Units

Topics

Applications of Matrices and Determinants

Introduction, Inverse of a Non-Singular Square Matrix, Adjoint of a square Matrix, Properties of inverses of matrices, Row-Echelon form and others.

Complex Numbers

Introduction to Complex Numbers, Powers of imaginary unit, Rectangular form, Properties of complex numbers, Geometrical representation of conjugate of a complex number, Properties of Complex Conjugates, others.

Theory of Equations

Introduction, Basics of Polynomial Equations, Different types of Polynomial Equations, Quadratic Equations, Vieta’s Formulae and Formation of Polynomial Equations and more.

Inverse Trigonometric Functions

Introduction, Some Fundamental Concepts, Domain and Range of trigonometric functions, Graphs of functions, Amplitude and Period of a graph, Inverse functions and more.

Two Dimensional Analytical Geometry-II

Introduction, Circle, Equation of a circle in standard form, Conics, The general equation of a Conic, Parabola, Hyperbola, Geometric description of conic section, and more.

Applications of Vector Algebra

Introduction, Geometric Introduction to Vectors, Scalar Product and Vector Product, Geometrical interpretation, Application of dot and cross products in Geometry, Vector triple product and more.

Applications of Differential Calculus

Early Developments, Meaning of Derivatives, Derivative as rate of change, Equations of Tangent and Normal, A Limit Process and more

Differentials and Partial Derivatives

Introduction, Linear Approximation and Differentials, Errors: Absolute Error, Relative Error, and Percentage Error, Differentials,

Applications of integration

Introduction, Fundamental Theorems of Integral Calculus and their Applications, Improper Integrals, Reduction Formulae, Gamma Integral, Evaluation of Bounded Plane Area by Integration

Ordinary Differential Equations

Introduction, Differential Equation, Order, and Degree, Formation of Differential Equations, Solution of First Order and First Degree Differential Equations, Applications of First Order Ordinary Differential Equations.

Probability Distributions

Random Variable , Types of Random Variable, Discrete random variables, Cumulative Distribution Function or Distribution Function, Continuous Distributions, Distribution function from Probability density function

Discrete Mathematics

Binary Operations, Definitions, Some binary operations on Boolean Matrices, Modular Arithmetic, Compound Statements, Logical Connectives, and Truth Tables, Duality.

Units

Topics

Electrostatics

Historical background of electric charges, Coulomb’s law, Super position principle, Electric Field, Electric dipole, Gauss Law, Electric Flux, Distribution of charges in a conductor and action at points, and more

Current Electricity

Electric Current, Ohm’s Law, Energy and power in electrical circuits, Kirchhoff’s rule, Thermo electric current

Magnetism and magnetic effects of electric current

Basic properties of magnets, Ampere Circuital law, Lorentz force,

Electromagnetic Induction and Alternating current

Electromagnetic Induction, Self-Induction, Methods of producing induced emf, Transformer, Alternating Current Power in AC circuits, Oscillation in LC circuits

Electromagnetic waves

Displacement current and Maxwell’s correction to Ampere’s circuital law, Electromagnetic waves, Types of spectrum emission and absorption spectrum fraunhofer lines

Ray optics

Ray optics, Spherical mirrors, Refraction, Thin lens, Prism,

Wave optics

Theories on light, Wave nature of light, Interference, Diffraction, Optical instruments,

Dual nature of radiation and mater

Electron Emission, Matter waves, Photo Electric Effect, X - ray Spectra Continuous X Ray Spectra, Characteristic X Ray Spectra

Atomic and nuclear physics

Electric Discharge Through gases Properties of Cathode Rays, Atomic Spectra, Nuclear Force, Nuclear fission, Nuclear fusion

Electronics and communication systems

Energy Band Diagram, DIODES, The Bipolar Junction transistor, Digital Electronics, Modulation,

Recent developments in physics

Nano science and Nano technology, Robotics

Units

Chapters

Metallurgy

Occurrence of metals, Concentration of ores, Extraction of crude metal, Refining process,

P-block elements -I

General trends in properties of p-block elements, Group 13 (Boron group) elements, Group 14 (Carbon group) elements,

P-block elements -II

Group 15 (Nitrogen group) elements, Oxygen, Group 17 (Halogen group) elements

Transition and inner transition elements

Position of d- block elements in the periodic table, Electronic configuration, General trend in properties, Important compound of Transition elements f-block elements

Coordination chemistry

Coordination compounds and double salts, Definition of important terms pertaining to co-ordination compounds, Nomenclature of coordination compounds, Theories of coordination compound

Solid state

General characteristics of solids, Crystal lattice and unit cell, Primitive and Non Primitive unit, Imperfections in solids,

Chemical kinetics

Rate of Chemical reaction, Molecularity, Integrated Rate Equation, Half life period of a reaction, Arrhenius Equation

Ionic Equillibrium

Acids and bases, Strength of Acids and Bases, Ionisation of water, The pH Scale, Ionistion of Weak Acids, Common ion effect, Buffer Solution, Solubility Product

Electro chemistry

Conductivity of electrolytic solution, Variation of molar conductivity with concentration, Thermodynamics of cell reactions, Nernst equation

Surface chemistry

Adsorption and Absorption, Characteristics of adsorption, Catalysis Positive and Negative Catalysis, Colloid, dispersion Phase and dispersion medium,

Hydroxy compounds and ethers

Classification of Alcohols, IUPAC Nomenclature,

Carbonyl compounds and carboxylic acids

Nomenclature of Aldehyde and Ketones, Structure of carbonyl group, General methods of preparation of Aldehydes and Ketones, Physical properties of Aldehydes and Ketones

Organic nitrogen compounds

Nitro Compounds, Amines - Classification

Bio molecules

Carbohydrate, Proteins, Nucleic acids,

Chapters

Topics

Organization

Meaning and Types of Organization

Sole trader

Meaning of sole trader, Special features of a sole trader, Merits of a sole trader, Demerits of a sole trader.

Partnership

Definition of partnership, Special features of partnership, Similarities between sole trader and partnership, Merits and Demerits of Partnership, Types of Partnership, Kinds of Partners, Rights and Duties of partners, Partner's express and Implied authority, Partnership Deed, Dissolution of partnership, and more.

Companies I and II

Definitions, Differences between partnership and company, Kinds of companies, public company, private company, Privileges of a private company, Differences between private company and public company, Formation of a company, Memorandum of Association, Articles of Association, Prospectus, Shares, Allotment of shares, DebenturesTypes, Differences between Shares and Debentures.

Stock Exchange

Introduction, Procedures regarding new Issues, Stock Exchange, Investors and speculatorsDifferences, SEBI, Mutual funds, Bombay Online Trading (BOLT).

Co-operatives

Definition, Merits, and Demerits, Types of Cooperatives, Differences between companies and cooperatives.

Government in Business

Introduction, Types, Public Corporation, Government Companies, Differences between the private sector and the public sector.

Units

Topics

Introduction to Macro Economics

Introduction to Macro Economics, Meaning of macro economics, Importance of macro economics, Economic Systems, Capitalist economy

National Income

Meaning of National Income, Gross Domestic Product (GDP), Gross National Product (GNP), Per capita Income, Real Income, GDP deflator

.Theories of Employment and Income

Theories of Employment and Income Introduction, Meaning of Full Employment, Unemployment and its types, Say’s Law of Market, Effective demand

Consumption and investment functions

Introduction, Consumption, Function, Meaning of Consumption function, Technical Attributes of the Consumption function, Multiplier, The Accelerator Principle

Monetary Economics

Money, Meaning, Functions of money, Supply of money, Quantity theories of money, Inflation, Meaning of inflation, Trade cycle

Banking

Commercial banks, Central Bank, NABARD and its role in Agricultural credit, Reserve bank of India and Industrial Finance, Recent advancements in banking sector, Money Market

International Economics

Meaning of International Economics, Subject matter of International Economics, Meaning of Trade, Gains from International Trade, Terms of Trade, Balance of Trade vs. Balance of payments

International Economic Organization

International monetary fund, International Bank for Reconstruction and Development of Bank or World Bank, World Trade Organization, Association of South East Asian Nations (ASEAN)

Fiscal Economics

Meaning of public finance, Definitions, Subject matter, Functions of Modern State, Public expenditure, Public Revenue

Environmental economics

Eco-system, Pollution, Global warming,

Economics of Development and Planning

Planning, Types of planning, NITI Aayog,

Introduction to Statistical Methods and Econometrics

Etymology and milestone of statistics in global level, Characteristics and Functions of Statistics,

Units

Chapters

Rise of Nationalism in India

Entire Unit

Rise of Extremism and Swadeshi Movement

Entire Unit

Impact of World War-I on Indian Freedom Movement

Entire Unit

Advent of Gandhi and Mass Mobilisation

Entire Unit

Period of Radicalism in Anti-imperialist Struggles

Entire Unit

Introduction to Communalism in Nationalist Politics

Entire Unit

Last Phase of Indian National Movement

Cripps Mission, Quit India Movement, Netaji Subhas Chandra Bose and the INA, Rajaji Proposals and the Wavell Plan, Cabinet Mission and Mountbatten Plan

Reconstruction of Post-colonial India

Consequences of Partition, Making of the Constitution, Merger of Princely States, Linguistic Reorganization of States

Envisioning a New Socio-Economic Order

Land Reforms and Rural Reconstruction, Development of Agriculture, Five Year Plans

The Age of Revolutions

The American War of Independence, The French Revolution, Industrial Revolution

Imperialism and its on slaught

Rise of Imperialism, World War I

Introduction to Outbreak of World War II and its Impact in Colonies

Second World War: Causes

The World after World War II

UNO and Global Disputes