JEE Main Mathematics (JEE Main) Syllabus 2026 PDF Download
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JEE Main Mathematics (JEE Main) Syllabus 2026
The JEE Main Mathematics (JEE Main) Syllabus for the JEE Main 2026 is available by the National Testing Agency. The JEE Main Mathematics (JEE Main) Syllabus is available for review from the link below. The JEE Main 2026 Mathematics (JEE Main) syllabus defines and describes each unit covered on the JEE Main 2026 Mathematics (JEE Main) exam.
Academic year:
B.E./B.Tech. Mathematics (JEE Main) Revised Syllabus
Units and Topics
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Syllabus
1 Sets, Relations, and Functions [Revision]
- Sets and Their Representations
- Roster or Tabular method or List method
- Set-Builder or Rule Method
- Classification of Sets
- Subsets
- Subsets of set of real numbers
- Intervals as subsets of R
- Subsets
- Venn Diagrams
- Basics of Relations & Functions
- Union of Sets
- Union of sets
- Some Properties of the Operation of Union
- Intersection of Sets
- Intersection of sets
- Some Properties of Operation of Intersection
- Difference of Sets
- Difference of sets
- Union of Sets
- Complement of a Set
- De Morgan's Law
- Some Properties of Complement Sets
- Practical Problems on Union and Intersection of Two Sets
- Algebra of Real Functions
- Sum, Difference,Product and Quotient of Function
- Addition of two real functions
- Subtraction of a real function from another
- Multiplication by a scalar
- Multiplication of two real functions
- Quotient of two real functions
- Algebraic Operations on Functions
2 Complex Numbers and Quadratic Equations [Revision]
- Introduction of Complex Number
- Concept of Complex Numbers
- Complex Numbers as Ordered Pairs of Reals
- Representation of Complex Numbers
- Expressing complex number in a + ib form and their representation in a plane
- Argand Plane and Polar Representation
- Algebraic Operations of Complex Numbers
- Properties of Conjugate, Modulus and Argument (or Amplitude) of Complex Numbers
- Square Root of a Complex Number
- Triangle Inequality
- Integral Powers of Iota
- Rotational Theorem of Complex Number
- Cube Root of Unity
- Geometry of Complex Numbers
- Demoiver's Theorem
- Powers of Complex Numbers
- Sum and Product of Root
- Nature of Roots of a Quadratic Equation
- Nature of roots(law)
- Formation of a Quadratic Equation with Given Roots
- Method of Solving a Quadratic Equation
- Quadratic Formula (Shreedharacharya's Rule)
- Definition: Discriminant
- Formula
- Examples
- Quadratic Formula (Shreedharacharya's Rule)
- Condition for Common Roots
- Maximum and Minimum Value of Quadratic Equation
- Quadratic Expression in Two Variables
- Solution of Quadratic Inequalities
3 Matrices and Determinants [Revision]
- Concept of Matrices
- Operations on Matrices> Addition and Subtraction of Matrices
- Operations on Matrices>Scalar Multiplication
- Operations on Matrices> Matrix Multiplication
- Types of Matrices
- Determinant of a Matrix
- Properties of Determinants
- Property 1 - The value of the determinant remains unchanged if its rows are turned into columns and columns are turned into rows.
- Property 2 - If any two rows (or columns) of a determinant are interchanged then the value of the determinant changes only in sign.
- Property 3 - If any two rows ( or columns) of a determinant are identical then the value of the determinant is zero.
- Property 4 - If each element of a row (or column) of a determinant is multiplied by a constant k then the value of the new determinant is k times the value of the original determinant.
- Property 5 - If each element of a row (or column) is expressed as the sum of two numbers then the determinant can be expressed as the sum of two determinants
- Property 6 - If a constant multiple of all elements of any row (or column) is added to the corresponding elements of any other row (or column ) then the value of the new determinant so obtained is the same as that of the original determinant.
- Property 7 - (Triangle property) - If all the elements of a determinant above or below the diagonal are zero then the value of the determinant is equal to the product of its diagonal elements.
- Evaluation of Determinants
- Application of Determinants
- Area of a Triangle Using Determinants
- Adjoint & Inverse of Matrix
- Test of Consistency
- Applications of Determinants and Matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Multiplication of Two Determinants
- Minors and Co-factors
- Some Special Cases of Matrix
- Rank of a Matrix
- Concept
- Elementary Transformations and Equivalent matrices
- Echelon form and finding the rank of the matrix (upto the order of 3×4)
- A system of equations with exactly one solution
- A system of equations with infinitely many solutions
- A system of equations that has no solution
- Testing the consistency of non homogeneous linear equations (two and three variables) by rank method
4 Permutations and Combinations [Revision]
- Permutations
- Fundamental Principles of Counting
- Combination
- Meaning of P (n,r) and C (n,r)
- Simple Applications of Permutations and Combinations
- Factorials
- Division and Distribution of Objects
- Dearrangement Theorem
- Sum of Numbers
- Important Result About Point
5 Mathematical Inductions [Revision]
- Mathematical Induction
- Principle of Mathematical Induction
- Motivation
- Motivating the Application of the Method by Looking at Natural Numbers as the Least Inductive Subset of Real Numbers
- Simple Applications of Mathematical Induction
- Problems Based on Sum of Series
- Problems Based on Inequality and Divisibility
6 Binomial Theorem and Its Simple Applications [Revision]
- Introduction of Binomial Theorem
- History of Binomial Theorem
- Binomial Theorem for Positive Integral Indices
- Statement and Proof of the Binomial Theorem for Positive Integral Indices
- Proof of Binomial Therom by Induction
- Special Case in Binomial Therom
- Pascal's Triangle
- Binomial theorem for any positive integer n
- Some special cases-(In the expansion of (a + b)n)
- General and Middle Terms
- Binomial Theorem
- Properties of Binomial Coefficient with Simple Application
- Binomial Theorem for Any Index (Without Proof)
- Expansion of Binomial
- Coefficient of Any Power of 'X'
- Greatest Term
- Independent Term
- Particular Term from End in Binomial Expansion
- Greatest Binomial Coefficients
- Number of Terms in the Expansion of (x + y + z)n
- Multinomial Theorem
- Infinite Series
7 Sequence and Series [Revision]
- Sequence, Series, and Progression
- Relation Between Arithmetic Mean (A.M.), Geometric Mean (G.M.), Harmonic Mean (H.M.)
- Arithmetico-geometric Sequence
- Arithmetic Progression (A.P.)
- Geometric Progression (G. P.)
- Nth Term of Geometric Progression (G.P.)
- General Term of a Geometric Progression (G.P.)
- Sum of First N Terms of a Geometric Progression (G.P.)
- Sum of infinite terms of a G.P.
- Geometric Mean (G.M.)
- Harmonic Progression (H. P.)
- Insertion of Arithmetic
- Geometric Mean
- Sum to' n' Terms of a Geometric Progression
- Sum to infinite terms of a G.P.
- Some Special Sequences
8 Limit, Continuity, and Differentiability [Revision]
- Concept of Limits
- Limits of Logarithmic Functions
- Limits of Exponential Functions
- Limits by Factorisation, Substitution and Rationalisation
- Algebra of Limits
- Limits of Trigonometric Functions
- Inverse Functions
- Graphs of Simple Functions
- Continuous and Discontinuous Functions
- Concept of Differentiability
- Differentiation of the Sum, Difference, Product, and Quotient of Two Functions
- Derivative of Inverse Function
- Exponential and Logarithmic Functions
- Derivatives of Composite Functions
- Derivative of Implicit Functions
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Mean Value Theorem
- Rolle’s Theorem
- Lagrange’s Mean Value Theorem
- Applications
- Simple Problems on Applications of Derivatives
Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)
- Rate of Change of Quantities
- Increasing and Decreasing Functions
- Maxima and Minima
- Tangents and Normals
- Limits Using L-hospital's Rule
- Evaluation of Limits
- Evaluation of Limits when X → ∞
- Evaluation of Limits of the form 1∞
- Infinite Series
- Successive Differentiation
- nth Derivative of Standard Functions
- Algebra of Derivative (Leibnitz or Product Rule)
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Approximations
9 Integral Calculas [Revision]
- Integration
- Integration as an Inverse Process of Differentiation
- Fundamental Integrals Involving Algebraic Functions
- Fundamental Integrals Involving Trigonometric Functions
- Fundamental Integrals Involving Exponential Functions
- Fundamental Integrals Involving Logarithms Functions
- Methods of Integration> Integration by Substitution
- Methods of Integration> Integration by Parts
- Methods of Integration> Integration Using Partial Fraction
- Methods of Integration>Integration Using Trigonometric Identities
- Integrals of Some Particular Functions
- Definite Integral as the Limit of a Sum
- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals
- Evaluation of Definite Integrals by Substitution
- Area Bounded by Two Curves
- Area Under Simple Curves
- Integration of Some Special Irrational Algebraic Functions
- Summation of Series by Integration
10 Diffrential Equations [Revision]
- Introduction to Ordinary Differential Equations
- Formation of Ordinary Differential Equations
- Definition of ordinary differential equation
- Order and degree of a differential equation
- Formation of ordinary differential equation
- Solution of a Differential Equation
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- General and Particular Solutions of a Differential Equation
- Solutions of Linear Differential Equation
- Solutions of linear differential equation of the type:
- `dy/dx` + py = q, where p and q are functions of x or constants.
- `dx/dy` + px = q, where p and q are functions of y or constants.
- Differential equations, order and degree.
- Solution of differential equations.
- Variable separable.
- Homogeneous equations
- Linear form `dy/dx` + Py = Q where P and Q are functions of x only. Similarly, for `dx/dy`.
- Methods of Solving First Order, First Degree Differential Equations
- Methods of Solving Differential Equations> Variable Separable Differential Equations
- Methods of Solving Differential Equations> Homogeneous Differential Equations
- Methods of Solving Differential Equations>Linear Differential Equations
- Solution by Inspection Method
11 Co-ordinate Geometry [Revision]
- Brief Review of Cartesian System of Rectanglar Co-ordinates
- Distance Formula
- Section Formula in Coordinate Geometry
- Formula
- Division of Line Segment
- Proof
- Examples
- Locus
- Equation of a locus
- Translation of Axes
- Concept of Slope (or, gradient)
- Parallel and Perpendicular Lines
- Intercepts on Axes
- Various Forms of the Equation of a Line
- Angle Between Two Lines
- Conditions for Concurrence of Three Lines
- Equations of Line in Different Forms
- Equations of Internal and External by Sectors of Angles Between Two Lines Co-ordinate of the Centroid, Orthocentre, and Circumcentre of a Triangle
- 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 Family of Lines Passing Through the Point of Intersection of Two Lines
- Equations of a Circle in Standard Form
- Equations of a Circle in General Form
- Equation of a Circle When the Endpoints of a Diameter Are Given
- Point of Intersection of a Line and a Circle
- 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 Tangent and Condition of Tangency
- Fundamentals of Conic Sections
- Parabola and its types
- Hyperbola and its Types
- Ellipse and its Types
- Condition for Y = mx + c to Be a Tangent and Point(s) of Tangency
- Results of Triangle
- Various Forms of Equation of a Line
- Shortest Distance Between Two Lines
- Bisector of the Angle Between the Two Lines
- Distance in Lines (Point & Parallel Lines)
- Foot of the Perpendicular
- Position of a Point with Respect to a Line
- Pedal Points
- Pair of Straight Lines
3.3.1 Combined equation of the pair of straight lines
3.3.2 Pair of straight lines passing through the origin
3.3.3 Angle between pair of straight lines passing through the origin
3.3.4 The condition for general second degree equation to represent the pair of straight
lines
- Equation of the bisectors of the angle between the lines
- General form of Pair of Straight Lines
- Advanced Concept of Circle
- Standard Equation of a Circle
12 Three Dimensional Geometry [Revision]
- Three - Dimensional Geometry
- Distance Between Two Points
- Distance Between Two Points in 3-D Space
- Distance Between Two Points
- Section Formula in Coordinate Geometry
- Formula
- Division of Line Segment
- Proof
- Examples
- Direction Ratios, Direction Cosine & Direction Angles
- Direction Cosines and Direction Ratios of a Line
- The Angle Between Two Intersecting Lines
- Skew Lines
- Equations of Line in Different Forms
- Equations of a Plane in Different Forms
- Intersection of the Line and Plane
- Coplanarity of Two Lines
- Angle Between Two Lines
- Projection of a Point on a Line
- Projection of a Line Segment Joining Two Points
- Equation of a Straight Line in Cartesian and Vector Form
- Concept of Slope (or, gradient)
- Distance in Lines (Point & Parallel Lines)
- Shortest Distance Between Two Lines
- Different Forms of Equation of a Plane
- Equation of a plane when a normal to the plane and the distance of the plane from the origin are given
- Equation of a plane perpendicular to a vector and passing through a given point
- Intercept form of the equation of a plane
- Equation of a plane passing through three given non-collinear points
- Equation of a plane passing through a given point and parallel to two given non-parallel vectors
- Equation of a plane passing through two given distinct points and is parallel to a non-zero vector
- Condition for a line to lie in a plane
- Condition for coplanarity of two lines
- Equation of plane containing two non-parallel coplanar lines
- Angle between two planes
- Angle between a line and a plane
- Distance of a point from a plane
- Distance between two parallel planes
- Equation of line of intersection of two planes
- Equation of a plane passing through the line of intersection of two given planes
- Equation of a Plane
- Angle Between Two Planes
- Angle Between Line and a Plane
- Distance Between Two Parallel Planes
- Position of Point and Line wrt a Plane
- Projection of a Line on a Plane
13 Vector Algebra [Revision]
- Vector Analysis
- Introduction
- Scalars and Vectors
- Scalar vs Vector
- Key Points to Remember
- Vector Operations>Addition and Subtraction of Vectors
- Statement
- Vector Addition: Parallel Vectors
- Vector Subtraction: Anti-Parallel Vectors
- Real-Life Applications
- Components of Vector in Algebra
- Multiplication of Vectors>Scalar Product(Dot Product)
- Introduction
- Definition: Scalar Product
- Characteristics of Scalar Product
- Scalar Product Using Rectangular Components
- Significance
- Example
- Real-Life Examples
- Scalar Triple Product
- Vector Triple Product
- Basic Concepts of Vector Algebra
- Section Formula in Coordinate Geometry
- Formula
- Division of Line Segment
- Proof
- Examples
- Linear Dependent and Independent Vectors
- Vector and Cartesian Equations of a Line
- Position Vector of a Point in a Space
- Modulus of a Vector
- Collinearity of Three Points
- Coplanarity of Three Vectors and Four Points
- Vector Inequality
- Product of Two Vectors
- Projection of a Vector Along Any Other Vector
- Area of a Parallelogram
- Geometric Interpretation of the Area of a Triangle
14 Statistics and Probability [Revision]
- Measures of Discretion
- Arithmetic Mean
- Mean of Grouped Data
- Basic Concept of Median
- Definition: Median
- Formula: Odd Number of Observations
- Formula: Even Number of Observations
- Example 1
- Example 2
- Example 3
- Key Points Summary
- Basic Concept of Mode
- Standard Deviation
- Variance and Standard Deviation for raw data
- Variance and Standard Deviation for ungrouped frequency distribution
- Variance and Standard Deviation for grouped frequency distribution
- Variance
- Mean Deviation
- Mean deviation for grouped data
- Mean deviation for ungrouped data
- Geometric Mean
- Harmonic Mean (H.M.)
- Coefficient of Variation
- Addition Theorem of Probability
- Multiplication Theorem on Probability
- Bayes’ Theorem
- Probability using Binomial Distribution
- Concept of Probability
- Odds in Favour and Against
- Elementary Types of Events and Properties of Probability
- Boole's Inequality
- Demorgan's Law
- Independent Events
- Conditional Probability
- Probability Distribution of Discrete Random Variables
- Poisson Distribution
15 Trigonometry [Revision]
- Trigonometric Identities (Square Relations)
- Trigonometric Equations
- Properties of Δ
- Sine formula: `a/sinA=b/sinB=c/sinC`
- Cosine formula:`cosA=(b^2+c^2-a^2)/(2bc)`, etc
- Area of triangle:Δ = `1/2`bc A etc
- Simple applications of the above
- Trigonometric Functions
- Properties of Inverse Trigonometric Functions
- Angles of Elevation and Depression
- Definition: Line of Sight
- Definition: Angles of Elevation
- Definition: Angle of Depression
- Measures of Angles with Various Systems
- Circular System
- Trigonometric Ratios
- Domain and Range of Trigonometric Functions
- Domain and Range of Trignometric Functions and Their Graphs
- Trigonometric Functions of Allied Angels
- Conditional Trigonometric Identities
- Greatest and Least Value of Trigonometric Expressions
- Solution of Trigonometric Equations (Solution in the Specified Range)
- Intervals for Inverse Trigonometric Functions
- Infinite Series of Inverse Trigonometric Functions
16 Mathematical Reasoning [Revision]
- Mathematical Reasoning
- Introduction of Validating Statements
- Validating the Statements Involving the Connecting Words
- statement with “and”
- Statements with “or”
- “Implies”
- “Implied by”
- Statements with “If then”
- Statements with “if and only if”
- Mathematically Acceptable Statements
- Statements and Truth Values in Mathematical Logic
- Tautology, Contradiction, and Contingency
- Logical Connective
- Truth Tables
- Logical Equivalance
- Quantifier, Quantified and Duality Statements in Logic
- Converse, Inverse and Contrapositive of the Conditional Staternent
- Negative of a Compound Statement
- Algebra of Statements
17 Linear Inequality [Revision]
- Linear Inequations
- Definition: Linear lnequations
- Signs of Inequality
- Definition: Replacement Set / Domain of Variable
- Definition: Solution Set
- Properties
- Method of Solving a Linear Inequality
- Rules to solve inequation
- System of Linear Inequalities
- Inequalities of Various Functions
18 Properties of Triangles [Revision]
- Properties of Triangle
- The Law of Sines or Sine Formula
- Law of Sines
- Law of Cosines
- Projection Formula
- Projection Formula
- Half-Angle formula
- Area of a triangle (Heron’s Formula )
- Solutions of Triangle
- Geometrical Concepts Related to a Circle
- Advanced Regular Polygon
- If all the sides and all the angles of a polygon are equal, it is called a regular polygon.
- Sum of interior angles of an 'n' sided polygon ( whether it is regular or not) = ( 2n - 4 )rt. angles and sum of its exterior angles = 4 right angles = 360°
- At each vertex of every polygon, Exterior angle + Interior angle = 180°.
- Each interior angle of a regular polygon = `[( 2n - 4 ) "rt. angles"]/[n] = [( 2n - 4 ) xx 90°]/n`
- Each exterior
- Angles of Elevation and Depression
- Definition: Line of Sight
- Definition: Angles of Elevation
- Definition: Angle of Depression
