JEE Exam Prep Course in Denver

Paper I- Module 1: Mathematics
1. SETS, Relations, and Functions
- Power Set
- Union, Intersection and Complement of sets
- Algebra Properties of Sets
- Into and Onto Functions
- The Composition of Functions
1. Complex Numbers and Quadratic Equations
- Representation of Complex Numbers
- Argand Diagram
- Algebra of Complex Numbers, Modulus
- Argument of Complex Numbers
- Square Root of a Complex Numbers
- Triangle Inequality
- Quadratic Equations
- Formation of Quadratic Equations with given roots
1. Matrices and Determinants
- Algebra of Matrices
- Type of Matrices
- Determinants
- Matrices of Order two and three
- Properties of determinants
- Evaluation of determinants
- Area of Triangle using determinants
- Adjoint
- Evaluation of inverse of a square matrix using determinants and elementary transformation
- Simultaneous Linear Equations
1. Permutations and Combinations
- Fundamental principle of counting
- Permutation as an arrangement and combination as section
- Meaning of P (n,r) and C (n,r)
- Simple Applications
1. Mathematical Inductions
- Principle of Mathematical Induction
- Simple Applications
1. Binomial Theorem and Its Simple Applications
- Binomial theorem for a positive integral index
- General Term and Middle Term
- Properties of Binomial Coefficients
- Simple Applications
1. Sequence and Series
- Arithmetic and Geometric Progressions
- Insertion of Arithmetic and Geometric means between two numbers
- Relation between A.M and G.M sum up to n terms
- Arithmetico-Geometric Progression
1. Limit, Continuity, and Differentiability
- Real-Valued Functions
- Algebra of Functions
- Polynomials
- Rational Trigonometric
- Logarithmic
- Exponential and Inverse Functions
- Graphs of Simple Functions
- Limits, Continuity, and Differentiability
- Differentiation of the sum, difference, product, and Quotient of two functions
- Differentiation of Trigonometric, Inverse Trigonometric, Logarithmic, exponential, Composite and Implicit Functions
- Rolle’s and Lagrange’s Mean Value Theorems
- Application of Derivatives
- Increasing and Decreasing Functions
- Maxima and Minima of Functions of one variable,tangents, and Normal
1. Integral Calculus
- Integral as an antiderivative
- Fundamental Integrals involving algebraic, Trigonometric, Exponential, and Logarithmic Functions
- Integration by Substitution by part and by partial functions
- Integration using Trigonometric identities
- Integral as limit of a sum
- The Fundamental theorem of Calculus
- Properties of Definite Integrals
- Determining areas of the regions bounded by simple curves in standard form
1. Differential Equations
- Ordinary Differential Equations
- Differential Equation order and degree
- The Formation of Differential Equations
- Solution of differential Equation by the method of separation of variables
- Solution of a homogeneous and linear differential equation of the type
1. Coordinate Geometry
- Cartesian system of Rectangular Coordinates in a plane
- Distance Formula
- Sections Formula
- Locus and its Equation
- Translation of Axes
- The Slope of a line
- Parallel and Perpendicular Lines
- Intercepts of a line on the coordinate axis
Straight Line
- Various forms of Equations of a line
- Intersection of lines
- Angles between two Lines
- Conditions for concurrence of three lines
- The distance of a point from a line equations of internal and external by sectors of angles between two lines coordinate of the centroid
- Orthocentre and circumcentre of a triangle equation of the family of lines passing through the point of intersection of two lines
Circle, Conic Sections
- A standard form of equations of a circle the general form of the equation of a circle
- Radius and central equation of a circle when the endpoints of a diameter are given points of intersection of a line and a circle with the center at the origin and condition for a line to be tangent to a circle equation of the tangent
- Sections of conics
- Equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency
12: Three Dimensional Geometry
- Coordinates of a point in space
- The distance between two points
- Section formula, directions ratios, and direction cosines
- The angle between two intersecting lines
- Skew lines
- The shortest distance between them
- Equations of a line and a plane in different forms
- The intersection of a line and a plane, coplanar lines
13: Vector Algebra
- Vectors and scalars
- The addition of vectors
- Components of a vector in two dimensions and three-dimensional space
- Scalar and vector products
- Scalar and vector triple product
14: Statistics and Probability
- Measures of discretion; calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation
- Variance and mean deviation for grouped and ungrouped data
Probability
- Probability of an event
- Addition and multiplication theorems of probability
- Bayes theorem
- Probability distribution of a random variate
- Bernoulli trials
- Binomial distribution
15: Trigonometry
- Trigonometric identities and equations
- Trigonometric functions
- Inverse trigonometric functions their properties, heights, and distance
16: Mathematical Reasoning
- Statement logical operations or, implies, implied by, if and only if, understanding of tautology
- Contradiction, converse, and contrapositive
Module 2: Physics
1. Physics and Measurements
- Physics, technology, and society
- S I Units
- Fundamental and derived units
- Least count
- Accuracy and precision of measuring instruments
- Errors in measurement
- Dimensions of Physics quantities
- Dimensional analysis and its analysis
1. 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
- Addition and subtraction
- Zero vector
- Scalar and vector Products
- Unit Vector
- Resolution of a Vector
- Relative Velocity
- Motion in a plane
- Projectile Motion
- Uniform Circular Motion
1. 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 and its applications
1. Work, Energy and Power
- Work done by a content force and a variable force
- Kinetic and potential energies
- Work-energy theorem
- Power
- The potential energy of spring
- Conservation of mechanical energy, conservative and neoconservative forces
1. Rotational Motion
- Centre of the mass of a two-particle system
- Centre of the mass of a rigid body
- Basic concepts of rotational motion
- A 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 axis theorems
- Rigid body rotation equations of rotational motion
1. 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
- Orbital velocity of a Satellite
- Geostationary satellites
1. Properties of Solids and Liquids
- Elastic behavior, 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
- Viscosity Stokes' law terminal velocity, streamline, and turbulent flow
- Reynolds number
- Bernoulli's principle and its applications
- Surface energy and surface tension, angle of contact, application of surface tension - drops, bubbles, and capillary rise
- Heat, temperature, thermal expansion
- Specific heat capacity, calorimetry; change of state,latent heat
- Heat transfer-conduction, convection,and radiation
- Newton's law of cooling
1. Thermodynamics
- Thermal equilibrium, zeroth law of thermodynamics, the concept of temperature,heat, work, and internal energy
- The first law of thermodynamics
- The second law of thermodynamics: reversible and irreversible processes
- Carnot engine and its efficiency
1. Kinetic Theory of Gases
- Equation of state of a perfect gas, work done on compressing a gas, Kinetic theory of gasses -assumptions, the concept of pressure
- Kinetic energy and temperature: RMS speed of gas molecules: Degrees of freedom
- Law of equipartition of energy, applications to specific heat capacities of gasses
- Mean free path
- Avogadro's number
1. Oscillations and Waves
- Periodic motion - period, frequency, displacement as a function of time
- Periodic functions. Simple harmonic motion (S.H.M.) and its equation; phase: oscillations of a spring -restoring force and force constant: energy in S.H.M
- Kinetic and potential energies; Simple pendulum - derivation of expression for its time period: Free, forced and damped oscillations
- Resonance
- Wave motion
- Longitudinal and transverse waves,speed of a wave
- Displacement relation for a progressive wave
- Principle of superposition of waves, a reflection of waves
- Standing waves in strings and organ pipes, fundamental mode and harmonics
- Beats doppler effect in sound
1. 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 fields due to infinitely 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; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field
- Conductors and insulators
- Dielectrics and electric polarization, capacitor, 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
1. Current Electricity
Electric current
- Drift velocity, Ohm's law
- Electrical resistance
- Resistances of different materials
- V-l characteristics of Ohmic and non-ohmic conductors
- Electrical energy and power. Electrical resistivity
- Color code for resistors
- Series and parallel combinations of resistors
- Temperature dependence of resistance
- Electric Cell and its Internal resistance, potential difference and emf of a cell, a combination of cells in series and parallel
- Kirchhoff’s laws and their applications
- Wheatstone bridge
- Metre Bridge
- Potentiometer - principle and its applications
1. Magnetic Effects of Current and Magnetism
BIOT
- Savart law and its application to current carrying a circular loop
- Ampere's law and its applications to infinitely long current carrying straight wire and solenoid
- Force on a moving charge in uniform magnetic and electric fields
- Cyclotron
- 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 current sensitivity, and 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; Earth's magnetic field and magnetic elements
- Para-, dia- and ferromagnetic substances. Magnetic susceptibility and permeability
- Hysteresis
- Electromagnets and permanent magnets
1. 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
- LCR series circuit
- Resonance
- Quality factor
- Power in AC circuits
- Wattless current
- AC generator and transformer
1. Electromagnetic Waves
- 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
1. Optics
- Reflection and refraction of light at plane and spherical surfaces, mirror formula
- Total internal reflection and its applications
- Deviation and Dispersion of light by a; prism; Lens Formula
- Magnification
- Power of a Lens
- Combination of thin lenses in contact
- 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, and sustained interference of light
- Diffraction due to a single slit, width of central maximum
- Resolving power of microscopes and astronomical telescopes. Polarization, plane,polarized light: Brewster's law, uses of plane,polarized light and Polaroid.
1. 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
- Davisson,Germer experiment
1. Atoms and Nuclei
- Alpha-particle scattering experiment
- Rutherford's model of atom
- Bohr model
- Energy levels,
- Hydrogen spectrum
- Composition and size of nucleus
- Atomic masses
- Isotopes
- Isobars
- Radioactivityalpha
- Beta and gamma particles/rays and their properties
- Radioactive decay law
- Mass-energy relation
- Mass defect
- Binding energy per nucleon and its variation with mass number
- Nuclear fission and fusion
1. Electronic Devices
- Semiconductors
- Semiconductor diode
- 1-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
- Junction transistor
- Transistor action
- Characteristics of a transistor
- Transistor as an amplifier (common emitter configuration) and oscillator
- Logic gates (OR. AND. NOT. NAND and NOR)
- Transistor as a switch
1. Communication Systems
- Propagation of electromagnetic waves in the atmosphere
- Sky and space wave propagation
- Need for modulation
- Amplitude and Frequency Modulation
- Bandwidth of signals
- The bandwidth of Transmission medium
- Basic Elements of a Communication System (Block Diagram only)
1. 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 thickness/ 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
- Surface tension of water by capillary rise and effect of detergents
- Coefficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body
- Plotting a cooling curve for the relationship between the temperature of a hot body and time
- 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 meter bridge
- The resistance of a given wire using Ohm's law
- Potentiometer: i. Comparison of emf of two primary cells and ii. Determination of internal resistance of a cell
- Resistance and figure of merit of a galvanometer by half deflection method
- The focal length of: (i) Convex mirror (ii) Concave mirror, and (ii) Convex lens, using the parallax method
- The plot of the angle of deviation vs angle of incidence for a triangular prism
- Refractive index of a glass slab using a traveling microscope
- Characteristic curves of a p-n junction diode in forward and reverse bias
- Characteristic curves of a Zener diode and finding reverse breakdown voltage
- Characteristic curves of a transistor and finding current gain and voltage gain
- Identification of Diode. LED, Transistor. IC. Resistor. A capacitor from a mixed collection of such items
- Using a multimeter to: (i) Identify the base of a transistor (ii) Distinguish between NPN and PNP type transistor (iii) See the unidirectional current in case of a diode and an LED (iv) Check the correctness or otherwise of a given electronic component (diode, transistor, or IC)
Module 2: Aptitude
1. Awareness of persons, buildings, materials
- Objects
- Texture related to Architecture and Built-environment
- Visualizing three dimensional objects from two-dimensional drawings
- Visualizing. Different sides of three-dimensional objects. Analytical Reasoning Mental Ability (Visual. Numerical and Verbal)
1. Three dimensional- perception
- Understanding and appreciation of scale and proportions of objects
- Building forms and elements
- Color texture harmony and contrast
- Design and drawing of geometrical or abstract shapes and patterns in pencil
- Transformation of forms both 2D and 3D union
- Subtraction rotation
- Development of surfaces and volumes
- Generation of Plan,
- Elevations and 3D views of objects
- Creating two-dimensional and three-dimensional compositions using given shapes and forms
Module 3: Chemistry
1:1 Physical Chemistry
1. Some basic concepts in chemistry
- Matter and its nature
- Dalton's atomic theory
- Concept of atom, molecule, element, and compound
- Physical quantities and their measurements in Chemistry, precision, and accuracy, significant figures
- S.I.Units
- Laws of chemical combination
- Atomic and molecular masses, mole concept, molar mass
- percentage composition, empirical and molecular formulae
- Chemical equations and stoichiometry
1. States of matter
Classification of matter into solid, liquid, and gaseous states

Gaseous State
- Measurable properties of gasses
- Gas laws
- Boyle's
- Law, Charle’s law & Graham's law of diffusion
- Avogadro's law, Dalton's law of partial pressure
- Concept of Absolute scale of temperature; Ideal gas equation; Kinetic theory of gasses (only postulates)
- Concept of average, root mean square and most probable velocities
- Real gasses, deviation from Ideal behavior, compressibility factor, and van der
- Waals equation
Liquid State
- Properties of liquids - vapor pressure, viscosity and surface tension, and effect of temperature on them (qualitative treatment only)
Solid State
- Classification of solids: molecular, ionic, covalent
- and metallic solids, amorphous and crystalline solids (elementary idea)
- Bragg's Law and its applications
- Unit cell and lattices, packing in solids (fcc, bcc and hcp lattices), voids, calculations involving unit cell parameters, an imperfection in Solids
- Electrical and magnetic properties
1. Atomic Structure
- Thomson and Rutherford atomic models and their limitations
- 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 and 2 with r for 1s and 2s orbitals; various quantum numbers (principal, angular momentum,and magnetic quantum numbers) and their
- Significance; shapes of s, p, and d - orbitals, electron
- Spin and spin quantum number
- Rules for filling electrons in orbitals – Aufbau principle
- Pauli's exclusion principle and Hund's rule, electronic
- Configuration of elements, extra stability of half, filled and completely filled orbitals
1. 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
- LCAOs
- Types of molecular orbitals (bonding, antibonding)
- Sigma and pi-bonds
- Molecular orbital electronic configurations of homonuclear diatomic the concept of bond order, bond length, bond energy
- Elementary idea of metallic bonding
- Hydrogen bonding and its applications
1. 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 and enthalpy, heat capacity, molar heat capacity
- Hess’s law 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; S of the universe and G of the system as criteria for spontaneity
- G (Standard Gibbs energy change) and equilibrium constant
1. Solutions
- Different methods for expressing the concentration of solution - molality, molarity, mole fraction, percentage (by volume and mass both) the vapor
- Pressure of solutions and Raoult's Law - Ideal and non-ideal solutions, vapor pressure - composition, plots for ideal and non-ideal solutions; Colligative properties of dilute solutions - a relative lowering of vapor pressure, depression of freezing point, the elevation of boiling point and osmotic pressure
- Determination of molecular mass using colligative properties; Abnormal value of molar mass
- Hoff factor and its significance
1. Equilibrium
Equilibria involving physical processes
- Solid, liquid - gas and solid-gas equilibria, Henry's law
- General characteristics of equilibrium involving physical processes
Equilibrium involving chemical processes
- Chemical equilibrium
- Equilibrium constants (Kpand Kc) and their significance, the significance of G and G in chemical equilibrium, factors affecting equilibrium concentration, pressure, temperature, the effect of catalyst
- Le Chatelier’s principle
1. 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 and Galvanic cells
- Different types of electrodes, electrode potentials including standard electrode potential half - cell and cell reactions
- Emf of a Galvanic cell and its measurement: Nernst equation and its applications
- Relationship between cell potential and Gibbs' energy change: Dry cell and lead accumulator; Fuel cells
1. 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)
1. Surface Chemistry
Adsorption
- Physisorption and chemisorption and their characteristics
- Factors affecting adsorption of gasses on solids
- Freundlich and Langmuir adsorption isotherms
- Adsorption from solutions
Catalysis
- Homogeneous and heterogeneous
- Activity and selectivity of solid catalysts
- Enzyme catalysis, and its mechanism
Colloidal state
- Distinction among true solutions
- Colloids, and suspensions
- Classification of colloids - lyophilic. lyophobic; multi-molecular
- Macromolecular and associated colloids (micelles)
- Preparation and properties of colloids -Tyndall effect
- Brownian movement
- Electrophoresis
- Dialysis
- Coagulation, and flocculation: Emulsions and their characteristics
1:2 Inorganic Chemistry
1. 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
1. General Principles and Processes of Isolation of Metals
- Modes of occurrence of elements in nature minerals, ores
- Steps involved in the extraction of metals - concentration, reduction (chemical and electrolytic methods), and refining with special reference to the extraction of Al, Cu, Zn, and Fe
- Thermodynamic and electrochemical principles involved in the extraction of metals
1. Hydrogen
- Position of hydrogen in periodic table
- Isotopes, preparation, properties and uses of hydrogen
- Physical and chemical properties of water and heavy water
- Structure, preparation, reactions, and uses of hydrogen peroxide
- Classification of hydrides - ionic, covalent, and interstitial
- Hydrogen as a fuel
1. S-Block Elements (Alkali and Alkaline earth metals)
Group -1 and 2 Elements
- General introduction, electronic configuration, and general trends in physical and chemical properties of elements
- anomalous properties of the first element of each group
- diagonal relationships
- Preparation and properties of some important compounds - sodium carbonate and sodium hydroxide and sodium hydrogen carbonate
- Industrial uses of lime, limestone
- Plaster of Paris and cement
- Biological significance of Na, K. Mg, and Ca
1. P-Block Elements
Group -13 to Group 18 Elements
- Electronic configuration and general trends in physical and chemical
- properties of elements across the periods and down the groups
- unique behavior of the first element in each group.
Groupwise study of the p - block elements Group -13
- Preparation, properties, and uses of boron and aluminum
- Structure, properties, and uses of borax, boric acid, diborane, boron trifluoride, aluminum chloride, and alums.
Group -14
- The tendency for catenation
- Structure, properties, and uses of Allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites, and silicones
Group -15
- Properties and uses of nitrogen and phosphorus
- Allotropic forms of phosphorus; Preparation, properties, structure, and uses of ammonia, nitric acid, phosphine, and phosphorus halides, (PCl3. PCl5)
- Structures of oxides and oxoacids of nitrogen and phosphorus.
Group -16
- Preparation, properties, structures, and uses of ozone
- Allotropic forms of Sulphur; Preparation, properties, structures, and uses of sulphuric acid (including its industrial preparation)
- Structures of oxoacids of Sulphur
Group-17
- Preparation, properties, and uses of hydrochloric acid
- Trends in the acidic nature of hydrogen halides
- Structures of Interhalogen compounds and oxides and oxoacids of halogens
Group-18
- Occurrence and uses of noble gasses
- Structures of fluorides and oxides of xenon
1. 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 K2Cr2O7, and KMnO4
Inner Transition Elements
1. Lanthanide
- Electronic configuration
- oxidation states, and lanthanide contraction.
1. Actinoids
- Electronic configuration and oxidation states
7. Coordination Compounds
- Introduction to coordination compounds
- Werner's theory; ligands, coordination number, denticity. Chelation
- IUPAC nomenclature of mononuclear coordination compounds, isomerism
- BondingValence bond approach and basic ideas of Crystal field theory
- Color and magnetic properties
- Importance of coordination compounds (in qualitative analysis, extraction of metals and in biological systems)
8. Environmental Chemistry
1. Environmental pollution
- Atmospheric, water, and soil
1. Atmospheric pollution
- Tropospheric and Stratospheric
1. Tropospheric pollutants - Gaseous pollutants
- Oxides of carbon, nitrogen, and sulphur, hydrocarbons
- their sources, harmful effects, and prevention
- Greenhouse effect and Global warming: Acid rain
1. Particulate pollutants
- Smoke, dust, smog, fumes, mist
- their sources, harmful effects, and prevention
1. Stratospheric pollution
- Formation and breakdown of ozone
- Depletion of the ozone layer - its mechanism and effects
1. Water Pollution
- Major pollutants such as. pathogens, organic wastes, and chemical pollutants
- Their harmful effects and prevention
1. Soil pollution
- Major pollutants such as; Pesticides (insecticides. herbicides and fungicides)
- their harmful effects, and prevention
- Strategies to control environmental pollution
1:3 Organic Chemistry
1. Purification and Characterisation of Organic Compounds
Purification
- Crystallization
- Sublimation
- Distillation
- differential extraction, and chromatography
- principles and their applications
Qualitative analysis
- Detection of nitrogen
- sulphur, phosphorus, and halogens
Quantitative analysis
- (basic principles only)
- Estimation of carbon, hydrogen, nitrogen, halogens, sulphur, phosphorus.
Calculations of empirical formula and molecular formulae
- Numerical problems in organic quantitative analysis
1. 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 those containing halogens, oxygen, nitrogen, and sulphur
- Homologous series: Isomerism - structural and stereoisomerism
Nomenclature (Trivial and IUPAC)
- Covalent bond fission - Homolytic and heterolytic
- Free radicals, carbocations, and carbanions
- Stability of carbocations and free radicals, electrophiles, and nucleophiles
Electronic displacement in a covalent bond
- Inductive effect
- Electromeric effect, resonance
- Hyperconjugation
Common types of organic reactions
- Substitution, addition, elimination, and rearrangement
1. 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 (Markovnikov's 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
1. 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
1. Oxygen Compounds Containing Oxygen
- General methods of preparation, properties, reactions, and uses
Alcohols, Phenols, and Ethers
1. Alcohols
- Identification of primary, secondary, and tertiary alcohols mechanism of dehydration
1. Phenols
- Acidic nature
- electrophilic substitution reactions
- halogenation. nitration and sulphonation
- Reimer - Tiemann reaction
1. 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 - hydrogen. aldol condensation
- Cannizzaro reaction
- Haloform reaction
- Chemical tests to distinguish between aldehydes and Ketones.
6. Oxygen Compounds Containing Nitrogen
- General methods of preparation. Properties, reactions, and uses
Amines
- Nomenclature, classification structure
- basic character, and identification of primary, secondary, and tertiary amines
- their basic character
Diazonium Salts
- Importance in synthetic organic chemistry
7. Polymers
- General introduction and classification of polymers
- General methods of polymerization
- Addition and condensation, copolymerization
- Natural and synthetic, rubber and vulcanization
- Some important polymers with emphasis on their monomers
- Uses – polythene, nylon, polyester, and bakelite
8. Biomolecules

Carbohydrates
- Classification; aldoses and ketoses
- monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose, and maltose)
PROTEINS
- Elementary Idea of -amino acids, peptide bond, polypeptides
- Proteins: primary, secondary, tertiary
- 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
9. Chemistry in Everyday Life
- Chemicals in Medicines
- Analgesics
- Tranquilizers
- Antiseptics
- Disinfectants
- Antimicrobials
- anti-fertility drugs
- antibiotics, antacids
- Antihistamines -their meaning and common examples.
Chemicals in food
- Preservatives
- artificial sweetening agents
- common examples
Cleansing Agents
- Soaps and detergents
- cleansing action
10. 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), carbonyl (aldehyde and ketones) carboxyl, and 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+, Al3+, Fe3+, Zn2+, Ni2+ , Ca2+, Ba2+, Mg2+ , NH4 + Anions- CO3 2− , S 2- ,SO4 2− , NO3- , NO2- , Cl- , Br- , I- ( 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
Paper II- Module 1: Mathematics
1. SETS, Relations, and Functions
- Sets and their representation
- Union, intersection and complement of sets and their algebraic properties
- Power set; Relation, Type of relations, equivalence relations, functions
- One-one, into and onto functions, the composition of functions
1. Complex Numbers and Quadratic Equations
- Complex numbers as ordered pairs of reals
- Representation of complex numbers in the form a+ib and their representation in a plane
- Argand diagram, algebra of complex number, modulus and argument (or amplitude) of a complex number triangle inequality
- Quadratic equations in real and complex number system and their solutions
- Relations between roots and coefficient, nature of roots the formation of quadratic equations with given roots
1. Matrix and Determinants
- Matrices
- Algebra of matrices
- Type of matrices
- Determinants, and matrices of order two and three
- Properties of determinants
- Evaluation of determinants
- Area of triangles using determinants
- Adjoint, and evaluation of inverse of a square matrix using determinants and elementary transformations
- Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices
1. Permutations and Combinations
- The fundamental principle of counting, permutation as an arrangement and combination as section
- Meaning of P (n,r) and C (n,r), simple applications
1. Mathematical Inductions
- Principle of Mathematical Induction and its simple applications
1. Binomial Theorem and its Simple Applications
- Binomial theorem for a positive integral index
- General term and middle term
- properties of Binomial coefficients, and simple applications
1. Sequence and Series
- Arithmetic and Geometric progressions
- Insertion of arithmetic, geometric means between two given numbers
- Relation between A.M and G.M sum up to n terms of special series; Sn, Sn2, Sn3
- Arithmetico-Geometric progression
1. Limit, Continuity and Differentiability
- Real–valued functions
- Algebra of functions, polynomials
- Rational
- Trigonometric, logarithmic, and exponential functions, inverse function
- Graphs of simple functions
- Limits, continuity, and differentiability
- Differentiation of the sum, difference, product, and quotient of two functions
- Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions
- derivatives of order up to two, Rolle’s and Lagrange's Mean value Theorems
- Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions
- Maxima and minima of functions of one variable, tangents and normal
1. Integral Calculus
- Integral as an antiderivative
- Fundamental Integrals involving algebraic
- trigonometric, exponential, and logarithmic functions
- Integrations by substitution, by parts, and by partial functions
- 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 ∫ √𝑎 2 ± 𝑥 2 𝑑𝑥 , ∫√𝑥 2 − 𝑎 2 𝑑𝑥 Integral as limit of a sum
- The fundamental theorem of calculus, properties of definite integrals
- Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form
1. Coordinate Geometry
Straight line
- Various forms of equations of a line
- Intersection of lines
- Angles between two lines
- Conditions for concurrence of three lines
- The distance of a point form a line
- Equations of internal and external by sectors of angles between two lines
- Coordinate of the centroid, orthocentre, and circumcentre of a triangle
- Equation of the family of lines passing through the point of intersection of two lines
Module 3: Planning
1. General Awareness
- General knowledge questions and knowledge about prominent cities
- Development issues
- Government programs, etc
1. Social Sciences
- The idea of nationalism
- Nationalism in India
- Pre-modern world
- 19th -century global economy
- Colonialism, and colonial cities
- Industrialization, resources, and development
- Types of resources
- Agriculture
- Water
- Mineral resources
- Industries
- National economy
- Human Settlements Power-sharing
- Federalism
- Political parties
- Democracy
- the constitution of India Economic development- economic sectors, globalization the concept of development
- Poverty
- Population structure
- social exclusion, and inequality
- Urbanization
- Rural development
- Colonial cities
1. Thinking Skills
- Comprehension (unseen passage)
- map reading skills
- Scale
- Distance
- Direction, area, etc.
- Critical reasoning
- Understanding of charts, graphs, and tables
- Basic concepts of statistics and quantitative reasoning

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