राजस्थान बोर्ड
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
- 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 and fussion
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
- 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
- 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 cells
- 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 carbocations
- 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 cells
- Galvanic cells
- Different types of electrodes
- Eectrode 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
- Sets and their representation: Union, intersection, complement of sets, Power set
- Algebraic properties of sets
UNIT II: RELATIONS AND FUNCTIONS
- Relation
- Type of relations
- Equivalence relations
- one-one, into and onto functions
- The composition of functions
UNIT III: TRIGONOMETRIC FUNCTIONS
- Trigonometrical identities and trigonometrical functions
- Inverse trigonometrical functions
- Properties of inverse trigonometrical functions
UNIT IV: COMPLEX NUMBER 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
UNIT V: LINEAR INEQUALITIES
Introduction, Inequalities, Algebraic Solutions of Linear, Inequalities in One Variable and their Graphical Representation
UNIT VI: 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
UNIT VII: BINOMIAL THEOREM
- Binomial theorem for a positive integral index
- General term and middle term
- Simple applications
UNIT VIII: SEQUENCES 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 IX: STRAIGHT LINES
- 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
UNIT X: 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
- Eequations of ellipse in standard forms
- Equations of hyperbola in standard forms
UNIT XI: INTRODUCTION TO 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 XII: 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 XIII: STATISTICS
- Measures of discretion
- Ccalculation 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
UNIT XIV: 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 IN LIVING WORLD
- 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 regulators auxin, 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
- Polyembryony
- 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(Elementary idea)
- 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 — IVF, 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 syndrome
- Klinefelter’s syndromes
- Molecular basis of Inheritance
- Search for genetic material
- And 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 parks and sanctuaries
- Sacred Groves
