Bihar Board 12th Syllabus 2025-26 Released : Download Latest and Revised Bihar Class 12th Syllabus PDF with Subject-wise

Unit 1: Relations and Functions

i) Relations and Functions: Types of relations: reflexive, symmetric, transitive, and equivalence relations. One-to-one and onto functions, composite functions, inverse of a function, binary operations.

ii) Inverse Trigonometric Functions: Definition, range, domain, principal value branch. Graphs and elementary properties of inverse trigonometric functions.

Unit 2: Algebra

i) Matrices: Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose, symmetric and skew-symmetric matrices. Matrix operations: addition, scalar multiplication, multiplication (non-commutative), elementary operations, invertible matrices, uniqueness of inverse.

ii) Determinants: Determinants (up to 3×3), properties, minors, cofactors, area of triangle, adjoint and inverse, system of linear equations (consistency, uniqueness, inverse method).

Unit 3: Calculus

i) Continuity and Differentiability: Derivative of composite, inverse trigonometric, exponential, logarithmic, implicit, parametric functions. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof).

ii) Applications of Derivatives: Rate of change, increasing/decreasing functions, tangents/normals, approximations, maxima and minima (first/second derivative tests), real-life applications.

iii) Integrals: Integration as inverse of differentiation, methods (substitution, partial fractions, by parts), definite integrals, properties, Fundamental Theorem (without proof).

iv) Applications of Integrals: Area under curves (lines, circles, parabolas, ellipses), area between curves.

v) Differential Equations: Order, degree, general/particular solutions, formation, variable separation, homogeneous equations, linear equations (dy/dx + py = q).

Unit 4: Vectors and 3-D Geometry

i) Vectors: Scalars/vectors, magnitude, direction, direction cosines/ratios, vector types, position vector, vector addition, scalar multiplication, section formula, scalar and vector products, scalar triple product.

ii) 3-D Geometry: Direction cosines/ratios of a line, Cartesian/vector equations of lines and planes, skew lines, shortest distance, distance from point to plane, angles between lines/planes.

Unit 5: Linear Programming

Introduction to LPP, terms: constraints, objective function, optimization, types of problems. Formulation of LPP, graphical solutions (2 variables), feasible/infeasible regions and solutions, optimal solutions (up to 3 constraints).

Unit 6: Probability

Multiplication theorem, conditional probability, independence, total probability, Bayes’ theorem, random variable and distribution, mean and variance, Bernoulli trials, binomial distribution.

Electrostatics

Electric Charges, Conservation of charge, Coulomb’s law force between two-point charges, forces between multiple charges, the electrical potential energy of a system of two-point charges and electric dipole in an electrostatic field, etc.

Current Electricity

Ohm’s law, electrical resistance, V-I characteristics (linear and nonlinear), electrical energy and power, electrical resistivity and conductivity, Kirchhoff’s laws and simple applications. Wheatstone bridge, metre bridge, etc.

Magnetic Effect of Current and Magnetism

Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, Force on a moving charge in a uniform magnetic and electric field, Earth’s magnetic field and magnetic elements, etc.

Electromagnetic Induction and Alternating Currents

Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, peak and RMS value of alternating current/voltage; reactance and impedance, etc.

Electromagnetic Waves

Electromagnetic waves, their characteristics, their transverse nature, Electromagnetic spectrum, including elementary facts about their uses, etc.

Optics

Refraction of light, total internal reflection and its applications, lensmaker’s formula. Magnification, power of a lens, Reflection of light, spherical mirrors, mirror formula, a combination of thin lenses in contact, etc.

Dual Nature of Matter

Matter waves-wave nature of particles, de Broglie relation, Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light, Davisson-Germer experiment, etc.

Atoms and Nuclei

Bohr model, energy levels, hydrogen spectrum, Composition and size of nucleus, Alpha-particle scattering experiment; Rutherford’s model of atom; atomic masses, isotopes, radioactive decay law, etc.

Electronic Devices

transistor as a switch, I-V characteristics of the transistor, transistor as an amplifier (common emitter configuration), the basic idea of analogue and digital signals, etc.

Communication Systems

Propagation of electromagnetic waves in the atmosphere, amplitude modulation.

Production and detection of an amplitude-modulated wave, etc.

Unit 1: Solid State

Electrical and magnetic properties, Packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects, etc.

Unit 2: Solutions

Osmotic pressure, determination of molecular masses using colligative properties, Elevation of boiling point, depression of freezing point, abnormal molecular mass, etc

Unit 3: Electrochemistry

Kohlrausch’s Law, lead accumulator, Conductance in electrolytic solutions, specific, variations of conductivity with concentration, etc.

Unit 4: Chemical Kinetics

Integrated rate equations and half-life, the concept of collision theory (elementary idea, no mathematical treatment), etc

Unit 5: Surface Chemistry

Brownian movement, electrophoresis, Lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, coagulation, emulsion-types of emulsions, etc

Unit 6: General Principles and Processes of Isolation of Elements

Occurrence and principles of extraction of aluminium, copper, zinc and iron, Principles and methods of extraction – concentration, oxidation, reduction – electrolytic method and refining; etc

Unit 7: p-block Elements

Halides PCl3, Ozone, Sulphur-allotropic forms; Phosphorus – allotropic forms, Preparation properties and uses of sulphur-dioxide, etc.

Unit 8: d and f-block elements

Magnetic properties, interstitial compounds, Metallic character, ionization enthalpy, preparation and properties of K2Cr2O7 and KMnO4, etc

Unit 9: Coordination Compounds

IUPAC nomenclature of mononuclear coordination compounds. Bonding, Introduction, ligands, coordination number, Werner’s theory, VBT, and CFT; structure and stereoisomerism, etc

Unit 10: Haloalkanes and Haloarenes

Nomenclature, nature of C-X bond, physical and chemical properties, substitution reactions, etc

Unit 11: Alcohols, Phenols, and Ethers

Mechanism of dehydration, physical and chemical properties, uses, uses with special reference to methanol and ethanol, etc

Unit 12: Aldehydes, Ketones, and Carboxylic Acids

Nomenclature, nature of carbonyl group, methods of preparation, physical, uses, methods of preparation, etc

Unit 13: Amines (Organic Compounds and containing Nitrogen)

Classification, structure, methods of preparation, secondary and tertiary amines, etc

Unit 14: Biomolecules

Monosaccharides (glucose and fructose), polysaccharides (starch, cellulose, glycogen) importance, etc

Unit 15: Polymers

Biodegradable and non-biodegradable polymers, etc, Some important polymers: natural and bakelite, rubber, etc

Unit 16: Chemistry in Everyday Life

Tranquillizers antiseptics, disinfectants, antacids, antihistamines, artificial sweetening agents, etc

1.

Reproduction and development

06

2.

Genetics and organic evolution

18

3.

Biotechnology & its application

18

4.

Applied Biology and Human Welfare

18

5.

Man and Environment

10

Total

70

Unit 1: Programming in C++

Review of C++ (Class XI Concepts); Structures: Definition, accessing elements, passing structures to functions, arrays of structures; Object-Oriented Programming (OOP): Data hiding, encapsulation, classes, objects, polymorphism (function overloading); Inheritance (single, multilevel, multiple), abstract and concrete classes; Constructors & Destructors: Default, parameterized, copy constructors; File Handling: Text files (creation, reading, modification), Binary files (searching, appending, deletion); Pointers & Dynamic Memory Allocation: new, delete, reference variables

Unit 2: Data Structures

Arrays: 1D & 2D arrays (traversal, searching, sorting, merging); Stack & Queue: Array and linked implementations, Operations (PUSH, POP, INSERT, DELETE), Infix to Postfix Conversion & Evaluation

Unit 3: Database and SQL

Relational Database Concepts: Keys (primary, candidate, alternate), relational algebra; SQL Commands: CREATE, DROP, ALTER, SELECT, INSERT, UPDATE, DELETE; Functions: SUM, AVG, COUNT, MAX, MIN

Unit 4: Boolean Algebra

Laws & Theorems: De Morgan’s Law, Duality Principle; Logic Gates: AND, OR, NOT, NAND, NOR; Karnaugh Maps (up to 4 variables)

Unit 5: Communication & Network Concepts

Transmission Media: Optical fiber, satellite, microwave; Network Devices: Router, switch, modem; Protocols: TCP/IP, FTP, HTTP; Cyber Security: Firewalls, hacking prevention

1

Indian History Part I: Harappan Archaeology, Political & Economic History, Social History, History of Buddhism and other religions, etc.

2

Indian History Part II: Agrarian Relations, The Mughal Court, New Architecture, Religious Histories, etc.

3

Colonialism & Rural Society, Colonialism & Indian Towns, The Nationalist Movement, Nationalism, Communalism & Partition, The Making of the Constitution, Independence & New Nation-State, etc.

4

Map Work

Unit 1: Making of Indian Constitution and its Goal

(i) Constitutional Development, (ii) Sources of Constitution, (iii) Constituent Assembly, (iv) Preamble

Unit 2: Salient features of Indian Constitution

Unit 3: Working of Federalism in India

(i) Indian federation and its units, (ii) Process of changes of name, boundary and territory of state, (iii) Controversial issues, (iv) Aim and characteristics of federal state, (v) Unitary features

Unit 4: Fundamental Rights and Duties

(i) Meaning, (ii) Importance, (iii) Characteristics, (iv) Amendments in fundamental rights

Unit 5: Directive Principles of State Policy

(i) Nature and sources, (ii) Difference between fundamental rights and directive principles of state policy, (iii) Importance

Unit 6: Union Executives

(i) President – Election, Powers, functions, real position, impeachment, (ii) Vice-President – Election, Power & Function, (iii) Council of Ministers – Composition (with special reference to coalition politics), (iv) Prime Minister – Power, functions & Role

Unit 7: Parliament

(i) Lok Sabha – Composition, Power, function, (ii) Rajya Sabha – Composition, Power, function

Unit 8: State Executive

(i) Governor – Power, Function and Position, (ii) Council of Ministers – Power, function and role with special reference to coalition politics, (iii) Chief Minister – Power, function, duties and role

Unit 9: State Legislature

(i) Bihar Legislative Assembly – Composition, power and function, (ii) Bihar Legislative Council – Composition, power and function

Unit 10: Indian Judiciary

(i) Supreme Court of India – Organisation and function, (ii) Patna High Court – Organisation and functions, (iii) Lok Adalat, Fast Track Courts, Family Courts, PIL

Unit 11: Electoral System in India

(i) Election Commission, (ii) Electoral Process – Maladies and reforms, (iii) Importance of Voting, (iv) Party system and role of opposition

Unit 12: Working of Local Self Government with special reference to Bihar

(i) 73rd and 74th constitutional amendments, (ii) Bihar Panchayati Raj (Amendment) Act – 2006, (iii) Rural and Urban local govt.

Unit 13: National Integration and Challenges

(i) Communalism, (ii) Regionalism, (iii) Casteism, (iv) Naxalism

Unit 14: Foreign Policy of India

(i) Determinants, (ii) Basic principles with special reference to nuclear policy, (iii) NAM, SAARC, UNO

Unit

Key Concepts

1. Fundamentals of Human Geography

- Nature and Scope

2. People

- Population of the world: distribution, density, and growth

- Population change, spatial pattern and structure, determinants of population changes, age and sex ratio, rural-urban composition

- Human development, concept, selected indicators, international comparison

3. Human Activities

- Primary activities: Concept and changing trends, gathering, pastoral mining, subsistence agriculture

- Secondary activities: Concept, manufacturing, agro-processing, household, small scale, large scale

- Tertiary activities: Concept, trade, transport, and communication

- Quaternary activities: Knowledge-based industry, information technology – USA, Britain, India, its contribution

4. Transport, Communication & Trade

- Land Transport: Road, Railways, Air, Water

- Satellite Communication, Cyber Zone

- International Technology – USA, Britain, India, its contribution

5. Human Settlement

- Types, characteristics & problems: Rural & Urban

- Morphology of cities

- Problems related to human settlements in developing countries

India: People and Economy

6. Introduction

- Location, Neighbourhood relations and place of India in world

7. Physical Aspects & Drainage System

- Physiography, relief, drainage system, physical divisions

8. Climate, Vegetation and Soil

- Weather & climate, distribution of temperature, pressure, winds & rainfall

- Indian monsoons, natural vegetation – types and distribution

- Wildlife conservation

- Soil, major types (ICAR classification), their distribution and conservation

9. Resources and Development

- Land resources: Agriculture land use, major crops, and agricultural development and problems

- Water resources: Achievement and usages, problems and conservation

- Mineral and energy resources: Metals and non-metals, minerals and its distribution and conservation, conventional and non-conventional resources of energy

10. Transport, Communication & International Trade

- Road, railways, waterways, airways, gas and oil pipeline, national electricity grid

11. Population

- Distribution, density & growth

- Composition of population, language and religion, rural-urban population

12. Natural Hazards and Management

- Flood and drought, earthquake and volcano, landslides, cyclones, tsunami

Part A: Foundations of Business

1. Nature & Purpose of Business

2. Forms of Business Organization

3. Private, Public & Global Enterprises

4. Business Services

5. Emerging Modes of Business

6. Social Responsibility & Ethics

Part B: Corporate Org., Finance & Trade

1. Formation of a Company

2. Sources of Business Finance

3. Small Business & Entrepreneurship

4. Internal Trade

5. International Business

Part C: Project Work

Project Report + Viva

Total