BOTANY

Morphology of plants: Root, Stem, Leaf, Inflorescence, flower, Fruit and seeds.

Functions of different parts of flowering plants: Roots, Stem, leaf, inflorescence, flower, fruit and

seeds.

Plant anatomy : Root, Stem and leaf. Different types of plant tissues.

Plant Physiology : Movement of water, food, nutrients, and gases. Plants and water relationship,

Mineral nutrition, Respiration, Photosynthesis. Plant growth, Phytohormones and development.

Biomolecules : Basic Chemical Constituents of living bodies, structure and function of carbohydrates,

proteins, lipids and nucleic acids. Enzymes : types, properties and function.

Diversity of living organisms.

Classification of living organisms : Five kingdom classification, major groups and principles of

classification with each kingdom. Systematics and binomial system of nomenclature. Salient features

of plant (major groups; angiosperms up to subclass level of classification).

Botanical gardens and herbaria.

Reproduction in flowering plants : Vegetative, asexual and sexual.

Flowers : pre fertilization, double fertilization, structure and events, apomixes and polyembryony.

Development of seeds and fruits.

Ecosystem : Components, types, energy and food.

Species, Population and community ecology.

Ecological adaptation, colour of diversity and conservation of biodiversity

Environmental issues, pollution and deforestation

Global warming, Ozone layer depletion, underground wake level, and threat to biodiversity(with

reference to wild life).

Mendelian inheritance, Chromosome theory of inheritance,

Deviations from Mendelian ratio(gene interaction)

Linkage and crossing over.

Genetic code, DNA-replication, transcription and translation.

Gene expression and regulation.

Recombinant DNA technology and B.T. Cotton.

ZOOLOGY

Salient features of animal classification(non chordates up to phylum level, and chordates up to class

level).

Different types of animal tissues.

Morphology, anatomy and functions of different systems of an annelid(earthworm), an

insect(cockroach) and an amphibian(frog).

Human physiology : Digestion and absorption, breathing and respiration, body fluids and circulation,

excretory products and elimination, locomotion and movement(skeleton system), control and

coordination.

Cell : Cell wall, cell membrane and cell organelles(plastids, mitochondria, endoplasmic reticulum,

Golgi apparatus, dictyosomes, ribosomes, lysosomes, vacuoles, centrioles) and nuclear organization.

Mitosis, meiosis and cell cycle.

Reproduction in organism : asexual sexual and vegetative.

Human reproduction : The male and female reproductive system, Gametogenesis menstrual cycle,

Fertilization and implantation, pregnance and embryonic development, parturition and lactation.

Reproductive health problem and strategies, population explosion and birth control, medical termination of pregnancy, STD infertility.

Basic concepts of immunology, vaccines, insulin, pathogens, parasite.

Sex determination in human being XX, XY.

Inheritance, pattern of hemophilia and blood groups in human being.

DNA Finger printing,

Evolution : Theories and evidences.

Cancer and AIDS, Adolescence and drug/alcohol abuse.

Zoological parks, museums and sanctuaries.

INORGANIC CHEMISTRY

1. Classification of elements and periodicity in properties. Significance of classification, genesis of periodic classification, modern periodic law and

present form of periodic table. Nomenclature of elements with atomic number > 100.

Electronic configuration, types of elements : s-, p-, d-, f- blocks. Periodic trends in properties

of elements Atomic radii, ionic radii, ionization enthalpy, electron gain enthalpy, electro negativity, valence.

2. Chemical Bonding and Molecular Structure : Kossel Lewis approach to chemical bonding, covalent bond, ionic bond, bond parameters, resonance, VSEPR theory, Valence bond theory, hybridization, molecular orbital theory,

bonding in some homonuclear diatomic molecules, hydrogen bonding.

3. Hydrogen Position of hydrogen in periodic table, isotopes, preparation and properties of dihydrogen,

hydrides, water(H2O), heavy water(D2O), hydrogen peroxide(H2O2), dihydrogen as a fuel.

4. General Principles and processes of isolation of elements Principles and methods of extraction concentration, oxidation, reduction, electrolytic method and refining, occurrence and principles of extraction of aluminum, copper, zinc and

iron.

5. s- Block Elements General Characteristics of the alkali metals and their compounds.

General characteristics of the alkaline earth metals and their compounds. Manufacture,

properties and uses of industrially important sodium and calcium compounds including

Portland cement. Biological importance of sodium, potassium magnesium and calcium.

6. p-Block elements Gp 13 elements :- General introduction, variation of properties, oxidation states, trends in

chemical reactivity, anomalous properties of first element of gp, Boron- physical and

chemical properties. Some important compounds : borax, boric acid, boron hydrides.

Aluminium : reactions with acids and alkalis.

Gp 14 elements : General introduction, variation of properties, oxidation states, trends in

chemical reactivity, anomalous behavious of first element of gp : carbon catenation, allotropic forms, physical and chemical properties, uses of some important compounds oxides. Important compounds of silicon and a few uses : silicon tetracholoride, silicones,

silicates and zeolites.

Gp 15 elements : General introduction, oxidation states, trend in physical and chemical

properties. Preparation and properties and uses of nitrogen, ammonia and nitric acid. Oxides

of nitrogen(structures only). Phosphorus allotropic forms, compounds of phosphrous : preparation and properties of hosphine, halides(Pcl3, Pcl5) and oxoacids.

Gp 16 elements : General introduction, oxidation states, trends in physical and chemical

properties. Preparation properties and uses of O2, O3. Sulphur allotropic forms, preparation, properties and uses of SO2, H2SO4, Industrial process of manufacture of H2SO4. Oxoacids

of sulphur(structures only).

Gp 17 elements : General introduction, oxidation states, trends in physical and chemical

properties. Preparation, properties and uses of chlorine and hydrochloric acid. Interhalogen

compounds, oxoacids of halogens(structures only).

Gp 18 elements : General introduction, trends in physical and chemical properties. Xenon-

fluorine compounds, xenon oxygen compounds.

7. d and f- block elements General introduction, electronic configuration, characteristics of transition metals. General

trends in properties of first row transition metals metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial

compounds, alloy formation. Preparation and properties of K2Cr2O7 and KMnO4.

Lanthanoids electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction.

Actinoids : Electronic configuration oxidation states.

8. Co-ordination compounds Werners theory of co-ordination compounds, definition of some important terms pertaining to co-ordination compounds, nomenclature, isomerism and bonding in co-ordination

compounds. Bonding in metal carbonyls, stability of co-ordination compounds, importance

and applications of co-ordination compounds.

9. Environmental Chemistry Environmental pollution, air, water and soil pollution, industrial waste, strategies to control

environmental pollution, green chemistry.

Physical Chemistry

1. Some basic concepts of chemistry Laws of chemical combinations, Daltons atomic theory, atomic and molecular masses, mole

concept and molar masses, percentage composition, stoichiometry and stoichiometric

calculations.

2. Structure of Atom : Sub atomic particles, atomic models, Bohrs model and its limitations, concept of shell and

sub-shells, dual nature of matter and light, de Broglie relationship, Heisenberg uncertainty

Principle, concepts of orbitals, quantum numbers, shapes of s,p and d- orbitals, Aufbau

Principle, Pauli exclusion principle, Hunds rule, electronic configuration of atoms, stability of half-filled and completely filled orbitals.

3. States of Matter Three states of matter, intermolecular forces, thermal energy.

Gasseous state : the gas laws, ideal gas equation, kinetic molecular theory of gases, behavior of

real gases, deviation from ideal behavior, liquification of gases.

Liquid state : Vapour pressure, viscosity and surface tension (no mathematical derivations).

Solid State : General characteristics of solid state, amorphous and crystallins solids,

classification of crystalline solids, crystal lattices and unit cells, no. of atoms in a unit cell,

calculation of density of unit cell, close packed structures, packing efficiency, imperfections in solids, electrical and magnetic properties.

4. Thermodynamics Concepts of system, types of systems, surrounding, work, heat, energy, extensive and intensive

properties. State functions, first law of thermodynamics, internal energy and enthalpy, heat

capacity and specific heat, measurement of U and H, Hesss law of constant heat summation, enthalpy of : bond dissociation, combustion, formation, atomization, sublimation,

phase transformation, ionization and dilution. Entropy, spontaneity, Gibbs energy change and equilibrium.

5. Equilibrium Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of

chemical equilibrium and equilibrium constant, homogenous and heterogenous eqilibria.

Application of equilibrium constants. Factors effecting equilibrium Le Chatliers Principle. Ionic equilibrium : ionisation of acids and bases, strong and weak electrolytes, degree of

ionisation, concept of pH, hydrolysis of salts (elementary idea), buffer solutions, solubility

product, common-ion effect.

6. Solutions

Types of solutions, expressing concentration of solutions, solubility, vapour pressure of liquid

solutions. Ideal and non-ideal solutions, colligative properties osmotic pressure, relative lowering of vapour pressure, elevation of boiling point, depression of freezing point. Determination of molecular masses using colligative properties, abnormal molecular masses.

7. Redox-reactions and electrochemistry Redox-reactions : Oxidation and reduction reactions, redox-reactions in terms of electron

transfer reaction oxidation number, redox-reaction and electrode processes.

Conductance in electrolytic solutions, specific and molar conductivity, variations of

conductivity with concentration, Kohlraushs law, electrochemical cells, Galvanic cells, Nernst equation. Electrolysis and laws of electrolysis, electrolytic cells, Batteries, fuel cells, corrosion.

8. Chemical Kinetics Rate of chemical reaction, factors effecting rate of reaction, order and molecularity of a

reaction, rate law and specific rate constant, integrated rate equations, and half life (only for

zero and first order reactions). Pseudo first order reaction, collision theory of chemical reaction

(no mathematically treatment).

9. Surface chemistry Adsorption, catalysis, colloids, classification of colloids, emulsions, colloids around us.

Organic Chemistry

1. Some basic concepts and techniques Classification of organic compounds, nomenclature of organic compounds, isomerism,

fundamental concepts in organic reaction mechanism, methods of purification of organic

compounds, qualitative and quantitative analysis of organic compounds.

2. Hydrocarbons Alkanes : Nomenclature, isomerism, conformations (only ethane), physical properties,

chemical reaction including free radical mechanism of halogenations, combustion and

pyrolysis.

Alkenes : Nomenclature, structure of double bond (ethane) geometrical isomerism, methods

of preparation, physical properties, chemical reaction : addition of hydrogen, halogen, water,

hydrogenhalides (Markovnikovs addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition.

Alkynes : Nonenclature, structure of triple bond (ethyne) methods of preparation, physical

properties, chemical properties; acidic nature of alkynes, addition reactions of hydrogen,

halogens, hydrogen halides and water.

Aromatic Hydrocarbons : Benzene, resonance, aromaticity, chemical properties, mechanism

of electrophilic substitution nitration, sulphonation, halogenations, friedel Craft alkylation and acylation, directive influence of functional gp in monosubstituted benezene,

carcinogenicity and toxicity.

3. Haloalkanes and haloarenes Classfication, nomenclature, nature of c-x bond, methods of preparation, physical properties,

chemical reactions, polyhalogen compounds.

4. Alcohols, phenols and ethers Classification, nomenclature, methods of preparation of alcohols, phenols and ethers. Physical

and chemical properties of alcohols, phenols and ethers.

5. Aldehydes, ketones and carboxylic acids Nomenclature of aldehydes, ketones and carboxylic acids. Structures of compounds

containing functional gps namely carbony1 and caboxy1 groups. Important methods of

preparation of aldehydes and ketones.

General methods of preparation of carboxylic acids. Acidity of carboxylic acids and various

factors effecting the acidity of carboxylic acids. Physical and chemical properties of

carboxylic acids.

6. Organic compounds containing nitrogen Amines : Structure, classification, nomenclature, methods of preparation of amines. Physical

and chemical properties of amines, distinction between primary, secondary and tertiary

amines.

Diagzonium salts : Methods of preparation, physical and chemical properties, importance in

the synthesis of a series of aromatic compounds including azo dyes.

7. Polymers Explanation of terms : monomer, polymer and polymerisation and their importance.

Distinction between various types of polymers and different types of polymerisation

processes, formation of polymers from mono and bi-functional monomer molecules.

Preparation of some important synthetic polymers and their properties and their importance in

daily life.

8. Biomolecules Define biomolecules like carbohydrates, proteins and nucleic acids, classify carbohydrates,

proteins, nuclear acids and vitamin on the basis of their structures. Difference between DNA

and RNA, role of biomolecules in biosystem.

9. Chemistry in everyday life Importance of chemistry in daily life, chemotherapy, basis of classification of drugs and drug-

target interaction of enzymes and receptors. Function of various types of drugs in the body,

artificial sweetening agents and food preservatives, chemistry of cleaning agents.

PHYSICS

Unit I: Physical World and Measurement

Unit of Measurement; systems of units; SI units, fundamental and derived units. Accuracy and

precision of measuring instruments; errors in measurement; significant figures and rounding off the

numbers. Dimensions of physical quantities, dimensional analysis and its applications.

Unit II: 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. Relation for uniformly accelerated motion (graphical treatment).

Scalar and vector quantities; Position and displacement vectors, multiplication of vectors by a real

number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a

plane rectangular components. Scalar and vector product of vectors. Projectile motion.

Unit III: Laws of Motion

Concept of force. Inertia, Newtons first law of motion; momentum and Newtons second law of motion; impulse; Newtons third law of motion. Law of conservation of linear momentum and applications.

Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction,

Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on level

circular road, vehicle on banked road).

Unit IV: Work, Energy and Power

Work done by a constant force and a variable force; kinetic energy, Potential energy, potential energy

of a spring, work-energy theorem, power, conservative forces: conservation of mechanical energy

(kinetic and potential energies); non-conservative forces: motion in a vertical circle; elastic and

inelastic collisions in one and two dimensions.

Unit V: Motion of System of Particles and Rigid Body

Centre of mass of a two-particle system, momentum conservation and centre of mass motion.

Centre of mass of a rigid body; centre of mass of uniform rod. Moment of a force, torque, angular

momentum, conservation of angular momentum with some examples.

Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of

linear and rotational motions; moment of inertia, radius of gyration. Values of moments of inertia, for

simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and

their applications.

Unit VI: Gravitation

Keplars laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy; gravitational potential. Escape

velocity. Orbital velocity of a satellite. Geo-stationary satellites.

Unit VIII: Heat & Thermodynamics

Heat, temperature, thermal expansion; thermal expansion of solids, liquids and gases, anomalous

expansion; specific heat capacity; Cp, Cv calorimetry; change of state- latent heat capacity. Heat transfer-conduction, convention and radiation, Qualitative ideas of Blackbody radiation, thermal

conductivity, Newtons law of cooling, Stefans law, Weins displacement Law. Thermal equilibrium and definition of temperature ( zeroth law of thermodynamics). Heat, work and

internal energy. First law of thermodynamics. Isothermal and adiabatic processes. Second law of

thermodynamics: reversible and irreversible processes. Heat engines and refrigerators.

Unit IX: 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 and forced and damped oscillation ( qualitative ideas only),

resonance.

Wave motion. Transverse and longitudinal waves, speed of wave motion. 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.

Unit X: Electrostatics

Electric Charges; Conservation of charge, Coulombs law-force between two point charges, forces between multiple charges; superposition principle and continuous charges 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 uniform electric field. Electric flux, statement of Gausss theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane

sheet and uniformly charged thin spherical shell (field inside and outside).

Electric potential, potential difference, electric potential due to a point charge, a dipole and system of

charges; equipotential surfaces, electrical potential energy of a system of two point charges and of

electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and

electric polarization, capacitors and capacitance, 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. Van de Graaff generator.

Unit XI : Current Electricity

Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their

relation with electric current; Ohms law, electrical resistance, V-I characteristics ( linear and non-linear ), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour

code for carbon resistors; series and parallel combinations of resistors; temperature dependence of

resistance Internal resistance of a cell, potential difference and emf of a cell, combination of cells in

series and in parallel. Kirchhoffs laws and simple applications. Wheatstone bride, Metre Bridge. Potentiometer principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell. Electric power, heating effect of current &

joules law. Unit XII : Magnetic Effects of Current and Magnetism

Concept of magnetic field, Oersteds experiment. Biot Savart law and its application to current carrying circular loop. Amperes law and its applications to infinitely long straight wire. Straight and toroidal solenoids, Force on a moving charge in uniform magnetic and electric fields. Cyclotron.

Force on a current-carrying conductor in a uniform magnetic ield. 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. Magnetic dipole moment of a

revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and

perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field bar

magnet as an equivalent solenoid, magnetic field lines; Earths magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances, with examples. Electromagnets and factors affecting their

strengths. Permanent magnets.

Unit XIII: Electromagnetic Induction and Alternating Currents

Electromagnetic induction; Faradays laws, induced emf and current; Lenzs Law, Eddy currents. Self and mutual induction.

Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC

oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattles

current. AC generator and transformer.

Unit XIV : Optics

Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and

its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens makers formula. Magnification, power of a lens, combination of thin lenses in contact combination of a lens

and a mirror. Refraction and dispersion of light through a prism. Scattering of light blue colour of sky and reddish apprearance of the sun at sunrise and sunset.

Optical instruments : Human eye, image formation and accommodation correction of eye defects

(myopia, hypermetropia) using lenses. Microscopes and astronomical telescopes ( reflecting and

refracting ) and their magnifying powers.

Unit XV: Dual Nature of Matter and Radiation

Dual nature of radiation. Photoelectric effect, Einsteins photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de Broglie relation

Unit XVI: Nuclei

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, nuclear fusion.

Unit XVII : Electronic Devices

Energy bands in solids (Qualitative ideas only) conductors, insulator and 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. Logic gates (OR, AND , NOT, NAND and NOR).

Mathematics

1. Sets, Relations and Functions Sets and their Representations, Union, intersection and complements of sets, and their algebraic properties, Relations, equivalence relations,

mappings, one-one, into and onto mappings, composition of mappings.

2. Complex Numbers 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. Cube roots of unity, triangle inequality.

3. Matrices and Determinants Determinants and matrices of order two and three, properties of determinants, Evaluation of determinants. Area of triangles using determinants, Addition and

multiplication of matrices, adjoint and inverse of matrix. Test of consistency and solution of

simultaneous linear equations using determinants and matrices

4. Quadratic Equations Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic

equations with given roots; Symmetric functions of roots, equations reducible to quadratic

equations application to practical problems 5. 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.

6. Mathematical Induction and Its applications

7. Binomial Theorem and its Applications Binomial Theorem for a positive integral index; general term and middle term; Binomial Theorem for any index. Properties of Binomial Co-

efficients. Simple applications for approximations.

8. Sequences and Series Arithmetic, Geometric and Harmonic progressions. Insertion of Arithmetic Geometric and Harmonic means between two given numbers. Relation between

A.M., G.M. and H.M.Special series: Sn, Sn2, Sn3 . Arithmetico-Geometric Series,

Exponential and Logarithmic series.

9. Differential Calculus Polynomials, rational, trigonometric, logarithmic and exponential functions, Inverse functions. Graphs of simple functions. Limits, Continuity; 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. Applications of derivatives: Rate of change of quantities, monotonic -

increasing and decreasing functions, Maxima and minima of functions of one variable,

tangents and normals, Rolles and Lagranges Mean Value Theorems. 10. 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. Integral as limit of a sum.

Properties of definite integrals. Evaluation of definite integrals; Determining areas of the

regions bounded by simple curves

11. 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, and those of the type

d2y dx2 = f(x)

12. Two dimensional Geometry Recall of Cartesian system of rectangular co-ordinates in a plane, distance formula, area of a triangle, condition for the collinearity of three points and

section formula, centroid and in-centre of a triangle, locus and its equation, translation of

axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate

axes.

The straight line and pair of 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, homogeneous equation of second degree in x and y, angle between

pair of lines through the origin, combined equation of the bisectors of the angles between a

pair of lines, condition for the general second degree equation to represent a pair of lines,

point of intersection and angle between two lines.

Circles and Family of Circles

Standard form of equation of a circle, general form of the equation of a circle, its radius and

centre, equation of a circle in the parametric form, 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 the circle, length of the tangent, equation of the

tangent, equation of a family of circles through the intersection of two circles, condition for

two intersecting circles to be orthogonal.

Conic Sections

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.

13. 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, equation of a

sphere, its centre and radius. Diameter form of the equation of a sphere.

14. 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. Application of vectors to plane geometry.

15. Measures of Central Tendency and Dispersion Calculation of Mean, median and mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation

for grouped and ungrouped data.

16. Probability Probability of an event, addition and multiplication theorems of probability and their applications; Conditional probability; Bayes Theorem, Probability distribution of a random variate; Binomial and Poisson distributions and their properties.

17. TrigonometryTrigonometrical identities and equations. Inverse trigonometric functions and their properties. Properties of triangles, including centroid, incentre, circum- centre and

orthocentre, solution of triangles. Heights and Distances

18. Statics Introduction, basic concepts and basic laws of mechanics, force, resultant of forces acting at a point, parallelogram law of forces, resolved parts of a force, Equilibrium of a

particle under three concurrent forces, triangle law of forces and its converse, Lamis theorem and its converse, Two parallel forces, like and unlike parallel forces, couple and its moment.

Dynamics Speed and velocity, average speed, instantaneous speed, acceleration and retardation,

resultant of two velocities. Motion of a particle along a line, moving with constant acceleration.

Motion under gravity. Laws of motion, Projectile motion.