## Jharkhand State Board

## PHYSICS-XI

#### UNIT I: Physical World and Measurement

- Introduction to Physics
- Scope and excitement of physics
- Physics, technology, and society
- Need for measurement:
- Units of measurement
- systems of units
- SI units
- fundamental and derived units
- Measurement of length,
- mass,
- and time.

#### UNIT II: Kinematics

- Position,
- path length,
- and displacement
- Average velocity and average speed
- Instantaneous velocity and speed
- Acceleration
- Uniformly accelerated motion
- Relative velocity

#### UNIT III: Laws of Motion

- Intuitive concept of force
- Inertia, Newton’s first law of motion
- Momentum, Newton’s second law of motion
- Impulse, Newton’s third law of motion
- Law of conservation of linear momentum and its applications

#### UNIT IV: Work, Energy, and Power

- Work done by a constant force and a variable force
- Kinetic energy
- work-energy theorem
- power
- Notion of potential energy,
- gravitational potential energy
- elastic potential energy
- Conservative forces: Conservation of mechanical energy (kinetic and potential energies)
- Non-conservative forces:
- Motion in a vertical circle
- elastic and inelastic collisions in one and two dimensions

#### UNIT V: Motion of System of Particles and Rigid Body

- Centre of mass of a two-particle system
- momentum conservation and centre of mass motion
- Centre of mass of a rigid body
- centre of mass of uniform rod
- Moment of a force
- torque
- angular momentum
- conservation of angular momentum with some examples.
- Equilibrium of rigid bodies
- rigid body rotation and equations of rotational motion
- comparison of linear and rotational motions
- moment of inertia
- radius of gyration.
- Rolling motion,
- kinematics of rolling motion,
- dynamics of rolling motion.

#### UNIT VI: Gravitation

- Kepler’s laws of planetary motion
- 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
- Geostationary satellites

#### UNIT VII: Properties of Bulk Matter

- Elastic behaviour
- stress-strain relationship
- Hooke’s law
- Young’s modulus
- bulk modulus
- shear modulus of rigidity
- Poisson’s ratio;
- elastic energy.
- 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,
- streamline
- turbulent flow,
- Reynolds number.
- Bernoulli’s theorem and its applications.

#### UNIT VIII: Thermodynamics

- Thermal equilibrium
- definition of temperature (zeroth law of thermodynamics)
- Heat,
- work and internal energy.
- First law of thermodynamics.
- Second law of thermodynamics
- reversible and irreversible processes
- Carnot engine and its efficiency.

#### UNIT IX: 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 interpretation of temperature
- rms speed of gas molecules;
- degrees of freedom
- law of equipartition of energy (statement only) and application to specific heat capacities of gases;
- concept of mean free path
- Avogadro’s number

#### UNIT X: Oscillations and Waves

- Periodic motion - time 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 in sound.

## PHYSICS-XII

#### UNIT I: Electrostatics

- Electric charges
- and their conservation;
- Coulomb’s law - force between two point charges
- forces between multiple charges;
- superposition principle and continuous charge distribution.

#### UNIT II: Current Electricity

- Electric current
- flow of electric charges in a metallic conductor,
- drift velocity
- mobility,
- 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.

#### UNIT III: 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
- its applications to infinitely long current carrying straight wire and solenoid
- force on a moving charge in uniform magnetic and electric fields
- cyclotron.

#### UNIT IV: Electromagnetic Induction and Alternating Currents

- Electromagnetic induction; Faraday’s laws
- induced EMF and current
- Lenz’s Law
- Eddy currents
- Self and mutual induction;
- Alternating currents
- peak and RMS value of alternating current/voltage;
- reactance and impedance;
- LC oscillations (qualitative treatment only),
- LCR series circuit
- resonance;
- power in AC circuits
- wattless current.

#### UNIT V: Electromagnetic Waves

- 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 VI: Optics

- Reflection of light
- spherical mirrors
- mirror formula
- Refraction of light,
- total internal reflection and its applications
- Optical fibres,
- refraction at spherical surfaces,
- lenses,
- thin lens formula
- lens-maker’s formula;
- Magnification
- power of a lens,
- combination of thin lenses in contact
- Refraction and dispersion of light through a prism.

#### UNIT VII: Dual Nature of Matter and Radiation

- Photoelectric Effect
- Hertz and Lenard’s observations;
- Einstein’s photoelectric equation - particle nature of light.

#### UNIT VIII: Atoms and Nuclei

- Alpha-particle scattering experiment
- Rutherford’s model of atom
- Bohr model
- energy levels,
- hydrogen spectrum;
- Composition and size of nucleus
- atomic masses
- isotopes,
- isobars;
- Radioactivity - alpha,
- beta and gamma particles/rays and their properties;
- radioactive decay law.

#### UNIT IX: Electronic Devices

- Energy bands in solids (qualitative ideas only),
- conductors,
- insulators and semiconductors
- semiconductor diode - I-V characteristics in forward and reverse bias,
- diode as a rectifier;
- Special purpose p-n junction diodes: LED,
- photodiode,
- solar cell and Zener diode and their characteristics,
- Zener diode as a voltage regulator.

## CHEMISTRY-XI

#### UNIT I: Some Basic Concepts of Chemistry

- Importance of studying chemistry,
- physical quantities and their measurement in chemistry,
- laws of chemical combination,
- atomic and molecular masses,
- mole concept,
- molar mass,
- percentage composition,
- empirical and molecular formulas,
- chemical reactions,
- stoichiometry and calculations based on stoichiometry.

#### UNIT II: 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
- 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’s exclusion principle and Hund’s rule
- electronic configuration of atoms,
- stability of half filled and completely filled orbitals.

#### UNIT III: Classification of Elements and Periodicity in Properties

- Need for classification of elements,
- genesis of periodic classification,
- modern periodic law and present form of periodic table,
- Nomenclature of elements with atomic number greater than 100:
- Electronic configurations of elements and periodic table and properties:
- Ionization enthalpy
- electron gain enthalpy
- atomic size,
- electronegativity.

#### UNIT IV: Chemical Bonding and Molecular Structure

- Kossel - Lewis approach to chemical bond formation
- concept of ionic and covalent bonds.
- Ionic Bonding
- Lattice energy,
- Born Haber cycle;
- Covalent Bonding - The Lewis structure,
- polar character of covalent bond,
- valence bond theory,
- resonance structures,
- geometry of molecules,
- VSEPR 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 bonding.

#### UNIT V: States of Matter: Gases and Liquids

- Three states of matter,
- intermolecular interactions,
- types 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 behavior of gases,
- empirical derivation of gas equation,
- Avogadro number,
- ideal gas equation,
- deviation from ideal behavior,
- liquefaction of gases,
- critical temperature,
- kinetic energy,
- intermolecular forces,
- the liquid state,
- vapor pressure,
- viscosity,
- surface tension and its effect on the shape of the drop,
- vaporization of a liquid,
- evaporation,
- osmotic pressure,
- solid state,
- classification of solids based on different binding forces,
- amorphous and crystalline solids (elementary idea),
- the unit cell in two-dimensional and three-dimensional lattices,
- calculation of density of unit cell,
- packing in solids,
- packing efficiency,
- voids,
- number of atoms per unit cell in a cubic unit cell,
- point defects,
- electrical and magnetic properties.

#### UNIT VI: 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
- molar heat capacity
- Hess’s law of constant heat summation,
- enthalpy change of reactions,
- calculation of enthalpy change of reactions (enthalpy of formation,
- enthalpy of combustion,
- enthalpy of neutralization,
- bond enthalpy,
- numerical problems).
- Second law of thermodynamics: Spontaneity of processes,-
- entropy,
- Gibbs free energy,
- Gibbs free energy change for a spontaneous process,
- equilibrium constant.

#### UNIT VII: 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,
- ionization of polybasic acids,
- acid-base equilibria,
- factors affecting acid strength and the position of equilibrium,
- the concept of pH,
- buffer solutions
- solubility equilibria of sparingly soluble salts,
- solubility product,
- common ion effect (with illustrative examples).

#### UNIT VIII: Redox Reactions

- Concept of oxidation and reduction,
- redox reactions
- oxidation number
- balancing redox reactions
- in terms of loss and gain of electrons and change in oxidation number
- applications of redox reactions

#### UNIT IX: 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,
- reactions and structure,
- use of hydrogen peroxide.

#### UNIT X: s-Block Element (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 relationships.

#### UNIT XI: 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 acid,
- boron hydrides. Aluminium: Reactions with acids and alkalis,
- uses.

#### UNIT XII: Organic Chemistry - Some Basic Principles and Techniques

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

#### UNIT XIII: Hydrocarbons

- Classification of hydrocarbons,
- alkanes - nomenclature,
- isomerism
- conformation (ethane only),
- physical properties,
- chemical reactions including free radical mechanism of halogenation,
- combustion,
- preparation of alkanes (from unsaturated hydrocarbons) and Wurtz reaction.
- Alkenes - nomenclature,
- structure of double bond (ethene),
- geometrical isomerism,
- physical properties,
- methods of preparation: from alcohols,
- from alkynes,
- 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: from calcium carbide,
- from vicinal dihalides,
- from alkynes,
- chemical reactions: acidic character of alkynes,
- addition reaction of - hydrogen,
- halogen,
- water and hydrogen halides,
- polymerization.

#### UNIT XIV: 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,
- strategies for controlling environmental pollution.

## CHEMISTRY-XII

#### UNIT I: 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,
- packing efficiency,
- voids,
- number of atoms per unit cell in a cubic unit cell,
- point defects,
- electrical and magnetic properties,
- band theory of metals,
- conductors,
- semiconductors and insulators.

#### UNIT II: 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 III: Electrochemistry

- Redox Reactions
- conductance in electrolytic solutions
- specific and molar conductivity,
- variations of conductivity with concentration,
- Kohlrausch’s Law,
- electrolysis and law of electrolysis (elementary idea),
- dry cell - electrolytic cells andGalvanic cells
- lead accumulator,
- EMF of a cell,
- standard electrode potential,
- Nernst equation and its application to chemical cells,
- fuel cells
- corrosion.

#### UNIT IV: 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 rate constant
- integrated rate equations and half-life (only for zero and first order reactions);
- concept of collision theory (elementary idea,
- no mathematical treatment),
- activation energy
- Arrhenius equation.

#### UNIT V: 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 suspension;
- lyophilic,
- lyophobic multimolecular and macromolecular colloids;
- properties of colloids;
- Tyndall effect,
- Brownian movement,
- electrophoresis,
- coagulation and peptization;
- emulsions - types of emulsions.

#### UNIT VI: 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 VII: 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),
- preparation,
- properties,
- structure and uses of phosphine,
- halides (PCI3,
- PCI5) and oxoacids (elementary idea only).

#### UNIT VIII: d and f Block Elements

- General introduction,
- electronic configuration
- occurrence
- 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 $K_2Cr_2O_7$ and $KMnO_4$

#### UNIT IX: Coordination Compounds

- Coordination compounds - Introduction,
- ligands
- Coordination Number
- colour,
- magnetic properties and shapes,
- IUPAC nomenclature of mononuclear coordination compounds
- bonding - Werner’s theory
- VBT,
- CFT;
- isomerism (geometrical and optical),
- importance of coordination compounds (in qualitative analysis,
- biological system).

#### UNIT X: Haloalkanes and Haloarenes

- Haloalkanes - Nomenclature,
- nature of C-X bond
- physical and chemical properties,
- mechanism of substitution reactions,
- optical rotation.
- Haloarenes - Nature of C-X bond
- substitution reactions (directive influence of halogen for monosubstituted compounds only).

#### UNIT XI: 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 with special reference to methanol and ethanol.
- Phenols - Nomenclature,
- methods of preparation,
- physical and chemical properties,
- acidic nature of phenol,
- electrophilic substitution reactions,
- uses of phenols
- Ethers - Nomenclature,
- methods of preparation
- physical and chemical properties,
- uses

#### UNIT XII: Aldehydes, Ketones and Carboxylic Acids

- Aldehyde 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 XIII: 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 - Nomenclature,
- structure,
- methods of preparation,
- physical and chemical properties,
- uses.
- Diazonium Salts - Preparation,
- chemical reactions and importance in synthetic organic chemistry.

#### UNIT XIV: Biomolecules

- Carbohydrates - Classification (aldoses and ketoses),
- monosaccharides (glucose and fructose),
- D-L configuration,
- oligosaccharides (sucrose,
- lactose,
- maltose),
- polysaccharides (starch,
- cellulose,
- glycogen);
- importance of carbohydrates.
- Proteins - Elementary idea of - amino acids,
- peptide bond, polypeptides
- proteins,
- structure of proteins - primary,
- secondary,
- tertiary structure and quaternary structures (qualitative idea only),
- denaturation of proteins;
- enzymes
- Vitamins - Classification and functions
- Nucleic Acids - DNA and RNA

#### UNIT XV: 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 XVI: Chemistry in Everyday Life

- Chemicals in medicines - analgesics,
- tranquilizers,
- antiseptics,
- disinfectants,
- antimicrobials,
- antifertility drugs,
- antibiotics,
- antacids,
- antihistamines.
- Chemicals in food - preservatives,
- artificial sweetening agents,
- elementary idea of antioxidants.
- Cleansing agents - soaps and detergents,
- cleansing action.

## MATHEMATICS-XI

#### UNIT I: Sets and Functions

- Sets
- subsets,
- universal set,
- Venn diagrams,
- operations on sets,
- complement of a set,
- algebraic properties of sets
- Relations
- Types of relations
- functions
- types of functions
- composition of functions,
- inverse of a function,
- binary operations.

#### UNIT II: Algebra

- Principle of mathematical induction,
- types of induction,
- proof by induction,
- binomial theorem for a positive integral index
- general and middle term,
- properties of binomial coefficients,
- Pascal’s triangle,
- arithmetic,
- geometric and harmonic progression.

#### UNIT III: Coordinate Geometry

- Cartesian system of rectangular coordinates,
- distance formula
- section formula
- area of a triangle,
- condition of collinearity of three points in a plane,
- slope of a line,
- parallel and perpendicular lines
- intercepts of a line on the coordinate axes.

#### UNIT IV: Calculus

- Limits
- derivatives,
- continuity and differentiability
- mean value theorem,
- chain rule,
- concept of exponential and logarithmic functions,
- derivatives of exponential and logarithmic functions.

#### UNIT V: Mathematical Reasoning

- Statements,
- logical operations,
- compound statements,
- negation,
- conjunction,
- disjunction,
- implication,
- equivalence,
- truth tables,
- tautology,
- contradiction,
- logical equivalence,
- proof of implication,
- problems related to logic.

#### UNIT VI: Statistics and Probability

- Measures of dispersion,
- range,
- mean deviation,
- standard deviation of ungrouped and grouped data,
- variance,
- analysis of frequency distribution with equal means but different variances,
- concept of probability,
- addition theorem,
- multiplication theorem,
- conditional probability,
- independent events,
- Bayes’ theorem

## MATHEMATICS-XII

#### UNIT I: Relations and Functions

- Types of relations
- reflexive,
- symmetric,
- transitive and equivalence relations. One-to-one and onto functions
- composite functions,
- inverse of a function. Binary operations.

#### UNIT II: Inverse Trigonometric Functions

- Definition,
- range,
- domain,
- principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions

#### UNIT III: Matrices

- Concept,
- notation,
- order,
- equality,
- types of matrices
- zero matrix,
- transpose of a matrix,
- symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. 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; (Here all matrices will have real entries).

#### UNIT IV: Determinants

- Determinant of a square matrix (up to 3 × 3 matrices),
- properties of determinants
- minors,
- cofactors and applications of determinants
- in finding the area of a triangle. Adjoint
- inverse of a square matrix.

#### UNIT V: Continuity and Differentiability

- Continuity and differentiability
- derivative of composite functions,
- chain rule,
- derivatives of inverse trigonometric functions
- derivative of implicit functions
- Concept of exponential and logarithmic functions.

#### UNIT VI: Application of Derivatives

- Rate of change of bodies,
- increasing and decreasing functions
- tangents and normals,
- use of derivatives in approximation,
- 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).

#### UNIT VII: Integrals

- Integration as inverse process of differentiation. Integration of a variety of functions by substitution,
- by partial fractions and by parts,
- Evaluation of simple integrals of the following types and problems based on them.

#### UNIT VIII: Applications of Integrals

- Applications in finding the area under simple curves,
- especially lines,
- circles/parabolas/ellipses (in standard form only),
- Area between any of the two above said curves (the region should be clearly identifiable).

#### UNIT IX: 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,
- solutions of homogeneous differential equations of first order and first degree.

#### UNIT X: Vectors

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

#### UNIT XI: Three-dimensional Geometry

- Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line,
- coplanar and skew lines
- shortest distance between two lines. Cartesian and vector equation of a plane,
- distance of a point from a plane.

#### UNIT XII: Linear Programming

- Introduction,
- 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 (bounded),
- feasible and infeasible solutions,
- optimal feasible solutions (up to three non-trivial constraints).

#### UNIT XIII: Probability

- Conditional probability,
- multiplication theorem on probability,
- independent events,
- total probability,
- Bayes’ theorem
- random variable and its probability distribution,
- mean and variance of random variable.

## BIOLOGY-XI

#### UNIT I: Diversity in Living World

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

#### UNIT II: Structural Organisation in Animals and Plants

- Morphology and modifications
- Tissues
- anatomy and functions of different systems (digestive,
- circulatory,
- respiratory,
- nervous and reproductive) in animals and plants.

#### UNIT III: Cell Structure and Function

- Cell theory,
- structure of prokaryotic and eukaryotic cell
- Plant cell and animal cell;
- Cell envelope
- cell membrane
- cell wall
- Cell organelles - structure and function;
- Endomembrane system,
- mitochondria
- chloroplast,
- nucleus,
- microbodies;
- Cytoskeleton,
- cilia
- flagella
- centrioles (ultrastructure and function);
- Plastids
- vacuoles,
- structure,
- storage functions,
- pigments,
- chemiosmotic hypothesis
- Eukaryotic chromosome,
- chromatin,
- chromosomal theory of inheritance;
- Cell cycle
- Cell Division
- Phases of cell cycle,
- mitosis
- meiosis and their significance

#### UNIT IV: Plant Physiology

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

#### UNIT V: Human Physiology

- Digestion and absorption: Alimentary canal and digestive glands,
- role of digestive enzymes,
- peristalsis,
- digestion,
- absorption and assimilation of proteins,
- carbohydrates and fats;
- Caloric value of proteins,
- Egestion;
- Nutrition in human beings - Balanced diet,
- obesity,
- eating disorders;
- Cellular respiration
- Exchange of gases,
- transport of gases
- regulation of respiration
- respiratory volumes;
- Respiratory organs in animals,
- Respiration in Plants;
- Body fluids and circulation - Blood,
- blood group,
- coagulation of blood
- Human circulatory system - Structure of human heart and blood vessels,
- cardiac cycle
- cardiac output
- double circulation
- Regulation of cardiac activity
- disorders of circulatory system (hypertension,
- coronary artery disease
- angina pectoris
- heart failure).

## BIOLOGY-XII

#### UNIT I: Reproduction

- Reproduction in organisms - Types of reproduction,
- asexual reproduction,
- sexual reproduction;
- Modes of reproduction - fission,
- fragmentation,
- regeneration,
- budding,
- vegetative propagation in plants;
- Human reproduction - Male and female reproductive systems
- Menstrual cycle
- Fertilisation
- embryo development upto blastocyst formation,
- implantation
- Pregnancy and embryonic development,
- parturition and lactation;
- Reproductive health - Need for reproductive health,
- population explosion and birth control,
- medical termination of pregnancy (MTP),
- Sexually transmitted diseases (STDs) - infertility.

#### UNIT II: Genetics and Evolution

- Heredity and variation
- Mendelian inheritance
- deviations from Mendelism - Incomplete dominance
- co-dominance
- multiple alleles
- inheritance of blood groups
- pleiotropy
- Elementary idea of polygenic inheritance
- Chromosome theory of inheritance
- Sex determination and sex-linked inheritance - Human genetics - Blood groups
- genetic disorders
- haemophilia
- thalassemia
- Mendelian disorders in humans - Autosomal dominant,
- autosomal recessive and X-linked inheritance.

#### UNIT III: Biology and Human Welfare

- Health and its failure: infectious and non-infectious diseases,
- drugs - alcoholism and drug abuse - addiction and prevention;
- Basic concepts of immunology
- vaccines
- Cancer - causes and remedies;
- Adolescent problems: obesity,
- drug addiction;
- Biomedical technologies - synthetic insulin,
- artificial limbs,
- pace-maker,
- artificial kidney,
- cataract lens,
- gene therapy

#### UNIT XI: Biotechnology and Its Applications

- Principles and process of biotechnology
- Genetic engineering (Recombinant DNA technology)
- Application of biotechnology in health and agriculture
- Human insulin
- vaccine production
- gene therapy
- Genetically modified organisms - Bt crops
- Ethical issues:
- Transgenic animals
- Plant tissue culture: Micropropagation.

#### UNIT V: Ecology and Environment

- Organisms and environment: habitat and niche;
- Population and ecological adaptations;
- Population interactions - mutualism,
- competition,
- predation,
- parasitism;
- Population attributes - growth,
- birth rate and death rate,
- age distribution;
- Ecosystems: Patterns,
- components;
- Productivity and decomposition;
- Energy flow;
- Ecological pyramids;
- Ecological succession;
- Nutrient cycling (carbon and phosphorous);
- Ecological services - carbon fixation,
- pollination,
- seed dispersal,
- oxygen release (in brief);
- Biodiversity
- its conservation:
- Concept of biodiversity
- Patterns of biodiversity
- Importance of biodiversity
- Loss of biodiversity
- Biodiversity conservation;
- Hotspots
- endangered organisms
- extinction
- Red Data Book
- biosphere reserves
- national parks,
- sanctuaries.