JEE Main Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in JEE Main, not a summary of it.

1. 1

   Sets, Relations and Functions

   3 topics

   • Sets and their representation
     • Union, intersection, and complement of sets and their algebraic properties
     • Power set
   • Relation
     • Type of relations
     • Equivalence relations
   • Functions
     • One-one, into and onto functions
     • Composition of functions
2. 2

   Complex numbers and quadratic equation

   2 topics

   • 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 co-efficient
     • Nature of roots
     • Formation of quadratic equations with given roots
3. 3

   Matrices and Determinants

   3 topics

   • Matrices
     • Algebra of matrices
     • Type of matrices
   • Determinants
     • Evaluation of determinants
     • Area of triangles using determinants
     • Adjoint
     • 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
4. 4

   Permutation and Combination

   3 topics

   • The fundamental principle of counting
   • Permutation as an arrangement and combination as section
   • Meaning of P (n,r) and C (n,r)
     • Simple applications
5. 5

   Binomial Therorem

   2 topics

   • Binomial theorem for a positive integral index
     • General term and middle term
   • Simple applications
6. 6

   Sequence and Series

   3 topics

   • Arithmetic and Geometric progressions
   • Insertion of arithmetic, geometric means between two given numbers
   • Relation between A.M and G.M
7. 7

   Limit, Continuity, and Differentiability

   23 topics

   • Real–valued functions
   • Algebra of functions
   • Polynomials
   • Rational functions
   • Trigonometric functions
   • Logarithmic functions
   • Exponential functions
   • Inverse function
   • Graphs of simple functions
   • Limits
   • Continuity
   • Differentiability
   • Differentiation of the sum, difference, product, and quotient of two functions
   • Differentiation of trigonometric functions
   • Differentiation of inverse trigonometric functions
   • Differentiation of logarithmic functions
   • Differentiation of exponential functions
   • Differentiation of composite functions
   • Differentiation of implicit functions
   • Derivatives of order up to two
   • Applications of derivatives: Rate of change of quantities
   • Applications of derivatives: Monotonic-Increasing and decreasing functions
   • Applications of derivatives: Maxima and minima of functions of one variable
8. 8

   Integral Calculus

   9 topics

   • Integral as an anti-derivative
   • 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
   • 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
9. 9

   Differential Equations

   2 topics

   • Ordinary Differential Equations
     • Order and Degree
   • Solution of Differential Equations
     • Method of Separation of Variables
     • Solution of Homogeneous Equations
     • Solution of Linear Equations
10. 10

    Co-ordinate Geometry

    9 topics

    • Cartesian system of rectangular coordinates in a plane
    • Distance formula
    • Sections formula
    • Locus and its equation
    • 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
      • Co-ordinate of the centroid
      • Orthocentre, and circumcentre of a triangle
    • Circle, conic sections
      • Standard form of equations of a circle
      • General form of the equation of a circle
      • Radius and central of a circle
      • 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
      • Sections of conics
      • Equations of conic sections (parabola, ellipse, and hyperbola) in standard forms
11. 11

    Three Dimensional Geometry

    8 topics

    • Coordinates of a Point in Space
    • Distance Between Two Points
    • Section Formula
    • Directions Ratios and Direction Cosines
    • Angle Between Two Intersecting Lines
    • Skew Lines
    • Shortest Distance Between Skew Lines
    • Equations of a Line
12. 12

    Vector Algebra

    4 topics

    • Vectors and Scalars
    • Addition of Vectors
    • Components of a Vector in Two Dimensions and Three-Dimensional Space
    • Scalar and Vector Products
13. 13

    Statistics and Probability

    4 topics

    • Measures of Discretion
    • Calculation of Mean, Median, Mode
      • Of Grouped Data
      • Of Ungrouped Data
    • Calculation of Standard Deviation, Variance, Mean Deviation
      • For Grouped Data
      • For Ungrouped Data
    • Probability
      • Probability of an Event
      • Addition and Multiplication Theorems of Probability
      • Bayes' Theorem
      • Probability Distribution of a Random Variate
14. 14

    Trigonometry

    3 topics

    • Trigonometrical identities
    • Trigonometrical functions
    • Inverse trigonometrical functions
      • Properties

Mathematics flashcards for JEE Main

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What is a set, and what are the two standard ways of representing a set?

   A set is a well-defined collection of distinct objects (elements). It can be represented in (1) Roster (tabular) form, listing all elements, e.g. $A=\{1,2,3\}$; and (2) Set-builder form, stating a defining property, e.g. $A=\{x : x \in \mathbb{N},\ x<4\}$.

2. Define the empty set, a singleton set, and a finite vs. infinite set.

   The empty (null) set $\varnothing$ contains no elements. A singleton set contains exactly one element. A finite set has a countable, definite number of elements; an infinite set has unlimited elements (e.g. $\mathbb{N}$).

3. When are two sets said to be equal, and when is $A$ a subset of $B$?

   Two sets are equal if they have exactly the same elements: $A=B \iff (A\subseteq B \text{ and } B\subseteq A)$. $A$ is a subset of $B$, $A\subseteq B$, if every element of $A$ is also in $B$.

4. What is the power set of a set $A$, and how many elements does it have if $|A|=n$?

   The power set $P(A)$ is the set of all subsets of $A$ (including $\varnothing$ and $A$ itself). If $|A|=n$, then $|P(A)|=2^{n}$, and the number of proper subsets is $2^{n}-1$.

5. Define the union and intersection of two sets $A$ and $B$ using set-builder notation.

   $A\cup B=\{x : x\in A \text{ or } x\in B\}$ (elements in at least one set). $A\cap B=\{x : x\in A \text{ and } x\in B\}$ (elements common to both).

6. Define the complement $A'$ of a set $A$ and the difference $A-B$.

   With respect to a universal set $U$, the complement is $A'=U-A=\{x : x\in U,\ x\notin A\}$. The difference $A-B=\{x : x\in A \text{ and } x\notin B\}$.

7. State the commutative and associative laws for union and intersection of sets.

   Commutative: $A\cup B=B\cup A$ and $A\cap B=B\cap A$. Associative: $(A\cup B)\cup C=A\cup(B\cup C)$ and $(A\cap B)\cap C=A\cap(B\cap C)$.

8. State the distributive laws of sets.

   $A\cap(B\cup C)=(A\cap B)\cup(A\cap C)$ and $A\cup(B\cap C)=(A\cup B)\cap(A\cup C)$.

9. State De Morgan's laws for sets.

   $(A\cup B)'=A'\cap B'$ and $(A\cap B)'=A'\cup B'$.

10. State the identity, complement, and idempotent laws for sets.

    Identity: $A\cup\varnothing=A$, $A\cap U=A$. Complement: $A\cup A'=U$, $A\cap A'=\varnothing$. Idempotent: $A\cup A=A$, $A\cap A=A$.

11. State the formula for $|A\cup B|$ and for $|A\cup B\cup C|$ (inclusion-exclusion).

    $|A\cup B|=|A|+|B|-|A\cap B|$. For three sets: $|A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|B\cap C|-|A\cap C|+|A\cap B\cap C|$.

12. What is the Cartesian product $A\times B$, and how many elements does it contain?

    $A\times B=\{(a,b) : a\in A,\ b\in B\}$, the set of all ordered pairs. If $|A|=m$ and $|B|=n$, then $|A\times B|=mn$.

13. Define a relation $R$ from set $A$ to set $B$. How many relations are possible from $A$ to $B$?

    A relation $R$ from $A$ to $B$ is any subset of $A\times B$. If $|A|=m$ and $|B|=n$, the total number of relations from $A$ to $B$ is $2^{mn}$.

14. Define the domain and range of a relation $R$.

    The domain is the set of all first elements of the ordered pairs in $R$; the range is the set of all second elements. For $R\subseteq A\times B$, the codomain is $B$, and the range is a subset of the codomain.

15. Define a reflexive relation and a symmetric relation on a set $A$.

    $R$ is reflexive if $(a,a)\in R$ for all $a\in A$. $R$ is symmetric if $(a,b)\in R \implies (b,a)\in R$ for all $a,b\in A$.

16. Define a transitive relation and an antisymmetric relation on a set $A$.

    $R$ is transitive if $(a,b)\in R$ and $(b,c)\in R \implies (a,c)\in R$. $R$ is antisymmetric if $(a,b)\in R$ and $(b,a)\in R \implies a=b$.

17. What is an equivalence relation?

    A relation $R$ on a set $A$ is an equivalence relation if it is simultaneously reflexive, symmetric, and transitive.

18. What is an equivalence class, and what key property do the equivalence classes of a relation have?

    For $a\in A$, the equivalence class is $[a]=\{x\in A : (x,a)\in R\}$. The distinct equivalence classes are mutually disjoint and their union is $A$; thus they form a partition of $A$.

19. Define the identity relation and the universal relation on a set $A$.

    Identity relation: $I_A=\{(a,a) : a\in A\}$. Universal relation: $A\times A$ (relates every element to every element). Both, along with the empty relation, are special cases.

20. Define a function (mapping) $f:A\to B$.

    A function $f:A\to B$ is a relation that assigns to each element of $A$ exactly one element of $B$. Every element of the domain $A$ must have one and only one image in $B$.

21. Define a one-one (injective) function.

    A function $f:A\to B$ is one-one (injective) if distinct elements have distinct images: $f(x_1)=f(x_2) \implies x_1=x_2$, equivalently $x_1\neq x_2 \implies f(x_1)\neq f(x_2)$.

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