JEE Main 2023: List of Chapters & Topics Covered Under Mathematics Section

Exam

Joint Entrance Exam - JEE Main

Subject to be discussed

Mathematics

Type of questions to be asked

• MCQs
• Numerical Value

Total Number of Questions

• Section A- 20
• Section B- 10

Number of questions to be attempted

• Section A- 20
• Section B- 5

Marking Scheme

• Correct +4
• Incorrect -1
• Unanswered- No deduction

1

Set, Relations and Functions

Set, and their representation

Union, intersection, and complement of sets and their algebraic properties

Powerset

Relation, Types of relations, equivalence relations

Functions; one-one, into and onto functions, the composition of functions

2

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 numbers, 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.

The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

3

Matrices and Determinants

Matrices: Algebra of matrices, types of matrices, and matrices of order two and three.

Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants.

Adjoint and evaluation of the 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.

4

Permutations and Combinations

The fundamental principle of counting.

Permutation as an arrangement and combination is a selection.

The meaning of P (n,r) and C (n,r). Simple applications.

5

Mathematical Induction

The Principle of Mathematical Induction and its simple applications.

6

Binomial Theorem

Binomial theorem for a positive integral index.

General term and middle term.

Properties of Binomial coefficients and simple applications.

7

Sequence and Series

Arithmetic and Geometric progressions, insertion of arithmetic.

Geometric means between two given numbers.

The relation between A.M. and G.M.

Sum up to n terms of special series: Sn, Sn2, Sn3.

Arithmetic Geometric progression.

8

Limit, Continuity, and Differentiability

Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic, and exponential functions, inverse functions.

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, monotonic increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals.

9

Integral Calculus

Integral as an antiderivative.

Fundamental integrals involving algebraic, trigonometric, exponential, and logarithmic functions.

Integration by substitution, by parts, and by partial fractions.

Integration using trigonometric identities.

Integral as the limit of a sum.

Evaluation of simple integrals

Fundamental Theorem of Calculus.

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

10

Differential Equations

Ordinary differential equations, their order, and degree.

Formation of differential equations.

The solution of differential equations by the method of separation of variables.

The solution of homogeneous and linear differential equations.

11

Coordinate Geometry

Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus, and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

Straight lines: 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, equations of internal and external bisectors of angles between two lines, coordinates of the centroid, orthocentre, and circumcentre of a triangle, and equation of the family of lines passing through the point of intersection of two lines.

Circles, conic sections: Standard form of the equation of a circle, the general form of the equation of a circle, its radius and center, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the center at the origin and condition for a line to be tangent to a circle, equation of the tangent.

Sections of cones, 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.

12

3D Geometry

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

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

Skew lines, the shortest distance between them, and their equation.

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

13

Vector Algebra

Scalars and Vectors. Addition, subtraction, multiplication, and division of vectors.

Vector’s Components in 2D and 3D space.

Scalar products and vector products, triple products.

14

Statistics and Probability

Measures of Dispersion: Calculation of mean, mode, median, variance, standard deviation, and mean deviation of ungrouped and grouped data.

Probability: Probability of events, multiplication theorems, addition theorems, Baye’s theorem, Bernoulli trials, Binomial distribution, and probability distribution.

15

Trigonometry

Identities of Trigonometry and Trigonometric equations.

Functions of Trigonometry.

Properties of Inverse trigonometric functions.

Problems on Heights and Distances.

16

Mathematical Reasoning

Statements and logical operations: or, and, implied by, implies, only if and if.

Understanding of contradiction, tautology, contrapositive, and converse.

Chapter

Number of Questions

Total Marks

Sets, Relation, and Function

1

4

Binomial Theorem and Its Application

1

4

Sequences and Series

1

4

Trigonometry

1

4

Mathematical Reasoning

1

4

Differential Equation

1

4

Differential Calculus

1

4

Statics and Dynamics

1

4

Permutations and Combinations

1

4

Statistics and Probability

2

8

Complex numbers and Quadratic Equation

2

8

Vector Algebra

2

8

Matrices and Determinants

2

8

Three Dimensional Geometry

2

8

Integral Calculus

3

12

Limits, Continuity and Differentiability

3

12

Coordinate Geometry

5

20

Objective Mathematics for JEE

R.D. Sharma

Degree level Differential Calculus

A Das Gupta

Higher Algebra

Hall and Knight

IIT Mathematics

M.L. Khanna

Problems in Calculus of One Variable

I.A. Maron

Mathematics for Class 11 and 12

R.D. Sharma