Mathematics (JEE Main)

This is a complete, free study companion for Mathematics (JEE Main) — built around what the exam actually asks. The topics examiners repeat most are Limits using standard limits and algebraic simplification, Definite integrals using properties, symmetry and substitution, and Continuity of piecewise functions with parameter values. The syllabus runs to 14 chapters. Below you'll find the full topic-frequency ranking, the exam paper pattern, every chapter, a step-by-step study plan, and the official downloads — everything in one place.

Everything here is free. We're an independent student resource, not the official JEE body, so always confirm the current syllabus and exam dates on the official JEE website before you rely on them.

Key information

Level: Paper 1, Paper 2A, Paper 2B
Programme: Paper 1 B.E./B.Tech., Paper 2A B.Arch., Paper 2B B.Planning
Stream: B.E./B.Tech., B.Arch., B.Planning
Conducted by: National Testing Agency (NTA)

Most frequently examined topics

#	Topic	Times asked
1	Limits using standard limits and algebraic simplification	9
2	Definite integrals using properties, symmetry and substitution	9
3	Continuity of piecewise functions with parameter values	8
4	Differentiability of modulus, greatest integer and piecewise functions	8
5	Indefinite integration by substitution and standard forms	8
6	Circle: centre, radius, tangent, chord and normal	8
7	Domain and range of real-valued functions	7
8	Modulus and argument of complex numbers	7
9	Matrix inverse and solution of simultaneous linear equations	7
10	Determinant evaluation using properties	7
11	Coefficient or independent term in binomial expansion	7
12	Special finite series using Σn, Σn², Σn³ and telescoping	7

Counted across the official previous-year question papers we have analysed for this subject. It shows what has been asked before — it does not predict what will appear in your exam. Always confirm the current syllabus on the official portal.

What you will study (chapters)

Chapter 1: Sets, Relations and Functions
Chapter 2: Complex Numbers and Quadratic Equations
Chapter 3: Matrices and Determinants
Chapter 4: Permutations and Combinations
Chapter 5: Binomial Theorem and Its Simple Applications
Chapter 6: Sequence and Series
Chapter 7: Limit, Continuity and Differentiability
Chapter 8: Integral Calculus
Chapter 9: Differential Equations
Chapter 10: Coordinate Geometry
Chapter 11: Three Dimensional Geometry
Chapter 12: Vector Algebra
Chapter 13: Statistics and Probability
Chapter 14: Trigonometry

How to study Mathematics (JEE Main) and score well

Start with the highest-frequency topics — In Mathematics (JEE Main), Limits using standard limits and algebraic simplification, Definite integrals using properties, symmetry and substitution, Continuity of piecewise functions with parameter values, and Differentiability of modulus, greatest integer and piecewise functions appear again and again in past papers. Master these first — they return the most marks for the time you put in.
Practise with previous-year papers — Solve the last 5–10 years of JEE Mathematics (JEE Main) papers under timed, exam-like conditions. Past papers show exactly which topics repeat and how questions are worded.
Revise actively, not passively — Write a one-page summary for each of the 14 chapters — key definitions, formulas and the points examiners reward — then re-test yourself instead of re-reading.
Mark your answers with the official scheme — After each practice paper, score yourself against the official marking scheme. It shows how marks are awarded step-by-step, so you learn to present answers the way examiners expect.

Exam tips: how to score higher in Mathematics (JEE Main)

Where students lose marks: attempting questions they have not truly eliminated options for, spending too long on one hard question, and rushing the sections they know best. Read the whole paper first, bank the marks you are sure of, and come back to the rest.

Manage your time and guess carefully: split your time in proportion to the marks each section carries and keep a few minutes at the end to check. This paper carries negative marking, so attempt a question only when you can rule out at least one or two options — a blind guess costs you marks. Confirm the exact marking scheme for your session on the official portal.

Frequently asked questions

What are the most important topics in Mathematics (JEE Main)?

Based on past papers, the most frequently asked topics include Limits using standard limits and algebraic simplification, Definite integrals using properties, symmetry and substitution, Continuity of piecewise functions with parameter values. The full ranked list with how often each appears is in the "Most important topics" section above.

Where can I download Mathematics (JEE Main) previous-year question papers?

Official JEE previous-year question papers are available on the official JEE website. Open the Question Papers section for the direct link, plus the exam pattern and the topics that repeat most.

How can I prepare for Mathematics (JEE Main) faster?

Start with the highest-frequency topics, learn the exam pattern so you know how each section is marked, and practise with past papers. A subject-aware study tutor can quiz you on exactly these topics.

A Gyani AI tutor trained on the Mathematics (JEE Main) syllabus and past papers can quiz you on the most-asked topics and show you exactly what to revise.