JEE Main Maths Syllabus 2027: Chapter-Wise Topics and PDF Download

Unit

Chapter Name

Topics Covered

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-one, into and onto functions, the composition of

functions.

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, the formation of

quadratic equations with given roots

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.

4

Permutations and Combinations

The fundamental principle of counting; permutations and combinations; Meaning of P(n, r) and C(n, r). Simple applications

5

Binomial Theorem and Its Simple Applications

Binomial theorem for a positive integral index, general term and middle term and simple applications.

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.

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.

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

$$\int \frac{dx}{x^2+a^2}, \quad \int \frac{dx}{\sqrt{x^2 \pm a^2}}, \quad \int \frac{dx}{a^2-x^2}, \quad \int \frac{dx}{\sqrt{a^2-x^2}}, \quad \int \frac{dx}{ax^2+bx+c}, \quad \int \frac{dx}{\sqrt{ax^2+bx+c}}, \quad \int \frac{(px+q)\,dx}{ax^2+bx+c},\int \frac{(px+q)\,dx}{\sqrt{ax^2+bx+c}}, \quad \int \sqrt{a^2 \pm x^2}\, dx, \quad \int \sqrt{x^2 - a^2}\, dx$$

The fundamental theorem of calculus, properties of definite integrals. Evaluate definite integrals and determine the areas of regions bounded by simple curves in standard forms.

9

Differential Equations

Ordinary differential equations, their order and degree, the solution of differential

equation by the method of separation of variables, solution of a homogeneous

and linear differential equation of the type $$\frac{dy}{dx} + p(x)\,y = q(x)$$

10

Coordinate Geometry

Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis.

Straight line: 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 the centroid, orthocentre, and circumcentre 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 centre, equation of a circle when the endpoints 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. 

11

Three-Dimensional Geometry

Coordinates of a point in space; the distance between two points; the section formula; direction ratios and direction cosines; the angle between two intersecting lines; the equation of a line; skew lines; the shortest distance between them and its equation.

12

Vector Algebra

Vectors and scalars; vector addition; components of a vector in two- and three-dimensional space; scalar and vector products. 

13

Statistics and Probability

Measures of dispersion; calculating the mean, median, and mode for grouped and ungrouped data; calculating the standard deviation, variance, and mean deviation for grouped and ungrouped data. Probability: probability of an event, addition and multiplication theorems of probability, Bayes' theorem, probability distribution of a random variable. 

14

Trigonometry

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions, and their properties.