Special OJEE 2025 BTech Syllabus PDF - Download Special OJEE BTech Syllabus Topic wise

Logic

Logic

Statement, Negation, Implication, Converse, Contrapositive, Conjunction, Disjunction, Tautology, Truth Table, Principle of Mathematical induction

Sets, Relation and Function

Sets, Relation, and Function

Union, Intersection, Difference, Symmetric Difference, and Complement of Sets, De Morgan’s Laws, Venn Diagram, Cartesian Product of Sets, Power Set, Domain, Codomain, Range of a Relation, Types of Relations, Equivalence Relation, Representation of 3D Space by RxRxR

Types of Functions

Constant Function, Identity Function, Modulus Function, Logarithm Function, Exponential Function, Greatest Integer Function

Composite and Inverse Functions

Surjective, Injective, and Bijective Functions, Sum, Difference, and Quotient of Functions and Their Range, Composite Function, Inverse of a Function

Number System

Real and Complex Numbers

Real Numbers, Rational and Irrational Numbers, Absolute Value, Triangle Inequality, AM ≥ GM, Simple Inequalities, Complex Numbers as Ordered Pairs of Reals, Representation in the Form a+ib, Argand Diagram

Algebra of Complex Numbers

Modulus, Argument, Conjugate, Quadratic Equation in Real Numbers, Relation between Roots and Coefficients, Nature of Roots, Formation of Quadratic Equation with Roots

Permutations and Combinations

Counting Principles

Fundamental Principle of Counting, Permutation as an Arrangement, Combination as a Selection, P(n,r), C(n,r), Simple Applications

Binomial Theorem

Binomial Theorem

Binomial Theorem for Positive Integral Index, General Term, Middle Term, Properties of Binomial Coefficient, Identities Involving Binomial Coefficients

Determinants and Matrices

Determinants and Matrices up to Third Order

Minors, Cofactors, Properties of Determinants, Types of Matrices, Algebra of Matrices, Evaluation of Determinants, Adjoint and Inverse of Matrix, Application to Linear Equations (in Three Unknowns)

Trigonometry

Trigonometric Functions and Identities

Compound Angles, Multiple and Submultiple Angles, Trigonometric Identities, Solution of Trigonometric Equations, Properties of Triangles, Inverse Trigonometric Function and Their Properties

Coordinate Geometry (2D)

Cartesian System, Lines, and Circles

Cartesian System of Rectangular Coordinates, Distance Formula, Section Formula, Locus, Translation of Axes, Slope of a Line, Parallel and Perpendicular Lines, Equation of a Line, Intersection of Lines

Circle, Parabola, Ellipse, and Hyperbola

Equations of Circles, Standard and General Forms, Tangents, Condition of Tangency, Intersection of Lines and Circles, Parabola, Ellipse, Hyperbola Equations and Tangents

Coordinate Geometry (3D)

Coordinates in 3D Space

Coordinates of a Point in Space, Distance between Two Points, Section Formula, Direction Cosines and Ratios, Projections, Angles between Lines and Planes, Equations of Lines and Planes, Coplanar Lines

Sequences and Series

Types of Series

Definition of Sequences, Infinite Geometric Series, Arithmetico-geometric Series, Exponential and Logarithmic Series, Geometric Mean, Relation between AM and GM

Vectors

Vectors and Scalars

Addition of Vectors, Components of a Vector in Two and Three Dimensions, Scalar and Vector Products, Scalar and Vector Triple Product

Differential Calculus

Limits, Continuity, Differentiability

Concept of Limit, Limits of Polynomial, Rational, Trigonometric, Exponential and Logarithmic Functions, Continuity and Differentiability, Derivative of Algebraic and Transcendental Functions

Applications of Derivatives

Rate of Change of Quantities, Monotonic Functions, Maxima and Minima, Tangents and Normals, Geometrical Applications to Finding Tangents and Normals to Plane Curves

Integral Calculus

Methods of Integration

Standard Methods (Substitution, By Parts, By Partial Fraction), Integration of Rational, Irrational, Trigonometric Functions, Definite Integrals, Fundamental Theorem of Calculus

Applications of Integration

Evaluation of Definite Integrals, Determining Areas Bounded by Simple Curves in Standard Form

Differential Equations

Definition, Order, Degree

General and Particular Solution, Formation of Differential Equations, Solution by Separation of Variables, Homogeneous and Linear Differential Equations of First Order and First Degree

Probability and Statistics

Measures of Dispersion

Calculation of Mean, Median, Mode (Grouped and Ungrouped Data), Calculation of Standard Deviation, Variance, Mean Deviation

Probability

Probability of an Event, Addition and Multiplication Theorems, Mutually Exclusive and Independent Events, Compound Events, Conditional Probability, Baye’s Theorem, Random Variables, Binomial Distribution

Measurements and Motion

Fundamental and derived physical quantities, Concept of Mass, Length and Time, Measurement of different quantities in SI Units. Practical units for measurement of microscopic and macroscopic lengths (AU, light year, parsec, nanometer, A⁰). Accuracy and precision of measuring instruments. Errors in measurement, Combination of errors, significant figures. Dimension of physical quantities, Dimension analysis of physical quantities - Conversion of physical quantities from one system of units to another. Concepts of vectors and scalars, Components of vectors, Unit vectors, Addition (triangles law, parallelogram law, polygons law), Subtraction and Multiplication (vector & scalar) of vectors. Lami’s theorem. Frame of reference. Equations of linear motion for uniformly accelerated bodies (by calculus and graphical method). Newton’s laws of motion, impulse momentum theorem, Conservation of energy and momentum, laws of friction, sliding and rolling friction.

Motion in a Plane

Projectile motion, Circular Motion - radial and tangential acceleration, Centripetal force, Banking of tracks, Work, energy, power: work done by constant and variable force, work energy theorem, potential energy of a spring, motion in a vertical circle, elastic and inelastic collision in one and two dimensions. Kepler’s laws of Planetary Motion (Statements only). Newton’s law of Gravitation. Gravitational field and potential, variation of g with altitude and depth. Earth satellites - Orbital and Escape velocities. Geostationary satellites. Moment of inertia, radius of gyration, theorems of moment of inertia, Moment of Inertia for rod, ring and circular disc. Center of mass of two particle systems and rigid body, motion of center of mass, moment of force, torque, angular momentum, laws of conservation of angular momentum and its applications.

Heat & Thermodynamics

Concept of heat and temperature, Scales of Temperature (Celsius, Fahrenheit, Kelvin), Definition of mechanical equivalent of heat (J), Thermal energy, Heat Capacity, Specific heat of solids and liquids, Latent heat, principle of calorimetry, thermal expansion of solids, liquids and gases. Heat transfer - Thermal conductivity of solids, Steady state, determination of thermal conductivity by Searles method. Kirchhoff’s laws of heat radiation, Stefan’s law of heat radiation, Wien’s law, Newton’s Law of cooling. Kinetic Theory of gases - Pressure of an ideal gas, mean and RMS speed, Kinetic interpretation of temperature, Degrees of freedom, Law of equipartition of energy. Concept of mean free path. Zeroth law of thermodynamics, first Law of thermodynamics, Specific heats of a gaseous system, Relation between Cp and Cv, Work done during Isothermal and Adiabatic processes, Carnot’s conceptual heat engine and its efficiency, coefficient of performance of refrigerator, Second law of thermodynamics, Absolute Scale of Temperature.

Characteristics of Materials

Elastic and Plastic behavior of solids, Elastic limit, Hooke’s law. Young’s modulus, Shear and Bulk modulus, Poisson’s ratio.

Liquids

Pressure due to the liquid column, Pascal’s law and its applications. Surface Tension and Surface Energy, Excess pressure across a spherical liquid surface, angle of contact and expression for capillary rise. Streamlined and turbulent flow, equation of continuity, Bernoulli’s equation and its application, Viscosity - coefficient of viscosity and its variation with temperature and pressure, Stokes law and terminal speed.

Electricity & Magnetism

Coulomb's law and conservation of charge, electric flux, Gauss law and its applications. Electric field intensity and Potential at a point in an electric field, Relation between them, electric potential and field due to an electric dipole, torque and potential energy of a dipole in external electric field. Capacitance - dielectric constant and its effect on capacitance. Series and parallel grouping of capacitances, Energy stored in a charged capacitor, dielectrics and electric polarization. Electric current, drift velocity and mobility of charge carriers. Ohm’s law, Variation of resistance of metallic conductors with temperature, Kirchhoff’s laws and its application to a balanced Wheatstone bridge. Internal resistance of a cell, potential difference and emf of a cell. Combination of Cells and resistors - series and parallel. Heating effect of electric current and Joule’s law, Electric power and electric energy.

Magnetism

Magnetic Permeability and Susceptibility of materials, Properties of dia, para and ferro magnetic materials. magnetic elements of Earth. Biot–Savart’s and Ampere’s law - Magnetic Field due to a straight conductor and circular coil. Moving coil galvanometer (dead beat only). Force on a moving charge and current carrying conductor in a uniform magnetic field. Force between two parallel current carrying straight conductors. Torque, experienced by a current loop, moving coil galvanometer and its conversion to ammeter and voltmeter. Faraday’s laws of electromagnetic induction, Lenz’s law, emf induced in a rotating coil in a magnetic field. Self and Mutual induction, Alternating current: Phase relation between Voltage and Current in pure resistive, pure capacitive, pure inductive and series LCR circuits. Power factors, wattless current. Principle of transformer, elementary idea on electromagnetic waves. Electromagnetic spectrum, basic idea of displacement current.

Wave Motion

Simple harmonic motion, oscillation of a loaded spring, simple pendulum, qualitative ideas about free, damped and forced oscillations. Wave propagation, characteristics of wave motion, longitudinal and transverse waves, superposition of waves: Stationary waves, Beats. Open and closed organ pipes, velocity of sound in air - effect of pressure, temperature and humidity on it. Doppler Effect, laws of transverse vibration of string (Statement only).

Optics

Reflection and refraction at curved surfaces. Spherical mirror and thin lens formula and refraction through prism. Total internal reflection, Dispersion, Huygens principle (statement only), Young’s double slit experiment. Interference in light.

Optical Instruments

Simple magnifier, compound microscope and astronomical telescope.

Electronic Devices

Thermionic emission, Statement of Richardson’s equation and Child’s Law, Vacuum triode - construction and characteristics, relationship between valve constants. Descriptive idea of energy bands: conductors, insulators and semiconductors. Intrinsic and extrinsic semiconductors, p-type and n-type semiconductors. PN junction, PNP and NPN transistor, PN Junction as a rectifier. Working of solar cells, photo diodes and LEDs. Elementary idea about OR, AND, NOT, NOR, NAND, XOR, XNOR gates.

Atomic and Nuclear Physics

Bohr’s atomic model, expression for radius, velocity, energy, frequency of an electron in nth orbit. Rydberg constant and Hydrogen spectra. Einstein photoelectric equation, dual nature of radiation and De Broglie wavelength. Mass energy equivalence relation (Statement only). Atomic nucleus, nuclear forces, nuclear mass, binding energy, mass defect, artificial radioactivity, radio isotopes and their uses. Nuclear fission, energy released during nuclear fission, chain reaction, controlled chain reaction, nuclear fusion, energy generation in the Sun, radiation hazards.

General Behaviour of Matter

Solid State

Characteristics, Classification, Solubility, Melting points, Crystal structure of simple ionic compounds. Radius ratio and coordination number: density calculation, lattice points and voids.

Liquid State

Characteristics, Boiling and Freezing points, Viscosity, Surface tension, Osmosis and Osmotic Pressure, Raoult’s law, Lowering of vapour pressure, Depression of freezing points, Elevation of boiling points, Anomalous molecular masses; Association and dissociation.

Solutions

Types of solutions, concentration and different ways of expressing concentration (percentage, ppm, strength, normality, molarity, molality and formality); Interrelations

Gaseous State

Gas laws, Kinetic model of gases, ideal gas equation, Van der waals’ equation, compressibility factor, Average, root mean square and most probable velocities.

Basic Concepts of Chemistry (Atoms and Molecules)

Symbols, Valency, Atomic mass, Molecular mass, Avogadro’s law, Mole concept, Equivalent mass of acid base salt Oxidant and Reductant. Percentage composition, empirical and molecular formula, chemical reactions and calculations based on stoichiometry.

Structure of Atoms and Molecules

Fundamentals particles and their properties, Rutherford and Bohr’s models of atom, Hydrogen spectrum, defects of Bohr’s model, dual nature of matter de-Broglie theory of matter wave, Heisenberg’s uncertainty principle. Energy levels, Shells and Sub-shells, s,p and d orbitals, Quantum numbers, Pauli’s exclusion principle, Aufbau principle, Hund’s rule, Electronic configuration of atoms, Extra stability of half filled and filled subshells.

Chemical Bonds

Ionic, Covalent, Coordinate and Hydrogen bond, Hybridisation- sp, sp², sp³, dsp², dsp³, d²sp³ shapes of molecules, VSEPR theory, Molecular Orbital Theory of simple diatomic molecules.

Periodic Classification

Periodic table and periodic laws, s, p, d and f block elements, Periodicity in properties such as atomic and ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity and oxidation states.

Chemical Energetics, Equilibrium and Kinetics

Energetics

Internal energy, Enthalpy, Heats of reactions, Bond energy, Hess’s law, Idea on enthalpy, entropy and free energy, spontaneity and conditions of equilibrium.

Equilibria

Reversible reaction, Law of mass action, Equilibrium constant Kₚ, Kc, Kx and their relation. Relationship between Equilibrium constant, reaction quotient and Gibbs energy. application of Equilibrium constant to ammonia synthesis and dissociation of HI, Decomposition and thermal dissociation. Theory of acids and bases, Dissociation of weak acids and bases, Ostwald’s dilution law, Ionic product of water, Common ion effect, Solubility product and their applications, pH, Hydrolysis of salts, Buffer solutions.

Kinetics

Rate of chemical reaction, Factors affecting the rate, Rate constant, Order and Molecularity of a reaction, Simple zero and First order reaction, Half life period, Arrhenius equation and Activation Energy, Collision theory (qualitative idea only)

Types of Chemical Reaction

Neutralisation and oxidation– Reduction reaction, Equivalent mass, Oxidation number, Balancing chemical reactions, by Ion electron method, Reactions involving KMnO₄, K₂Cr₂O₇, Na₂S₂O₃, oxalate etc.

Non-Metals

Group study, Preparation, Properties and uses of compounds of the elements. hydrogen (ortho and para hydrogen, isotopes of hydrogen, D₂O and H₂O₂). Dihydrogen as fuel. Allotropes of carbon. Nitrogen family (NH₃ and HNO₃). Oxygen, ozone and sulphur. Oxygen family (O₂, O₃, H₂S, SO₂, H₂SO₄ and its manufacturer by contact process). Halogens, Hydrogen halides and Interhalogen compounds. Zero group elements: Electronic configuration occurrence, physical and chemical properties and uses.

Electrochemistry

Electrolysis, Electrical Conductivity (Specific, Equivalent and molar), Faraday’s laws, Kohlrausch law, Galvanic cell, Cell reaction, Nernst equation, Standard electrode potential, Electro chemical series, e.m.f. of simple cells. Fuel cells.

Surface Chemistry

Colloids: Preparation, purification, properties and uses. Emulsion, Adsorption: Types and applications.

Metals and Metallurgy

Occurrence of metal, Minerals and ores, flux, slag, calcination, roasting, smelting (by reduction of oxides) and refining. General trends in the characteristics. Principles of extraction of Na, Mg, Ca, Al, Cu and Fe and their oxides, hydroxides, chlorides, nitrates and sulfates.

Organic Chemistry

Introductory:

Functional Groups and organic radicals, Nomenclature by IUPAC system (substitutive method) , Isomerism (Structural and stereoisomerism – optical and geometrical) EZ & RS nomenclature, Electron mobility – Inductive effect, Resonance, Electromeric effect and Hyperconjugation; their applications. Types of organic reactions – addition, substitution, elimination reactions. Idea of electrophiles and nucleophiles; Reaction intermediates – idea of carbocations, carbanion & free radicals; their stabilities.

Aliphatic Compounds

Methods of preparation and properties of alkanes, alkenes, alkynes (acidity of terminal alkynes), haloalkanes, alcohols, ether, aldehydes, ketones, carboxylic acids, acid derivatives (acid chlorides, esters and amides), nitroalkanes and amines.

Aromatic Compounds

Aromaticity (Huckel’s rule), Aromatic hydrocarbon (Preparation and reactions – Substitution, addition, ozonolysis) Directive influence of functional group. Phenols (Preparation and reactions) : Aldehydes (Preparations and reactions); Acids (Preparation and reactions). Amines (Preparation and reactions); Diazonium salts (synthetic application).

Biochemistry

Biological importance of organic compounds such as carbohydrates, amino acids, proteins, Vitamins and nucleic acids (only by metabolic process).

Chemistry in the Service of Mankind

Polymers (nylon, terylene, neoprene, buna-S, PVC, Teflon & bakelite). Biodegradable Polymer Medicine-analgesic, antipyretic, antibiotic, antacid and antiseptic (structure and preparation not required).

Environmental Chemistry

Source, effect and control measures of air and water pollution.

Mathematics

Logic

Logic

Statement, Negation, Implication, Converse, Contrapositive, Conjunction, Disjunction, Tautology, Truth Table, Principle of Mathematical induction

Sets, Relation, and Function

Sets, Relation, and Function

Union, Intersection, Symmetric Difference, De Morgan’s Laws, Venn Diagram, Types of Relations, Equivalence Relation

Types of Functions

Constant, Identity, Modulus, Logarithm, Exponential, Greatest Integer Function

Composite and Inverse Functions

Surjective, Injective, Bijective, Inverse Function, Sum/Difference/Quotient of Functions

Number System

Real and Complex Numbers

Real Numbers, Rational/Irrational, AM ≥ GM, Complex Numbers as Ordered Pairs of Reals, Argand Diagram

Algebra of Complex Numbers

Modulus, Argument, Conjugate, Quadratic Equations, Nature of Roots

Permutations and Combinations

Counting Principles

Fundamental Principle of Counting, Permutation, Combination

Binomial Theorem

Binomial Theorem

General Term, Middle Term, Properties of Binomial Coefficient

Determinants and Matrices

Determinants and Matrices up to Third Order

Minors, Cofactors, Types of Matrices, Adjoint, Inverse, Application to Linear Equations

Trigonometry

Trigonometric Functions

Compound Angles, Trigonometric Identities, Solution of Trigonometric Equations, Inverse Trigonometric Functions

Coordinate Geometry (2D)

Cartesian System, Lines, and Circles

Distance Formula, Slope of Line, Equation of Line, Equations of Circles, Tangents, Parabola, Ellipse, Hyperbola

Coordinate Geometry (3D)

Coordinates in 3D Space

Distance between Points, Direction Cosines, Angles between Lines, Planes

Sequences and Series

Types of Series

Arithmetic-Geometric Series, AM and GM Relations

Vectors

Vectors and Scalars

Addition of Vectors, Scalar and Vector Products, Triple Product

Differential Calculus

Limits, Continuity, Differentiability

Limits of Polynomial, Rational, Trigonometric Functions, Continuity, Derivatives

Applications of Derivatives

Rate of Change, Maxima and Minima, Tangents and Normals

Integral Calculus

Methods of Integration

Integration by Substitution, Parts, Partial Fractions, Definite Integrals

Applications of Integration

Definite Integrals, Areas Bounded by Curves

Differential Equations

Differential Equations

Formation of Equations, Separation of Variables, Linear and Homogeneous Differential Equations

Probability and Statistics

Probability

Addition/Multiplication Theorems, Mutually Exclusive Events, Conditional Probability, Bayes’ Theorem

Measures of Dispersion

Calculation of Mean, Median, Mode, Standard Deviation, Variance

Chemistry

General Behaviour of Matter

Solid State

Crystal structure, Radius ratio, Coordination number, Lattice points and voids, Solubility, Melting points

Liquid State

Boiling and Freezing points, Viscosity, Surface tension, Osmosis, Raoult’s law, Anomalous molecular masses, Association and dissociation

Solutions

Types of solutions, Concentration (ppm, molarity, molality), Depression of freezing points, Elevation of boiling points

Gaseous State

Gas laws, Ideal gas equation, Van der Waals’ equation, Compressibility factor, Molecular velocities (Average, RMS, Most probable)

Basic Concepts of Chemistry

Atoms and Molecules

Atomic mass, Molecular mass, Mole concept, Avogadro’s law, Stoichiometry, Empirical and molecular formula, Percentage composition

Structure of Atoms

Rutherford and Bohr’s models, Dual nature of matter, Quantum numbers, Pauli’s exclusion principle, Aufbau principle, Hund’s rule

Chemical Bonds

Ionic, Covalent, Coordinate bonds, Hybridization (sp, sp², sp³), VSEPR theory, Molecular Orbital Theory

Periodicity and Properties

Atomic radii, Ionization energy, Electron gain enthalpy, Electronegativity, Oxidation states

Thermodynamics and Energy

Internal energy, Enthalpy, Bond energy, Hess's law, Entropy, Free energy

Equilibrium and Kinetics

Law of mass action, Equilibrium constants, Le Chatelier’s principle, pH, Buffer solutions, Rate of reaction, Collision theory

Electrochemistry and Electrolysis

Faraday’s laws, Galvanic cell, Nernst equation, Electrochemical series, Conductivity, Fuel cells

Colloids and Adsorption

Preparation, Properties of colloids, Adsorption types, Emulsion, Applications

Organic Chemistry

Introductory Organic Chemistry

Functional groups, IUPAC nomenclature, Isomerism, Inductive effect, Resonance, Reaction intermediates (carbocations, carbanions, free radicals)

Aliphatic Compounds

Alkanes, Alkenes, Alkynes, Haloalkanes, Alcohols, Ethers, Aldehydes, Ketones, Carboxylic acids, Amines

Aromatic Compounds

Aromaticity, Reactions of aromatic hydrocarbons, Phenols, Diazonium salts, Amines, Aldehydes, Acids

Biochemistry

Carbohydrates, Amino acids, Proteins, Vitamins, Nucleic acids

Physics

Measurements and Motion

Units and Measurement

SI units, Accuracy and precision, Errors in measurement, Dimensional analysis, Vector and scalar quantities

Motion in a Straight Line

Linear motion equations, Uniformly accelerated motion, Impulse, Conservation of momentum, Energy and work, Projectile motion

Circular Motion

Radial and tangential acceleration, Centripetal force, Banking of tracks, Rotational dynamics, Angular momentum

Heat and Thermodynamics

Heat Transfer and Laws

Heat capacity, Specific heat, Thermal conductivity, Stefan's law, Newton's law of cooling, First and second laws of thermodynamics

Elasticity

Hooke’s law, Young’s modulus, Bulk modulus, Poisson’s ratio

Electricity & Magnetism

Electrostatics and Magnetism

Coulomb’s law, Electric potential, Gauss’s law, Capacitance, Ohm’s law, Kirchhoff’s laws, Biot-Savart law, Faraday’s law, Electromagnetic induction

Wave Motion

Wave Properties

Simple harmonic motion, Wave propagation, Superposition, Doppler effect

Optics

Reflection and Refraction

Mirror and lens formula, Total internal reflection, Dispersion, Interference, Young's double-slit experiment

Electronic Devices

Semiconductors and Circuits

Semiconductors, PN junction, Transistors, Solar cells, LEDs, Logic gates (OR, AND, NOT, NOR, NAND, XOR, XNOR)

Atomic and Nuclear Physics

Atomic Structure and Radioactivity

Bohr's model, Photoelectric effect, Mass-energy equivalence, Nuclear fission and fusion, Artificial radioactivity