JEE (MAIN) SYLLABUS
Part I: MATHEMATICS
UNIT 1: SETS, RELATIONS, AND FUNCTIONS:
Sets and their representation; union, intersection, and complement of sets and their algebraic properties;
Power set; relations, types of relations, equivalence relations, functions; one-to-one, into, and onto functions; and 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, Quadratic equations in real and complex number systems and their solutions; relations between roots and coefficients, nature of roots, and the 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; evaluation of determinants; area of triangles using determinants; Adjoint and inverse of a square matrix;
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, permutations, and combinations; the meaning of P(n, r) and C(n, r); and simple applications.
UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term, middle term, and simple applications.
UNIT 6: SEQUENCE AND SERIES:
Arithmetic and geometric progressions, insertion of arithmetic and 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; polynomial, 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 up to two, Applications of derivatives: rate of change of quantities, monotonic-increasing and decreasing functions, Maxima and minima of functions of one variable.
UNIT 8: INTEGRAL CALCULUS
Integral as an antiderivative, 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 The fundamental theorem of calculus, properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves.
UNIT 9: DIFFERENTIAL EQUATIONS
Ordinary differential equations, their order and degree, the solution of a differential equation by the method of separation of variables, and the solution of a homogeneous and linear differential equation of the type
UNIT 10: COORDINATE GEOMETRY
Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, the slope of a line, parallel and perpendicular lines, and intercepts of a line on the coordinate axis. Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point from a line, the coordinates of the centroid, the orthocenter, and the circumcenter of a triangle. Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and center, the equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the center 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, the distance between two points, the section formula, direction ratios and direction cosines, and the angle between two intersecting lines. Equation of a line; skew lines, the shortest distance between them, and its equation. UNIT 12: VECTOR ALGEBRA :
Vectors and scalars, the addition of vectors, components of a vector in two-dimensional and three-dimensional spaces, and scalar and vector products.
UNIT 13: STATISTICS AND PROBABILITY :
Measures of dispersion: calculation of the mean, median, and 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, Bayes's theorem, and probability distribution of a random variable.
UNIT 14: TRIGONOMETRY :
Trigonometric identities and trigonometric functions, inverse trigonometric functions, and their properties.
Part II: APTITUDE TEST
UNIT - 1 Awareness of persons, buildings, materials, objects, and textures related to architecture and the built environment, Visualizing three-dimensional objects from two-dimensional drawings. Visualizing different sides of three-dimensional objects Analytical Reasoning Mental Ability (Visual, Numerical, and Verbal)
UNIT 2: Three-dimensional perception: Understanding and appreciation of scale and proportions of objects, building forms and elements, color, texture, harmony, and contrast. Design and drawing of geometrical or abstract shapes and patterns in pencil. Transformation of forms, both 2D and 3D; union, subtraction, rotation; development of surfaces and volumes; generation of plans, elevations, and 3D views of objects; creating two-dimensional and three-dimensional compositions using given shapes and forms.
Part III: PLANNING
UNIT-1 GENERAL AWARENESS. General knowledge questions and knowledge about prominent cities, development issues, government programs, etc.
UNIT 2: SOCIAL SCIENCES
The idea of nationalism, nationalism in India, pre-modern world, 19
th-century global economy, colonialism and colonial cities, industrialization, resources and development, types of resources, agriculture, water, mineral resources, industries, national economy, and human settlements. Power-sharing, federalism, political parties, democracy, the constitution of India. Economic development: economic sectors, globalization, the concept of development, poverty, population structure, social exclusion and inequality, urbanization, rural development, and colonial cities. UNIT 3: THINKING SKILLS
Comprehension (unseen passage); map reading skills, scale, distance, direction, area, etc.; critical reasoning; understanding of charts, graphs, and tables; and basic concepts of statistics and quantitative reasoning.
JEE ADVANCED SYLLABUS
1. Sets, Relations, and Functions
Sets and their representations, different kinds of sets (empty, finite, and infinite), algebra of sets, intersection, complement, difference, and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, and difference (for a finite number of sets), and practical problems based on them.
Cartesian product of finite sets, ordered pairs, relations, domain and codomain of relations, equivalence relation.
Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto, and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product, and composition of functions.
2. Algebra
Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. Statement of the fundamental theorem of algebra, Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, the sum of the first n natural numbers, and sums of squares and cubes of the first n natural numbers. Logarithms and their properties, permutations and combinations, the binomial theorem for a positive integral index, and properties of binomial coefficients.
3. Matrices
Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar, product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties, and solutions of simultaneous linear equations in two or three variables.
3. Probability and Statistics
Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes
Theorem: Computation of probability of events using permutations and combinations.
Measures of central tendency and dispersion: mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data; analysis of the frequency distribution with the same mean but different variance; random variable; mean and variance of the random variable.
4. Trigonometry
Trigonometric functions, their periodicity and graphs, addition and subtraction formulas, formulas involving multiple and sub-multiple angles, and the general solution of trigonometric equations. Inverse trigonometric functions (principal value only) and their elementary properties.
5. Analytical Geometry
Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, the equation of the bisector of the angle between two lines, and the concurrency of lines; the centroid, orthocenter, incenter, and circumcenter of a triangle. Equation of a circle in various forms, equations of tangent, normal, and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles, and those of a circle and a straight line. Equations of a parabola, ellipse, and hyperbola in standard form; their foci, directrices, and eccentricity; parametric equations; and equations of tangent and normal.
Locus problems.
Three dimensions: distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two lines, angle between two planes, angle between a line and the plane, and coplanar lines.
6. Differential Calculus
Limit of a function at a real number, continuity of a function, limit and continuity of the sum, difference, product, and quotient of two functions, and L'Hospital's rule of evaluation of limits of functions. Continuity of composite functions, intermediate value property of continuous functions.
Derivative of a function, derivative of the sum, difference, product, and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential, and logarithmic functions. Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems, derivatives up to order two of implicit functions, geometric interpretation of derivatives.
7. Integral Calculus
Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integrals and their properties, and the fundamental theorem of integral calculus.
Integration by parts, integration by the methods of substitution and partial fractions, and the application of definite integrals to the determination of areas bounded by simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, separation of variables method, linear first order differential equations.
8. Vectors
Addition of vectors, scalar multiplication, dot and cross products, scalar and vector triple products, and their geometrical interpretations.
