KCET

Unit I: Units and Measurements

4 टॉपिक

• Units of measurement
• Systems of Units
• SI units, fundamental and derived units, significant figures.
• Dimensions of physical quantities, dimensional formulae and equations, dimensional analysis and its applications.

Unit II: Kinematics

6 टॉपिक

• The 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 and relations for uniformly accelerated motion (graphical treatment).
• Elementary concepts of differentiation and integration for describing motion.
• Scalars and vectors: Position and displacement vectors, equality of vectors, multiplication of vectors by real numbers
• addition and subtraction of vectors, unit vector, Resolution of a vector in a plane- rectangular components. Scalar and vector products.
• Motion in a plane: projectile motion, uniform circular motion.

Unit III: Laws of Motion

6 टॉपिक

• Force and 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, common forces in mechanics, static and kinetic friction, laws of friction, rolling friction, methods of reducing 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

5 टॉपिक

• Work done by a constant force and a variable force
• kinetic energy, work-energy theorem, power. Notion of potential energy, the potential energy of a spring, 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: System of Particles and Rotational Motion

4 टॉपिक

• Centre of mass of a two-particle system, motion of centre of mass, centre of mass of rigid bodies.
• Moment of a force (torque), angular momentum, conservation of angular momentum with some examples.
• Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear and rotational motions
• moment of inertia, radius of gyration, moment of inertia of some regular bodies about specific axes. (no derivation).

Unit VI: Gravitation

3 टॉपिक

• Kepler's laws of planetary motion. The universal law of gravitation and gravitational constant. Acceleration due to gravity and its variation with altitude and depth.
• Gravitational potential energy
• gravitational potential, escape velocity, Earth satellites - orbital velocity and time period of a satellite, energy of an orbiting satellite.

Unit VII: Properties of Solids and Fluids

10 टॉपिक

• Elastic behaviour, stress and strain, Hooke's law, stress-strain curve, Young's modulus, bulk modulus, shear modulus, Poisson's ratio
• elastic potential energy. Applications of elastic behavior of materials.
• Pressure due to a fluid column
• Pascal's law and its applications (hydraulic lift & hydraulic brakes).
• Fluid Dynamics - Equation of continuity, streamline and turbulent flow. Bernoulli's theorem and its applications.
• Viscosity: Stokes' law, terminal velocity.
• Surface tension: Surface energy, angle of contact, excess of pressure, application of surface tension - drops, bubbles and capillary rise.
• Thermal properties of matter: Heat and temperature, ideal gas equation and absolute temperature, thermal expansion of solids, liquids and gases. Specific heat capacity: Cp, Cv, calorimetry
• change of state - latent heat.
• Heat transfer: Conduction and thermal conductivity, convection and radiation. Qualitative ideas of Black Body Radiation, Wein's displacement law, Stefan-Boltzmann's law and Newton's law of cooling.

Unit VIII: Thermodynamics

1 टॉपिक

• Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics). Heat, work and internal energy. First law of thermodynamics. Specific heat capacity, thermodynamic state variables and equation of state, thermodynamic processes- Isothermal and adiabatic processes. Second law of thermodynamics: Reversible and irreversible processes. Carnot engine.

Unit IX: Kinetic Theory

4 टॉपिक

• Equation of state of a perfect 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 its application to specific heat capacities of gases and solids
• concept of mean free path.

Unit X: Oscillations and Waves

5 टॉपिक

• Periodic motion - time period, frequency, displacement as a periodic function of time. Simple harmonic motion (SHM) and its equation
• phase, oscillations of a spring - restoring force and force constant
• energy in SHM - kinetic and potential energies
• simple pendulum - derivation of expression for its time period.
• Wave motion: Longitudinal and transverse waves, speed of travelling 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 XI: Experimental Skills

8 टॉपिक

• Familiarity with the basic approach and observations of the experiments and activities:
• Vernier Callipers - its use to measure the internal and external diameter and depth of a vessel.
• Screw gauge - its use to determine thickness / diameter of thin sheet / wire.
• Simple Pendulum - length of second's pendulum by plotting a graph of the square of time period vs length of the pendulum.
• Surface tension of water by capillary rise method.
• Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a spherical body.
• Speed of sound in air at room temperature by using a resonance tube,
• Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.

Unit I: Electrostatics

9 टॉपिक

• Electric charges and their basic properties: Coulomb's law - force between two point-charges, forces between multiple charges
• superposition principle.
• Electric field: electric field due to a point charge, electric field lines
• electric dipole, electric field due to a dipole
• torque on a dipole in a uniform electric field.
• Electric flux, continuous charge distribution, Gauss's law 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 and potential difference, electric potential due to a point charge, a dipole and system of charges
• equipotential surfaces, electrical potential energy of a system of charges and of electric dipole in an electric field.
• Conductors and insulators, electrostatics of conductors. Dielectrics and electric polarisation, 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 (no derivation).

Unit II: Current Electricity

3 टॉपिक

• Electric current: 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, temperature dependence of resistance.
• Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel. Kirchhoff's laws and its simple applications. Wheatstone bridge.

Unit III: Magnetic Effects of Current and Magnetism

7 टॉपिक

• Concept of magnetic field, Oersted's experiment. Biot-Savart's law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields.
• 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 a 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. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field
• bar magnet as an equivalent solenoid (only expression), magnetic field lines
• dipole in a uniform magnetic field, Gauss's law in magnetism. Magnetization and magnetic intensity.
• Dia-, para- and ferro - magnetic substances, with examples.

Unit IV: Electromagnetic Induction and Alternating Currents

7 टॉपिक

• Electromagnetic induction
• Faraday's law, induced emf and current
• Lenz's Law, motional emf. Self and mutual inductance. AC generator.
• Alternating currents, peak and rms value of alternating current/voltage
• AC applied to a resistor, an inductor and a capacitor, reactance and impedance
• LCR series circuit, resonance
• power in AC circuits, wattless current. Transformer.

Unit V: Electromagnetic Waves

2 टॉपिक

• 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), applications of electromagnetic waves.

Unit VI: Optics

6 टॉपिक

• Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, lens-maker's formula. Magnification, power of a lens, combination of thin lenses in contact. Refraction of light through a prism.
• Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
• Wave optics: Wavefront and Huygens' principle, proof of laws of reflection and refraction using Huygens' principle.
• Interference, Young's double hole experiment, coherent sources and sustained interference of light.
• Diffraction due to a single slit, Polarisation, plane polarized light
• uses of Polaroids.

Unit VII: Dual Nature of Matter and Radiation

3 टॉपिक

• Electron emission and types, Photoelectric effect, Hertz and Lenard's observations
• Einstein's photoelectric equation - particle nature of light.
• Matter waves - wave nature of particles, de Broglie relation.

Unit VIII: Atoms and Nuclei

7 टॉपिक

• Alpha-particle scattering experiment
• Rutherford's model of atom
• Bohr model, energy levels, hydrogen spectrum, de Broglie explanation of Bohr's second postulate.
• Composition and size of nucleus, atomic masses, isotopes, isobars, isotones, nuclear forces.
• Mass-energy relation, mass defect
• binding energy per nucleon and its variation with mass number.
• Radioactivity (only types of radioactive decay). Nuclear fission and fusion.

Unit IX: Electronic Devices

2 टॉपिक

• Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors
• semiconductor: intrinsic and extrinsic semiconductors, semiconductor diode, I-V characteristics in forward and reverse bias, diode as a rectifier.

Unit X: Experimental Skills

8 टॉपिक

• Familiarity with the basic approach and observations of the experiments and activities:
• The resistivity of the material of a given wire using Ohm's law.
• The resistance per unit length of a given wire using Ohm's law.
• Resistance and figure of merit of a galvanometer by half deflection method.
• The focal length of (i) Convex mirror, (ii) Concave mirror, and (iii) Convex lens, by parallax method.
• The plot of the angle of deviation vs angle of incidence for a triangular prism.
• Refractive index of a glass slab using a travelling microscope.
• Characteristic curves of a p-n junction diode in forward and reverse bias.

Unit I: Some Basic Concepts of Chemistry

2 टॉपिक

• Matter and its nature, Dalton's atomic theory: Concept of atom, molecule, element, and compound: Laws of chemical combination
• Atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae: Chemical equations and stoichiometry

Unit II: Structure of Atom

5 टॉपिक

• Nature of electromagnetic radiation, photoelectric effect
• Spectrum of the hydrogen atom. Bohr model of a hydrogen atom - its postulates, derivation of the relations for the 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, the quantum mechanical model of the atom, its important features. Concept of atomic orbitals as one-electron wave functions: Variation of Y and Y2 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 III: Classification of Elements & Periodicity in Properties

1 टॉपिक

• 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 IV: Chemical Bonding and Molecular Structure

8 टॉपिक

• Kossel - Lewis approach to chemical bond formation, the 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, the 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, the concept of bond order, bond length, and bond energy.
• Hydrogen bonding and its applications.

Unit V: Thermodynamics

6 टॉपिक

• Fundamentals of thermodynamics: System and surroundings, extensive and intensive properties, state functions, types of processes.
• The 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 bonddissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization, and solution.
• The second law of thermodynamics - Spontaneity of processes
• DS of the universe and DG of the system as criteria for spontaneity. DG0 (Standard Gibbs energy change) and equilibrium constant.

Unit VI: Equilibrium

5 टॉपिक

• Meaning of equilibrium, the 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.
• Equilibrium involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, the significance of DG and DG0 in chemical equilibrium, factors affecting equilibrium: concentration, pressure, temperature, the 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, the solubility of sparingly soluble salts and solubility products, buffer solutions.

Unit VII: Redox Reactions

1 टॉपिक

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

Unit VIII: Organic Chemistry- Some Basic Principles & Techniques

8 टॉपिक

• Tetravalency of carbon: Shapes of simple molecules - hybridization (s and p): Classification of organic compounds based on functional groups: and those containing halogens, oxygen, nitrogen, and sulphur
• Homologous series: Isomerism - structural and stereoisomerism.
• Nomenclature (Trivial and IUPAC) Covalent bond fission - Homolytic and heterolytic: free radicals, carbocations, and carbanions
• stability of carbocations and free radicals, electrophiles, and nucleophiles.
• Electronic displacement in a covalent bond - Inductive effect, electromeric effect, resonance, and hyperconjugation. Common types of organic reactions- Substitution, addition, elimination, and rearrangement.
• 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 IX: Hydrocarbons

5 टॉपिक

• 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 (Markownikoffs and peroxide effect): Ozonolysis and polymerization.
• Alkynes - Acidic character: Addition of hydrogen, halogens, water, and hydrogen halides: Polymerization.
• Aromatic hydrocarbons - Nomenclature, benzene - structure and aromaticity: Mechanism of electrophilic substitution: halogenation, nitration. Friedel - Craft's alkylation and acylation, directive influence of the functional group in monosubstituted benzene.

Unit X: Principles related to Practical Chemistry-I

2 टॉपिक

• Detection of extra elements (Nitrogen, Sulphur and halogens) in organic compounds
• The chemistry involved in the titrimetric exercises - Acids, bases and the use of indicators.

Unit I: Solutions

4 टॉपिक

• Different methods for expressing the concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both), the 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 - a relative lowering of vapour pressure, depression of freezing point, the 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 II: Electrochemistry

3 टॉपिक

• Electrolytic and metallic conduction, conductance in electrolytic solutions, conductivity, molar conductivity and their variation with concentration: Kohlrausch's law and its applications. Electrolysis and laws of electrolysis.
• 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 storage battery, Fuel cells, corrosion.

Unit III: Chemical Kinetics

2 टॉपिक

• 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, the effect of temperature on the rate of reactions, Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).

Unit IV: d and f Block Elements

6 टॉपिक

• 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, and lanthanoid contraction.
• Actinoids - Electronic configuration and oxidation states.

Unit V: Coordination Compounds

6 टॉपिक

• Introduction to coordination compounds. Werner's theory
• ligands, coordination 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
• Metal carbonyls.
• Importance of co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems)

Unit VI: Haloalkanes and Haloarenes

5 टॉपिक

• General methods of preparation, properties, and reactions
• Nature of C-X bond
• Mechanisms of substitution reactions. Optical activity.
• Uses
• Environmental effects of chloroform, iodoform freons, and DDT.

Unit VII: Alcohols, Phenols and Ethers

4 टॉपिक

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

Unit VIII: Aldehydes, Ketones and Carboxylic Acids

7 टॉपिक

• 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 (Wolf Kishner and Clemmensen)
• the acidity of a-hydrogen. aldol condensation, Cannizzaro reaction. Haloform reaction, Chemical tests to distinguish between aldehydes and Ketones.
• Carboxylic Acids : Acidic strength and factors affecting it.

Unit IX: Amines

3 टॉपिक

• General methods of preparation. Properties, reactions and uses.
• Amines: Nomenclature, classification, structure and identification of primary, secondary, and tertiary amines and their basic character.
• Diazonium Salts: Importance in synthetic organic chemistry.

Unit X: Biomolecules

7 टॉपिक

• General introduction and importance of biomolecules.
• CARBOHYDRATES - Classification
• aldoses and ketoses: monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose, and maltose).
• PROTEINS - Elementary Idea of a-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.
• HORMONES: (General introduction).

Unit XI: Principles related to Practical Chemistry-II

15 टॉपिक

• 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 titrimetric exercises - Oxalic acid vs KMnO4
• Mohr's salt vs KMnO4
• Chemical principles involved in the qualitative salt analysis:
• Cations - Al3+, Zn2+, Ca2+, Ba2+, Mg2+, NH4+
• Anions- CO3 2-, SO4 2-, NO3 -, Cl -, Br - (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. Kinetic study of the reaction of iodide ions with hydrogen peroxide at room temperature.
• 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.

1. SETS

1 टॉपिक

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

2. Relations & Functions

1 टॉपिक

• Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finites sets. Cartesian product of the reals with itself (up to Rx Rx R). Definition of Relation, Pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, Domain, Co-domain and Range of a function. Real valued function of a 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

3 टॉपिक

• Positive and Negative angles, Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2 x + cos2 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 identities like following:
• Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.

1. Complex Numbers and Quadratic Equations

1 टॉपिक

• Need for complex numbers, especially the square root of -1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane.

2. Linear Inequalities

1 टॉपिक

• Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.

3. Permutations and Combinations.

1 टॉपिक

• Fundamental principle of counting. Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications.

4. Binomial Theorem.

1 टॉपिक

• Statement and proof of the binomial theorem for positive integral indices. Pascal's triangle. Simple applications.

5. Sequence and Series

1 टॉपिक

• Sequence, Series. Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., Arithmetic and Geometric series, infinite G.P. and its sum, geometric mean (G.M.). Relation between A.M. and G.M.

1. Straight Lines.

1 टॉपिक

• Brief recall of 2-D from earlier classes, 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. Distance of a point from a line.

2. Conic Sections.

1 टॉपिक

• Sections of a cone: Circles, 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.

1 टॉपिक

• Coordinate Axes and Coordinate planes in three-dimensions. Coordinates of a point. Distance between two points.

1.Limits and Derivatives

1 टॉपिक

• 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, product, quotient of functions. Derivative of polynomials and trigonometric functions.

1. Statistics

1 टॉपिक

• Measure of dispersion: Mean deviation, Variance and Standard deviation of ungrouped/ grouped data.

2. Probability

1 टॉपिक

• Events: Occurrence of events, 'not', 'and' & 'or' events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of 'not', 'and', & 'or' events.

1. Relations and Functions

1 टॉपिक

• Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

2. Inverse Trigonometric Functions

1 टॉपिक

• Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

1. Matrices

1 टॉपिक

• 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). Invertible matrices and proof of the uniqueness of inverse, if it exists (Here all matrices will have real entries).

2. Determinants

1 टॉपिक

• Determinant of a square matrix (up to 3 x 3 matrices), minors, cofactors 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.

1. CONTINUITY AND DIFFERENTIABILITY

1 टॉपिक

• Continuity and Differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions. Derivatives of loge x and ex. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives.

2.Application of Derivatives

1 टॉपिक

• Applications of derivatives: Rate of change, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals

2 टॉपिक

• 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 -
• Definite Integral. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Application of Integrals

1 टॉपिक

• Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses (in standard form only).

5. Differential Equations

2 टॉपिक

• Definition, order and degree, general and particular solutions of a differential equation. 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 - dy/dx + Py = Q, where P and Q are function of x or constant.
• dx/dy + Px = Q , where P and Q are function of y or constant.

1. Vectors

1 टॉपिक

• 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

1 टॉपिक

• Direction cosines/direction ratios of a line joining two points. Cartesian and vector equation of a line, coplanar & skew lines, shortest distance between two lines. Angle between two lines.

UNIT V: LINEAR PROGRAMMING

1 टॉपिक

• Introduction, related terminology such as constraints, objective function, optimization, 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 VI: PROBABLITY

1 टॉपिक

• Multiplication theorem on probability. Conditional probability, independent events, total probability, Bayes' theorem.

Chapter-1: The Living world: Biodiversity

3 टॉपिक

• Need for classification, Taxonomy & Systematics
• Binomial nomenclature
• Concept of species and taxonomical hierarchy.

Chapter- 2: Biological Classification

5 टॉपिक

• Three domain of life, five kingdom classification
• Salient features and classification of Monera
• Protista and Fungi into major groups
• Lichens
• Viruses and Viroids.

Chapter- 3: Plant Kingdom

1 टॉपिक

• Salient Features and Classification of plants into major groups - Algae, Bryophytes, Pteridophytes and Gymnosperms.

Chapter- 4: Animal Kingdom

1 टॉपिक

• Salient features and classification of animals - non chordate up to phyla level and chordate up to classes level (Salient features and examples).

Chapter-5: Morphology of Flowering Plants

2 टॉपिक

• Morphology and functions of different parts of flowering plants - Root, stem, leaf, inflorescence - cymose and racemose, flower, fruit and seed (To be dealt along with the relevant practical of the Practical Syllabus). Semi-technical description of a typical flowering plant
• Family Solanaceae features and its economic importance.

Chapter-6: Anatomy of Flowering Plants

2 टॉपिक

• Tissue systems
• Anatomy of Root, stem and leaf (Dicotyledonous and Monocotyledonous plants).

Chapter-7: Structural Organization in Animals

1 टॉपिक

• Morphology, anatomy and functions of different systems (digestive, circulatory, respiratory, nervous and reproductive) of frog. (Brief account only).

Chapter- 8: Cell: The Unit of Life

9 टॉपिक

• Cell theory and cell as the basic unit of life
• Structure of prokaryotic and eukaryotic cell
• Plant cell and animal cell
• Cell envelope, cell membrane, cell wall
• Cell organelles - structure and function
• Endomembrane system - endoplasmic reticulum, Golgi bodies, lysosomes, vacuoles
• mitochondria, ribosomes, plastids, microbodies
• Cytoskeleton, cilia, flagella, centrioles (ultra structure & function)
• Nucleus - nuclear membrane, chromatin, nucleolus, chromosome structure and types.

Chapter - 9: Biomolecules

2 टॉपिक

• Biomicromolecules and biomacromolecules, Chemical constituents of living cells
• structure and function of, proteins, carbohydrates, lipids, nucleic acids, primary and secondary metabolites, Enzymes - Types and nomenclature, properties, enzyme action, factors affecting enzyme activity.

Chapter-10: Cell Cycle and Cell division

1 टॉपिक

• Phases of Cell cycle, mitosis, meiosis and their significance.

Chapter-11: Photosynthesis in Higher Plants

10 टॉपिक

• Photosynthesis as a means of Autotrophic nutrition
• Where does photosynthesis take place
• Early experiments on photosynthesis, Pigments are involved in Photosynthesis (Elementary idea)
• Photochemical and biosynthetic phases of
• photosynthesis
• Cyclic and non-cyclic photophosphorylation
• Chemiosmotic hypothesis
• Photorespiration
• C3 and C4 pathways
• Factors affecting photosynthesis.

Chapter-12: Respiration in Plants

5 टॉपिक

• Exchange of gases
• Cellular respiration - glycolysis, fermentation (anaerobic), TCA cycle and electron transport system (aerobic)
• Energy relations - Number of ATP molecules generated
• Amphibolic pathways
• Respiratory quotient.

Chapter-13: Plant Growth and Development

6 टॉपिक

• Seed germination
• Phases of plant growth and plant growth rates
• Conditions for growth
• Differentiation, dedifferentiation and redifferentiation
• development and sequence of developmental process in a plant cell
• Growth regulators, characteristics, discovery and physiological effects of auxin, gibberellin, cytokinin, ethylene and ABA.

Chapter-14: Breathing and Exchange of Gases

3 टॉपिक

• Respiratory organs in animals (recall only)
• Respiratory system in humans
• Mechanism of breathing and its regulation in humans- Exchange of gases, transport of gases and regulation of respiration, Respiratory volumes and capacities, Disorders related to respiration-Asthma, Emphysema, Occupational respiratory disorders.

Chapter-15: Body Fluids and Circulation

7 टॉपिक

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

Chapter-16: Excretory Products and their Elimination

6 टॉपिक

• Modes of excretion -Ammonotelism, ureotelism, uricotelism
• Human excretory system-structure and function
• Urine formation, mechanism of concentration of the filtrate, and micturition, Osmoregulation
• Regulation of kidney function- Renin-angiotensin, Atrial Natriuretic Factor, ADH and Diabetes insipidus, Role of other organs in excretion
• Disorders-Uremia, Renal failure, Renal calculi, Nephritis
• Dialysis and artificial kidney.

Chapter- 17: Locomotion and Movement

5 टॉपिक

• Types of movement - ciliary, flagellar, muscular
• Skeletal muscle - contractile proteins and muscle contraction
• Skeletal system and its functions (To be dealt with the relevant practical of Practical syllabus)
• Joints
• Disorders of muscular and skeletal system- Myasthenia gravis, Tetany, Muscular dystrophy, Arthritis, Osteoporosis and Gout.

Chapter- 18: Neural Control and Coordination

3 टॉपिक

• Neuron and nerves
• Nervous system in humans- central nervous system, peripheral nervous system and visceral nervous system
• Generation and conduction of nerve impulse.

Chapter -19: Chemical Coordination and Integration

4 टॉपिक

• Endocrine glands and hormones
• Human endocrine system - Hypothalamus, Pituitary, Pineal, Thyroid, Parathyroid, Thymus, Adrenal, Pancreas, Gonads
• Heart, kidney and Gastrointestinal tracts, Mechanism of hormone action (Elementary Idea)
• Role of hormones as messengers and regulators, Hypo-and hyperactivity and related disorders (Common disorders e.g. Dwarfism, Acromegaly, Cretinism, goiter, exophthalmic goiter, diabetes, Addison's disease).

VI: PRINCIPLES RELATED TO PRACTICAL BIOLOGY

9 टॉपिक

• Study and describe locally available common flowering plants of family Solanaceae
• floral formula and floral diagram.
• To study anatomy of monocot and dicot roots and stems (primary).
• To study the distribution of stomata in the upper and lower surfaces of leaves.
• To study and identify different types of inflorescences.
• Study of external morphology of frog.
• Study of mitosis.
• To detect the presence of carbohydrates (glucose, sucrose and starch), proteins and lipids.
• To detect the presence of urea, sugar, albumin and bile salts in urine.

Chapter- 1: Sexual Reproduction in Flowering Plants

8 टॉपिक

• Flower structure
• Development of male and female gametophytes
• Pollination-types, agencies and examples
• Outbreeding devices
• Pollen-Pistil interaction
• Double fertilization
• Post fertilization events- Development of endosperm and embryo, Development of seed and formation of fruit (Types of fruits and seeds) Special modes- apomixis, parthenocarpy, polyembryony
• Significance of seed and fruit formation.

Chapter- 2: Human Reproduction

8 टॉपिक

• Male and female reproductive systems
• Microscopic anatomy of testis and ovary
• Gametogenesis- spermatogenesis & oogenesis
• Menstrual cycle
• Fertilization, embryo development up to blastocyst formation, implantation
• Pregnancy and placenta formation (Elementary idea)
• Parturition (Elementary idea)
• Lactation (Elementary idea).

Chapter- 3: Reproductive Health: Problems and strategies

4 टॉपिक

• Need for reproductive health and prevention of sexually transmitted diseases (STD)
• Population stabilization and Birth control- Need and Methods, Contraception and Medical Termination of Pregnancy (MTP)
• Amniocentesis
• Infertility and assisted reproductive technologies - IVF, ZIFT, GIFT, ICSI, AI, IUI & IUT (Elementary idea for general awareness).

Chapter- 4: Principles of Inheritance and Variation

11 टॉपिक

• Mendelian Inheritance
• Deviations from Mendelism- Incomplete dominance, Co-dominance, Multiple alleles and Inheritance of blood groups, Pleiotropy
• Elementary idea of polygenic inheritance
• Chromosome theory of inheritance
• Chromosomes and genes
• Sex determination- In humans, birds, honey bee
• Drosophila and grasshopper
• Linkage and crossing over
• Mutation, Genetic disorders
• Pedigree analysis, Mendelian disorders in humans - Sex linked inheritance (Haemophilia and Colour blindness) and Autosome linked inheritance (Sickle cell anemia, Phenylketonuria and Thalassemia)
• Chromosomal disorders in humans (Down's syndrome, Turner's and Klinefelter's syndromes).

Chapter-5: Molecular Basis of Inheritance

9 टॉपिक

• Search for genetic material and DNA as genetic material
• Structure of DNA and RNA
• DNA packaging
• Properties of genetic material (DNA vs RNA), DNA replication
• Central dogma
• Transcription, genetic code, mutation and genetic code, translation
• Gene expression and regulation- Lac Operon
• Genome and human genome project
• DNA finger printing.

Chapter-6: Evolution

8 टॉपिक

• Origin of life
• Evolution of life forms a theory, Biological evolution and evidences for biological evolution (Paleontological, comparative anatomy, embryology and molecular evidence)
• Darwin's contribution, Modern Synthetic theory of Evolution
• Mechanism of evolution- Variation (Mutation and Recombination) and Natural Selection with examples, types of natural selection
• Gene flow and genetic drift
• Founder effect A brief account of evolution, Hardy- Weinberg's principle
• Adaptive radiation
• Human evolution.

Chapter- 7: Human Health and Disease

6 टॉपिक

• Pathogens
• parasites causing human diseases (Malaria, Filariasis, Ascariasis, Typhoid, Pneumonia, common cold, amoebiasis, ring worm)
• Basic concepts of
• immunology- Immunity and its types, autoimmunity, immune system in the body, vaccines
• Allergy, Cancer, HIV and AIDs
• Adolescence, drug and alcohol abuse.

Chapter- 8: Microbes in Human Welfare

1 टॉपिक

• In household food processing, industrial production, sewage treatment, energy generation and as biocontrol agents and biofertilizers.

Chapter-9: Biotechnology: Principles and Processes

2 टॉपिक

• Genetic engineering (Recombinant DNA technology)
• Tools, techniques and processes.

Chapter-10: Biotechnology and its Applications

5 टॉपिक

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

Chapter-11: Organisms and Populations

2 टॉपिक

• Population- Population attributes- Population Growth, birth rate, death rate, immigration and emigration, age distribution
• Life history variations, Population interactions-mutualism, competition, predation, parasitism, amensalism and commensalism.

Chapter- 12: Ecosystem

5 टॉपिक

• Patterns, components
• productivity and decomposition
• Energy flow
• Ecological pyramids
• Pyramids of number, biomass and energy.

Chapter-13: Biodiversity and Conservation

6 टॉपिक

• Concept, of Biodiversity
• Patterns of Biodiversity
• Importance of Biodiversity
• Loss of Biodiversity
• Biodiversity conservation approaches
• Hotspots, endangered organisms, extinction, Red Data Book, National parks and sanctuaries, Biosphere reserves and sacred grooves, Botanical gardens, zoological parks, seed banks, tissue culture and cryopreservation.

VI: PRINCIPLES RELATED TO PRACTICAL BIOLOGY

13 टॉपिक

• To study reproductive parts of commonly available flowers.
• To calculate the percentage of pollen germination.
• To study pollen tube growth of stigma.
• To study discrete stages of gametogenesis in mammalian testes and ovary.
• To study and identify various stages of female gametophyte development in the ovary of a flower.
• To perform emasculation, bagging and tagging for controlled pollination.
• To study the blastula stage of embryonic development in mammals.
• Preparation and analysis of pedigree charts.
• To verify Mendel's law of segregation.
• To verify Mendel's law of independent assortment.
• Staining of nucleic acids by acetocarmine.
• Study of homologous and analogous organs in plants and animals.
• To study disease causing organisms and symptoms of the diseases.