• Arithmetic Progression
• Geometrics Progression
• Harmonic Progression
• General term; Summation of first n-terms of series ∑n, ∑n², ∑n3; Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum.

• Definition
• General properties
• Change of base

• Definition in terms of ordered pair of real numbers and properties of complex numbers
• Complex conjugate
• Triangle inequality
• Amplitude of complex numbers and its properties
• Square root of complex numbers
• Cube roots of unity
• De Moivre’s theorem (statement only) and its elementary applications
• Solution of quadratic equation in complex number system.

• nth degree equation has exactly n roots (statement only)
• Quadratic Equations: Quadratic equations with real coefficients
• Relations between roots and coefficients
• Nature of roots
• Formation of a quadratic equation, sign and magnitude of the quadratic expression ax2 +bx+c (where a, b, c are rational numbers and a ≠ 0).

• Permutation of n different things taken r at a time (r ≤ n)
• Permutation of n things not all different. Permutation with repetitions (circular permutation excluded)
• Combinations of n different things taken r at a time (r ≤ n)
• Combination of n things not all different
• Basic properties
• Problems involving both permutations and combinations.

• Concepts of m x n (m ≤ 3, n ≤ 3) real matrices
• Operations of addition
• Scalar multiplication and multiplication of matrices
• Transpose of a matrix
• Determinant of a square matrix
• Properties of determinants (statement only)
• Minor, cofactor and adjoint of a matrix
• Nonsingular matrix. Inverse of a matrix
• Finding the area of a triangle. Solutions of systems of linear equations. (Not more than 3 variables).

• Idea of sets
• Subsets
• Power set
• Complement
• Union
• Intersection and difference of sets
• Venn diagram
• De Morgan’s Laws
• Inclusion formula for two or three finite sets
• Exclusion formula for two or three finite sets
• Cartesian product of sets.

• Statement of the theorem, general term
• Middle term
• Equidistant terms
• Properties of binomial coefficients.

• Equivalence relation — definition and elementary examples
• Mappings
• Range and Domain
• Injective
• Surjective and bijective mappings
• Composition of mappings
• Inverse of a mapping

• Measure of dispersion
• Mean
• Variance and Standard Deviation
• Frequency distribution
• Addition and Multiplication rules of probability
• Conditional probability and Bayes’ Theorem
• Independence of events
• Repeated independent trails 
• Binomial distribution.

• Statement of the principle
• Proof by induction for the sum of squares
• Sum of cubes of first n natural numbers
• Divisibility properties like 22n — 1 is divisible by 3 (n ≥ 1), 7divides 32n+1+2n+2 (n ≥ 1)

• Distance formula
• Section formula
• Area of a triangle
• Condition of collinearity of three points in a plane
• Polar coordinates
• Transformation from Cartesian to polar coordinates and vice versa
• Parallel transformation of axe
•  Concept of locus
• Locus problems involving all geometrical configurations
• Slope of a line
• Equation of lines in different forms
• Angle between two lines
• Condition of perpendicularity and parallelism of two lines
• Distance of a point from a line
• Distance between two parallel lines
• Lines through the point of intersection of two lines
• Angle bisector
• Equation of a circle with a given centre and radius
• Condition that a general equation of second degree in x, y may represent a circle
• Equation of a circle in terms of endpoints of a diameter
• Equation of tangent, normal and chord
• Parametric equation of a circle
• Intersection of a line with a circle
• Equation of the common chord of two intersecting circles.
• Definition of conic section
• Directrix
• Focus and Eccentricity
• Classification based on eccentricity
• Equation of Parabola
• Ellipse and Hyperbola in standard form, their foci, directrices, eccentricities and parametric equations.

• Direction cosines and direction ratios
• Distance between two points and section formula
• Equation of a straight line
• Equation of a plane
• Distance of a point from a plane

• Differential calculus: Functions, domain and range set of functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule and derivative of functions in various forms. Concept of differential.
• Rolle’s Theorem 
• Lagrange’s Mean Value theorem (statement only)
• Their geometric interpretation and elementary application
• L’Hospital’s rule (statement only) and applications. Second order derivative.

• Integral calculus: Integration as a reverse process of differentiation, indefinite integral of standard functions. Integration by parts. Integration by substitution and partial fraction.
• Definite integral as a limit of a sum with equal subdivisions
• Fundamental theorem of integral calculus and its applications
• Properties of definite integrals.
• Differential Equations: Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
• Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines. The area of the region included between two elementary curves.
• Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple product

• Trigonometric functions
• Addition and subtraction formulae
• Formulae involving multiple and submultiple angles
• General solution of trigonometric equations
• Properties of triangles
• Inverse trigonometric functions and their properties.

Dimensions of Physical Quantities.

Error in Measurement.

Vector in 3D

Dot & Cross product

Elementary Differential

Time and Velocity

Equations of Motion

Impulse Centripetal force

Inertial & Non-Inertial Frames

Elastic & Inelastic Collisions

Banking of Roads

Motion of Connected System

Torque

Equilibrium of rigid bodies

Friction and Laws of Friction

Universal Law of Gravitation

Acceleration due to gravity

Escape Velocity

Geostationary Orbits

Escape Velocity

Hooke’s Law

Young’s Modulus

Shear

Rigidity Modulus

Angle of Contact

Capillary Rise

Fluid Pressure

Bulk Modulus

Surface Tension

Heat Transfer

Conduction

Latent Heat Capacity

Ideal Gas Laws

Heat and Temperature

Reynolds Number

Liquids and Gases

Newton’s Law of Cooling

Stefan Law

1st Law of Thermodynamics

2nd Law of Thermodynamics

Reversible and Irreversible Processes

Concept of Pressure and Temperature

Mean Free Oath

Avogadro Number

Speed of Gas Molecules

Assumptions in Kinetics Theory of Gases

Equation of State of Perfect Gas

Restoring Force & Force Const, 

Energy In S.H.M.- Ke & Pe, 

Free, Forced & Damped Oscillations (Introductory Ideas), 

Resonance Wave Motion, 

Equation For Progressive Wave, Longitudinal & Transverse Waves, Sound Waves, 

Newton’s Formula & Laplace’s Correction, 

Factors Affecting The Velocity Of Sound In Air, 

Principles Of Superposition Of Waves,

 Reflection Of Waves, 

Standing Waves In Strings & Organ Pipes, 

Fundamental Mode, 

Harmonics & Overtones

Coulomb’s Law-force Between Two Point Charges, 

Forces Between Multiple Charges;

Superposition Principle & Continuous Charge Distribution. 

Electric Field, & Potential Due To A Point Charge & Distribution Of Charges,

Electric Field Lines Electric Field Due To A Dipole; 

Torque On A Dipole In Uniform Electric Field; 

Electric Flux, 

Gauss’ Theorem & Its Simple Applications, 

Conductors & Insulators, 

Drift Velocity’ Mobility & Their Relation With Electric Current; 

Ohm’s Law, 

Electrical Resistance

Ohmic And Non-ohmic Conductors

Electrical Energy & Power 

Carbon Resistors 

Colour Codes

Combination Of Resistances

Temperature Dependence Of Resistances,

Oersted’s Experiment, 

Biot – Savart Law & Its Application To Current Carrying Circular Loop;

Ampere’s Law & Its Applications To Infinitely Long Straight Wire, Straight And Toroidal Solenoids; 

Force On A Moving Charge In Uniform Magnetic & Electric Fields, Cyclotron Frequency; 

Force On A Current-carrying Conductor In A Uniform Magnetic Field, Force Between Two Parallel Current-carrying Conductors– Definition Of Ampere.

 Torque Experienced By A Current Loop In A Uniform Magnetic Field

Wave Optics

Bohr Model Of Hydrogen Atom, Energy Levels In A Hydrogen Atom, Hydrogen Spectrum, Continuous & Characteristic Xrays.

Isotones, Radioactivity – Alpha, Beta & Gamma Particles/ Rays & Their Properties; 

Radioactive Decay Law; 

Mass Energy Relation, Mass Defect;

 Binding Energy Per Nucleon & Its Variation With Mass Number; 

Nuclear Fission & Fusion.

Magnet As An Equivalent Solenoid, Magnetic Field Lines; 

Earth’s Magnetic Field & Its Magnetic Elements. Para-, Dia- & Ferro- Magnetic Substances, With Examples.

Electromagnets & The Factors Affecting Their Strengths, Permanent Magnets.

• Avogadro’s Hypothesis and its applications; Gay Lussac’s law of gaseous volume; Dalton’s atomic hypothesis.
• Gram atomic weight, Gram molecular weight, Gram equivalent weight and mole concept, valency, atomic mass, molecular mass, and equivalent weight; chemical equations equilibrium in chemical equations
• computations (using the mole concept) pertaining to neutralisation, displacement, and reduction reactions in common oxidation;
• concentration as measured by molality, molarity, normalcy, and mole fraction.
• composition in percentage terms, empirical formula, and molecular formula; numerical issues.

• The concept of a nuclear atom includes the electron, mass, charge, and atomic number.
• The shortcomings of Rutherford’s model;
• additional nuclear structure Atoms of hydrogen have line spectra.
• energy quantization (Planck’s equation E = hv);
• Bohr’s hydrogen atom model and its limits, Sommerfeld’s adjustments (basic concept);
• The ground state electronic configurations of many electron atoms and monoatomic ions, as well as the four quantum numbers;
• The Aufbau Principle, Hund’s Rule, and Pauli’s Exclusion Principle.
• The principle of uncertainty, the duality of matter and light, and de Broglie’s relationship
• The idea of atomic orbitals and the forms of the s, p, and d orbitals (illustrative method).

• The characteristics of α-, β-, and γ-ray radioactivity;
• synthetic transformation; The average age, half-life, decay constant, and rate of radioactive decay of radioactive elements. radioactive units; numerical issues.
• Group displacement law, the stability of the atomic nucleus, and the impact of the neutron-proton (n/p) ratio on the modes of decay
• Applications of radioisotopes (using C, P, Co, and I as examples) definitions and examples of isobars and isotones
• Basic understanding of the reactions of nuclear fission and fusion.

• The modern periodic chart is based on electrical configurations, groups (Gr. 1–18), and periods; the modern periodic law is based on atomic numbers.
• elements’ general characteristics include representative elements (s- and p-blocks), transition elements (d-blocks), and inner transition elements (f-block/lanthanides and actinides).
• Atomic radii, valency, ionisation energy, electron affinity, electronegativity, metallic character, and basic and acidic characteristics of oxides and hydrides of the typical elements (up to Z = 36) are examples of periodic patterns in physical and chemical properties.
• Position of noble gases and hydrogen in the periodic table; correlations along diagonals.

• Properties of electrovalent and covalent compounds; valence electrons; the Octet rule; electrovalent, covalent, and coordinate covalent bonds with examples. Examples of the Octet rule’s limitations; Fajans Rule.
• instances include the directionality of covalent bonds and the forms of polyatomic compounds.
• A qualitative visual approach to the concept of atomic orbital hybridization: sp, sp2, sp3, and dsp2.
• Bond order and magnetic characteristics in molecular orbital energy diagrams of homonuclear diatomic species.
• Molecule shapes and the Valence Shell Electron Pair Repulsion (VSEPR) notion (basic premise). Concept of resonance (elementary idea), resonance structures (examples).
• basic understanding of hydrogen bonding between and within molecules, bond polarity, dipole moment, and electronegativity, as well as how these qualities affect solubility, mp, and bp;
• In diborane, the hydrogen bridge binds.

• Coordination compounds (just examples), double and complex salts,
• Coordination number in Werner’s theory (only instances of coordination numbers 4 and 6),
• Mononuclear coordination compounds: IUPAC name, colour, magnetic characteristics, and forms.

• Different binding forces are used to classify solids into molecular, ionic, covalent, and metallic solids as well as amorphous and crystalline solids (basic idea).
• Unit cell in two- and three-dimensional lattices; density computation; solid packing; packing efficiency; voids; number of atoms per unit cell in a cubic unit cell; point defects; electrical and magnetic characteristics and so on.
• Band theory of n & p type semiconductors, metals, conductors, semiconductors, and insulators.

• Surface tension, viscosity, and vapour pressure (just qualitative concepts; no mathematical derivations)

• Gases’ measurable characteristics.
• Boyle’s Law and Charles Law, the temperature scale in absolute terms, the kinetic theory of gases, the ideal gas equation, which shows the relationship between temperature and the average, root mean square, and most likely velocities.
• Graham’s Law of gaseous diffusion and Dalton’s Law of partial pressure.
• departures from the optimal way of acting.
• Van der Waals equation; liquefaction of gases; actual gases; numerical issues.

• Chemical Energetics: Energy changes in physical and chemical reactions, conservation of energy principle.
• Thermodynamics’ first law; internal energy, heat, pressure, volume work, and equilibrium. A chemical reaction’s enthalpy change (ΔH) and internal energy change (ΔE).
• Applications of Hess’s Law (numerical issues).
• Heat of vaporisation, fusion, and reaction; Entropy; Free energy; Second law of thermodynamics; Standard of spontaneity.
• Thermodynamics’ third law (short introduction).
• Chemical Equilibrium: The dynamic character of chemical equilibria and the Law of Mass Action. The principle of Le Chatelier and equilibrium constants.
• Gaseous reaction equilibrium constants (Kp and Kc) and their relationship (examples).
• The meaning of ΔG and ΔGº.

• Hybridization of carbon: σ – and π – bonds
• Isomerism – constitutional and stereoisomerism;
• Geometrical and optical isomerism of compounds containing up to two asymmetric carbon atoms.
• IUPAC nomenclature of simple organic compounds – hydrocarbons, mono and bifunctional molecules only (alicyclic and heterocyclic compounds excluded) Conformations of ethane and n-butane (Newman projection only)
• Electronic Effects: Inductive, resonance and hyperconjugation.
• Stability of carbocation, carbanion and free radicals; Rearrangement of carbocation;
• Electrophiles and nucleophiles, tautomerism in β-dicarbonyl compounds, acidity and basicity of simple organic compounds

• Alkanes – Preparation from alkyl halides and carboxylic acids; Reactions — halogenation and combustion
• Alkenes and Alkynes – Preparation from alcohols;
• Formation of Grignard reagents and their synthetic applications for the preparation of alkanes, alcohols, aldehydes, ketones and acids;
• SNl and SN2 reactions (preliminary concept).
• Markownikoff’s and anti-Markovnikov’s additions; Hydroboration; Oxymercuration-demercuration, reduction of alkenes and alkynes (H2/Lindler catalyst and Na in liquid NH3), metal acetylides

• Haloalkanes – Preparation from alcohols;
• Nomenclature, nature of C -X bond, physical and chemical properties, mechanism of substitution reactions, optical rotation
• Formation of Grignard reagents and their synthetic applications for the preparation of alkanes, alcohols, aldehydes, ketones and acids; SN1 and SN2 reactions (preliminary concept)
• Uses and environmental effects of – dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT

• Preparation of alcohols from carbonyl compounds and esters.
• Reaction – dehydration, oxidation, esterification, reaction with sodium, ZnCl2/HCl, phosphorus halides
• Ethers – Preparation by Williamson’s synthesis;
• Cleavage with HCl and HI
  Aldehydes and Ketones – Preparation from esters, acid chlorides, gem-dihalides,
• Ca-salt of carboxylic acids. Reaction – Nucleophilic addition with HCN, hydrazine, hydroxyl amines, semi carbazides, alcohols; Aldol condensation, Clemmensen and Wolff – Kishner reduction, haloform, Cannizzaro and Wittig reactions
• Carboxylic Acids – Hydrolysis of esters (mechanism excluded) and cyanides; Hunsdicker and HVZ reactions
• Aliphatic Amines – Preparation from nitro, cyano and amino compounds. Distinction of 1º, 2º and 3º amines (Hinsberg method); Reaction with HNO2; Carbylamine reaction