UNIT 1: 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.

UNIT 2: Atomic Structure

Discovery of sub-atomic particles (electron, proton and neutron); 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 Ψ and Ψ2 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.

UNIT 3: 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.

UNIT 4: Chemical Thermodynamics

Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes.
First law of thermodynamics: Concept of work, heat internal energy and enthalpy, heat capacity, 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; ΔS of the universe and ΔG of the system as criteria for spontaneity, ΔGo (Standard Gibbs energy change) and equilibrium constant.

UNIT 5: 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.

UNIT 6: 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 significance, significance of ΔG and ΔGo 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, Bronsted - 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.

UNIT 7: Redox Reactions and Electrochemistry - I

Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.

Eectrolytic and metallic conduction, conductance in electrolytic solutions, specific and molar conductivities and their variation with concentration: Kohlrausch’s law and its applications.

UNIT 8: Redox Reactions and Electrochemistry - II

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; Corrosion and its prevention.

UNIT 9: 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).

UNIT 10: Classification of Elements and Periodicity in Properties

Modem 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.

UNIT 11: 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.
Group wise study of the p – block elements
Group - 13
Preparation, properties and uses of Boron and Aluminium; Structure, properties and uses of Borax, Boric acid, Diborane, Boron tri-fluoride, Aluminium chloride and alums.
Group - 14
Tendency for catenation; Structure, properties and uses of allotropes and oxides of Carbon, Silicon tetrachloride, Silicates, Zeolites and Silicones.
Group - 15
Properties and uses of Nitrogen and Phosphorus; Allotrophic forms of Phosphorus; Preparation, properties, structure and uses of Ammonia, Nitric acid, Phosphine and Phosphorus halides, (PCl3, PCl5); Structures of oxides and oxoacids of Nitrogen and Phosphorus.

UNIT 12: p - Block Elements

Group - 16
Preparation, properties, structures and uses of dioxygen and ozone; Allotropic forms of Sulphur; Preparation, properties, structures and uses of Sulphur dioxide, 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 and oxoacids of halogens.
Group - 18
Occurrence and uses of noble gases; Structures of fluorides and oxides of xenon.

UNIT 13: 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 K2Cr2O7 and KMnO4.
Inner Transition Elements

Lanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction.
Actinoids - Electronic configuration and oxidation states.

UNIT 14: Co-ordination 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 (in qualitative analysis, extraction of metals and in biological systems).

UNIT 15: Purification and Characterization 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 (basic principles only) - Estimation of Carbon, Hydrogen, Nitrogen, Halogens, Sulphur, Phosphorus.
Calculations of empirical formulae and molecular formulae; Numerical problems in organic quantitative analysis.

UNIT 16: Some Basic Principles of Organic Chemistry - I

Tetravalency of Carbon; Shapes of simple molecules - hybridization (s and p); Classification of organic compounds based on functional groups: - C = C - , - C ≡ C - and those containing Halogens, Oxygen, Nitrogen and Sulphur; Homologous series; Isomerism - structural and stereoisomerism.

UNIT 17: Some Basic Principles of Organic Chemistry - II

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 hyper conjugation.
Common types of organic reactions - Substitution, addition, elimination and rearrangement.

UNIT 18: Hydrocarbons - I

Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.
Alkanes - Conformations: Sawhorse and Newman projections (of ethane); Mechanism of halogenation of Alkanes.
Alkenes - Geometrical isomerism; Mechanism of electrophilic addition: addition of hydrogen, halogens, water, hydrogen halides (Markownikoff’s and peroxide effect); Ozonolysis, oxidation, and polymerization.

UNIT 19: Hydrocarbons - II

Alkynes - Acidic character; Addition of hydrogen, halogens, water and hydrogen halides; Polymerization.
Aromatic hydrocarbons - Nomenclature, benzene - structure and aromaticity; Mechanism of electrophilic substitution: halogenation, nitration, Friedel - Craft’s alkylation and acylation, directive influence of functional group in mono-substituted benzene.

UNIT 20: 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, freons and DDT.

UNIT 21: Organic Compounds Containing Oxygen - I

General methods of preparation, properties, reactions and uses.
Alcohols, Phenols and Ethers
Alcohols: Identification of primary, secondary and tertiary Alcohols; mechanism of dehydration.
Phenols: Acidic nature, electrophilic substitution reactions: halogenation, nitration and sulphonation, Reimer - Tiemann reaction.
Ethers: Structure.

UNIT 22: Organic Compounds Containing Oxygen - II

General methods of preparation, properties, reactions and uses.
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, NH3 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.

UNIT 23: 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.

UNIT 24: PRINCIPLES RELATED TO PRACTICAL CHEMISTRY

Detection of extra elements (Nitrogen, Sulphur, halogens) in organic compounds; Detection of the following functional groups; hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketones) carboxyl, and amino groups in organic compounds.
• The chemistry involved in the preparation of the following:
Inorganic compounds; Mohr’s salt, potash alum.
Organic compounds: Acetanilide, p-nitro acetanilide, aniline yellow, iodoform.
• The chemistry involved in the titrimetric exercises – Acids, bases, and the use of indicators, oxalic-acid vs KMnO4, Mohr’s salt vs KMnO4
• Chemical principles involved in the qualitative salt analysis: Cations – Pb2+, Cu2+, Al3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+ , NH4+ Anions- CO32−, S2- ,SO42−, NO3- , NO2- , Cl- , Br- , I- ( Insoluble salts excluded).
Chemical principles involved in the following experiments:
1. Enthalpy of solution of CuSO4
2. Enthalpy of neutralization of strong acid and strong base.
3. Preparation of lyophilic and lyophobic sols.
4. Kinetic study of the reaction of iodide ions with hydrogen peroxide at room temperature.

UNIT 25: Bio Molecules

General introduction and importance of biomolecules.
Carbohydrates - Classification: aldoses and ketoses; monosaccharides (glucose and fructose), constituent monosaccharides of oligosacchorides (sucrose, lactose, maltose) and polysaccharides (starch, cellulose, glycogen).
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 nucleic acids.

UNIT 1: 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.

UNIT 2: LAWS OF MOTION

Static and Kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion: Centripetal force and its applications.
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.

UNIT 3: 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; motion in a vertical circle: Elastic & inelastic collisions in one and two dimensions.

UNIT 4: 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. Comparison of linear and rotational motions.

UNIT 5: 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.

UNIT 6: 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.

UNIT 7: 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;
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

UNIT 8: PROPERTIES OF SOLIDS AND LIQUIDS - I

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. Effect of gravity on fluid pressure.
Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow. Critical Velocity. Bernoulli’s principle and its applications.

UNIT 9: PROPERTIES OF SOLIDS AND LIQUIDS - II

Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, 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.

UNIT 10: 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.

UNIT 11: 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 12: ELECTROSTATICS - I

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 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.

UNIT 13: ELECTROSTATICS - II

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.

UNIT 14: CURRENT ELECTRICITY

Electric current, Drift velocity, mobility, and their relation with electric current. Ohm’s law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and non-ohmic conductors, Electrical energy and power, Electrical resistivity ;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.

UNIT 15: 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.

UNIT 16: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Magnetic field due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole in a uniform magnetic field. Para-, dia- and ferromagnetic substances with examples, the effect of temperature on magnetic properties.

UNIT 17: 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.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion.

UNIT 18: 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.

UNIT 19: OPTICS - I

Reflection of light, spherical mirrors, mirror formula. Refraction of light at plane and spherical surfaces, thin lens formula, and lens maker formula. Total internal reflection and its applications. Magnification. Power of a Lens. Combination of thin lenses in contact. Refraction of light through a prism. Microscope and Astronomical Telescope (reflecting and refracting ) and their magnifying powers.

UNIT 20: OPTICS - II

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, Polarization, plane polarized light; Brewster’s law, uses of plane polarized light and Polaroids.

UNIT 21: 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: power in AC circuits, wattless current. AC generator and transformer.

UNIT 22: ELECTRONIC DEVICES - I

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.

UNIT 23: ELECTRONIC DEVICES - II

Logic gates (OR, AND, NOT, NAND and NOR)

UNIT 24: ELECTROMAGNETIC WAVES

Displacement current. 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.

UNIT 25: EXPERIMENTAL SKILLS

Familiarity with the basic approach and observations of the experiments and activities:
1. Vernier calipers -its use to measure the internal and external diameter and depth of a vessel.
2. Screw gauge-its use to determine the thickness/ diameter of thin sheet/wire.
3. Simple Pendulum-dissipation of energy by plotting a graph between the square of amplitude and time.
4. Metre Scale - the mass of a given object by the principle of moments.
5. Young❜s modulus of elasticity of the material of a metallic wire.
6. Surface tension of water by capillary rise and effect of detergents,
7. Co-efficient of Viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body,
8. Speed of sound in air at room temperature using a resonance tube,
9. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.
10. The resistivity of the material of a given wire using a metre bridge.
11. The resistance of a given wire using Ohm❜s law.
12. Resistance and figure of merit of a galvanometer by half deflection method.
13. The focal length of; (i) Convex mirror (ii) Concave mirror, and (ii) Convex lens, using the parallax method.
14. The plot of the angle of deviation vs angle of incidence for a triangular prism.
15. The refractive index of a glass slab using a travelling microscope.
16. Characteristic curves of a p-n junction diode in forward and reverse bias.
17. Characteristic curves of a Zener diode and finding reverse breakdown voltage.
18. Identification of Diode. LED, Resistor. A capacitor from a mixed collection of such items

UNIT 1

Sets: Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set.
Relations: Relation, Types of relations, equivalence relations.

UNIT 2

Function, limit and Continuity: One-one, into and onto functions, composition of functions; Real valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions.Limits, continuity and differentiability.

UNIT 3

Complex numbers: 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.

UNIT 4

Quadratic equations: 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.

UNIT 5

Sequences and series: Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M.

UNIT 6

Matrices: Matrices, algebra of matrices, types of matrices, matrices of order two and three; Adjoint; transpose; symmetric and skew symmetric matrices.

UNIT 7

Determinants: Properties of determinants, evaluation of determinants, area of triangles using determinants.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

UNIT 8

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

UNIT 9

Permutations: Fundamental principle of counting, permutation as an arrangement. Meaning of P(n, r) , simple applications.

UNIT 10

Combinations: Combination as selection,Meaning ofC(n, r) , simple applications.

UNIT 11

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

UNIT 12

Derivatives: Differentiation of sum, difference, product and quotient of two functions;Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two.

UNIT 13

Application of Derivatives: Rate of change of quantities, monotonic increasing and decreasing functions, Maxima and minima of functions of one variable.

UNIT 14

Integral calculus (Part1): 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.

UNIT 15

Integral calculus (Part2): Evaluation of simple integrals of followingtype:

UNIT 16

Definite Integrals: Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form

UNIT 17

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 18

Coordinate geometry: Cartesian system of rectangular coordinates 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.

UNIT 19

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, coordinates of centroid, orthocentre and circumcentre of a triangle.

UNIT 20

Circles: 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.

UNIT 21

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) oftangency.

UNIT 22

Three Dimensional Geometry (Part1): 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 in different forms.

UNIT 23

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.

UNIT 24

Trigonometry: Trigonometrical Identities and equations, Trigonometrical functions;

UNIT 25

Inverse Trigonometric Functions: Definition, domain, range, elementary properties of inverse trigonometric functions, Heights and distances

Grammar: Parts of speech – Noun, Pronoun, Adjective, Adverb, Verb, Preposition, Conjunction Interjection; Tenses – Present, Past and Future Tense in Active and Passive Form; Modal Verbs – Can, Could, May, might, Should, Will, would, punctuation, independent and dependent clauses, sentence and its types, determiners

Associative Language Skills: Vocabulary – Antonyms, Synonyms, Homonyms, Homographs, one-word substitution, Word Analogies, Idioms and Phrases.

Common Errors: Sentence Correction and Error Finding Exercises.

Comprehension Passages: Closed and Open paragraphs, identifying key ideas or theme.

Area and production of various horticultural crops and current status. Importance of fruits and vegetables in human diets, crops diversification and processing industries.
Orchard- location, layout, ornamental gardening and kitchen garden.
Planting system, training, pruning, intercropping, protection from frost and sunburn.
Trees, shrubs, climbers, annuals, perennials.
Propagation by seeds, cutting, budding, layering and grafting.
Cultivation practices, processing and marketing of: Fruits- mango, papaya, banana, guava, citrus, grapes.
Vegetables- radish, carrot, potato, onion, cauliflower, brinjal, tomato, spinach and cabbage.
Flowers- gladiolus, canna, chrysanthemums, roses and marigold.
Principles and methods of fruit and vegetable preservation. Preparation of jellies, jams, ketchup, chips and their packing.

Unit-1: Livestock ProductionScope and importance: (a) Importance of livestock in agriculture and industry, White revolution in India. (b) Important breeds Indian and exotic, distribution of cows, buffaloes and poultry in India.
Care and management: (a) Systems of cattle and poultry housing (b) Principles of feeding, feeding practices. (c) Balanced ration-definition and ingredients. (d) Management of calves, bullocks, pregnant and milch animals as well as chicks crockrels and layers, poultry. (e) Signs of sick animals, symptoms of common diseases in cattle and poultry, Rinderpest, black quarter, foot and mouth, mastitis and haemorrhagic septicaemia coccidiosis, Fowl pox and Ranikhet disease, their prevention and control.
Artificial Insemination: Reproductive organs, collection, dilution and preservation of semen and artificial insemination, role of artificial insemination in cattle improvement. Livestock Products: Processing and marketing of milk and Milk products.

Unit-2: Crop Production Introduction: (a) Targets and achievements in foodgrain production in India since independence and its future projections, sustainable crop production, commercialization of agriculture and its scope in India. (b) Classification of field crops based on their utility-cereals, pulses, oils seeds, fibre, sugar and forage crops.
Soil, Soil fertility, Fertilizers and Manures: (a) Soil, soil pH, Soil texture, soil structure, soil organisms, soil tilth, soil fertility and soil health. (b) Essential plant nutrients, their functions and deficiency symptoms. (c) Soil types of India and their characteristics. (d) Organic manure, common fertilizers including straight, complex, fertilizer mixtures and biofertilizers; integrated nutrient management system.
Irrigation and Drainage: (a) Sources of irrigation (rain, canals, tanks, rivers, wells, tubewells). (b) Scheduling of irrigation based on critical stages of growth, time interval, soil moisture content and weather parameters. (c) Water requirement of crops. (d) Methods of irrigation and drainage. (e) Watershed management Weed Control: Principles of weed control, methods of weed control (cultural, mechanical, chemical, biological and Integrated weed management).
Crops: Seed bed preparation, seed treatment, time and method of sowing/planting, seed rate; dose, method and time of fertilizer application, irrigation, interculture and weed control; common pests and diseases, caused by bacteria, fungi virus and nematode and their control, integrated pest management, harvesting, threshing, post-harvest technology: storage, processing and marketing of major field crops-Rice, wheat, maize, sorghum, pearl millet, groundnut, mustard, pigeon-pea, gram, sugarcane, cotton and berseem.