NCERT Solutions Class 11 Maths

Class 11 is the year that decides how easy or how hard Class 12 will feel. The Class 11 exam is set by your school, not by the board. But every topic you learn this year comes back in Class 12, and in entrance exams like JEE, CUET and NDA. So a strong Class 11 base is worth the effort.

Maths is the subject most students worry about. It is also the subject where full marks are possible, because every answer is either right or wrong — there is no guesswork. Our NCERT Solutions for Class 11 Maths give you step-by-step answers to every exercise question in the NCERT textbook, so you can check your own working and find exactly where you went wrong.

NCERT stands for the National Council of Educational Research and Training. CBSE (Central Board of Secondary Education) sets its papers from NCERT books, so solving the NCERT exercises well is the single best use of your study time.

Quick facts

All 14 Chapters of Class 11 Maths

The Class 11 Maths NCERT book has 14 chapters, grouped into 5 units. Here is the full list with the number of exercises in each chapter.

Two chapters have been removed from the older Class 11 Maths book: Principle of Mathematical Induction and Mathematical Reasoning. If you are studying from an old book or an old website, you will see 16 chapters and different chapter numbers. Use the list above instead.

Chapter-wise NCERT Solutions for Class 11 Maths

Chapter 1 – Sets

A set is simply a collection of things. This chapter teaches you how to write a set, and the different types of sets: empty set, finite and infinite sets, equal sets, subsets, universal set and power set. You also learn set operations — union, intersection, difference and complement — and how to show them using Venn diagrams.

This is the base for Chapter 2, and it is also used in probability. Do not skip it because it looks easy.

Solutions: Exercise 1.1, 1.2, 1.3, 1.4, 1.5 and Miscellaneous Exercise.

Chapter 2 – Relations and Functions

This chapter connects two sets. You learn ordered pairs, the Cartesian product of sets, what a relation is, and how a function is a special kind of relation. Key ideas here are domain, co-domain and range. You also study common real functions and their graphs, such as the identity function, constant function, modulus function and greatest integer function.

Solutions: Exercise 2.1, 2.2, 2.3 and Miscellaneous Exercise.

Chapter 3 – Trigonometric Functions

Here trigonometry moves from right-angled triangles to the whole circle. You learn to measure angles in degrees and in radians, and to convert between them. Then come the trigonometric functions, their signs in each quadrant, their domain and range, and their graphs. The chapter also covers the formulas for the sum and difference of two angles, and the identities that follow from them.

Learn the formulas properly here. Almost every later step in trigonometry depends on them.

Solutions: Exercise 3.1, 3.2, 3.3 and Miscellaneous Exercise.

Chapter 4 – Complex Numbers and Quadratic Equations

Some quadratic equations have no real solution. To solve them, we need a new kind of number. This chapter introduces the imaginary unit i, complex numbers of the form a + ib, and their algebra — addition, subtraction, multiplication and division. You also learn the modulus and the conjugate of a complex number, and how to solve quadratic equations that have complex roots.

Solutions: Exercise 4.1 and Miscellaneous Exercise.

Chapter 5 – Linear Inequalities

An equation says two things are equal. An inequality says one is bigger or smaller. This chapter shows how to solve linear inequalities in one variable using algebra, and how to show the answer on a number line. Word problems here are common in exams, so practise turning a sentence into an inequality.

Solutions: Exercise 5.1 and Miscellaneous Exercise.

Chapter 6 – Permutations and Combinations

This chapter is about counting without listing everything out. A permutation is an arrangement, where the order matters. A combination is a selection, where the order does not matter. You learn the fundamental principle of counting, factorial notation, the formulas for nPr and nCr, and how to apply them to real problems.

The main skill is deciding whether a question is asking for an arrangement or a selection. Read every question twice.

Solutions: Exercise 6.1, 6.2, 6.3, 6.4 and Miscellaneous Exercise.

Chapter 7 – Binomial Theorem

Expanding (a + b) to a high power by hand takes forever. The Binomial Theorem gives you the answer in one formula, for any positive whole number power. You learn Pascal's triangle, the general term, and how to find the middle term or the coefficient of a particular term.

Solutions: Exercise 7.1 and Miscellaneous Exercise.

Chapter 8 – Sequences and Series

A sequence is a list of numbers in order. A series is the sum of that list. This chapter covers Arithmetic Progression (AP), Geometric Progression (GP), the nth term and the sum of n terms of each, Arithmetic Mean (AM) and Geometric Mean (GM), the relation between AM and GM, and the sum of an infinite GP.

This chapter has many formulas. Write them all on one sheet and revise that sheet often.

Solutions: Exercise 8.1, 8.2 and Miscellaneous Exercise.

Chapter 9 – Straight Lines

This chapter puts lines on the coordinate plane. You learn slope, the angle between two lines, and when two lines are parallel or perpendicular. Then come the different forms of the equation of a line — point-slope form, two-point form, slope-intercept form, intercept form and normal form — the general equation of a line, and the distance of a point from a line.

Solutions: Exercise 9.1, 9.2, 9.3 and Miscellaneous Exercise.

Chapter 10 – Conic Sections

Cut a cone with a flat plane and you get a curve. Depending on the angle of the cut, that curve is a circle, a parabola, an ellipse or a hyperbola. These are the conic sections. For each one you learn the standard equation, and terms like focus, directrix, axis, vertex, eccentricity and latus rectum.

Solutions: Exercise 10.1, 10.2, 10.3, 10.4 and Miscellaneous Exercise.

Chapter 11 – Introduction to Three Dimensional Geometry

So far every point had two coordinates. In space, a point has three: x, y and z. This chapter introduces the three coordinate axes and the three coordinate planes, the eight octants, how to write the coordinates of a point in space, the distance between two points, and the section formula in three dimensions.

This is a short chapter and a scoring one. Do not leave it for the last day.

Solutions: Exercise 11.1, 11.2 and Miscellaneous Exercise.

Chapter 12 – Limits and Derivatives

This is your first taste of calculus. A limit tells you the value a function moves towards. A derivative tells you how fast a function is changing. You learn the algebra of limits, limits of polynomial, rational and trigonometric functions, the definition of a derivative from first principles, and the rules for the derivative of a sum, difference, product and quotient.

Calculus carries forward directly into Class 12, so understand it now rather than memorising it.

Solutions: Exercise 12.1, 12.2 and Miscellaneous Exercise.

Chapter 13 – Statistics

In earlier classes you found the average. Now you find out how spread out the data is. This chapter covers the measures of dispersion: range, mean deviation, variance and standard deviation, for both grouped and ungrouped data.

The steps are long but they repeat. Once you get the table format right, the marks are easy.

Solutions: Exercise 13.1, 13.2 and Miscellaneous Exercise.

Chapter 14 – Probability

Probability measures how likely something is. This chapter builds on the sets you learnt in Chapter 1. You study random experiments, sample space, events, and types of events such as mutually exclusive and exhaustive events. You then learn the axiomatic approach to probability, and how to find the probability of 'not', 'and' and 'or' events.

Solutions: Exercise 14.1, 14.2 and Miscellaneous Exercise.

Class 11 Maths Marks Distribution (Unit-wise)

The Class 11 Maths paper is of 80 marks and 3 hours. Another 20 marks come from internal assessment, making 100 in total.

CBSE gives the marks unit-wise, not chapter-wise. So no chapter can be skipped.

Internal assessment (20 marks)

What this table tells you: Sets and Functions plus Algebra together carry 48 of the 80 marks. That is 60 per cent of the paper from 8 chapters. Give these chapters your first and best hours.

How to Use These Solutions the Right Way

1. Read the chapter in the NCERT book first - Look carefully at the solved examples.
2. Try the exercise on your own - Give each question a real attempt before you look anywhere else.
3. Only then open the solution - Compare your method with ours, not just the final answer.
4. Mark the questions you got wrong - Do those same questions again after two days, without help.
5. Keep a formula sheet - One page per chapter. Revise it every week.
6. Do the Miscellaneous Exercise - It is harder, and it is where exam questions usually come from.

Preparation Tips for Class 11 Maths

• Make a weekly timetable and give more hours to Sets and Functions and to Algebra, since they carry the most marks.
• Do a little maths every day. Three hours on Sunday will not beat forty minutes daily.
• Write short notes while you revise. Writing shows you what you have not understood.
• After finishing the syllabus, solve sample papers with a timer set to 3 hours.
• Test yourself often. A weak topic is easier to fix in August than in February.
• Take breaks. A tired brain makes silly calculation mistakes.

Why Students Use Extramarks NCERT Solutions

• All 14 chapters, exercise by exercise, matched to the latest CBSE syllabus.
• Step-by-step methods, not just final answers, so you can see where your working went wrong.
• Free PDF download — study offline, on a phone, tablet or laptop.
• Simple language, useful for self-study and for last-minute revision.
• Useful beyond Class 11 — the same topics appear in Class 12 and in entrance exams such as JEE and CUET.

Frequently Asked Questions (FAQs)

Q1. How many chapters are there in Class 11 Maths?
There are 14 chapters in the current Class 11 Maths NCERT book. Two chapters from the older book — Principle of Mathematical Induction and Mathematical Reasoning — are no longer part of the syllabus.

Q2. Is Class 11 Maths a board exam?
No. The Class 11 exam is conducted by your own school. But the syllabus is the base for the Class 12 board exam and for entrance exams, so it matters just as much.

Q3. Which chapters carry the most marks in Class 11 Maths?
Algebra (Chapters 4 to 8) carries 25 marks and Sets and Functions (Chapters 1 to 3) carries 23 marks. Together that is 48 out of 80.

Q4. Is NCERT enough for Class 11 Maths?
For school exams, yes — if you finish every exercise including the Miscellaneous Exercise. For JEE and other entrance exams, finish NCERT first, then move to NCERT Exemplar and previous year papers.

Q5. Which is the hardest chapter in Class 11 Maths?
Most students find Trigonometric Functions and Conic Sections the hardest, because both need many formulas. Permutations and Combinations feels tricky at first, but becomes easy with practice.

Q6. How many marks is the Class 11 Maths paper?
The theory paper is 80 marks for 3 hours, plus 20 marks of internal assessment, making 100 marks in total.

Q7. Can I download these NCERT Solutions for Class 11 Maths in PDF?
Yes. All 14 chapters are available as free PDF downloads, chapter-wise and exercise-wise, so you can study offline.