JEE Main Maths Syllabus 2027 (OUT): PDF Download

Sets, Relations and Functions

• Sets and their representation: Union, intersection and complement of sets and their algebraic properties

• Power set: Relation, types of relations, equivalence relations, functions

• One-one, into and onto functions, the composition of functions.

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 number

• Modulus and argument (or amplitude) of a complex number

• Square root of a complex number

• Triangle inequality

• Quadratic equations in real and complex number system and their solutions

• Relations between roots and coefficient, nature of roots, the formation of quadratic equations with given roots.

Matrices and Determinants

• Matrices

• Algebra of matrices

• Type of matrices,

• Determinants and matrices of order two and three

• Properties of determinants

• Evaluation of determinants

• Area of triangles using determinants

• Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations

• Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices

Permutations and Combinations

• Fundamental principle of counting

• Permutation as an arrangement and combination as section,

• Meaning of P (n,r) and C (n,r)

• Simple applications.

Binomial Theorem and its Simple Applications

• Binomial theorem for a positive integral index

• General term and middle term

• Properties of Binomial coefficients and simple applications.

Sequence and Series

• Arithmetic and Geometric progressions

• Insertion of arithmetic

• Geometric means between two given numbers,

• Relation between A.M and G.M sum up to n terms of special series

• Sn, Sn2, Sn3

• Arithmetico-Geometric progression

Limit, Continuity and Differentiability

• Real-valued functions

• Algebra of functions

• polynomials, rational, trigonometric, logarithmic and exponential functions

• Inverse function. 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

• Rolle’s and Lagrange's Mean value Theorems, Applications of derivatives

• Rate of change of quantities, monotonicI ncreasing and decreasing functions,

• Maxima and minima of functions of one variable, tangents and normal.

Integral Calculus

• Integral as an anti-derivative

• Fundamental Integrals involving algebraic, Trigonometric, exponential and logarithms functions.

• Integrations by substitution, by parts and by partial functions.

• Integration using trigonometric identities. Integral as limit of a sum.

• The fundamental theorem of calculus, properties of definite integrals.

• Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

Differential Equations

• Ordinary differential equations, their order and degree,

• Formation of differential equations

• Solution of differential equation by the method of separation of variables

• Solution of a homogeneous and linear differential equation.

Co-ordinate Geometry

• Cartesian system of rectangular coordinates in a plane

• Distance formula, sections formula

• Locus and its equation,

• Translation of axes, 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, the distance of a point form a line, equations of internal and external by sectors of angles between two lines co-ordinate of the centroid, orthocentre and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.

• Circle, Conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and central, 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 condition for a line to be tangent to a circle, equation of the tangent, sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for Y = mx +c to be a tangent and point (s) of tangency

3D Geometry

• Coordinates of a point in space

• Distance between two points

• Section formula, directions ratios and direction cosines, the angle between two intersecting lines.

• Skew lines, the shortest distance between them and its equation.

• Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

Vector Algebra

• Vectors and scalars,

• Addition of vectors, components of a vector in two dimensions and three-dimensional space

• Scalar and vector products, scalar and vector triple product.

Statistics and Probability

• Measures of discretion

• Calculation of mean, median, 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, Baye's theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.

Trigonometry

• Trigonometrical identities and equations

• Trigonometrical functions,

• Inverse trigonometrical functions and their properties, heights and distance.