweetening agents
- common examples.

**Cleansing agents** - Soaps and detergents, cleansing action.

#### Physics

#### UNIT 1: Motion

**Laws of motion:** Force and Inertia, Newton’s First Law of motion;
Momentum, Newton’s Second Law of motion; Impulse; Newton’s Third Law of motion.
Law of conservation of linear momentum and its applications; equilibrium of concurrent
forces. Static and Kinetic friction, laws of friction, rolling friction. Dynamics
of uniform circular motion: Centripetal force and its applications.

**Work, energy and power:** Work done by a constant force and a variable
force; kinetic and potential energies, work energy theorem, power. Potential energy
of a spring, conservation of mechanical energy, conservative and non-conservative
forces; Elastic & inelastic collisions in one and two dimensions.

**Rotational motion:** Centre of mass of a two-particle system, Centre
of mass of a rigid body; Basic concepts of rotational motion; moment of a force,
torque, angular momentum, conservation of angular momentum and its applications;
moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical
objects, parallel and perpendicular axes theorems and their applications. Rigid
body rotation, equations of rotational motion.

#### UNIT 2: Kinematics, Gravitation & Oscillations

**Physics and measurement:** Physics, technology and society, SI units,
Fundamental and derived units. Least count, accuracy and precision of measuring
instruments, Errors in measurement, Dimensions of Physical quantities, dimensional
analysis and its applications.

**Kinematics:** Frame of reference. Motion in a straight line: Position-time
graph, speed and velocity. Uniform and non- uniform motion, average speed and instantaneous
velocity, uniformly accelerated motion, velocity- time, position-time graphs, relations
for uniformly accelerated motion. Scalars and Vectors, Vector addition and Subtraction,
Zero Vector, Scalar and Vector products, Unit Vector, Resolution of a Vector. Relative
Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.

**Gravitation:** The universal law of gravitation. Acceleration due
to gravity and its variation with altitude and depth. Kepler’s laws of planetary
motion. Gravitational potential energy; gravitational potential. Escape velocity.
Orbital velocity of a satellite. Geo-stationary satellites.

**Oscillations and waves: **Periodic motion - period, frequency, displacement
as a function of time. Periodic functions. Simple harmonic motion (S.H.M.) and its
equation; phase; Oscillations of a spring - restoring force and force constant;
energy in S.H.M. : kinetic and potential energies; Simple pendulum - derivation
of expression for its time period; Free, forced and damped oscillations, resonance;
Wave motion; Longitudinal and transverse waves, speed of a wave; Displacement relation
for a progressive wave; Principle of superposition of waves, reﬂection of waves
Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats,
Doppler effect in sound.

#### UNIT 3: Thermal Physics

**Properties of solids and liquids:** Elastic behaviour, Stress- strain
relationship, Hooke’s Law, Young’s modulus, Bulk modulus, modulus of rigidity. Pressure
due to a ﬂuid column; Pascal’s law and its applications. Viscosity, Stokes’ law,
terminal velocity, streamline and turbulent ﬂow, Reynolds number. Bernoulli’s principle
and its applications. Surface energy and surface tension, angle of contact, application
of surface tension - drops, bubbles and capillary rise. Heat, temperature, thermal
expansion; specific heat capacity, calorimetry; change of state, latent heat. Heat
transfer conduction, convection and radiation, Newton’s law of cooling.

**Thermodynamics:** Thermal equilibrium, zeroth law of thermodynamics,
concept of temperature. Heat, work and internal energy. First law of thermodynamics.
Second law of thermodynamics: reversible and irreversible processes. Carnot engine
and its efficiency.

**Kinetic theory of gases: **Equation of state of a perfect gas, work
done on compressing a gas. Kinetic theory of gases - assumptions, concept of pressure.
Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom,
Law of equipartition of energy, applications to specific heat capacities of gases;
Mean free path, Avogadro’s number.

#### UNIT 4: Electricity & Magnetism

**Electrostatics:** Electric charges: Conservation of charge, Coulomb’s
law-forces between two point charges, forces between multiple charges; superposition
principle and continuous charge distribution. Electric field: Electric field due
to a point charge, Electric field lines, Electric dipole, Electric field due to
a dipole, Torque on a dipole in a uniform electric field. Electric ﬂux, Gauss’s
law and its applications to find field due to infinitely long uniformly charged
straight wire, uniformly charged infinite plane sheet and uniformly charged thin
spherical shell. Electric potential and its calculation for a point charge, electric
dipole and system of charges; Equipotential surfaces, Electrical potential energy
of a system of two point charges in an electrostatic field. Conductors and insulators,
Dielectrics and electric polarization, capacitor, combination of capacitors in series
and in parallel, capacitance of a parallel plate capacitor with and without dielectric
medium between the plates, Energy stored in a capacitor.

**Current electricity:** Electric current, Drift velocity, Ohm’s law,
Electrical resistance, Resistances of different materials, V-I characteristics of
Ohmic and nonohmic conductors, Electrical energy and power, Electrical resistivity,
Colour code for resistors; Series and parallel combinations of resistors; Temperature
dependence of resistance. Electric Cell and its internal resistance, potential difference
and emf of a cell, combination of cells in series and in parallel. Kirchhoff’s laws
and their applications. Wheatstone bridge, Metre bridge. Potentiometer - principle
and its applications.

**Magnetic effects of current and magnetism:** Biot - Savart law and
its application to current carrying circular loop. Ampere’s law and its applications
to infinitely long current carrying straight wire and solenoid. Force on a moving
charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying
conductor in a uniform magnetic field. Force between two parallel current-carrying
conductors- definition of ampere. Torque experienced by a current loop in uniform
magnetic field; Moving coil galvanometer, its current sensitivity and conversion
to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole
moment. Bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic
field and magnetic elements. Para-, dia- and ferro- magnetic substances. Magnetic
susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.

#### UNIT 5: Atomic Structure & Optics

**Atoms and nuclei:** Alpha-particle scattering experiment; Rutherford’s
model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size
of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity-alpha, beta
and gamma particles/rays and their properties; radioactive decay law. Mass-energy
relation, mass defect; binding energy per nucleon and its variation with mass number,
nuclear fission and fusion.

**Dual nature of matter and radiation:** Dual nature of radiation.
Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric
equation; particle nature of light. Matter waves-wave nature of particle, de Broglie
relation. Davisson-Germer experiment.

**Optics: **Reﬂection and refraction of light at plane and spherical
surfaces, mirror formula, Total internal reﬂection and its applications, Deviation
and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens,
Combination of thin lenses in contact, Microscope and Astronomical Telescope (reﬂecting
and refracting) and their magnifying powers.

**Wave optics: **wavefront and Huygens’ principle, Laws of reﬂection
and refraction using Huygen’s principle. Interference, Young’s double
slit experiment and expression for fringe width. Diffraction due to a single slit,
width of central maximum. Resolving power of microscopes and astronomical telescopes,
Polarisation, plane polarized light; Brewster’s law, uses of plane polarized
light and Polaroids.

#### UNIT 6: Electrical & Electronics

**Electromagnetic induction and alternating currents:** Electromagnetic
induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self
and mutual inductance. Alternating currents, peak and rms value of alternating current/
voltage; reactance and impedance; LCR series circuit, resonance; Quality factor,
power in AC circuits, wattless current. AC generator and transformer.

**Electromagnetic waves: **Electromagnetic waves and their characteristics.
Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves,
microwaves, infrared, visible, ultraviolet, X- rays, gamma rays). Applications of
e.m. waves.

**Electronic devices:** Semiconductors; semiconductor diode: I-V characteristics
in forward and reverse bias; diode as a rectifier; I-V characteristics of LED, photodiode,
solar cell and Zener diode; Zener diode as a voltage regulator. Junction transistor,
transistor action, characteristics of a transistor; transistor as an amplifier (common
emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR).
Transistor as a switch. Communication systems: Propagation of electromagnetic waves
in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude
and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium,
Basic Elements of a Communication System.

#### Mathematics

#### UNIT 1: Algebra

**Sets, relations and functions:** Sets and their representation; Union,
intersection and complement of sets and their algebraic properties; Power set; Relation,
Types of relations, equivalence relations, functions;. oneone, into and onto functions,
composition of functions.

**Complex numbers and quadratic equations:** Complex numbers as ordered
pairs of reals, Representation of complex numbers in the form a+ib and their representation
in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or
amplitude) of a complex number, square root of a complex number, triangle inequality,
Quadratic equations in real and complex number system and their solutions. Relation
between roots and coefficients, nature of roots, formation of quadratic equations
with given roots.

**Sequences and series: **Arithmetic and Geometric progressions, insertion
of arithmetic, geometric means between two given numbers. Relation between A.M.
and G.M. Sum upto n terms of special series: S n, S n2, Sn3. Arithmetico – Geometric
progression.

#### UNIT 2: Matrices, Vectors & Reasoning

**Matrices & Determinants:** Matrices, algebra of matrices, types of
matrices, determinants and matrices of order two and three. Properties of determinants,
evaluation of determinants, area of triangles using determinants. Adjoint and evaluation
of inverse of a square matrix using determinants and elementary transformations,
Test of consistency and solution of simultaneous linear equations in two or three
variables using determinants and matrices.

**Vector algebra:** Vectors and scalars, addition of vectors, components
of a vector in two dimensions and three dimensional space, scalar and vector products,
scalar and vector triple product.

**Mathematical reasoning:** Statements, logical operations and, or,
implies, implied by, if and only if. Understanding of tautology, contradiction,
converse and contrapositive.

#### UNIT 3: Permutation-Combinations & Binomial Theorem

**Permutations and Combinations:** Fundamental principle of counting,
permutation as an arrangement and combination as selection, Meaning of P (n, r)
and C (n, r), simple applications.

**Mathematical induction: **Principle of Mathematical Induction and
its simple applications.

**Binomial theorem and its simple applications:** Binomial theorem
for a positive integral index, general term and middle term, properties of Binomial
coefficients and simple applications.

#### UNIT 4: Limit, Integration & Differentiation

**Limit, continuity and differentiability:** Real valued functions,
algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential
functions, inverse functions. Graphs of simple functions. Limits, continuity and
differentiability. Differentiation of the sum, difference, product and quotient
of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic,
exponential, composite and implicit functions; derivatives of order upto two. Rolle’s
and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change
of quantities, monotonic increasing and decreasing functions, Maxima and minima
of functions of one variable, tangents and normals.

**Integral calculus:** Integral as an anti derivative. Fundamental
integrals involving algebraic, trigonometric, exponential and logarithmic functions.
Integration by substitution, by parts and by partial fractions. Integration using
trigonometric identities. Evaluation of simple integrals of the type:

Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite
integrals. Evaluation of definite integrals, determining areas of the regions bounded
by simple curves in standard form Differential equations: Ordinary differential
equations, their order and degree. Formation of differential equations. Solution
of differential equations by the method of separation of variables, solution of
homogeneous and linear differential equations of the type:

#### UNIT 5: Geometry

**Coordinate geometry:** Cartesian system of rectangular coordinates
10 in a plane, distance formula, section formula, locus and its equation, translation
of axes, slope of a line, parallel and perpendicular lines, intercepts of a line
on the coordinate axes.

**Straight lines:** Various forms of equations of a line, intersection
of lines, angles between two lines, conditions for concurrence of three lines, distance
of a point from a line, equations of internal and external bisectors of angles between
two lines, coordinates of centroid, orthocentre and circumcentre of a triangle,
equation of family of lines passing through the point of intersection of two lines.

**Circles, conic sections: **Standard form of equation of a circle,
general form of the equation of a circle, its radius and centre, equation of a circle
when the end points of a diameter are given, points of intersection of a line and
a circle with the centre at the origin and condition for a line to be tangent to
a circle, equation of the tangent. Sections of cones, equations of conic sections
(parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to
be a tangent and point (s) of tangency.

**Three Dimensional Geometry:** Coordinates of a point in space, distance
between two points, section formula, direction ratios and direction cosines, angle
between two intersecting lines. Skew lines, the shortest distance between them and
its equation. Equations of a line and a plane in different forms, intersection of
a line and a plane, coplanar lines.

#### UNIT 6: Probability & Trigonometry

**Statistics and probability:** Measures of Dispersion: Calculation
of mean, median, mode of grouped and ungrouped data calculation of standard deviation,
variance and mean deviation for grouped and ungrouped data.

**Probability:** Probability of an event, addition and multiplication
theorems of probability, Baye’s theorem, probability distribution of a random variate,
Bernoulli trials and Binomial distribution.

**Trigonometry:** Trigonometrical Identities and equations, Trigonometrical
functions, Inverse trigonometrical function and their properties, heights and Distances.

#### Biology

#### Unit 1: Diversity & Structural Organisation

What is living? Biodiversity; Need for classification; Three domains of life; Taxonomy
& Systematics; Concept of species and taxonomical hierarchy; Binomial nomenclature;
Tools for study of Taxonomy – Museums, Zoos, Herbaria, Botanical gardens.

**Five kingdom classiﬁcation:** salient features and classification
of Monera; Protista and Fungi into major groups; Lichens; Viruses and Viroids, Salient
features and classification of plants into major groups-Algae, Bryophytes, Pteridophytes,
Gymnosperms and Angiosperms; Angiosperms- classification up to class, characteristic
features and examples, Salient features and classification of animals-nonchordate
up to phyla level and chordate up to classes level.

**Structural Organisation in Animals and Plants:** Morphology and modifications;
Tissues; Anatomy and functions of different parts of ﬂowering plants: Root, stem,
leaf, inﬂorescence- cymose and recemose, ﬂower, fruit and see, Animal tissues; Morphology,
anatomy and functions of different systems (digestive, circulatory, respiratory,
nervous and reproductive) of an insect (cockroach).

**Cell Structure and Function :** Cell theory and cell as the basic
Unit of life; Structure of prokaryotic and eukaryotic cell; Plant cell and animal
cell; Cell envelope, cell membrane, cell wall; Cell organelles-structure and function;
Endomembrane system-endoplasmic reticulum, Golgi bodies, lysosomes, vacuoles; mitochondria,
ribosomes, plastids, micro bodies; Cytoskeleton, cilia, ﬂagella, centrioles (ultra
structure and function); Nucleus-nuclear membrane, chromatin, nucleolus. Chemical
constituents of living cells: Biomolecules-structure and function of proteins, carbodydrates,
lipids, nucleic acids; Enzymes-types, properties, enzyme action;

**B Cell division:** Cell cycle, mitosis, meiosis and their significance.

#### Unit 2: Plant Physiology

**Transport in plants:** Movement of water, gases and nutrients; Cell
to cell transport-Diffusion, facilitated diffusion, active transport; Plant – water
relations – Imbibition, water potential, osmosis, plasmolysis; Long distance transport
of water – Absorption, apoplast, symplast, transpiration pull, root pressure and
guttation; Transpiration-Opening and closing of stomata; Uptake and translocation
of mineral nutrients- Transport of food, phloem transport, Mass ﬂow hypothesis;
Diffusion of gases.

**Mineral nutrition:** Essential minerals, macro and micronutrients
and their role; Deficiency symptoms; Mineral toxicity; Elementary idea of Hydroponics
as a method to study mineral nutrition; Nitrogen metabolism-Nitrogen cycle, biological
nitrogen fixation.

**Photosynthesis:** Photosynthesis as a means of Autotrophic nutrition;
Site of photosynthesis take place; pigments involved in Photosynthesis (Elementary
idea); Photochemical and biosynthetic phases of photosynthesis; Cyclic and non cyclic
and photophosphorylation; Chemiosmotic hypothesis; Photorespiration C3 and C4 pathways;
Factors affecting photosynthesis.

**Respiration:** Exchange gases; Cellular respiration- glycolysis,
fermentation (anaerobic), TCA cycle and electron transport system (aerobic); Energy
relations- Number of ATP molecules generated; Amphibolicpathways; Respiratory quotient.

**Plant growth and development:** Seed germination; Phases of Plant
growth and plant growth rate; Conditions of growth;Plant growth and development:
Seed germination; Phases of Plant growth and plant growth rate; Conditions of growth;
Differentiation, dedifferentiation and redifferentiation; Sequence of developmental
process in a plant cell; Growth regulators-auxin, gibberellin, cytokinin, ethylene,
ABA; Seed dormancy; Vernalisation; Photoperiodism.

#### Unit 3: Human Physiology

**Digestion and absorption:** Alimentary canal and digestive glands;
Role of digestive enzymes and gastrointestinal hormones; Peristalsis, digestion,
absorption and assimilation of proteins, carbohydrates and fats; Caloric value of
proteins, carbohydrates and fats; Egestion; Nutritional and digestive disorders
– PEM, indigestion, constipation, vomiting, jaundice, diarrhea.

**Breathing and Respiration:** Respiratory organs in animals; Respiratory
system in humans; Mechanism of breathing and its regulation in humans- Exchange
of gases, transport of gases and regulation of respiration Respiratory volumes;
Disorders related to respiration-Asthma, Emphysema, Occupational respiratory disorders.

**Body ﬂuids and circulation:** Composition of blood, blood groups,
coagulation of blood; Composition of lymph and its function; Human circulatory system-Structure
of human heart and blood vessels; Cardiac cycle, cardiac output, ECG, Double circulation;
Regulation of cardiac activity; Disorders of circulatory system-Hypertension, Coronary
artery disease, Angina pectoris, Heart failure.

**Excretory products and their elimination:** Modes of excretion- Ammonotelism,
ureotelism, uricotelism; Human excretory system-structure and fuction; Urine formation,
Osmoregulation; Regulation of kidney function-Renin- angiotensin, Atrial Natriuretic
Factor, ADH and Diabetes insipidus; Role of other organs in excretion; Disorders;
Uraemia, Renal failure, Renal calculi, Nephritis; Dialysis and artificial kidney.

**Locomotion and Movement:** Types of movement- ciliary, fiagellar,
muscular; Skeletal muscle- contractile proteins and muscle contraction; Skeletal
system and its functions; Joints; Disorders of muscular and skeletal system-Myasthenia
gravis, Tetany, Muscular dystrophy, Arthritis, Osteoporosis, Gout.

**Neural control and coordination:** Neuron and nerves; Nervous system
in humans- central nervous system, peripheral nervous system and visceral nervous
system; Generation and conduction of nerve impulse; Reﬂex action; Sense organs;
Elementary structure and function of eye and ear.

**Chemical coordination and regulation:** Endocrine glands and hormones;
Human endocrine system-Hypothalamus, Pituitary, Pineal, Thyroid, Parathyroid, Adrenal,
Pancreas, Gonads; Mechanism of hormone action; Role of hormones as messengers and
regulators, Hypo-and hyperactivity and related disorders (Common disorders e.g.
Dwarfism, Acromegaly, Cretinism, goiter, exopthalmicgoiter, diabetes, Addison’s
disease).

#### Unit 4: Reproduction, Genetics and Evolution

**Reproduction in organisms:** Reproduction, a characteristic feature
of all organisms for continuation of species; Modes of reproduction – Asexual and
sexual; Asexual reproduction; Modes-Binary fission, sporulation, budding, gemmule,
fragmentation; vegetative propagation in plants.

**Sexual reproduction in ﬂowering plants:** Flower structure; Development
of male and female gametophytes; Pollination- types, agencies and examples; Outbreeding
devices; Pollen- Pistil interaction; Double fertilization; Post fertilization events-
Development of endosperm and embryo, Development of seed and formation of fruit;
Special modes-apomixis, parthenocarpy, polyembryony; Significance of seed and fruit
formation.

**Human Reproduction:** Male and female reproductive systems; Microscopic
anatomy of test is and ovary; Gametogenesis- spermatogenesis & oogenesis; Menstrual
cycle; Fertilisation, embryo development upto blastocyst formation, implantation;
Pregnancy and placenta formation; Parturition; Lactation.

**Reproductive health:** Need for reproductive health and prevention
of sexually transmitted diseases (STD); Birth control-Need and Methods, Contraception
and Medical Termination of Pregnancy (MTP); Amniocentesis; Infertility and assisted
reproductive technologies – IVF, ZIFT, GIFT.

**Genetics and Evolution: **Heredity and variation: Mendelian Inheritance;
Deviations from Mendelism- Incomplete dominance, Co-dominance, Multiple alleles
and Inheritance of blood groups, Pleiotropy; Elementary idea of polygenic inheritance;
Chromosome theory of inheritance; Chromosomes and genes; Sex determination-In humans,
birds, honey bee; Linkage and crossing over; Sex linked inheritance-Haemophilia,
Colour blindness; Mendelian disorders in humans-Thalassemia; Chromosomal disorders
in humans; Down’s syndrome, Turner’s and Klinefelter’s syndromes.

**Molecular basis of Inheritance:** Search for genetic material and
DNA as genetic material; Structure of DNA and RNA; DNA packaging; DNA replication;
Central dogma; Transcription, genetic code, translation; Gene expression and regulation-
Lac Operon; Genome and human genome project; DNA finger printing.

**Evolution:** Origin of life; Biological evolution and evidences for
biological evolution from Paleontology, comparative anatomy, embryology and molecular
evidence); Darwin’s contribution, Modern Synthetic theory of Evolution; Mechanism
of evolution-Variation (Mutation and Recombination) and Natural Selection with examples,
types of natural selection; Gene ﬂow and genetic drift; Hardy-Weinberg’s principle;
Adaptive Radiation; Human evolution.

#### Unit 5: Biology, Biotechnology and Human Welfare

**Health and Disease:** Pathogens; parasites causing human diseases
(Malaria, Filariasis, Ascariasis Typhoid, Pneumonia, common cold, amoebiasis, ring
worm); Basic concepts of immunology-vaccines; Cancer, HIV and AIDS; Adolescence,
drug and alcohol abuse.

**Improvement in food production:** Plant breeding, tissue culture,
single cell protein, Biofortification; Apiculture and Animal husbandry.

**Microbes in human welfare:** In household food processing, industrial
production, sewage treatment, energy generation and as biocontrol agents and biofertilizers.

**Biotechnology and Its Applications:** Principles and process of Biotechnology:
Genetic engineering (Recombinant DNA technology).

**Application of Biotechnology in health and agriculture:** Human insulin
and vaccine production, gene therapy; Genetically modified organisms-Bt crops; Transgenic
Animals; Biosafety issues-Biopiracy and patents.

#### Unit 6: Ecology and environment

**Organisms and environment:** Habitat and niche; Population and ecological
adaptations; Population interactions- mutualism, competition, predation, parasitism;
Population attributes-growth, birth rate and death rate, age distribution.

**Ecosystem:** Patterns, components; productivity and decomposition;
Energy ﬂow; Pyramids of number, biomass, energy; Nutrient cycling (carbon and phosphorous);
Ecological succession; Ecological Services-Carbon fixation, pollination, oxygen
release.

**Biodiversity and its conservation:** Concept of Biodiversity; Patterns
of Biodiversity; Importance of Biodiversity; Loss of Biodiversity; Biodiversity
conservation; Hotspots, endangered organisms, extinction, Red Data Book, biosphere
reserves, National parks and sanctuaries.

**Environmental issues:** Air pollution and its control; Water pollution
and its control; Agrochemicals and their effects; Solid waste management; Radioactive
waste management; Greenhouse effect and global warning; Ozone depletion; Deforestation;
Any three case studies as success stories addressing environmental issues.