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.
