JEE Advanced 2022 Syllabus

General:

• Units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments: Experiments based on using Vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young’s modulus by Searle’s method, Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using a meter bridge and a post office box.

Mechanics:

• Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Uniform
• circular motion; Relative velocity.
• Newton’s laws of motion; Inertial and uniformly accelerated frames of reference; Static
• and dynamic friction; Kinetic and potential energy; Work and power; Conservation of
• linear momentum and mechanical energy.
• Systems of particles; Centre of mass and its motion; Impulse; Elastic and inelastic
• collisions.
• Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion
• of planets and satellites in circular orbits; Escape velocity.
• Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of
• inertia of uniform bodies with simple geometrical shapes; Angular momentum; Torque;
• Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation;
• Rolling without slipping of rings, cylinders and spheres; Equilibrium of rigid bodies;
• Collision of point masses with rigid bodies.
• Linear and angular simple harmonic motions.
• Hooke’s law, Young’s modulus.
• Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy and surface tension, capillary
• rise; Viscosity (Poiseuille’s equation excluded), Stoke’s law; Terminal velocity,
• Streamline flow, equation of continuity, Bernoulli’s theorem and its applications.
• Wave motion (plane waves only), longitudinal and transverse waves, superposition of
• waves; Progressive and stationary waves; Vibration of strings and air columns;
• Resonance; Beats; Speed of sound in gases; Doppler effect (in sound).

Thermal Physics:

• Thermal expansion of solids, liquids and gases; Calorimetry, latent heat; Heat conduction in one dimension; Elementary concepts of convection and radiation; Newton’s law of cooling; Ideal gas laws; Specific heats (Cv and Cp for monatomic and diatomic gases);
• Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and work; First law of thermodynamics and its applications (only for ideal gases); Blackbody radiation: absorptive and emissive powers; Kirchhoff’s law; Wien’s displacement law, Stefan’s law.

Electricity and Magnetism

• Coulomb’s law; Electric field and potential; Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines;
• Flux of electric field; Gauss’s law and its application in simple cases, such as, to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Capacitance; Parallel plate capacitor with and without dielectrics; Capacitors in series and parallel; Energy stored in a capacitor.
• Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells;
• Kirchhoff’s laws and simple applications; Heating effect of current.
• Biot–Savart’s law and Ampere’s law; Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside a long straight solenoid; Force on a moving charge and on a current-carrying wire in a uniform magnetic field.
• Magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop;
• Moving coil galvanometer, voltmeter, ammeter and their conversions.
• Electromagnetic induction: Faraday’s law, Lenz’s law; Self and mutual inductance; RC, LR and LC circuits with d.c. and a.c. sources.

Optics:

• Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces;
• Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses;
• Combinations of mirrors and thin lenses; Magnification.
• Wave nature of light: Huygen’s principle, interference limited to Young’s double-slit experiment.

Modern Physics

• Atomic nucleus; α, β and γ radiations; Law of radioactive decay; Decay constant; Halflife and mean life; Binding energy and its calculation; Fission and fusion processes;
• Energy calculation in these processes.
• Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays, Moseley’s law; de Broglie wavelength of matter waves.

General topics:

• The concept of atoms and molecules, Mole concept, Dalton’s atomic theory.
• Balanced chemical equations, Chemical formulas, Calculations on mole concept involving common oxidation and reduction.
• Neutralization and displacement reactions.
• Concentration in terms of mole fraction, molality, molarity, and normality.

Liquid and Gaseous States:

• The absolute scale of temperature, ideal gas equation, Deviation from ideality, van der Waals equation.
• Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature.
• Law of partial pressures, Vapour pressure and Diffusion of gases.

Atomic Structure and Chemical Bonding:

• Bohr model, the spectrum of a hydrogen atom, quantum numbers, Wave-particle duality, de Broglie hypothesis and Uncertainty principle.
• Qualitative quantum mechanical picture of the hydrogen atom, shapes of s, p and d orbitals, Electronic configurations of elements (up to atomic number 36), Aufbau principle, Pauli exclusion principle and Hund’s rule.
• Orbital overlap and the covalent bond; Hybridization involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond.
• Polarity in molecules, dipole moment (qualitative aspects only), VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).

Energetics:

• First law of Thermodynamics, Internal energy, work, and heat.
• Pressure-Volume work, Enthalpy, Hess’s law; Heat of reaction, fusion, and vaporization.
• The second law of Thermodynamics, Entropy, Free energy, and criterion of spontaneity.

Chemical Equilibrium:

• Law of mass action, Equilibrium constant, and Le Chatelier’s principle (effect of concentration, temperature and pressure).
• The significance of Delta G and Delta G0 in chemical equilibrium, Solubility product, common ion effect, pH, and buffer solutions.
• Acids and bases (Bronsted and Lewis concepts) and Hydrolysis of salts.

Electrochemistry:

• Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to Delta G.
• Electrochemical series, emf of galvanic cells, Faraday’s laws of electrolysis.
• Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law, and Concentration cells.

Chemical Kinetics:

• Rates of chemical reactions, Order of reactions, and Rate constant.
• First order reactions, Temperature dependence of rate constant (Arrhenius equation).

Solid State:

• Classification of solids, crystalline state, and seven crystal systems (cell parameters a, b, c, Alpha, Beta, Gamma).
• Close-packed structure of solids (cubic), packing in fcc, bcc and hcp lattices.
• Nearest neighbours, ionic radii, simple ionic compounds, point defects.

Solutions:

• Raoult’s law, Molecular weight determination from lowering of vapour pressure, the elevation of boiling point and depression of freezing point.
• Surface chemistry: Elementary concepts of adsorption (excluding adsorption isotherms).
• Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants, and micelles (only definitions and examples).

Nuclear chemistry:

• Radioactivity: isotopes and isobars, Properties of Alpha, Beta, and Gamma rays.
• Kinetics of radioactive decay (decay series excluded), carbon dating.
• Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions.

Isolation/preparation and properties of the non-metals:

• Boron, silicon, nitrogen, phosphorus, oxygen, sulphur, and halogens.
• Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur.

Preparation and properties of the compounds:

• Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium.
• Boron: diborane, boric acid, borax, and Aluminium: alumina, aluminium chloride and alums.
• Carbon: oxides and oxyacid (carbonic acid), and Silicon: silicones, silicates and silicon carbide.
• Nitrogen: oxides, oxyacids and ammonia, and Phosphorus: oxides, oxyacids (phosphorus acid phosphoric acid) and phosphine.
• Oxygen: ozone and hydrogen peroxide, and Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate.
• Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.

Transition elements (3d series):

• Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment.
• Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).

• Preparation and properties of the following compounds:

1. Oxides and chlorides of tin, and lead.

2. Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+.

3. Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate.

Ores and minerals:

• Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminum, zinc, and silver.
• Extractive metallurgy: Chemical principles, and reactions only (industrial details excluded).

Reduction Methods:

• Carbon reduction method (iron and tin), Self-reduction method (copper and lead), Electrolytic reduction method (magnesium and aluminium), Cyanide process (silver and gold).
• Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide.

Algebra:

Complex Numbers

• Algebra of complex numbers, addition, multiplication, conjugation.
• Polar representation, properties of modulus and principal argument.
• Triangle inequality, cube roots of unity.
• Geometric interpretations.

Quadratic Equations

• Quadratic equations with real coefficients.
• Relations between roots and coefficients.
• Formation of quadratic equations with given roots.
• Symmetric functions of roots.

Sequence and Series

• Arithmetic, geometric, and harmonic progressions.
• Arithmetic, geometric, and harmonic means.
• Sums of finite arithmetic and geometric progressions, infinite geometric series.
• Sums of squares and cubes of the first n natural numbers.

Logarithms

• Logarithms and their properties.

Permutation and Combination

• Problems on permutations and combinations.

Binomial Theorem

• Binomial theorem for a positive integral index.
• Properties of binomial coefficients.

Matrices and Determinants

• Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix.
• Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three.
• Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties.
• Solutions of simultaneous linear equations in two or three variables.

Probability

• Addition and multiplication rules of probability, conditional probability.
• Bayes Theorem, independence of events.
• Computation of probability of events using permutations and combinations.

Trigonometry:

Trigonometric Functions

• Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.
• Formulae involving multiple and submultiple angles.
• The general solution of trigonometric equations.

Inverse Trigonometric Functions

• Relations between sides and angles of a triangle, sine rule, cosine rule.
• Half-angle formula and the area of a triangle.
• Inverse trigonometric functions (principal value only).

Vectors:

Properties of Vectors

• The addition of vectors, scalar multiplication.
• Dot and cross products.
• Scalar triple products and their geometrical interpretations.

Differential Calculus:

Functions

• Real-valued functions of a real variable, into, onto and one-to-one functions.
• Sum, difference, product, and quotient of two functions.
• Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
• Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Limits and Continuity

• Limit and continuity of a function.
• Limit and continuity of the sum, difference, product and quotient of two functions.
• L’Hospital rule of evaluation of limits of functions.

Derivatives

• The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.
• Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
• Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.
• Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.
• Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus:

Integration

• Integration as the inverse process of differentiation.
• Indefinite integrals of standard functions, definite integrals, and their properties.
• Fundamental Theorem of Integral Calculus.
• Integration by parts, integration by the methods of substitution and partial fractions.

Application of Integration

• Application of definite integrals to the determination of areas involving simple curves.

Differential Equations

• Formation of ordinary differential equations.
• The solution of homogeneous differential equations, separation of variables method.
• Linear first-order differential equations.