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JOINT ENTRANCE EXAMINATION SYLLABUS 2025
JEE MAIN EXAM MATHEMATICS SYLLABUS
UNIT 1: Sets, Relations and Functions
Sets and their representation; Union, intersection and complement of sets and their algebraic properties; power set; Relation, Types of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.
UNIT 2: 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 numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, quadratic equations in real and complex number system and their solutions. Relation between roots and coefficients, nature of roots, formation of quadratic equations with given roots.
UNIT 3: Matrices and Determinants
Matrices, algebra of matrices, types 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 test of consistency and solution of simultaneous linear equations in two or three variables using matrices.
UNIT 4: Permutations and Combinations
The fundamental principle of counting, permutation as an arrangement and combination as selection, meaning of P (n, r) and C (n, r), simple applications.
UNIT 5: Binomial Theorem and its Simple Applications
Binomial theorem for a positive integral index, general term and middle term, and simple applications.
UNIT 6: Sequence and Series
Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M.
UNIT 7: Limit, Continuity and Differentiability
Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions, maxima and minima of functions of one variable, tangents and normals.
UNIT 8: Integral Calculus
Integral as an anti-derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type
Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
UNIT 9: Differential Equations
Ordinary differential equations, their order and degree. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:
UNIT 10: Co-ordinate Geometry
Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.
Straight lines:
Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, coordinates of centroid, orthocentre and circumcentre of a triangle.
Circles, conic sections:
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms.
UNIT 11: Three Dimensional Geometry
Coordinates of a point in space, distance between two points, section formula. direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line.
UNIT 12: Vector Algebra
Vectors and scalars, addition of vectors, components of a vector in two dimensions and three-dimensional space, scalar and vector products.
UNIT 13: Statistics and Probability
Measures of Dispersion: 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.
UNIT 14: Trigonometry
Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties.
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JEE MAIN EXAM PHYSICS SYLLABUS
Section A (Theory Part) weightage – 80%
Section B(Experimental Part) weightage – 20%
SECTION A
UNIT 1: PHYSICS AND MEASUREMENT
Units of measurements, System of Units, S I Units, fundamental and derived units, least count,significant figures, Errors in measurements, Dimensions of Physics quantities, dimensionalanalysis, and its applications.
UNIT 2: 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. Addition and subtraction, scalar and vector products, Unit Vector, Resolution of a Vector. Relative Velocity, Motion in a plane, Projectile Motion, Uniform Circular Motion.
UNIT 3: 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.Static and Kinetic friction, laws of friction, rolling friction.Dynamics of uniform circular motion: centripetal force and its applications: vehicle on a levelcircular road, vehicle on a banked road.
UNIT 4: WORK, ENERGY, AND POWER
Work done by a constant 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; motion in a vertical circle: Elastic and inelastic collisions in one and two dimensions.
UNIT5: ROTATIONAL MOTION
Centre of the mass of a two-particle system, Centre of the mass of a rigid body; Basic concepts of rotational motion; 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. Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions.
UNIT 6: 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, Motion of a satellite, orbital velocity, time period, and energy of satellite.
UNIT 7: PROPERTIES OF SOLIDS AND LIQUIDS
Elastic behaviour, Stress-strain relationship, Hooke's Law. Young's modulus, bulk modulus, and modulus of rigidity. Pressure due to a fluid column; Pascal's law and its applications. Effect of gravity on fluid pressure. Viscosity. Stokes' law. terminal velocity, streamline, and turbulent flow.critical velocity. Bernoulli's principle and its applications. Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension - drops, bubbles, and capillary rise. Heat, temperature, thermal expansion; specific heat capacity, calorimetry; change of state, latent heat. Heat transfer conduction, convection, and radiation.
UNIT 8: THERMODYNAMICS
Thermal equilibrium, zeroth law of thermodynamics, the concept of temperature. Heat, work, and internal energy. The first law of thermodynamics, isothermal and adiabatic processes. The second law of thermodynamics: reversible and irreversible processes.
UNIT 9: 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 interpretation of temperature: RMS speed of gas molecules: Degrees of freedom. Law of equipartition of energy and applications to specific heat capacities of gases; Mean free path. Avogadro's number.
UNIT 10: OSCILLATIONS AND WAVES
Oscillations and periodic motion – time 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: Wave motion. Longitudinal and transverse waves, speed of the travelling wave. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves. Standing waves in strings and organ pipes, fundamental mode, and harmonics. Beats.
UNIT 11: ELECTROSTATICS
Electric charges: Conservation of charge. Coulomb's law forces between two point charges, forces between multiple charges: superposition principle and continuous charge distribution. Electric field: Electric field due to a point charge, Electric field lines. Electric dipole, Electric field due to a dipole. Torque on a dipole in a uniform electric field. 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. Electric potential and its calculation for a point charge, electric dipole and system of charges; potential difference, Equipotential surfaces, Electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators. Dielectrics and electric polarization, capacitors and capacitances, the combination of capacitors in series and parallel, and capacitance of a parallel plate capacitor with and without dielectric medium between the plates. Energy stored in a capacitor.
UNIT 12: CURRENT ELECTRICITY
Electric current. Drift velocity, mobility, and their relation with electric current. Ohm's law. Electrical resistance. V-l characteristics of Ohmic and non-ohmic conductors. Electrical energy and power. Electrical resistivity and conductivity. Series and parallel combinations of resistors; Temperature dependence of resistance. 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.
UNIT 13: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
Biot - Savart law and its application to the current carrying circular loop. Ampere's law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields. Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel currents carrying conductors-definition of ampere. Torque experienced by a current loop in a uniform magnetic field: Moving coil galvanometer, its sensitivity, and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Magnetic field due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole in a uniform magnetic field. Para-, dia- and ferromagnetic substances with examples, the effect of temperature on magnetic properties.
UNIT 14: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS
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: LCR series circuit, resonance: power in AC circuits, wattless current. AC generator and transformer.
UNIT 15: ELECTROMAGNETIC WAVES
Displacement current. Electromagnetic waves and their characteristics, Transverse nature of Electro magnetic waves, Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet. X-rays. Gamma rays), Applications of e.m. waves.
UNIT 16: OPTICS
Reflection of light, spherical mirrors, mirror formula. Refraction of light at plane and spherical surfaces, thin lens formula, and lens maker formula. Total internal reflection and its applications. Magnification. Power of a Lens. Combination of thin lenses in contact. Refraction of light through a prism. Microscope and Astronomical Telescope (reflecting and refracting )and their magnifying powers.
Wave optics: wavefront and Huygens' principle. Laws of reflection and refraction usingHuygens principle. Interference, Young's double-slit experiment, and expression for fringe width, coherent sources, and sustained interference of light. Diffraction due to a single slit,width of central maximum. Polarization, plane-polarized light: Brewster's law, uses of planepolarized light and Polaroid.
UNIT 17: 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.
UNIT 18: 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, Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission, and fusion.
UNIT 19: ELECTRONIC DEVICES
Semiconductors; semiconductor diode: I-V characteristics in forward and reverse bias; diode as a rectifier; I-V characteristics of LED. the photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Logic gates (OR. AND. NOT. NAND and NOR).
SECTION-B
UNIT 20: EXPERIMENTAL SKILLS
Familiarity with the basic approach and observations of the experiments and activities:
1. Vernier calipers -its use to measure the internal and external diameter and depth of a vessel.
2. Screw gauge-its use to determine the thickness/ diameter of thin sheet/wire.
3. Simple Pendulum-dissipation of energy by plotting a graph between the square of amplitude and time.
4. Metre Scale - the mass of a given object by the principle of moments.
5. Young's modulus of elasticity of the material of a metallic wire.
6. Surf ace tension of water by capillary rise and effect of detergents,
7. Co-efficient of Viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body,
8. Speed of sound in air at room temperature using a resonance tube,
9. Specific heat capacity of a given (i) solid and (ii) liquid by method of mixtures.
10. The resistivity of the material of a given wire using a metre bridge.
11. The resistance of a given wire using Ohm's law.
12. Resistance and figure of merit of a galvanometer by half deflection method.
13. The focal length of;
(i) Convex mirror
(ii) Concave mirror, and
(ii) Convex lens, using the parallax method.
14. The plot of the angle of deviation vs angle of incidence for a triangular prism.
15. The refractive index of a glass slab using a travelling microscope.
16. Characteristic curves of a p-n junction diode in forward and reverse bias.
17. Characteristic curves of a Zener diode and finding reverse break down voltage.
18. Identification of Diode. LED, Resistor. A capacitor from a mixed collection of such items.
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JEE MAIN EXAM CHEMISTRY SYLLABUS
SECTION-A
PHYSICAL CHEMISTRY
UNIT 1: Some Basic Concepts in Chemistry
Matter and its nature, Dalton’s atomic theory; Concept of atom, molecule, element and compound; Laws of chemical combination; atomic and molecular masses, mole concept, molar mass, percentage composition, empirical and molecular formulae; chemical equations and stoichiometry.
UNIT 2: Atomic Structure
Nature of electromagnetic radiation, photoelectric effect; spectrum of hydrogen atom, Bohr model of hydrogen atom – its postulates, derivation of the relations for energy of the electron and radii of the different orbits, limitations of Bohr’s model; dual nature of matter, de-Broglie’s relationship, Heisenberg uncertainty principle. Elementary ideas of quantum mechanics, quantum mechanical model of atom, its important features. Concept of atomic orbitals as one electron wave functions; Variation of Ψ and Ψ2 with r for 1s and 2s orbitals; various quantum numbers (principal, angular momentum and magnetic quantum numbers) and their significance; shapes of s, p and d – orbitals, electron spin and spin quantum number; rules for filling electrons in orbitals – Aufbau principle, Pauli’s exclusion principle and Hund’s rule, electronic configuration of elements, extra stability of half-filled and completely filled orbitals.
UNIT 3: Chemical Bonding and Molecular Structure
Kossel – Lewis approach to chemical bond formation, concept of ionic and covalent bonds.
Ionic Bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds; calculation of lattice enthalpy.
Covalent Bonding: Concept of electronegativity, Fajan’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, 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, concept of bond order, bond length and bond energy.
Elementary idea of metallic bonding. Hydrogen bonding and its applications.
UNIT 4: Chemical Thermodynamics
Fundamentals of thermodynamics – System and surroundings, extensive and intensive properties, state functions, types of processes.
First law of thermodynamics – Concept of work, heat internal energy and enthalpy, heat capacity, molar heat capacity; Hess’s law of constant heat summation; enthalpies of bond dissociation, combustion, formation, atomization, sublimation, phase transition, hydration, ionization and solution.
Second law of thermodynamics – Spontaneity of processes; ΔS of the universe and ΔG of the system as criteria for spontaneity, ΔG° (Standard Gibbs energy change) and equilibrium constant.
UNIT 5: Solutions
Different methods for expressing concentration of solution – molality, molarity, mole fraction, percentage (by volume and mass both), vapour pressure of solutions and Raoult’s Law – Ideal and non-ideal solutions, vapour pressure – composition, plots for ideal and non-ideal solutions; colligative properties of dilute solutions – relative lowering of vapour pressure, depression of freezing point, elevation of boiling point and osmotic pressure; determination of molecular mass using colligative properties; abnormal value of molar mass, van’t Hoff factor and its significance.
UNIT 6: Equilibrium
Meaning of equilibrium, concept of dynamic equilibrium.
Equilibria involving physical processes: Solid -liquid, liquid – gas and solid – gas equilibria, Henry’s law, general characteristics of equilibrium involving physical processes.
Equilibria involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of ΔG and ΔG° in chemical equilibria, factors affecting equilibrium concentration, pressure, temperature, effect of catalyst; Le Chatelier’s principle.
Ionic equilibrium: Weak and strong electrolytes, 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, pH scale, common ion effect, hydrolysis of salts and pH of their solutions, solubility of sparingly soluble salts and solubility products, buffer solutions.
UNIT 7: Redox Reactions and Electrochemistry
Electronic concepts of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions.
Electrolytic and metallic conduction, conductance in electrolytic solutions, specific and 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; Nernst equation and its applications; relationship between cell potential and Gibbs’ energy change; dry cell and lead accumulator; fuel cells.
UNIT 8: 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, their characteristics and half – lives, effect of temperature on rate of reactions – Arrhenius theory, activation energy and its calculation, collision theory of bimolecular gaseous reactions (no derivation).
SECTION-B
INORGANIC CHEMISTRY
UNIT 9: 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.
UNIT 10: 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; unique behaviour of the first element in each group.
UNIT 11: d – and f – Block Elements
Transition Elements: General introduction, electronic configuration, occurrence and characteristics, general trends in properties of the first row transition elements – physical properties, ionization enthalpy, oxidation states, atomic radii, colour, catalytic behaviour, magnetic properties, complex formation, interstitial compounds, alloy formation; preparation, properties and uses of K2Cr2O7 and KMnO4.
Inner Transition Elements:
Lanthanoids – Electronic configuration, oxidation states and lanthanoid contraction.
Actinoids – Electronic configuration and oxidation states.
UNIT 12: Co-ordination Compounds
Introduction to co-ordination compounds, Werner’s theory; ligands, coordination number, denticity, chelation; IUPAC nomenclature of mononuclear co-ordination compounds, isomerism; bonding-valence bond approach and basic ideas of crystal field theory, colour and magnetic properties; importance of co-ordination compounds (in qualitative analysis, extraction of metals and in biological systems).
Section-C
ORGANIC CHEMISTRY
UNIT 13: Purification and Characterisation 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, phosphorus.
Calculations of empirical formulae and molecular formulae; numerical problems in organic quantitative analysis.
UNIT 14: 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.
UNIT 15: Hydrocarbons
Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions.
UNIT 16: 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.
UNIT 17: Organic Compounds Containing Oxygen
UNIT 18: Organic Compounds Containing Nitrogen
General methods of preparation, properties, reactions and uses.
UNIT 19: Biomolecules
General introduction and importance of biomolecules.
UNIT 20: Principles Related to Practical Chemistry
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