JEE Main Maths Syllabus

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Chapter Name

SubTopics

Sets, Relations and Functions

• Sets and their representation: Union, intersection
• Complement of sets and their algebraic properties; Power set
• Relation, Type of relations, equivalence relations
• Functions: one-one, into and onto functions, the composition of functions

Complex Numbers

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
• 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, evaluation of determinants, area of triangles using determinants
• Adjoint, and evaluation of inverse of a square matrix using determinants
• Test of consistency and solution of simultaneous linear equations in two or three variables using matrices

Permutations and Combinations

• The 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, 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

Limit

Continuity

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.
• Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima, and minima of functions of one variable.

Integral Calculus

• Integral as an antiderivative, Fundamental integral involving algebraic, trigonometric, exponential, and logarithmic functions. 
• Integrations by substitution, by parts, and by partial functions. Integration using trigonometric identities. 
• Evaluation of simple integrals of the type 

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

• 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
• The solution of differential equation by the method of separation of variables
• Solution of a homogeneous and linear differential equation of the type dydx+p(x)y=q(x)

Co-Ordinate 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, 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 form a line, Coordinate 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 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 sections of conics, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms

Three Dimensional Geometry 

Coordinates of a point in space, the distance between two points, section formula, Directions 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.

Vector Algebra

• Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional space, Scalar, and vector products.

Statistics

Probability

• Measures of dispersion; 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 variable.

Trigonometry

• Trigonometric identities and trigonometric functions
• Inverse trigonometric functions, and their properties

Units/ Chapters

Deleted Topics

Complex Numbers and Quadratic Equations

• Square root of a complex number, triangle inequality

Determinants and Matrices

• Properties of determinants, elementary transformations
• Test of consistency and solution of simultaneous linear equations in two or three variables using Determinants

Mathematical Induction

• Principle of Mathematical Induction and its simple applications

Binomial Theorem and its Simple Applications

• Properties of Binomial coefficients

Sequence and Series

• Sum up to n terms of special series; S${}_n$, S${}_{n2}$, S${}_{n3}$
• Arithmetic-Geometric progression.

Limits, Continuity, and Differentiability

• Rolle’s and Lagrange's Mean value Theorems
• Tangents and normal

Integral Calculus

• Integral as limit of a sum

Differential Equation

• Formation of differential equations

Co-Ordinate Geometry

• Translation of axes,
• Straight Line: equations of internal and external by sectors of angles between two lines, equation of the family of lines passing through the point of intersection of two lines. 
• Circle, Conic section: condition for a line to be tangent to a circle, equation of the tangent, condition for Y = mx +c to be a tangent and point (s) of tangency.

3D Geometry

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

Vector Algebra

• Scalar and vector triple product. 

Probability and Statistics

• Bernoulli trials, and binomial distribution. 

Trigonometry

• Trigonometric equations, heights, and distance. 

Mathematical Reasoning

• Statement logical operations and, or, implies, implied by, if and only if, understanding of tautology, contradiction, converse, and contrapositive. 

Paper

Subject

Section

Total No. of Questions

Marks for Each Correct Answer

Marks for Each Wrong Answer 

Paper-1(B.E./B.Tech.)

Physics

Section-A (MCQ)

20

4

-1

Section-B (Numerical Answer Type)

5

4

Chemistry

Section-A (MCQ)

20

4

Section-B (Numerical Answer Type)

5

4

Mathematics

Section-A (MCQ)

20

4

Section-B (Numerical Answer Type)

5

4

Total Question

75