## JEE Syllabus

## PHYSICS

#### UNIT 1: PHYSICS 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 2: 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 3: LAWS OF MOTION

- Newton’s First law of motion: Force and inertia
- Newton’s Second Law of motion: Momentum
- Newton’s Third Law of motion: Impulses
- Law of conservation of linear momentum and its applications
- Equilibrium of concurrent forces
- Static and Kinetic friction
- Laws of friction
- Rolling friction
- Dynamics of uniform circular motion
- Centripetal force
- Examples of circular motion (vehicle on level circular road, vehicle on banked road)

#### UNIT 4: WORK, ENERGY AND POWER

- 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 5: ROTATIONAL MOTION

- 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 6: 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 7: PROPERTIES OF SOLIDS AND LIQUIDS

- 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
- Streamline
- Bernoulli’s principle and its applications
- Surface energy and surface tension
- Angle of contact
- Application of surface tension - drops, bubbles, and turbulent flow
- Capillary rise
- Temperature
- Thermal expansion
- Specific heat capacity
- Calorimetry
- Change of state
- Latent heat
- Heat tansfer conduction
- Convection and radiation
- Excess of pressure across a curved surface
- Heat
- Stokes’ law
- Terminal velocity
- Critical velocity

#### UNIT 8: 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 9: 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
- Applications to specific heat capacities of gases
- Mean free path
- Avogadro’s number

#### UNIT 10: OSCILLATIONS AND WAVES

- Oscillations and periodic motion - time period
- Oscillations and periodic motion -frequency
- Oscillations and periodic motion - 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

#### UNIT 11: ELECTROSTATICS

- Electric charges: Conservation of charge
- Electric charges: 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
- 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 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 12: 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 law and their applications
- Wheatstone bridge
- Metre Bridge

#### UNIT 13: 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
- Torque experienced by a current loop in a uniform magnetic field: 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 14: 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 15: 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 16: 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 17: DUAL NATURE OF MATTER AND RADIATION

- Dual nature of radiation
- Photoelectric effect
- Hertz and Lenard’s observations
- Einstein’s photoelectric equation: particle nature of light
- Matter waves-wave nature of particle
- De Broglie relation

#### UNIT 18: 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 19: 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
- Zener diode
- Zener diode as a voltage regulator
- Logic gates (OR. AND. NOT. NAND and NOR)

#### UNIT 20: EXPERIMENTAL SKILLS

Familiarity with the basic approach and observations of the experiments and activities:

- Vernier calipers-its use to measure the internal and external diameter and depth of a vessel.
- Screw gauge-its use to determine thicknes/ diameter of thin sheet/wire.
- Simple pendulum-dissipation of energy by plotting a graph between the square of amplitude and time.
- Metre Scale - the mass of a given object by the principle of moments.
- Young’s modulus of elasticity of the material of a metallic wire.
- Surf ace tension of water by capillary rise and effect of detergents.
- Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
- Speed of sound in air at room temperature using a resonance tube.
- Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.
- The resistivity of the material of a given wire using a metre bridge.
- The resistance of a given wire using Ohm’s law.
- Resistance and figure of merit of a galvanometer by half deflection method.
- The focal length of: (i) Convex mirror (ii) Concave mirror, and (iii) Convex lens, using the parallax method.
- The plot of the angle ofdeviation vs angle of incidence for a triangular prism.
- Refractive index of a glass slab usinq a travelling microscope.
- characteristic curves of a p-njunction diode in forward and reverse bias.
- characteristic curves of a Zener diode and finding reverse break down voltage.
- Identificationn of Diode, LED. Resistor. A capacitor from a mixed collection of such items

## CHEMISTRY

#### 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: ATOMIC STRUCTURE

- 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’
- Extra stability of half-filled and completely filled orbitals’

#### UNIT III: 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
- Molecular orbital Theory - LCAOs
- Molecular orbital Theory - Types of molecular orbitals (bonding, antibonding)
- Molecular orbital Theory - sigma and pi-bonds
- Molecular orbital Theory - Molecular orbital electronic configurations of homonuclear diatomic molecules
- Molecular orbital Theory - The concept of bond order, bond length, and bond energy
- Elementary idea of metallic bonding
- Hydrogen bonding and its application

#### UNIT IV: CHEMICAL THERMODYNAMICS

- Fundamentals of thermodynamics: system and surroundings
- Fundamentals of thermodynamics: extensive and intensive properties
- Fundamentals of thermodynamics: state functions
- Fundamentals of thermodynamics: 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 V : SOLUTIONS

- Different methods for expressing the concentration of solution - molality
- Different methods for expressing the concentration of solution - molarity
- Different methods for expressing the concentration of solution - mole fraction
- Different methods for expressing the concentration of solution - 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 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
- Ionic equilibrium: ionization of electrolytes
- Ionic equilibrium: various concepts of acids and bases (Arrhenius, Bronsted - Lowry and Lewis) and their ionization
- Ionic equilibrium: 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 AND 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 VIII: CHEMICAL KINETICS

- Rate of a chemical reaction
- Factors affecting the rate of reactions: concentration
- Factors affecting the rate of reactions: Temperature
- Factors affecting the rate of reactions: Pressure
- Factors affecting the rate of reactions: 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)

SECTION-B INORGANIC CHEMISTRY

#### UNIT IX: 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
- Chemical reactivity

#### UNIT X: P- BLOCK ELEMENTS

- Group -13 to Group 18 Elements
- General Introduction: Electronic configuration and general trends in physical and chemical properties of elements across the periods and down the groups
- Unique behaviour of the first element in each group

#### UNIT XI: d - and f- BLOCK ELEMENTS

- Transition Elements General introduction
- Electronic configuration
- Occurrence
- Characteristics
- General trends in properties of the first-row transition elements - physical properties
- General trends in properties of the first-row transition elements - ionization enthalpy
- General trends in properties of the first-row transition elements - oxidation states
- Atomic radii
- Colour
- Catalytic behaviour
- Magnetic properties
- Complex formation
- Interstitial compounds
- Alloy formation
- Preparation, properties, and uses of K2CrO7
- Preparation, properties, and uses of KMnO4
- Inner Transition Elements Lanthanoids - Electronic configuration
- Inner Transition Elements Lanthanoids - Oxidation states
- Inner Transition Elements Lanthanoids - lanthanoid contraction
- Actinoids - Electronic configuration and oxidation states

#### UNIT XII: CO-ORDINATION 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)

SECTION-C ORGANIC CHEMISTRY

#### UNIT XIII: PURIFICATION AND CHARACTERISATION OF ORGANIC COMPOUNDS

- Purification - Crystallization
- Purification - sublimation
- Purification -distillation
- Purification -differential extraction
- Purification - chromatography - principles and their applications
- Qualitative analysis - Detection of nitrogen
- Qualitative analysis -sulphur
- Qualitative analysis - phosphorus and
- Qualitative analysis - halogens
- Quantitative analysis (basic principles only) - Estimation of carbon, hydrogen, nitrogen, halogens, sulphur, phosphorus
- Calculations of empirical formulae and molecular formulae: Numerical problems in organic quantitative analysis

#### UNIT XIV: SOME BASIC PRINCIPLES OF ORGANIC CHEMISTRY

- 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
- Common types of organic reactions - addition
- Common types of organic reactions - elimination
- Common types of organic reactions - rearrangement

#### UNIT XV: HYDROCARBONS

- Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties, and reactions
- 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
- Mechanism of halogenationn
- Mechanism of nitration
- Friedel - Craft’s alkylation and acylation
- Friedel - directive influence of the functional group in monosubstituted benzene

#### UNIT XVI: ORGANIC COMPOUNDS CONTAINING HALOGENS

- 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 XVII: ORGANIC COMPOUNDS CONTAINING OXYGEN

- General methods of preparation of alcohol
- Properties of alcohol
- Reactions of alcohol
- Preparation of phenol
- Properties of phenol
- Reactions of phenol
- Preparation, properties, and reactions of ethers
- Uses of ALCOHOLS
- Uses of PHENOLS
- Uses of ETHERS
- Alcohols: Identification of primary, secondary, and tertiary alcohols: mechanism of dehydration
- Phenols: Acidic nature
- Electrophilic substitution reactions: halogenation
- Nitration and sulphonation. Reimer - Tiemann reaction
- Reimer - Tiemann reaction
- Ethers: Structure
- 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 XVIII: ORGANIC COMPOUNDS CONTAINING NITROGEN

- General methods of preparation
- Properties, reactions, and uses-1
- Properties, reactions, and uses-2
- Amines: Nomenclature
- Amines: classification structure
- Amines: basic character
- Amines: identification of primary, secondary, and tertiary amines
- Amines: their basic character
- Diazonium Salts: Importance in synthetic organic chemistry

#### UNIT XIX: 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)

#### UNIT XX: PRINCIPLES RELATED TO PRACTICAL CHEMISTRY

- Detection of extra elements (Nitrogen, Sulphur, halogens) in organic compounds
- Detection of the following functional groups:
- Hydroxyl (alcoholic and phenolic) groups in organic compounds
- Carbonyl (aldehyde and ketones)
- Carboxyl groups in organic compounds
- Amino groups in organic compounds
- The chemistry involved in the preparation of the following: Inorganic compounds
- Mohr’s salt, potash alum
- Organic compounds: Acetanilide, p-nitro acetanilide, aniline yellow, iodoform
- The chemistry involved in the titrimetric exercises — Acids, bases and the use of indicators, oxalic acid vs KMnO4, Mohr’s salt vs KMnO4 Chemical principles involved in the qualitative salt analysis: Cations - Pb2+, Cu2+, A13+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+, NH4+ Anions- CO32-, S2-, SO42-, NO3-, NO2-, Cl-, Br-, Insoluble salts excluded
- Chemical principles involved in the following experiments:

- Enthalpy of solution of CuSO4
- Enthalpy of neutralization of strong acid and strong base
- Preparation of lyophilic and lyophobic sols
- Kinetic study of the reaction of iodide ions with hydrogen peroxide at room temperature

## MATHEMATICS

#### UNIT 1: SETS, RELATIONS, AND FUNCTIONS:

- Sets and their representation: Union
- Sets and their representation: intersection
- Sets and their representation: complement of sets
- Sets and their representation: Power set
- Algebraic properties of sets
- Relation
- Type of relations, equivalence relations
- One-one, into and onto functions
- The composition of functions

#### UNIT 2: 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

#### UNIT 3: MATRICES AND DETERMINANTS:

- Matrices
- Algebra of matrices
- Type of matrices
- Matrices of order two and three
- Determinants
- Evaluation of determinants
- Adjoint
- 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 4: 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 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

- Binomial theorem for a positive integral index
- General term and middle term
- Simple applications

#### UNIT 6: 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 7: LIMIT, CONTINUITY, AND DIFFERENTIABILITY:

- Functions
- Algebra of functions
- Rational
- Graphs of simple functions
- 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
- 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 8: INTEGRAL 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

#### UNIT 9: DIFFRENTIAL EQUATIONS

- Ordinary differential equations, their order, and degree
- The solution of differential equation by the method of separation of variables
- Solution of linear differential equation of the type 𝑑𝑦/ 𝑑𝑥 + 𝑝(𝑥)𝑦 = 𝑞(𝑥)

#### UNIT 10: CO-ORDINATE GEOMETRY

- Cartesian system of rectangular coordinates in a plane
- Sections formula
- Distance formula
- The slope of a line
- Locus
- Equation of line
- Parallel and perpendicular lines
- Intercepts of a line on the coordinate axis
- 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

#### UNIT 11: 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 12: VECTOR ALGEBRA

- Vectors and scalars, the addition of vectors
- Components of a vector in two dimensions and threedimensional space
- Scalar products
- Vector products

#### UNIT 13: STATISTICS AND PROBABILITY

- 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