UP Board
PHYSICS-XI
UNIT I: PHYSICAL WORLD AND MEASUREMENT
- Units of measurements, System of Units, S I Units,
- Fundamental and Derived units
- least count
- significant figures
- Errors in measurements
- Dimensions of Physics quantities, Dimensional analysis and its applications
UNIT II: KINEMATICS
- 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, position-time graph, relations for uniformly accelerated motion-
- Scalars and Vectors. Vector Addition and Subtraction, scalar and vector products. Unit Vector. Resolution of a Vector
- Relative Velocity
- Motion in a plane, Projectile Motion. Uniform Circular Motion
UNIT III: LAWS OF MOTION
- Force and inertia, Newton’s First law of motion: Momentum, Newton’s Second Law of motion, Impulses: 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 IV: WORK, ENERGY AND POWER
- Work done by a constant force and a variable force;
- kinetic and potential energies
- work-energy theorem
- power
- The potential energy of spring conservation of mechanical energy
- conservative and 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 the mass of a two-particle system, Centre of the mass of a rigid body:
- Basic concepts of rotational motion
- moment of a force; torque, angular momentum, conservation of angular momentum and its applications;
- The moment of inertia, the radius of gyration, values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications
- Equilibrium of rigid bodies. rigid body rotation and equations of rotational motion
- comparison of linear and rotational motions
UNIT VI: GRAVITATION
- The universal law of gravitation
- Acceleration due to gravity and its variation with altitude and depth
- Kepler’s law of planetary motion
- Gravitational potential energy
- gravitational potential
- Escape velocity
- Motion of a satellite, orbital velocity, time period and energy of satellite
UNIT VII: PROPERTIES OF BULK MATTER
- Elastic behaviour, Stress-strain relationship, Hooke’s Law
- Young’s modulus
- bulk modulus, modulus of rigidity
- Pressure due to a fluid column
- Pascal’s law and its applications
- Effect of gravity on fluid pressure
- Viscosity
- Stokes’ law.
- terminal velocity,
- streamline
- turbulent flow.critical velocity
- Bernoulli’s principle and its applications
- Surface energy and surface tension, angle of contact
- excess of pressure across a curved surface,
- application of surface tension - drops, bubbles, and
- capillary rise
- Heat,
- temperature, thermal expansion;
- specific heat capacity, calorimetry; change of state, latent heat
- Heat tansfer conduction, convection, and radiation
UNIT VIII: THERMODYNAMICS
- Thermal equilibrium
- zeroth law of thermodynamics,
- the concept of temperature. Heat, work, and internal energy
- The first law of thermodynamics,
- isothermal and adiabatic processes.
- The second law of thermodynamics:
- reversible and irreversible processes
UNIT IX: BEHAVIOUR OF PERFECT GASES AND KINETIC THEORY OF GASES
- Equation of state of a perfect gas
- work done on compressing a gas
- Kinetic theory of gases - assumptions
- the concept of pressure
- Kinetic interpretation of temperature:
- RMS speed of gas molecules:
- Degrees of freedom
- Law of equipartition of energy
- and applications to specific heat capacities of gases
- Mean free path. Avogadro’s number
UNIT X: OSCILLATIONS AND WAVES
- Oscillations and periodic motion - time period, frequency, displacement as a function of time
- Periodic functions
- Simple harmonic motion (S.H.M.) and its equation’s 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:
- 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
PHYSICS-XII
UNIT I: ELECTROSTATICS
- Electric charges: Conservation of charge. Coulomb’s law forces between two point charges
- forces between multiple charges: superposition principle and continuous charge distribution
- Electric field
- Electric field due to a point charge, Electric field lines. Electric dipole, Electric field due to a dipole
- Torque on a dipole in a uniform electric field.
- Electric flux. Gauss’s law
- and its applications to find field due to infnitely long uniformly charged straight wire, uniformly charged infinite plane sheet
- and uniformly charged thin spherical shell
- Electric potential and its calculation for a point charge
- electric dipole and system of charges:
- potential difference
- Equipotential surfaces
- Electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field
- Conductors and insulators
- Dielectrics and electric polarization
- capacitors and capacitances
- the combination of capacitors in series and parallel
- capacitance of a parallel plate capacitor with and without dielectric medium between the plates
- Energy stored in a capacitor
UNIT II: CURRENT ELECTRICITY
- Electric current. Drift velocity,
- mobility and their relation with electric current. Ohm’s law
- Electrical resistance
- V-I characteristics of ohmic and non-ohmic conductors
- Electrical energy and power
- Electrical resistivity and conductivity
- Series and parallel combinations of resistors
- Temperature dependence of resistance
- Internal resistance
- potential difference and emf of a cell
- a combination of cells in series and parallel
- Kirchhoffs raws and their applications
- wheatstone bridge. Metre Bridge
UNIT III: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
- 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
- Force on a current-carrying conductor in a uniform magnetic field
- The force between two parallel currents carrying conductors-definition of ampere
- Torque experienced by a current loop in a uniform magnetic field: Moving coil galvanometer, its sensitivity,
- conversion to ammeter and voltmeter
- Current loop as a magnetic dipole and its magnetic dipole moment
- Bar magnet as an equivalent solenoid
- magnetic field lines
- Magnetic field due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis
- Torque on a magnetic dipole in a uniform magnetic field
- para- , dia and ferromagnetic substances with examples
- effect of temperature on magnetic properties.
UNIT IV: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS
- Electromagnetic induction: Faraday’s law
- Induced emf and current:
- Lenz’s Law
- Eddy currents. Self and mutual inductance
- Alternating currents, peak and RMS value of alternating current/ voltage: reactance and impedance:
- LCR series circuit
- resonance
- power in AC circuits
- wattless current.
- AC generator
- transformer
UNIT V: ELECTROMAGNETIC WAVES
- Displacement current
- Electromagnetic waves and their characteristics
- Transverse nature of electromagnetic waves, Electromagnetic spectrum(radio waves, microwaves, infrared, visible, ultraviolet. X-rays. Gamma rays)
- Applications of e.m. waves
UNIT VI: OPTICS
- Reflection of light
- spherical mirrors
- mirror formula
- Refraction of light at plane and spherical surfaces
- thin lens formula
- lens maker formula
- Total internal reflection and its applications
- Magnification
- Power of a Lens. Combination of thin lenses in contact
- Refraction of light through a prism
- Microscope and Astronomical Telescope (reflecting and refracting ) and their magnifying powers
- Wave optics: wavefront and Huygens’ principle
- Laws of reflection and refraction using Huygens principle
- Interference, Young’s double-slit experiment and expression for fringe width
- coherent sources
- sustained interference of light
- Diffraction due to a single slit, width of central maximum
- Polarization, plane-polarized light
- Brewster’s law,
- uses of plane-polarized light and Polaroid
UNIT VII: DUAL NATURE OF RADIATION AND MATTER
- Dual nature of radiation
- Photoelectric effect
- Hertz and Lenard’s observations;
- Einstein’s photoelectric equation: particle nature of light
- Matter waves-wave nature of particle, de Broglie relation
UNIT VIII: ATOMS AND NUCLEI
- Alpha-particle scattering experiment
- Rutherford’s model of atom
- Bohr model
- energy level’s hydrogen spectrum
- Composition and size of nucleus
- atomic masses
- Mass-energy relation
- mass defect; binding energy per nucleon and its variation with mass number
- nuclear fission
- fusion
UNIT IX: ELECTRONIC DEVICES
- Semiconductors
- semiconductor diode: I-V characteristics in forward and reverse bias,diode as a rectifier
- I-V characteristics of LED. the photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator
- Logic gates (OR. AND. NOT. NAND and NOR).
CHEMISTRY-XI
UNIT I: SOME BASIC CONCEPTS OF CHEMISTRY
- 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
- 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, quantum mechanics, the quantum mechanical model of the atom, its important features. Concept of atomic orbitals as one-electron wave functions: Variation of 𝚿 and 𝚿2 with r for ls 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 AND PERIODICITY IN PROPERTIES
UNIT IV: CHEMICAL BONDING AND MOLECULAR STRUCTURE
- 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
- Elementary idea of metallic bonding
- Hydrogen bonding and its application
UNIT V: CHEMICAL THERMODYNAMICS
- 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
- enthalpy
- heat capacity, molar heat capacity
- Hess’s laws of constant heat summation
- Enthalpies of bond dissociation, combustion formation, atomization, sublimation, phase transition, hydration, ionization, and solution
- The second law of thermodynamics - Spontaneity of processes: ΔS of the universe and ΔG of the system as criteria for spontaneity
- ΔG° (Standard Gibbs energy change)
- equiliribrium constant
UNIT VI: EQUILIBRIUM
- 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 ΔG and ΔG° 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)
- ionization constants, ionization of water. pH scale, common ion effect,
- hydrolysis of salts and pH of their solutions,
- the solubility of sparingly soluble salts
- solubility products,
- buffer solutions
UNIT VII: REDOX REACTIONS
- Electronic concepts of oxidation and reduction
- redox reactions
- oxidation number, rules for assigning oxidation number,
- balancing of redox reactions
- Electrolytic and metallic conduction, conductance in electrolytic solutions,
- molar conductivities and their variation with concentration:
- Kohlrausch’s law and its applications
- Electrochemical cells
- Electrolytic
- Galvanic cells
- different types of electrodes, electrode potentials including standard electrode potential, half-cell and cell reactions, emf of a Galvanic cell and its measurement:
- Nernst equation and its applications;
- Relationship between cell potential and Gibbs’ energy change:
- Dry cell and lead accumulator;
- Fuel cells
UNIT VIII: ORGANIC CHEMISTRY: SOME BASIC PRINCIPLES AND TECHNIQUES
- 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 earbocations
- 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
UNIT IX: HYDROCARBONS
- 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
CHEMISTRY-XII
UNIT I : SOLUTIONS
- 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 mass freezing point
- the elevation of boiling point
- osmotic pressure;
- Determination of molecular mass using colligative properties;
- Abnormal value of molar mass
- van’t Hoff factor and its significance.
UNIT II: ELECTROCHEMISTRY
- Electronic concepts of oxidation and reduction
- redox reactions
- oxidation number, rules for assigning oxidation number,
- balancing of redox reactions
- Electrolytic and metallic conduction, conductance in electrolytic solutions,
- molar conductivities and their variation with concentration:
- Kohlrausch’s law and its applications
- Electrochemical cells
- Electrolytic
- Galvanic cells
- different types of electrodes, electrode potentials including standard electrode potential, half-cell and cell reactions, emf of a Galvanic cell and its measurement:
- Nernst equation and its applications;
- Relationship between cell potential and Gibbs’ energy change:
- Dry cell and lead accumulator;
- Fuel cells
UNIT III: CHEMICAL KINETICS
- Rate of a chemical reaction
- factors affecting the rate of reactions: concentration, temperature, pressure, and catalyst;
- elementary and complex reactions,
- order and molecularity of reactions
- rate law
- rate constant and its units,
- differential and integral forms of zero and first-order reactions, their characteristics and half-lives,
- 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
- 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 K2CrO7, and KMnO4
UNIT V: COORDINATION COMPOUNDS
- Introduction to coordination compounds, Werner’s theory;
- ligands,
- co-ordination number, denticity, chelation;
- IUPAC nomenclature of mononuclear co-ordination compounds, isomerism;
- Bonding-Valence bond approach and basic ideas of Crystal field theory,
- colour and magnetic properties;
- Importance of co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems)
UNIT VI: HALOALKANES AND HALOARENES
- General methods of preparation, properties, and reactions
- Nature of C-X bond
- Mechanisms of substitution reactions
- Uses; Environmental effects of chloroform, iodoform, freons, and DDT
UNIT VII: ALCOHOLS, PHENOLS AND ETHERS
- General methods of preparation, properties, reactions, and uses
- Alcohols: Identification of primary, secondary, and tertiary alcohols: mechanism of dehydration
- Phenols: Acidic nature, electrophilic substitution reactions: halogenation. nitration and sulphonation. Reimer - Tiemann reaction
- Ethers: Structure
UNIT VIII: ALDEHYDES, KETONES AND CARBOXYLIC ACIDS
- 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 α-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
- General methods of preparation. Properties, reactions, and uses.
- Amines: Nomenclature, classification structure, basic character, and identification of primary, secondary, and tertiary amines and their basic character
- Diazonium Salts: Importance in synthetic organic chemistry
UNIT X: BIOMOLECULES
- General introduction and importance of biomolecules
- CARBOHYDRATES - Classification; aldoses and ketoses: monosaccharides (glucose and fructose)
- constituent monosaccharides of oligosaccharides (sucrose, lactose, and maltose)
- PROTEINS - Elementary Idea of α-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)
MATHEMATICS-XI
UNIT I: SETS AND FUNCTIONS
- Sets and their representation: Union, intersection, complement of sets, Power set
- algebraic properties of sets
- Relation
- Type of relations, equivalence relations
- one-one, into and onto functions, the composition of functions
- Trigonometric Functions:
- Trigonometrical identities and trigonometrical functions
- inverse trigonometrical functions
- properties of inverse trigonometrical functions
UNIT II: ALGEBRA
- Complex numbers and quadratic equations:
- Introduction to Complex Numbers, Complex numbers as ordered pairs of reals
- Representation of complex numbers in the form a + ib and their representation in a plane, modulus
- algebra of complex number,
- Argand diagram,and argument (or amplitude) of a complex number,
- Quadratic equations in real system and their solutions Relations between roots and co-efficient, nature of roots
- the formation of quadratic equations with given roots
- Permutations and combinations:
- The fundamental principle of counting
- permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r)
- Simple applications
- Binomial theorem:
- Binomial theorem for a positive integral index
- general term and middle term
- simple applications
- Sequence and series:
- Arithmetic and Geometric progressions,insertion of arithmetic means between two given numbers
- geometric means between two given numbers
- Relation between A.M and G.M
UNIT-III: COORDINATE GEOMETRY
- Straight line
- Various forms of equations of a line, angles between two lines
- intersection of lines
- conditions for concurrence of three lines
- the distance of a point from a line
- co-ordinate of the centroid, orthocentre, and circumcentre of a triangle.
- Circle, conic sections
- A standard form of equations of a circle, the general form of the equation of a circle,its radius
- central equation of a circle when the endpoints of a diameter are given
- points of intersection of a line and a circle with the centre at the origin
- sections of conics, equations of parabola in standard form
- equations of ellipse in standard forms
- equations of hyperbola in standard forms
- Three-Dimensional Geometry
- Coordinates of a point in space,directions ratios, and direction cosines, the angle between two intersecting lines, the distance between two points, section formula
- Skew lines
- the shortest distance between them Skew lines, the shortest distance between them, and its equation. Equations of a line
UNIT-IV: CALCULUS
- Limits and derivatives:
- functions, Graphs of simple functions
- algebra of functions, rational
- polynomial function
- Trigonometric function
- inverse function
- Limits
- Differentiation of the sum, difference, product, and quotient of two functions, Differentiation of trigonometric functions
- logarithmic Functions & its Derivatives
- Differentiation of Exponential, inverse trigonometric and implicit functions
- Differentiation of composite function
- derivatives of order up to two
- Rate of change of quantities, Applications of derivatives
- increasing and decreasing functions
- Maxima and minima of functions of one variable
UNIT-V STATISTICS AND PROBABILITY
- Statistics:
- Measures of discretion;calculation of mean, median, mode of grouped and ungrouped data , mean deviation for grouped and ungrouped data
- calculation of standard deviation, variance, for grouped and ungrouped data
- Probability:
- Probability of an event
- addition theorems of probability
- multiplication theorems of probability
- Baye’s theorem, probability distribution of a random variate
MATHEMATICS-XII
UNIT I: RELATIONS AND FUNCTIONS
- Relations function:
- Relation
- Type of relations, equivalence relations
- one-one, into and onto functions, the composition of functions
- Trigonometrical functions:
- Trigonometrical identities and trigonometrical functions
- inverse trigonometrical functions
- properties of inverse trigonometrical functions
UNIT II: ALGEBRA
- Matrices and determinants:
- Matrices, algebra of matrices, type of matrices,and matrices of order two and three,
- determinants
- evaluation of determinants,Adjoint, and evaluation of inverse of a square matrix using determinants
- area of triangles using determinants
- Test of consistency
- solution of simultaneous linear equations in two or three variables using matrices
UNIT III: CALCULAS
- Integral as an anti-derivative, fundamental theorem of calculus
- Fundamental integral involving algebraic, trigonometric, exponential, and logarithms functions. Integrations by substitution
- Integration by parts, and by partial fractions
- Integration using trigonometric identities
- Evaluation of simple integrals of the type ∫ 𝑑𝑥 𝑥 2+𝑎2 , ∫ 𝑑𝑥 √𝑥 2 ± 𝑎2 , ∫ 𝑑𝑥 𝑎2− 𝑥 2 , ∫ 𝑑𝑥 √𝑎2− 𝑥 2 , ∫ 𝑑𝑥 𝑎𝑥2+𝑏𝑥+𝑐 ,∫ 𝑑𝑥 √𝑎𝑥2+ 𝑏𝑥+𝑐 , ∫ (𝑝𝑥+𝑞)𝑑𝑥 𝑎𝑥2+𝑏𝑥+𝑐 , ∫ (𝑝𝑥+𝑞)𝑑𝑥 √𝑎𝑥2+ 𝑏𝑥+𝑐
- Evaluation of simple integrals of the type ∫ √𝑎 2 ± 𝑥 2 𝑑𝑥 , ∫√𝑥 2 − 𝑎 2 𝑑𝑥
- The properties of definite integrals
- Evaluation of definite integrals,
- determining areas of the regions bounded by simple curves in standard form
- Derivatives, continuity, and differentiability:
- functions, Graphs of simple functions
- algebra of functions, rational
- polynomial function
- Trigonometric function
- inverse function
- Limits
- continuity and differentiability
- Differentiation of the sum, difference, product, and quotient of two functions, Differentiation of trigonometric functions
- logarithmic Functions & its Derivatives
- Differentiation of Exponential, inverse trigonometric and implicit functions
- Differentiation of composite function
- derivatives of order up to two
- Rate of change of quantities, Applications of derivatives
- increasing and decreasing functions
- Maxima and minima of functions of one variable
UNIT IV: VECTOR AND THREE-DIMENSIONAL GEOMETRY
- Vectors and scalars, the addition of vectors
- components of a vector in two dimensions and threedimensional space
- scalar products
- vector products
- Coordinates of a point in space,directions ratios, and direction cosines, the angle between two intersecting lines, the distance between two points, section formula
- Skew lines
- the shortest distance between them Skew lines, the shortest distance between them, and its equation. Equations of a line
UNIT-V: LINEAR PROGRAMMING
- Introduction
- related terminology such as constraints
- objective function
- optimization
- graphical method of solution for problems in two variables
- feasible and infeasible regions (bounded or unbounded)
- feasible and infeasible solutions
- optimal feasible solutions (up to three non-trivial constraints).
UNIT VI: PROBABILITY
- Probability of an event
- addition theorems of probability
- multiplication theorems of probability
- Baye’s theorem, probability distribution of a random variate
BIOLOGY-XI
UNIT I: DIVERSITY OF LIVING ORGANISMS
- What is living? ;
- Biodiversity
- Need for classification
- Taxonomy & Systematics
- Concept of species and taxonomical hierarchy
- Binomial nomenclature
- Five kingdom classification
- salient features and classification of Monera
- Protista and Fungi into major groups
- Lichens
- Viruses and Viroids.
- Salient features and classification of plants into major groups-Algae
- Bryophytes
- Pteridophytes
- Gymnosperms (three to five salient and distinguishing features and at least two examples of each category);
- Salient features and classification of animals-nonchordate up to phyla level and chordate up to classes level (three to five salient features and at least two examples).
UNIT II: STRUCTURAL ORGANISATION IN PLANTS AND ANIMALS
- Morphology and modifications
- Tissues
- Anatomy and functions of different parts of flowering plants
- stem
- Root
- leaf
- inflorescence- cymose and recemose,
- flower
- fruit
- seed (To be dealt along with the relevant practical of the Practical Syllabus)
- Family (malvaceae, Cruciferae, leguminoceae, compositae, graminae).
- Animal tissues
- Morphology, anatomy and functions of different systems(digestive, circulatory, respiratory, nervous and reproductive)
- of an insect (Frog). (Brief account only)
UNIT III: CELL: STRUCTURE AND FUNCTION
- Cell theory and cell as the basic unit of life;
- Structure of prokaryotic and eukaryotic cell
- Plant cell and animal cell;
- cell membrane, cell wall,Cell envelope
- Cell organelles structure and function; Endomembrane system-endoplasmic reticulum, Golgi bodies; lysosomes
- vacuoles;
- mitochondria
- ribosomes
- plastids
- micro bodies; Cytoskeleton;
- cilia, flagella
- centrioles
- Nucleus-nuclear membrane, chromatin,(ultra structure and function);
- nucleolus
- Chemical constituents of living cells:
- Biomolecules-structure
- function of proteins
- carbodydrates
- lipids, nucleic acids
- Enzymes-types, properties, enzyme action, classification and nomenclature of anzymes
- B Cell division
- Cell cycle, mitosis,
- meiosis and their significance
UNIT IV: PLANT PHYSIOLOGY
- Photosynthesis
- Photosynthesis as a means of Autotrophic nutrition;
- Site of photosynthesis take place
- pigments involved in Photosynthesis (Elementary idea);
- Photochemical
- biosynthetic phases of photosynthesis
- Cyclic and non cyclic and photophosphorylation
- Chemiosmotic hypothesis;
- Photorespiration C3 and C4 pathways;
- Factors affecting photosynthesis
- Respiration
- Exchange gases;
- Cellular respiration-glycolysis
- fermentation (anaerobic)
- TCA cycle and electron transport system (aerobic)
- Energy relations-Number of ATP molecules generated
- Amphibolic pathways
- Respiratory quotient
- Plant growth and development
- Seed germination;
- Phases of Plant growth and plant growth rate; Conditions of growth, Differentiation, dedifferentiation and redifferentiation; Sequence of developmental process in a plant cell; Growth regulatorsauxin, gibberellin, cytokinin, ethylene, ABA;
UNIT V: HUMAN PHYSIOLOGY
- Breathing and Respiration:
- Respiratory organs in animals (recall only)
- Respiratory system in humans
- Mechanism of breathing and its regulation in humans-Exchange of gases
- transport of gases
- regulation of respiration Respiratory volumes
- Disorders related to respiration-Asthma
- Emphysema, Occupational respiratory disorders.
- Body fluids and circulation:
- Composition of blood, blood groups, coagulation of blood; Composition of lymph and its function
- Human circulatory system-Structure of human heart
- blood vessels;
- Cardiac cycle, cardiac output, ECG,
- Double circulation
- Regulation of cardiac activity
- Disorders of circulatory system-Hypertension
- Coronary artery disease, Angina pectoris, Heart failure
- Excretory products and their elimination
- Modes of excretion- Ammonotelism, ureotelism, uricotelism;
- Human excretory system-structure and fuction
- Urine formation Osmoregulation;
- Regulation of kidney function-Renin
- angiotensin
- Atrial Natriuretic Factor, ADH and Diabetes insipidus; Role of other organs in excretion; Disorders; Uraemia, Renal failure, Renal calculi, Nephritis; Dialysis and artificial kidney.
- Locomotion and Movement: Types of movement
- ciliary, fiagellar, muscular;
- Skeletal muscle-contractile proteins
- 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, Gout.
- Neural control and coordination:
- Neuron and nerves
- Nervous system in humans central nervous system
- peripheral nervous system and visceral nervous system
- Generation and conduction of nerve impulse;
- Chemical coordination and regulation:
- Endocrine glands and hormones
- Human endocrine system
- Hypothalamus, Pituitary,
- Pineal, Thyroid, Parathyroid, Adrenal, Pancreas, Gonads;
- 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
- exopthalmic goiter,
- diabetes
- Addison’s disease. (Imp: Diseases and disorders mentioned above to be dealt in brief.)
BIOLOGY-XII
UNIT I: REPRODUCTION
- Sexual reproduction in flowering plants:
- 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
- Special modes apomixis parthenocarpy, polyembryony
- Significance of seed and fruit formation
- Human Reproduction:
- Male and female reproductive systems
- Microscopic anatomy of testis and ovary;
- Gametogenesis-spermatogenesis
- oogenesis
- Menstrual cycle
- Fertilisation
- embryo development upto blastocyst formation,
- implantation
- Pregnancy and placenta formation
- Parturition (Elementary idea); Lactation (Elementary idea).
- Reproductive health: Need for reproductive health and prevention of sexually transmitted diseases (STD);
- Birth control-Need and Methods,
- Contraception and Medical Termination of Pregnancy (MTP);
- Amniocentesis;
- Infertility and assisted reproductive technologies — IV F, ZIFT, GIFT (Elementary idea for general awareness).
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
- Chromosomes and genes;
- Sex determination
- In humans
- birds
- honey bee
- Linkage and crossing over
- Sex linked inheritance
- Haemophilia
- Colour blindness
- Mendelian disorders in humans-
- Thalassemia
- Chromosomal disorders in humans
- Down’s syndrome
- Turner’s
- Klinefelter’s syndromes
- Molecular basis of Inheritance:
- Search for genetic material
- DNA as genetic material
- Structure of DNA
- RNA
- DNA packaging
- DNA replication
- Central dogma
- Transcription
- genetic code
- translation
- Gene expression and regulation- Lac Operon
- Genome and human genome project
- DNA finger printing
- protein biosynthesis
- Evolution: Origin of life
- Biological evolution and evidences for biological evolution from Paleontology, comparative anatomy, embryology and molecular evidence
- Darwin’s contribution,
- Modern Synthetic theory of Evolution;
- Mechanism of evolution
- Variation (Mutation and Recombination)
- Natural Selection with examples
- types of natural selection; Gene flow and genetic drift; Hardy-Weinberg’s principle
- Adaptive Radiation
- Human evolution
UNIT III: BIOLOGY AND HUMAN WELFARE
- Health and Disease; Pathogens
- parasites causing human diseases
- Malaria, Filariasis, Ascariasis. Typhoid, Pneumonia, common cold, amoebiasis, ring worm
- dengue, chikungunya;
- Basic concepts of immunology
- vaccines
- Cancer, HIV and AIDS
- Adolescence, drug and alcohol abuse.Tobacco abuse
- Microbes in human welfare:
- In household food processing, industrial production, sewage treatment, energy generation
- as biocontrol agents and biofertilizers
UNIT IV: 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
- Transgenic Animals
- Biosafety issues-Biopiracy and patents
UNIT V: ECOLOGY AND ENVIRONMENT
- Organisms and environment Population interactions mutualism, competition.
- predation, parasitism; Population attributes-growth, birth rate and death rate, age distribution.
- Ecosystem: Patterns, components; productivity and decomposition; Energy flow; Pyramids of number, biomass, energy
- Biodiversity and 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 par s and sanctuaries, Sacred Groves
BETA
