JEE Advanced Syllabus 2024 – Complete Subject-Wise Syllabus for Physics, Chemistry, and Mathematics

Topic

Subtopics

Sets, Relations, and Functions

Sets and representations, types of sets (empty, finite, infinite),

  algebra of sets, intersection, complement, difference, symmetric difference,

  De-Morgan’s laws (union, intersection, difference), practical applications;

  Cartesian product of finite sets, ordered pairs, relations, domain and

  codomain, equivalence relations; Functions as mappings, domain, codomain,

  range, invertible functions, even and odd functions, types of functions

  (into, onto, one-to-one), special functions (polynomial, trigonometric,

  exponential, logarithmic, power, absolute value, greatest integer), sum,

  difference, product, and composition of functions.

Algebra

Algebra of complex numbers (addition, multiplication, conjugation,

  polar representation), properties (modulus, principal argument, triangle

  inequality), cube roots of unity, geometric interpretations; Fundamental

  theorem of algebra, quadratic equations (real coefficients), relations

  between roots and coefficients, formation of quadratic equations, symmetric

  functions of roots; Arithmetic and geometric progressions,

  arithmetic/geometric means, sums of finite and infinite progressions, sums of

  the first n natural numbers, sums of squares and cubes of the first n natural

  numbers; Logarithms and properties, permutations, combinations, binomial

  theorem (positive integral index), binomial coefficients properties.

Matrices

Matrices as rectangular arrays, matrix equality, addition, scalar

  multiplication, matrix product, transpose of a matrix, elementary row/column

  transformations, determinant of a square matrix (up to order 3), adjoint,

  inverse of square matrices (up to order 3), properties of matrix operations,

  diagonal, symmetric, skew-symmetric matrices, solutions of simultaneous

  linear equations (2-3 variables).

Probability and Statistics

Random experiments, sample space, types of events (impossible,

  simple, compound), addition and multiplication rules, conditional

  probability, independence of events, total probability, Bayes’ theorem,

  probability computations using permutations and combinations; Measures of

  central tendency and dispersion, mean, median, mode, mean deviation, standard

  deviation, variance (grouped and ungrouped data), frequency distribution

  analysis with same mean and different variance, random variable, mean,

  variance of a random variable.

Trigonometry

Trigonometric functions, periodicity, graphs, addition/subtraction

  formulas, multiple/sub-multiple angle formulas, general solutions of

  trigonometric equations; Inverse trigonometric functions (principal value

  only) and elementary properties.

Analytical Geometry

Two Dimensions: Cartesian coordinates, distance between points,

  section formulae, origin shift; Equation of a line (various forms), angle

  between lines, point-to-line distance; Lines through the intersection point

  of two lines, angle bisectors, concurrency; Centroid, orthocenter, incenter,

  and circumcenter of triangles; Equation of a circle (various forms), tangent,

  normal, chord equations, parametric equations of circles, circle

  intersections (line or circle), circle equations through intersection points;

  Parabola, ellipse, hyperbola equations in standard form (foci, directrices,

  eccentricity, parametric equations, tangents, normals); Locus problems. Three

  Dimensions: Distance between points, direction cosines/ratios, line equations

  in space, skew lines, shortest distance, plane equations, point-to-plane

  distance, angles between lines, planes, and lines/planes, coplanarity of

  lines.

Differential Calculus

Limits, function continuity, limit/continuity of sum, difference,

  product, quotient, L'Hospital’s rule; Continuity of composite functions,

  intermediate value property; Derivatives of functions, sum, difference,

  product, quotient rules, chain rule, derivatives of polynomial, rational,

  trigonometric, inverse trigonometric, exponential, logarithmic functions;

  Tangents, normals, increasing/decreasing functions, second-order derivatives,

  maxima and minima, Rolle’s theorem, Lagrange’s mean value theorem (and geometric

  interpretation), derivatives of implicit functions (up to second order),

  geometric interpretation of derivatives.

Integral Calculus

Integration as inverse of differentiation, indefinite integrals of

  standard functions, definite integrals (limit of sums), properties of

  definite integrals, fundamental theorem of calculus; Integration by parts,

  substitution, partial fractions; Application of definite integrals for areas

  bounded by curves; Formation of ordinary differential equations, solutions of

  first-order/first-degree homogeneous differential equations, separation of

  variables, linear first-order differential equations.

Vectors

Vector addition, scalar multiplication, dot and cross products,

  scalar/vector triple products, geometric interpretations.

Topic

Subtopics

General

Units, dimensions, dimensional analysis; least count, significant figures; Measurement methods and error analysis (experiments with Vernier calipers, screw gauge, simple pendulum for g, Young’s modulus, capillary rise for surface tension, calorimeter for specific heat, concave mirror and convex lens focal length, speed of sound via resonance column, Ohm’s law, meter bridge for specific resistance).

Mechanics

Kinematics (1D, 2D, projectiles, circular motion, relative velocity); Newton’s laws, inertia, reference frames, friction, energy, work, power, conservation of momentum and energy; Systems of particles, center of mass, impulse, collisions; Rigid body dynamics, moment of inertia, torque, conservation of angular momentum, rotational motion, collisions; Oscillations (forced, damped, resonance, SHM); Gravitation, gravitational field and potential, Kepler’s laws, planetary motion, orbits, escape velocity; Fluid mechanics (pressure, Pascal’s law, buoyancy, surface tension, viscosity, Bernoulli’s theorem); Wave motion (longitudinal, transverse, superposition, stationary waves, resonance, speed of sound, Doppler effect).

Thermal Physics

Expansion of matter, calorimetry, heat conduction, convection, radiation, Newton’s law of cooling; Gas laws, specific heats, isothermal and adiabatic processes, first and second laws of thermodynamics, Carnot engine; Blackbody radiation, Kirchhoff’s law, Wien’s displacement law, Stefan’s law.

Electricity and Magnetism

Coulomb’s law, electric field and potential, energy in electrostatic fields, electric field lines, Gauss’s law and applications; Capacitance, capacitors (with/without dielectrics), energy storage, RC circuits; Electric current, Ohm’s law, resistances, Kirchhoff’s laws, heating effect of current; Magnetic fields (Biot-Savart’s law, Ampere’s law, fields due to currents), forces on charges and currents, magnetic moment, galvanometers, voltmeters, ammeters; Electromagnetic induction (Faraday’s law, Lenz’s law, inductance, LR/LC/LCR circuits with AC and DC).

Electromagnetic Waves

Characteristics of electromagnetic waves, electromagnetic spectrum (radio, microwave, infrared, visible, UV, X-rays, gamma rays) and their uses.

Optics

Light propagation, reflection, refraction, total internal reflection, prisms, thin lenses, mirrors; Wave nature (Huygens' principle, Young’s double-slit experiment, diffraction, polarization, Brewster’s law).

Modern Physics

Atomic structure, nuclear radiation (alpha, beta, gamma), radioactive decay, half-life, binding energy, fission, fusion; Photoelectric effect, Bohr’s model of atoms, X-rays, Moseley’s law, matter waves (de Broglie wavelength)