Name of Test

Topic

Mathematics

Sets, Relations and Functions

Complex Numbers and Quadratic Equations

Matrices and Determinants

Permutations and Combinations

Mathematical Induction

Binomial theorem and its Simple Applications

Sequences and Series

Limit, Continuity and Differentiability

Integral Calculus

Differential Equations

Coordinate Geometry

Three Dimensional Geometry

Vector Algebra

Statistics and Probability

Trigonometry

Mathematical Reasoning

Physics

Physics and Measurements 

Kinematics

Laws of Motion

Work, Energy and Power

Rotational Motion & Gravitation

Properties of Solids and Liquids

Thermodynamics

Kinetic theory of Gases

Oscillations and Waves

Electrostatics

Current Electricity

Magnetic Effects of Current and Magnetism

Electromagnetic Induction and Alternating Currents

Electromagnetic Waves

Optics

Dual Nature of Matter and Radiation

Atoms and Nuclei

Electronic Devices

Communication Systems

Chemistry

Section A – Physical Chemistry

Some Basic Concepts of Chemistry

States of Matter

Atomic Structure

Chemical Bonding and Molecular Structure

Chemical thermodynamics

Solutions

Equilibrium

Redox Reactions and Electrochemistry

Chemical Kinetics

Surface Chemistry

Section B – Inorganic Chemistry

Classification of Elements and Periodicity in Properties

General Principles and Process of Isolation of Metals

Hydrogen

s – block elements – Alkali and Alkaline Earth Metal

p – block Elements

D and f block Elements

Coordination Compounds

Environmental Chemistry

Section C – Organic Chemistry

Purification and Characteristics of Organic Compounds

Some Basic Principles of Organic Chemistry

Hydrocarbons

Organic Compounds containing Halogens

Organic Compounds containing Oxygen

Organic Compounds containing Nitrogen

Polymers

Biomolecules

Chemistry in Everyday Life

Principles Related to Practical Chemistry

Topics

Topics Description

Topic Difficulty Level

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 etc.

Class 11^th

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, square root of a complex number, triangle inequality etc.

Class 11^th & Class 12^th

Matrices 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 etc.

Class 12^th

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. etc.

Class 11^th

Mathematical Induction

Principle of Mathematical Induction and its simple applications.

Class 11^th

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.

Class 11^th

Sequences and Series

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, and Relation between A.M and G.M sum up to n terms of special series; Sn, Sn₂, Sn₃. Arithmetic-Geometric progression.

Class 11^th

Limit, Continuity and Dfferentiability

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 etc.

Class 12^th

Integral Calculus

Integral as an anti-derivative, Fundamental Integrals involve algebraic, trigonometric, exponential and logarithms functions. Integrations by substitution, by parts and by partial functions. Integration using trigonometric identities. etc.

Class 11^th & Class 12^th

Differential Equations

Ordinary differential equations, their 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
(d_y / d_x) + p(x)y = q(x)

Class 12^th

Coordinate Geometry

Straight line; Various forms of equations of a line, the 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 co-ordinate 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, its 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 centre at the origin and condition for a line to be tangent to a circle, equation of the tangent etc.

Class 12^th

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 and its equation. Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.etc.

Class 12^th

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.

Class 12^th

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, Baye’s theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.

Class 11^th & Class 12^th

Trigonometry

Trigonometrical identities and equations, trigonometrical functions, inverse trigonometrical functions and their properties, heights and distance.

Class 11^th & Class 12^th

Mathematical Reasoning

Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse and contrapositive.

Class 11^th

Topics

Topics Description

Topic Difficulty Level

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 applications. etc.

Class 11^th

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 etc.

Class 11^th

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. etc

Class 11^th

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; Elastic and inelastic collisions in one and two dimensions. etc.

Class 11^th

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 axes theorems and their applications. Rigid body rotation equations of rotational motion. etc.

Class 11^th

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. Geo stationary satellites.

Class 12^th

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. Viscosity. Stokes’ law. terminal velocity, streamline and turbulent flow. Reynolds number. etc.

Class 11^th

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. etc.

Class 11^th

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 energy and temperature: RMS speed of gas molecules: Degrees of freedom. Law of equipartition of energy etc.

Class 11^th

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. etc.

Class 11^th

Electrostatics

Electric charges: Conservation of charge. Coulomb’s law forces between two-point charges
Electric field: Electric field due to a point charge, Electric field lines.
Electric flux. Gauss’s law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.
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 etc.

Class 12^th

Current Electricity

Electric current; Drift velocity. Ohm’s law. Electrical resistance. Resistances of different materials.

Class 12^th

Magnetic Effects of Current and Magnetism

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 etc.

Class 12^th

Electromagnetic Induction and Alternating Currents

Biot – Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long current carrying straight wire and solenoid.
Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current-carrying conductors definition of ampere.
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. etc.

Class 12^th

Electromagnetic Waves

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 etc.

Class 12^th

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
Wave optics: wavefront and Huygens’ principle. Laws of reflection and refraction using the Huygens principle. Interference, Young’s double-slit experiment and expression for fringe width, coherent sources and sustained interference of light. etc.

Class 12^th

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. DavissonGermer experiment. etc.

Class 12^th

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: isotones. Radioactivity- alpha etc

Class 12^th

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 etc

Class 12^th

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). etc.

Class 12^th

Topics

Topics Description

Topic Difficulty Level

Section A – Physical Chemistry

Some Basic Concepts of Chemistry

Matter and its nature, Dalton’s atomic theory: Concept of atom, molecule, element and compound: Physical quantities and their measurements in Chemistry etc.

Class 11^th

States of Matter

Gaseous State: Measurable properties of gases: 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;
Liquid State: Properties of liquids – vapour 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) etc.

Class 11^th

Atomic Structure

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) etc.

Class 11^th

Chemical Bonding and Molecular Structure

Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy.
Covalent Bonding: Concept of electronegativity. Fagan’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.

Class 11^th

Chemical thermodynamics

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;
The second law of thermodynamics – Spontaneity of processes;

Class 11^th

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 etc

Class 12^th

Equilibrium

Equilibria involving physical processes: Solid-liquid, liquid – gas and solid-gas equilibria, Henry’s law.
Equilibrium involving chemical processes: Law of chemical equilibrium, equilibrium constants (K_p and K_c) and their significance, ionization of electrolytes, various concepts of acids and bases (Arrhenius. Bronsted – Lowry and Lewis) and their ionization, acid-base equilibria (including multistage ionization) and ionization constants, ionization of water. etc

Class 11^th

Redox Reactions and Electrochemistry

Electronic concepts of oxidation and reduction, redox reactions, oxidation numbers, rules for assigning oxidation numbers, and 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 etc.

Class 11^th

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 etc.

Class 12^th

Surface Chemistry

Adsorption- Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids
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;

Class 12^th

Section B – Inorganic Chemistry

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

Class 11^th

General Principles and Process 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.

Class 11^th

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.

Class 11^th

S – block elements – Alkali and Alkaline Earth Metal

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.
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. etc.

Class 11^th

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;
Groupwise study of the p – block elements Group-13
Preparation, properties and uses of boron and aluminium; Structure, properties and uses of borax, boric acid, diborane, boron trifluoride, aluminium 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; Allotrophic forms of 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)
Group-17
Preparation, properties and uses of hydrochloric acid;
Group-17 Preparation, properties and uses of hydrochloric acid etc.

Class 11^th

D and f block Elements

Transition Elements 
General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first-row transition elements
Inner Transition Elements
Lanthanoids – Electronic configuration, oxidation states and lanthanoid contraction. Actinoids – Electronic configuration and oxidation states. etc.

Class 12^th

Coordination Compounds

Introduction to coordination compounds. Werner’s theory; ligands, coordination number, denticity. chelation; IUPAC nomenclature of mononuclear coordination compounds, isomerism; etc.

Class 12^th

Environmental Chemistry

Environmental pollution – Atmospheric, water and soil.
Atmospheric pollution – Tropospheric and Stratospheric
Tropospheric pollutants – Gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons; their sources, harmful effects and prevention; Greenhouse effect and Global warming: Acid rain;
Particulate pollutants: Smoke, dust, smog, fumes, mist; their sources, harmful effects and prevention.
Stratospheric pollution- Formation and breakdown of ozone, depletion of the ozone layer – its mechanism and effects.
Water Pollution – Major pollutants such as. pathogens, organic wastes and chemical pollutants; their harmful effects and prevention.
Soil pollution – Major pollutants such as; Pesticides (insecticides. herbicides and fungicides), their harmful effects and prevention. Strategies to control environmental pollution. etc.

Class 11^th

Section C – Organic Chemistry

Purification and Characteristics 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, and phosphorus.
Calculations of empirical formulae and molecular formulae: Numerical problems in organic quantitative analysis,

Class 12^th

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 carbocations and 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.

Class 12^th

Hydrocarbons

Electronic displacement in a covalent bond – Inductive effect, electromeric effect, resonance and hyperconjugation. Common types of organic reactionsSubstitution, addition, elimination and rearrangement.
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
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.
Aromatic hydrocarbons – Nomenclature, benzene – structure and aromaticity: Mechanism of electrophilic substitution: halogenation, nitration.

Class 11^th

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.

Class 12^th

Organic Compounds containing Oxygen

General methods of preparation, properties, reactions and uses.
Alcohols: Identification of primary, secondary and tertiary alcohols: mechanism of dehydration.
Alcohols: Identification of primary, secondary and tertiary alcohols: mechanism of dehydration.
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 etc.

Class 12^th

Organic 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 and their basic character.
Diazonium Salts: Importance in synthetic organic chemistry

Class 12^th

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 and uses – polythene, nylon, polyester and bakelite.

Class 12^th

Biomolecules

General introduction and importance of biomolecules.

Class 12^th

Chemistry in Everyday Life

Carbohydrates – Classification; aldoses and ketoses: monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose and maltose).
Proteins – Elementary Idea of alpha-amino acids, peptide bonds, and 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.

Class 12^th