Indian Council of Agricultural Research All India Entrance Examination for Admission (ICAR-AIEEA )

Indian Council of Agricultural Research All India Entrance Examination for Admission (ICAR-AIEEA ) Exam Syllabus details are given below.

## Physics

**Unit- 1 : Physical World and Measurement**

Physics scope and excitement; nature of physical laws; Physics, technology and society. Need for measurement : Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures. Dimensions of physical quantities, dimensional analysis and its applications.

**Unit - 2 : 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 graph, position - time graphs, relations for uniformly accelerated motion ( graphical treatment ). Elementary concepts of differentiation and integration for describing motion. Scalar and vector quantities : Position and displacement vectors, general vectors and notation, equality of 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. Motion in a plane. Cases of uniform velocity and uniform acceleration - projectile motion. Uniform circular motion. Motion of objects in three dimensional space. Motion of objects in three dimensional space.

**Unit - 3 : Laws of Motion**

Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and 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, examples of circular motion ( vehicle on level circular road, vehicle on banked road ).

**Unit - 4 : Work, Energy and Power**

Scalar product of vectors. Work done by a constant force and a variable force; kinetic energy, work - energy theorem, power. Notion of potential energy, potential energy of a spring, conservative forces : conservation of mechanical energy ( kinetic and potential energies ); non - conservative forces : elastic and inelastic collisions in one and two dimensions.

**Unit - 5 : Motion of System of Particles and Rigid Body**

Centre of mass of a two - particle system, momentum conversation and centre of mass motion. Centre of mass of arigid body; centre of mass of uniform rod. Vector product of vectors; 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. Statement of parallel and perpendicular axes theorems and their applications.

**Unit - 6 : Gravitation**

Keplar’s 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 - 7 : Properties of Bulk Matter**

Elastic behaviour, Stress - strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity. Pressure due to a fluid column; Pascal’s law and its applications ( hydraulic lift and hydraulic brakes ). Effect of gravity on fluid pressure. Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Bernoulli’s theorem and its applications.

Surface energy and surface tension, angle of contact, application of surface tension ideas to drops, bubbles and capillary rise. Heat, temperature, thermal expansion; specific heat - calorimetry; change of state - latent heat. Heat transferconduction, convection and radiation, thermal conductivity, Newton’s law of cooling.

**Unit - 8 : Thermodynamics**

Thermal equilibrium and definition of temperature ( zeroth law of thermodynamics ). Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics : reversible and irreversible processes. Heat engines and refrigerators.

**Unit - 9 : Behaviour of Perfect Gas and Kinetic Theory**

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 ( statement only ) and application to specific heats of gases; concept of mean free path, Avogadro’s number.

**Unit -10 : 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 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 - 11 : Electrostatics**

Electric Charges; Conservation of charge, Coulomb’s law - force 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, statement of Gauss’s 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 - 12 : Current Electricity**

Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s 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. Kirchoff’s laws and simple applications. Wheatstone bridge, 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.

**Unit- 13 : Magnetic Effects of Current and Magnetism**

Concept of magnetic field, Oersted’s experiment. Biot - Savart law and its application to current carrying circular loop. Ampere’s 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 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. 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; Earth’s magnetic field and magnetic elements. Para - , dia - and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets.

**Unit - 14 : Electromagnetic Induction and Alternating Currents**

Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. Need for displacement current. 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, wattless current. AC generator and transformer.

**Unit - 15 : Electromagnetic waves**

Displacement current, Electromagnetic waves and their characteristics ( qualitative ideas only ). Transverse nature of electromagnetic waves. Electromagnetic spectrum ( radio waves, microwaves, infrared, visible, ultraviolet, X - rays, gamma rays ) including elementary facts about their uses.

**Unit - 16 : 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, lensmaker’s formula. Magnification, power of a lens, combination of thin lenses in contact. Refraction and dispersion of light through a prism. Scattering of light - blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments : Human eye, image formation and accommodation, correction of eye defects ( myopia, hypermetropia, presbyopia and astigmatism ) using lenses. Microscopes and astronomical telescopes ( reflecting and refracting ) and their magnifying powers.

**Wave optics :** wave front and Huygens’ principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’ principle. Interference, Young’s double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids.

**Unit - 17 : 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 particles, de Broglie relation. Davisson - Germer experiment.

**Unit - 18 : Atoms & 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, nuclear reactor, nuclear fusion.

**Unit - 19 : 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.

**Unit - 20 : Communication Systems**

Elements of a communication system ( block diagram only ); bandwidth of signals ( speech, TV and digital data ); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude - modulated wave.

## Chemistry

**Unit - 1 : Some Basic Concepts of Chemistry**

**General Introduction :** Importance and scope of chemistry. Historical approach to particulate nature of matter, laws of chemical combination. Dalton’s atomic theory : concept of elements, atoms and molecules. Atomic and molecular masses mole concept and molar mass : percentage composition, empirical and molecular formula chemical reactions, stoichiometry and calculations based on stoichiometry.

**Unit - 2 : Solid State**

Classification of solids based on different binding forces : molecular, ionic, covalent and metallic solids, amorphous and crystalline solids ( elementary idea ), unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties.

**Unit - 3 : Solutions**

Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties – relative lowering of vapour pressure, elevation of Boiling Point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass.

**Unit - 4 : Structure of Atom**

Discovery of electron, proton and neutron; atomic number, isotopes and isobars. Thomson’s model and its limitations, Rutherford’s model and its limitations. Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals - Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

**Unit - 5 : Classification of Elements and Periodicity in Properties**

Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements - atomic radii, ionic radii. Ionization enthalpy, electron gain enthalpy, electro negativity, valence.

**Unit - 6 : Chemical Bonding and Molecular Structure**

Valence electrons, ionic bond, covalent bond : bond parameters. Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR ( Valence shell electron pair repulsion ) theory, concept of hybridization, involving s, p and d orbitals and shapes of some simple molecules, molecular orbital; theory of homonuclear diatomic molecules ( qualitative idea only ), hydrogen bond.

**Unit - 7 : States of Matter : Gases and Liquids**

Three states of matter. Intermolecular interactions, type of bonding, melting and boiling points. Role of gas laws in elucidating the concept of the molecule, Boyle’s law. Charles law, Gay Lussac’s law, Avogadro’s law. Ideal behaviour, empirical derivation of gas equation, Avogadro’s number. Ideal gas equation. Derivation from ideal behaviour, liquefaction of gases, critical temperature. Liquid State - Vapour pressure, viscosity and surface tension ( qualitative idea only, no mathematical derivations ).

**Unit - 8 : Thermodynamics**

Concepts of System, types of systems, surroundings. Work, heat, energy, extensive and intensive properties, state functions. First law of thermodynamics -internal energy and enthalpy, heat capacity and specific heat, measurement of DU and DH, Hess’s law of constant heat summation, enthalpy of : bond dissociation, combustion, formation, atomization, sublimation. Phase transformation, ionization, and solution. Introduction of entropy as a state function, free energy change for spontaneous and non - spontaneous processes, criteria for equilibrium.

**Unit - 9 : Equilibrium**

Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium - Le Chatelier’s principle; ionic equilibrium - ionization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts. Buffer solutions, solubility product, common ion effect.

**Unit - 10 : Redox Reactions**

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, applications of redox reactions.

**Unit - 11 : Hydrogen**

Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides - ionic, covalent and interstitial; physical and chemical properties of water, heavy water; hydrogen peroxide - preparation, properties and structure; hydrogen as a fuel.

**Unit - 12 : s - Block Elements ( Alkali and Alkaline earth metals )**

**Group 1 and Group 2 elements**

General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties ( such as ionization enthalpy, atomic and ionic radii ), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses.

**Unit- 13 : Preparation and properties of some important compounds**

Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, biological importance of sodium and potassium. CaO, CaCO_{3} and industrial use of lime and limestone, biological importance of Mg and Ca.

**Unit - 14 : Some p - Block Elements**

**General Introduction to p - Block Elements : Group 13 elements**

General introduction, electronic configuration, occurrence. Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron - physical and chemical properties, some important compounds : borax, boric acids, boron hydrides. Aluminum : uses, reactions with acids and alkalies.

**Unit - 15 : Group 14 elements**

General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behaviour of first element, Carbon - catenation, allotropic forms, physical and chemical properties; uses of some important compounds : oxides. Important compounds of silicon and a few uses : silicon tetrachloride, silicones, silicates and zeolites.

**Unit - 16 : Organic Chemistry**

**Some Basic Principles and Techniques**

General introduction, methods of qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds, Electronic displacements in a covalent bond : inductive effect, electromeric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a covalent bond : free radicals, carbocations, carbanions; electrophiles and nucleophiles, types of organic reactions.

**Unit - 17 : Hydrocarbons**

**Classification of hydrocarbons**

**Alkanes -** Nomenclature, isomerism, conformations ( ethane only ), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis.

**Alkenes -** Nomenclature, structure of double bond ( ethene ) geometrical isomerism, physical properties, methods of preparation; chemical reactions : addition of hydrogen, halogen, water, hydrogen halides ( Markovnikov’s addition and peroxide effect ), ozonolysis, oxidation, mechanism of electrophilic addition.

**Alkynes -** Nomenclature, structure of triple bond ( ethyne ), physical properties. Methods of preparation, chemical reactions : acidic character of alkynes, addition reaction of - hydrogen, halogens, hydrogen halides and water.

**Aromatic hydrocarbons :** Introduction, IUPAC nomenclature; benzene : resonance, aromaticity; chemical properties : mechanism of electrophilic substitution. – nitration, sulphonation, halogenation, Friedel - Craft’s alkylation and acylation : directive influence of functional group in mono - substituted benzene; carcinogenicity and toxicity.

**Unit - 18 : Electrochemistry**

Conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis ( elementary idea ), dry cell – electrolytic cells and Galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion.

**Unit - 19 : Chemical Kinetics**

Rate of a reaction ( average and instantaneous ), factors affecting rate of reaction; concentration, temperature, catalyst; 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); concept of collision theory ( elementary idea, no mathematical treatment )

**Unit - 20 : Surface Chemistry**

Adsorption – physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis : homogenous and heterogeneous, activity and selectivity : enzyme catalysis; colloidal state : distinction between true solutions, colloids and suspensions; lyophilic, lyophobic, multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsion – types of emulsions.

**Unit - 21 : 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 aluminium, copper, zinc and iron.

**Unit- 22 : p - Block Elements**

**Group 15 elements**

General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen - preparation, properties and uses; compounds of nitrogen : preparation and properties of ammonia and nitric acid, oxides of nitrogen ( structure only ); Phosphorous - allotropic forms; compounds of phosphorous : preparation and properties of phosphine, halides ( PCl_{3}, PCl_{5} ) and oxoacids

**Unit - 23 : Group 16 elements**

General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen : preparation, properties and uses; simple oxides; Ozone. Sulphur - allotropic forms; compounds of sulphur : preparation, properties and uses of sulphur dioxide; sulphuric acid : industrial process of manufacture, properties and uses, oxoacids of sulphur ( structures only ).

**Unit - 24 : Group 17 elements**

General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens : preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens ( structures only ).

**Unit- 25 : Group 18 elements :**

General introduction, electronic configuration. Occurrence, trends in physical and chemical properties, uses.

**Unit - 26 : d and f Block Elements :**

General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the 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 K_{2}Cr_{2}O_{7} and KMnO_{4}.

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

**Actinoids -** Electronic configuration, oxidation states.

**Unit -27 : Coordination Compounds :**

Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. bonding; isomerism, importance of coordination compounds ( in qualitative analysis, extraction of metals and biological systems ).

**Unit- 28 : Haloalkanes and Haloarenes :**

**Haloalkanes :** Nomenclature, nature of C - X bond, physical and chemical properties, mechanism of substitution reactions.

**Haloarenes :** Nature of C - X bond, substitution reactions ( directive influence of halogen for monosubstituted compounds only ) Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT.

**Unit - 29 : Alcohols, Phenols and Ethers :**

**Alcohols**

Nomenclature, methods of preparation, physical and chemical properties ( of primary alcohols only ); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol.** Phenols :** Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols. **Ethers :** Nomenclature, methods of preparation, physical and chemical properties, uses.

**Unit - 30 : Aldehydes, Ketones and Carboxylic Acids**

**Aldehydes and Ketones :** Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses.

**Carboxylic Acids :** Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses.

**Unit - 31 : Organic compounds containing Nitrogen**

**Amines :** Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines.

**Cyanides and Isocyanides -** will be mentioned at relevant places in context.

**Diazonium salts :** Preparation, chemical reactions and importance in synthetic organic chemistry.

**Unit - 32 : Biomolecules**

**Carbohydrates -** Classification ( aldoses and ketoses ), monosaccharide ( glucose and fructose ), oligosaccharides ( sucrose, lactose, maltose ), polysaccharides ( starch, cellulose, glycogen ); importance.

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

**Vitamins -** Classification and functions.

**Nucleic Acids :** DNA and RNA.

**Unit - 33 : Polymers**

Classification - natural and synthetic, methods of polymerization ( addition and condensation ), copolymerization. Some important polymers : natural and synthetic like polythene, nylon, polyesters, Bakelite, rubber.

**Unit - 34 : Environmental Chemistry**

Environmental pollution - air, water and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warming - pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution.

**Unit - 35 : Chemistry in Everyday life**

**Chemicals in medicines -** analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines.

**Chemicals in food -** preservatives, artificial sweetening agents.

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

## Mathematics

**Unit - 1 : Sets and Functions**

**1. Sets :**

Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets, Subsets of the set of real numbers especially intervals ( with notations ). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set.

**2. Relations & Functions :**

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself ( upto R x R x R ). Definition of relation, Types of relations : reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations, Pictorial representation of a function, domain.

Co - domain and range of a relation. Function as a special kind of relation from one set to another. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

**3. Trigonometric Functions :** Positive and negative angles. Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^{2}x + cos^{2}x=1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin ( x+y ) and cos ( x+y ) in terms of sinx, siny, cosx & cosy. Deducing the identities like the following :

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type sin è ?= sin á, cos è ?= cos á ?and tan è ?= tan á.

**Inverse Trigonometric Functions :** Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Properties of triangles, including centroid, incentre, circum-centre and orthocentre, Solution of triangles. Heights and Distances.

**Unit - 2 : Algebra**

**1. Principle of Mathematical Induction :** Processes of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

**2. Complex Numbers and Quadratic Equations :** Need for complex numbers, especially -1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.

**3. Linear Inequalities :** Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables - graphically.

**4. Permutations & Combinations :** Fundamental principle of counting. Factorial n. (n!). Permutations and combinations, derivation of formulae and their connections, simple applications.

**5. Binomial Theorem :** History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.

**6. Sequence and Series :** Sequence and Series. Arithmetic progression ( A. P. ). arithmetic mean ( A.M. ) Geometric progression ( G.P. ), general term of a G.P., sum of n terms of a G.P., geometric mean ( G.M. ), relation between A.M. and G.M. Sum to n terms of the special series Ón, Ón2 and Ón3.

**7. Matrices :** Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non - zero matrices whose product is the zero matrix (restrict to square matrices of order 2 ). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists.

**8. Determinants :** Determinant of a square matrix ( up to 3 x 3 matrices ), properties of determinants, minors, co factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables ( having unique solution ) using inverse of a matrix.

**Unit - 3 : Coordinate Geometry**

**1. Straight Lines :** Slope of a line and angle between two lines. Various forms of equations of a line : parallel to axes, point - slope form, slope - intercept form, two - point form, intercepts form and normal form. General equation of a line. Distance of a point from a line.

**2. Conic Sections :** Sections of a cone : circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

**3. Introduction to Three - dimensional Geometry :** Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

**Unit - 4 : Calculus**

**1. Limits and Derivatives :** Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

**2. Continuity and Differentiability :** Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems ( without proof ) and their geometric interpretations.

**3. Applications of Derivatives :** Applications of derivatives : rate of change, increasing / decreasing functions, tangents & normals, approximation, maxima and minima ( first derivative test motivated geometrically and second derivative test given as a provable tool ). Simple problems.

**4. Integrals :** Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts; only simple integrals of the type :

p>to be evaluated. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus ( without proof ). Basic properties of definite integrals and evaluation of definite integrals.

**5. Applications of the Integrals :** Applications in finding the area under simple curves, especially lines, areas of circles / parabolas / ellipses ( in standard form only ), area between the two above said curves.

**6. Differential Equations :** Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree.

**Solutions of linear differential equation of the type :**

dx / dy + py = q, where p and q are functions of x.

**Unit - 5 : Vectors and Three- Dimensional Geometry**

**1. Vectors :** Vectors and scalars, magnitude and direction of a vector. Direction cosines / ratios of vectors. Types of vectors ( equal, unit, zero, parallel and collinear vectors ), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar ( dot ) product of vectors, projection of a vector on a line. Vector ( cross ) product of vectors.

**2. Three - dimensional Geometry :** Direction cosines / ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between ( i ) two lines, ( ii ) two planes. ( iii ) a line and a plane.

**Unit - 6 : Linear Programming**

**Linear Programming :** Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming ( L.P. ) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions ( up to three non - trivial constraints ).

**Unit - 7 : Mathematical Reasoning**

**Mathematical Reasoning :** Mathematically acceptable statements. Connecting words / phrases - consolidating the understanding of “if and only if ( necessary and sufficient ) condition”, “implies”, “and / or”, “implied by”, “and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words, difference between contradiction, converse and contrapositive.

**Unit - 8 : Statistics & Probability**

**1. Statistics :** Measures of central tendency, mean, median and mode from ungrouped / grouped data. Measures of dispersion, mean deviation, variance and standard deviation from ungrouped / grouped data. Correlation, regression lines.

**2. Probability :** Random experiments : outcomes, sample spaces ( set representation ). Events : occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events Axiomatic ( set theoretic ) probability, Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events. Multiplication theorem on probability. Conditional probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of stochastic variable. Repeated independent ( Bernoulli ) trials and Binomial distribution.

**Unit - 9 : 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, Lami’s theorem and its converse, Two Parallel forces, like and unlike parallel forces, couple and its moment.

**Unit - 10 : 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.

## Biology (Botany And Zoology)

**Unit 1 : The Living World**

Nature and scope of Biology. Methods of Biology. Our place in the universe. Laws that govern the universe and life. Level of organization. Cause and effect relationship. Being alive. What does it mean? Present approaches to understand life processes, molecular approach; life as an expression of energy; steady state and homeostasis; self duplication and survival; adaptation; death as a positive part of life.

Origin of life and its maintenance. Origin and diversity of life. Physical and chemical principles that maintain life processes. The living crust and interdependence. The positive and negative aspects of progress in biological sciences. The future of the living world, identification of human responsibility in shaping our future.

**Unit 2 : Unit of Life**

Cell as a unit of life. Small biomolecules; water, minerals, mono and oligosaccharides, lipids, amino acids, nucleotides and their chemistry, cellular location and function. Macromolecules in cells - their chemistry, cellular location and functional significance. Polysaccharides, proteins and nucleic acids. Enzymes; chemical nature, classification, mechanism in action - enzyme complex, allosteric modulation ( brief ), irreversible activation. Biomembranes; Fluid mosaic model of membrane, role in transport, recognition of external information ( brief ).

Structural organization of the cell; light and electron microscopic views of cell, its organelles and their functions; nucleus mitochondria, chloroplasts, endoplasmic reticulum. Golgi complex, lysosomes, microtubules, cell wall, cilia and flagella, vacuoles, cell inclusions. A general account of cellular respiration. Fermentation, biological oxidation ( A cycle outline ), mitochondrial electron transport chain, high energy bonds and oxidative phosphorylation, cell reproduction; Process of mitosis and meiosis.

**Unit 3 : Diversity of Life**

Introduction. The enormous variety of living things, the need for classification to cope with this variety; taxonomy and phylogeny; shortcomings of a two kingdom classification as plants and animals; the five kingdom classification, Monera, Protista, Plantae, Fungi and Animalia; the basic features of five kingdom classification. modes of obtaining nutrition - autotrophs and heterotrophs.

Life style producers, consumers and decomposers. Unicellularity and multicellularity, phylogenetic relationships. Concepts of species, taxon and categories - hierarchical levels of classification; binomial nomenclature; principles of classification and nomenclature; identification and nature of viruses and bacteriophages; kingdom Monera -archeabacteria- life in extreme environments; Bacteria, Actinomycetes, Cyanobacteria.

Examples & illustration of autotrophic and heterotrophic life; mineralizes- nitrogen fixers; Monera in cycling matter; symbiotic forms; disease producers. Kingdom Protista - Eukaryotic unicellular organisms, development of flagella and cilia; beginning of mitosis; syngamy and sex. Various life styles shown in the major phyla. Evolutionary precursors of complex life forms. Diatoms, dinoflagellates, slime moulds, protozons; symbiotic forms. Plant kingdomcomplex autotrophs, red brown and green algae; conquest of land, bryophytes, ferns, gymnosperms and angiosperms.

Vascularization; development of flower, fruit and seed. Kingdom fungi - lower fungi ( Zygomycetes ), higher fungi ( Ascomycetes and Basidiomycetes ); the importance of fungi. Decomposers; parasitic forms; lichens and mycorrhizae. Animal kingdom- animal body pattern and symmetry. The development of body cavity in invertebrate vertebrate physia. Salient features with reference to habitat and example of phylum porifera, coelenterata, helminthis, annelids, mollusca, arthropoda, echinoderms; chordata - ( classes - fishes, amphibians, reptiles, birds and mammals ) highlighting major characters.

**Unit 4 : Organisms and Environment**

Species : Origin and concept of species population, interaction between environment and population community. Biotic community, interaction between different species, biotic stability. Changes in the community. Succession. Ecosystem; interaction between biotic and abiotic components; major ecosystems, manmade ecosystem - Agro ecosystem. Biosphere; flow of energy, trapping of solar energy, energy pathway, food chain, food web, biogeochemical cycles, calcium and sulphur, ecological imbalance and its consequences.

Conservation of natural resources; renewable and non - renewable ( in brief ). Water and land management, wasteland development. Wild life and forest conservation; causes for the extinction of some wild life, steps taken to conserve the remaining species, concept of endangered species - Indian examples, conservation of forests; Indian forests, importance of forests, hazards of deforestation, concept of afforestation. Environmental pollution; air and water pollution, sources, major pollutants of big cities of our country, their effects and methods of control, pollution due to nuclear fallout and waste disposal, effect and control, noise pollution; sources and effects.

**Unit 5 : Multicellularity : Structure and Function - Plant Life**

Form and function. Tissue system in flowering plants; meristematic and permanent. Mineral nutrition - essential elements, major functions of different elements, passive and active uptake of minerals. Modes of nutrition, transport of solutes and water in plants. Photosynthesis; photochemical and biosynthetic phases, diversity in photosynthetic pathways, photosynthetic electron transport and photophosphorylation, photorespiration. Transpiration and exchange of gases.

Stomatal mechanism. Osmoregulation in plants : water relations in plant cells, water potential. Reproduction and development in Angiosperms; asexual and sexual reproduction. Structure and functions of flower : development of male and female gametophytes in angiosperms, pollination, fertilization and development of endosperm, embryo seed and fruit. Differentiation and organ formation. Plant hormones and growth regulation; action of plant hormones in relation to seed dormancy and germination, apical dominance, senescence and abscission. Applications of synthetic growth regulators. A brief account of growth and movement in plants.

**Unit 6 : Multicellularity : Structure and Function - Animal Life**

Animal tissues, epithelial, connective, muscular, nerve. Animal nutrition, organs of digestion and digestive process, nutritional requirements for carbohydrates, proteins, fats, minerals and vitamins; nutritional imbalances and deficiency diseases. Gas exchange and transport : Pulmonary gas exchange and organs involved, transport of gases in blood, gas exchange in aqueous media circulation : closed and open vascular systems, structure and pumping action of heart, arterial blood pressure, lymph. Excretion and osomoregulation.

Ammonotelism, Ureotelism, urecotelism, excretion of water and urea with special reference to man. Role of kidney in regulation of plasma, osmolarity on the basis of nephron structure, skin and lungs in excretion. Hormonal coordination; hormones of mammals, role of hormones as messengers and regulators. Nervous coordination, central autonomic and peripheral nervous systems, receptors, effectors, reflex action, basic physiology of special senses, integrative control by neuroendocrinal systems.

Locomotion : joints, muscle movements, types of skeletal muscles according to types of movement, basic aspects of human skeleton. Reproduction; human reproduction, female reproductive cycles. Embryonic development in mammals ( upto three germs layers ), growth, repair and ageing.

**Unit 7 : Continuity of Life**

Heredity and variation : Introduction, Mendel’s experiments with peas and concepts of factors. Mendel’s laws of inheritance. Genes : Packaging of heredity material in prokaryotes - bacterial chromosome and plasmid; and eukaryote chromosomes. Extranuclear genes, viral genes. Linkage ( genetic ) maps. Sex determination and sex linkage. Genetic material and its replication, gene manipulation. Gene expression; genetic code, transcription, translation, gene regulation. Molecular basis of differentiation.

**Unit 8 : Origin and Evolution of Life**

Origin of life : living and non - living, chemical evolution, organic evolution; Oparin ideas, Miller - Urey experiments. Interrelationship among living organisms and evidences of evolution : fossil records including geological scale, Morphological evidence - hematology, vestigeal organs, embryological similarities and biogeographical evidence. Darwin’s two major contributions. Common origin of living organisms and recombination as source of variability, selection and variation, adaptation ( Lederberg’s replica plating experiment for indirect selection of bacterial mutants ), reproductive isolation, speciation.

Role of selection, change and drift in determining composition of population. Selected examples : industrial melanism; drug resistance, mimicry, malaria in relation to G - 6 - PD deficiency and sickle cell disease. Human evolution : Palcontological evidence, man’s place among mammals. Brief idea of Dryopithecus, Australopithecus, Homo erectus, H. neanderthlensis, Cro - Magnon man and Homo sapiens. Human chromosomes, similarity in different racial groups. Comparison with chromosomes of non - human primates to indicate common origin; Cultural vs. biological evolution. Mutation : origin and types of mutation, their role in speciation.

**Unit 9 : Application of Biology**

Introduction, role of biology, in the amelioration of human problems. Domestication of plant - a historical account, improvement of crop plants; Principles of plant breeding and plant introduction. Use of fertilizers, their economic and ecological aspects. Use of pesticides : advantages and hazards. Biological methods of pest control. Crops today.

Current concerns, gene pools and genetic conservation. Underutilized crops with potential uses of oilseeds, medicines, beverages, spices, fodder, New crops - Leucaena ( Subabul ), Jojoba, Guayule, winged bean, etc. Biofertilizers - green manure, crop residues and nitrogen fixation ( symbiotic, non symbiotic ). Applications of tissue culture and genetic engineering in crops. Domestication and introduction of animals. Livestock, poultry, fisheries ( fresh water, marine, aquaculture ).

**Improvement of animals :** principles of animal breeding. Major animal diseases and their control. Insects and their products ( silk, honey, wax and lac ). Bioenergy -biomass, wood ( combustion; gasification, ethanol ). Cow dung cakes, gobar gas, plants as sources of hydrocarbons for producing petroleum, ethanol from starch and lignocellulose. Biotechnology, application in health and agriculture, genetically modified ( GM ) organisms, bio-safety issues. A brief historical account - manufacture of cheese. yoghurt, alcohol, yeast, vitamins, organic acids, antibiotics, steroids, dextrins.

Scaling up laboratory findings to Industrial production, sewage treatment. Production of insulin, human growth hormones, interferon. Communicable diseases including STD and diseases spread through ‘blood transfusion ( hepatitis, AIDS, etc ) Immune response, vaccine and antisera. Allergies and Inflammation. Inherited diseases and dysfunctions, sex- linked diseases, genetic incompatibilities, and genetic counseling. Cancer - major types, causes, diagnosis and treatment.

Tissue and organ transplantation. Community health services and measures; blood banks; mental health, smoking, alcoholism and drug addiction - physiological symptoms and control measures. Industrial wastes, toxicology, pollution - related diseases. Biomedical engineering- spare parts for man, instruments for diagnosis of diseases and care. Human population related diseases. Human population, growth, problems and control, inequality between sexes, control measures; test- tube babies aminocentesis. Future of Biology.

## Agriculture

**Unit – 1 : Agro meteorology, Genetics and Plant Breeding, Biochemistry and Microbiology**

**Agrometerology :**

Elements of Weather – rainfall, temperature, humidity, wind velocity, Sunshine weather forecasting, climate change in relation to crop production.

**Genetics & Plant Breeding :**

a) Cell and its structure, cell division – mitosis and meiosis and their significance.

b) Organisation of the genetic materials in chromosomes, DNA and RNA.

c) Mendel’s laws of inheritance. Reasons for the success of Mendel in his experiments, Absence of linkage in Mendel’s experiments.

d) Quantitative inheritance, continuous and discontinuous variation in plants.

e) Monogenic and polygenic inheritance.

f) Role of Genetics in Plant breeding, self and cross – pollinated crops, methods of breeding in field crops – introduction, selection, hybridization, mutation and polyploidy, tissue and cell culture.

g) Plant Biotechnology – definition and scope in crop production.

**Biochemistry :**

pH and buffers, Classification and nomenclature of carbohydrates; proteins; lipids; vitamins and enzymes.

**Microbiology :**

Microbial cell structure, Micro – organisms – Algae, Bacteria, Fungi, Actinomycetes, Protozoa and Viruses. Role of micro – organisms in respiration, fermentation and organic matter decomposition.

**Unit – 2 : Livestock Production**

**Scope 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 – 3 : 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 ).

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.

**Unit – 4 : Horticulture**

a) Importance of fruits and vegetables in human diet, Crop diversification & processing Industry.

b) Orchard – location and layout, ornamental gardening and kitchen garden.

c) Planting system, training, pruning, intercropping, protection from frost and sunburn.

d) Trees, shrubs, climbers, annuals, perennials – definition and examples. Propagation by seed, cutting, budding, layering and grafting.

**e) 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.

f) Principles and methods of fruit and vegetable preservation.

g) Preparation of jellies, jams, ketchup, chips and their packing.