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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

#Unit/TopicWeightage
1  Sets, Relations, and Functions 
2  Complex Numbers and Quadratic Equations 
3  Matrices and Determinants 
4  Permutations and Combinations 
5  Mathematical Inductions 
6  Binomial Theorem and Its Simple Applications 
7  Sequence and Series 
8  Limit, Continuity, and Differentiability 
9  Integral Calculas 
10  Diffrential Equations 
11  Co-ordinate Geometry 
12  Three Dimensional Geometry 
13  Vector Algebra 
14  Statistics and Probability 
15  Trigonometry 
16  Mathematical Reasoning 
17  Linear Inequality 
18  Properties of Triangles 
 Total -
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Syllabus

1 Sets, Relations, and Functions
2 Complex Numbers and Quadratic Equations
  • Introduction of Complex Number  
  • Concept of Complex Numbers  
    • Imaginary number
    • Complex Number
  • 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  
    • Equality of two Complex Numbers 
    • Conjugate of a Complex Number 
    • Properties of `barz`
    • Addition of complex numbers - Properties of addition, Scalar Multiplication
    • Subtraction of complex numbers - Properties of Subtraction
    • Multiplication of complex numbers - Properties of Multiplication
    • Powers of i in the complex number
    • Division of complex number - Properties of Division
    • The square roots of a negative real number
    • Identities
  • 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  
    • Properties of 1, w, w2
  • 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  
  • Condition for Common Roots  
  • Maximum and Minimum Value of Quadratic Equation  
  • Quadratic Expression in Two Variables  
  • Solution of Quadratic Inequalities  
3 Matrices and Determinants
  • Concept of Matrices  
    • Matrices
    • Determinants
    • Cramer’s Rule
    • Application in Economics
  • Properties of Matrix Addition  
    • Commutative Law
    • Associative Law
    • Existence of additive identity
    • The existence of additive inverse
  • Operation on Matrices  
  • Properties of Matrix Multiplication  
  • Types of Matrices  
    • Row Matrix
    • Column Matrix
    • Zero or Null matrix
    • Square Matrix
    • Diagonal Matrix
    • Scalar Matrix
    • Unit or Identity Matrix
    • Upper Triangular Matrix
    • Lower Triangular Matrix
    • Triangular Matrix
    • Symmetric Matrix
    • Skew-Symmetric Matrix
    • Determinant of a Matrix
    • Singular Matrix
    • Transpose of a Matrix
  • Determinants  
    • Determinants of Matrices of different order
    • Properties of Determinants
    • Application of Factor Theorem to Determinants
    • Product of Determinants
    • Relation between a Determinant and its Cofactor Determinant
    • Area of a Triangle
    • Singular and non-singular Matrices
  • 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 of a Matrix  
  • Test of Consistency  
  • Applications of Determinants and Matrices  
    • Consistent System
    • Inconsistent System
    • Solution of a system of linear equations using the inverse of a matrix
  • Transpose of a Matrix  
  • Symmetric and Skew Symmetric Matrices  
    • Define symmetric and skew symmetric matrix
  • 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)
    1. A system of equations with exactly one solution
    2. A system of equations with infinitely many solutions
    3. 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
  • Introduction of Permutations and Combinations  
  • Fundamental Principles of Counting  
    • Tree Diagram 
    • Addition Principle 
    • Multiplication principle
  • Permutations  
    • Permutation
    • Permutation of repeated things
    • Permutations when all the objects are not distinct
    • Number of Permutations Under Certain Restricted Conditions
    • Circular Permutations
  • Combination  
    • nCr , nCn =1, nC0 = 1, nCr = nCn–r, nCx = nCy, then x + y = n or x = y, n+1Cr = nCr-1 + nCr
    • When all things are different
    • When all things are not different.
    • Mixed problems on permutation and combinations.
  • 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
  • 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
  • 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
8 Limit, Continuity, and Differentiability
9 Integral Calculas
  • Integration  
  • Integration as an Inverse Process of Differentiation  
    Derivatives Integrals
    (Anti derivatives)
    `d/(dx) (x^(n+1)/(n+1)) = x^n`   `int x^n dx = x^(n+1)/(n+1) + "C"`, n ≠ –1     
    `d/(dx)`(x) = 1                                          `int dx` = x + C
    `d/(dx)`(sin x) = cos x `int` cos x dx = sin x +C
    `d/(dx)` (-cos x) = sin x `int`sin x dx = -cos x +C
    `d/(dx)` (tan x) = sec2x `int sec^2 x` dx = tanx + C
    `d/(dx)`(-cot x) = `cosec^2x ` `int cosec^2x` dx = -cot x +C
    `d/(dx)` (sec x) = sec x tan x  `int` sec x tan x dx = sec x +C
    `d/(dx)` (-cosecx) = cosec x cot x `int` cosec x cot x dx = -cosec x +C
    `d/(dx) (sin^-1) = 1/(sqrt(1-x^2))` `int (dx)/(sqrt(1-x^2))= sin^(-1) x +C `
    `d/(dx) (-cos^(-1)) = 1/(sqrt (1-x^2))` `int (dx)/(sqrt (1-x^2))= -cos^(-1) x + C `
    `d/(dx) (tan^(-1) x) = 1/(1+x^2)` `int (dx)/(1+x^2)= tan^(-1) x + C `
     `d/(dx) (-cot^(-1) x) = 1/(1+x^2)` `int (dx)/(1+x^2)= -cot^(-1) x + C `
    `d/(dx) (sec^(-1) x) = 1/(x sqrt (x^2 - 1))` `int (dx)/(x sqrt (x^2 - 1))`= `sec^(-1)` x + C
    `d/(dx) (-cosec^(-1) x) = 1/(x sqrt (x^2 - 1))` `int (dx)/(x sqrt (x^2 - 1))=-cosec^(-1) x + C `
    `d/(dx)(e^x) = e^x` `int e^x dx = e^x + C`
    `d/(dx) (log|x|) = 1/x` `int 1/x dx = log|x| +C`
    `d/(dx) ((a^x)/(log a)) = a^x` `int a^x dx = a^x/log a` +C
  • 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 Fractions  
  • Integration Using Trigonometric Identities  
  • Integrals of Some Particular Functions  

    1) `int (dx)/(x^2 - a^2) = 1/(2a) log |(x - a)/(x + a)| + C`

    2) `int (dx)/(a^2 - x^2) = 1/(2a) log |(a + x)/(a - x)| + C`

    3) `int (dx)/(x^2 - a^2) = 1/a  tan^(-1) (x/a) + C`

    4) `int (dx)/sqrt (x^2 - a^2) = log |x + sqrt (x^2-a^2)| + C`

    5) `int (dx)/sqrt (a^2 - x^2) = sin ^(-1) (x/a) +C`

    6)  `int (dx)/sqrt (x^2 + a^2) = log |x + sqrt (x^2 + a^2)| + C`

    7) To find the integral `int (dx)/(ax^2 + bx + c)`

    8) To find the integral of the type `int (dx)/sqrt(ax^2 + bx + c)`

    9) To find the integral of the type `int (px + q)/(ax^2 + bx + c) dx`

    10) For the evaluation of the integral of the type `int (px + q)/sqrt(ax^2 + bx + c) dx`

  • Definite Integral as the Limit of a Sum  
  • Fundamental Theorem of Calculus  

    Area function, First fundamental theorem of integral calculus and Second fundamental theorem of integral calculus

  • Properties of Definite Integrals  
  • Evaluation of Definite Integrals  
  • Area of the Region Bounded by a Curve and a Line  
    • Area of the Region Bounded by a Curve & X-axis Between two Ordinates
    • Area of the Region Bounded by a Curve & Y-axis Between two Abscissa 
    • Circle-line, elipse-line, parabola-line
  • Area Between Two Curves  
  • Area Under Simple Curves  
    • Simple curves: lines, parabolas, polynomial functions
  • Integration of Some Special Irrational Algebraic Functions  
  • Evaluation of Definite Integrals by Substitution  
  • Summation of Series by Integration  
10 Diffrential Equations
11 Co-ordinate Geometry
  • Brief Review of Cartesian System of Rectanglar Co-ordinates  
  • Distance Formula  
  • Section Formula  
    • Formula
    • Division of Line Segment
    • Proof
    • Examples
  • Locus  
    • Equation of a locus
  • Translation of Axes  
  • Concept of Slope (or, gradient)  
    • Slope of a Line Or Gradient of a Line.
    • Parallelism of Line
    • Perpendicularity of Line in Term of Slope
    • Collinearity of Points
    • Slope of a line when coordinates of any two points on the line are given
    • Conditions for parallelism and perpendicularity of lines in terms of their slopes
    • Angle between two lines
    • Collinearity of three points
  • 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  
  • Distance of a Point from a Line  
    • Introduction of Distance of a Point from a Line
    • Distance between two parallel lines
  • Equation of a Straight Line  
    • Inclination of a line
    • Slope of a line
    • Perpendicular Lines
    • Angle between intersecting lines
    • Different Forms of an equation of a straight line
    • General form to other 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.
  • General Equation of Tangents  
  • Conic Sections  
    • Geometric description of conic section
    • Degenerate Forms
    •  Identifying the conics from the general equation of the conic 
    • Parabola  
      • Standard equation of the parabola
      • Tracing of the parabola y2 = 4 ax (a>0)
      • Parametric expressions of standard parabola y2 = 4ax
      • General forms of the equation of a parabola
      • Tangent
      • Condition of tangency
      • Tangents from a point to a parabola
    • Ellipse  
      • Standard equation of the ellipse
      • Special cases of an ellipse
      • Tangent to an ellipse
      • Equation of tangent to the ellipse
      • Condition for tangency
      • Tangents from a point to the ellipse
      • Locus of point of intersection of perpendicular tangents
      • Auxilary circle and director circle of the ellipse
    • Hyperbola  
      • Standard equation of the hyperbola
      • Tangent to a hyperbola
      • Tangent at a point on a hyperbola
      • Equation of tangent to the hyperbola
      • Condition for tangency
      • Tangents from a point to the hyperbola
      • Locus of point of intersection of perpendicular tangents
      • Auxiliary Circle, Director Circle
      • Asymptote
  • Parabola  
  • Ellipse  
  • Hyperbola  
  • 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  
    • Coplanar
    • Skew lines
    • Distance between two skew lines
    • Distance between parallel lines
  • Bisector of the Angle Between the Two Lines  
  • Perpendicular Distance of a Point from a Line  
  • 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
  • Three - Dimensional Geometry  
  • Section Formula  
    • Formula
    • Division of Line Segment
    • Proof
    • Examples
  • Direction Ratios  
  • Direction Cosines and Direction Ratios of a Line  
    • Direction cosines of a line passing through two points.
  • The Angle Between Two Intersecting Lines  
  • Skew Lines  
  • Shortest Distance Between Two Lines  
    • Coplanar
    • Skew lines
    • Distance between two skew lines
    • Distance between parallel lines
  • Equations of Line in Different Forms  
    • Point-slope Form
    • Slope-Intercept form
    • Two-points Form
    • Double-Intercept form
    • Normal Form
  • 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)  
    • Slope of a Line Or Gradient of a Line.
    • Parallelism of Line
    • Perpendicularity of Line in Term of Slope
    • Collinearity of Points
    • Slope of a line when coordinates of any two points on the line are given
    • Conditions for parallelism and perpendicularity of lines in terms of their slopes
    • Angle between two lines
    • Collinearity of three points
  • Perpendicular Distance of a Point from a Line  
  • Distance Between Skew Lines and Parallel Lines  
    • Distance between skew lines
    • Distance between parallel 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  
    • Passing through a point and perpendicular to a vector
    • Passing through a point and parallel to two vectors
    • Passing through three non-collinear points
    • In normal form
    • Passing through the intersection of two planes
  • 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
14 Statistics and Probability
15 Trigonometry
  • 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  
  • Inverse Trigonometric Functions  
    • Introduction of Inverse Trigonometric Functions
  • Properties of Inverse Trigonometric Functions  

    Inverse of Sin, Inverse of cosin, Inverse of tan, Inverse of cot, Inverse of Sec, Inverse of Cosec

  • 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 Ratios of Allied Angles  
  • Conditional Trigonometric Identities  
  • Greatest and Least Value of Trigonometric Expressions  
  • Solution of Trigonometric Equations (Solution in the Specified Range)  
  • Domain and Range of Inverse Trigonometric Functions  
  • Principal Value of Inverse Trigonometric Functions  
  • Intervals for Inverse Trigonometric Functions  
  • Infinite Series of Inverse Trigonometric Functions  
16 Mathematical Reasoning
  • 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  
  • Truth Value of Statement  
  • Tautology, Contradiction, and Contingency  
  • Logical Connective  
  • Truth Tables  
  • Logical Equivalance  
  • Duality  
  • Converse, Inverse and Contrapositive of the Conditional Staternent  
  • Negative of a Compound Statement  
  • Algebra of Statements  
    • Idempotent law
    • Associative law
    • Commutative law
    • Distributive law
    • Identity law
    • Complement law
    • Involution law
    • DeMorgan’s laws
17 Linear Inequality
  • 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
  • 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  
    • Polar co-ordinates
    • Relation between the polar co-ordinates and the Cartesian co-ordinates
    • Solving a Triangle
    • The Sine rule
    • The Projection rule
    • Applications of the Sine rule, the Cosine rule and the Projection rule
  • 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

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