NCERT Solutions for Class 11 Maths

The Class 11 Maths Solutions for NCERT have been drafted by some of the best subject experts at Vedantu. To make the process of referring to these solutions even more convenient for the students, we provide a free PDF of the same. You can choose to download the same from the official website and keep it handy. Additionally, you can also choose to resolve your doubts by attending live classes on the platform offered by some of the expert academicians across the country.

These solutions of NCERT Class 11 Maths have been provided in a systematic manner. The methodical arrangement of these solutions chapter-wise ensures that students can utilise their time judiciously. The step-by-step explanations provided in these solutions will allow students to grasp the concept behind each topic. To ensure smooth learning, the experts have destructured even the most complex problems in a logical manner. Also, all the Class 11 chapters’ solutions are 100% accurate and as per the NCERT (CBSE Board) guidelines and syllabus.

Scoring high in Mathematics is not a dream too unattainable with these NCERT Solutions. All the exercises of the Class 11 Maths textbook as per the latest syllabus have been extensively covered in these NCERT Class 11 Maths Solutions. These solutions will allow students to learn about the applicability of the various concepts in real life. Additionally, these will also benefit them in Class 12 and while preparing for various competitive examinations. With students solving complex problems, their approach towards solving questions in entrance examinations like JEE will also be polished. Students can also refer to the important questions of Class 11 Mathematics as they prepare for different exams.

Students can refer to the Class 11 Maths syllabus to know the chapters that they will be learning throughout the year. In Class 11 Maths, there are 16 chapters. Students may feel like the syllabus is too vast, as compared to Class 10. However, with Vedantu’s help, they can easily understand all the concepts as well as score high marks in their Maths exam. The details of all the chapters included in Maths Class 11 NCERT Solutions are provided below:

NCERT Solutions Maths Chapter 1 Class 11 Sets

A set is defined as the characterized accumulation of the various items. Sets are an integral part of modern-day Mathematics. The concepts in this chapter include different types of sets, various set operations and Venn diagrams. The concepts of relations and functions are characterised by using sets. Learning of sets also aids in the understanding of the concepts of sequences, probability, geometry and more. This chapter provides hypotheses to deal with sets consistently. Students need a good grasp of this chapter for the understanding of more complex concepts. Students can download the Class 11 Maths NCERT Solutions for Chapter 1 in both English and Hindi from Vedantu. 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 1 of CBSE Class 11 Maths Solutions –

• Chapter 1: Important Questions

• Chapter 1: Important Formulas

• Chapter 1: Revision Notes

• Chapter 1: NCERT Exemplar Solutions

• Chapter 1: RD Sharma Solutions

Maths NCERT Solutions Class 11 Chapter 2 Relations and Functions

An upgrade on Sets, Relations and Functions explores the idea of linking pairs of objects from two different sets and then deriving relations between the said objects of the pair. Certain relations qualify as functions, a crucial concept in Mathematics for its capturing of the idea of two quantities corresponding with each other and the correspondence is mathematically precise. All this and much more has been explained in a fun and creative way in this chapter. The concepts in Chapter 2 of NCERT Maths Book Class 11 Solutions PDF include an introduction, Cartesian product of sets, relations, domain and range of a relation, inverse of a relation and functions, domain and range of a function, rules for finding domain and range, kinds of functions, methods to check one-one mapping, some standard real functions and their graphs, algebra of real functions, and periodic function.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 2 of CBSE Class 11 Maths Solutions –

• Chapter 2: Important Questions

• Chapter 2: Important Formulas

• Chapter 2: Revision Notes

• Chapter 2: NCERT Exemplar Solutions

• Chapter 2: RD Sharma Solutions

Class 11 Maths NCERT Solutions Chapter 3 Trigonometric Functions

This chapter generalises the concepts of trigonometric ratios to trigonometric functions along with the study of their properties. Students get to explore the dynamic world of trigonometry as they attempt and solve the various numerical problems provided in this chapter.

Chapter 3 of Class 11 Maths NCERT Solutions begins with the meaning of trigonometry and continues with basic trigonometric identities, trigonometric ratios of standard angles, trigonometric ratios of allied angles, trigonometric functions of sum or difference of two angles, multiple angles and half angles, transformation of products into sum or difference of sines and cosines, factorisation of the sum or difference of two sines or cosines, important trigonometric ratios, conditional identities, range of trigonometric expression, sine and cosine series, graphs of trigonometric functions, trigonometric equations, general solution, and results.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 3 of CBSE Class 11 Maths Solutions –

• Chapter 3: Important Questions

• Chapter 3: Important Formulas

• Chapter 3: Revision Notes

• Chapter 3: NCERT Exemplar Solutions 

• Chapter 3: RD Sharma Solutions
  
  

NCERT Solutions Maths Class 11 Chapter 4 Principle of Mathematical Induction

With just one exercise, this chapter can prove to be quite interesting for students who have a knack for Mathematical induction. Be sure to familiarize yourself with the concepts as they are useful in higher studies as well. 

Chapter 4 of NCERT Maths Book Class 11 Solutions PDF includes the topics deduction, induction, steps of principle of mathematical induction, and examples for demonstration of these principles. On Vedantu, students will find the Class 11 Maths NCERT Solutions for Chapter 4 in both Hindi and English. 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 4 of CBSE Class 11 Maths Solutions –

• Chapter 4: Important Questions

• Chapter 4: Important Formulas

• Chapter 4: Revision Notes

• Chapter 4: NCERT Exemplar Solutions

• Chapter 4: RD Sharma Solutions

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

The framework of real numbers is stretched to complex numbers to accommodate the square root of negative numbers. The concept of complex numbers finds a profound use in higher Mathematics, so ensure that you are thorough with all the concepts included in the chapter. In Class 11 Maths Chapters, the fifth chapter is “Complex Numbers and Quadratic Equations”. This chapter includes topics like definition of complex numbers, conjugate of a complex number, algebra of complex numbers, argand plane, modulus and argument of complex number, polar form, De-Moivre’s theorem, cube root and square root of complex number, loci in complex plane, vectorial representation of a complex, quadratic expression, nature of roots and graphs, max and min value of quadratic expression, theory of equations, max and min values of rational expression, resolution into two linear factors, formation of a polynomial equation and transformation of equations.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 5 of CBSE Class 11 Maths Solutions –

• Chapter 5: Important Questions

• Chapter 5: Important Formulas

• Chapter 5: Revision Notes

• Chapter 5: NCERT Exemplar Solutions

• Chapter 5: RD Sharma Solutions

NCERT Solutions Maths Chapter 6 Class 11 Linear Inequalities

A very important chapter from an examination point of view, this chapter can also prove to be very interesting if you are thorough with all the concepts. Two quantities are more often unequal than equivalent. The concepts and exercises included in this chapter will open up your mind to how inequalities are a part of everyday life. In NCERT Maths Book Class 11 Solutions PDF, Chapter 6 is “Linear Inequalities”. The topics in this chapter are introduction to linear inequalities, examples of inequality in daily life, notations, types of inequalities, solution for linear inequality in one variable solution and solution set, rules of inequality, and graphical solution of linear inequalities in 2 variables. It also talks about linear inequalities in one variable, linear inequalities in two variables, and quadratic inequalities.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 6 of CBSE Class 11 Maths Solutions –

• Chapter 6: Important Questions

• Chapter 6: Revision Notes

• Chapter 6: NCERT Exemplar Solutions

• Chapter 6: RD Sharma Solutions

NCERT Class 11 Maths Solutions Chapter 7 Permutations and Combinations

Students in this chapter are introduced to the advanced concepts of permutation and combinations which are a crucial part of learning mathematics as their applications are found in many other fields as well. There are a total of 4 exercises in this chapter with 31 questions based on the concepts of Permutations and Combinations. Chapter 7 “Permutations and Combinations” of CBSE Class 11 Maths Solutions includes the concepts of fundamental principles of counting (fundamental principle of multiplication, fundamental principle of addition), basic arrangements and selections (permutations, combinations), geometric applications of nCr, permutations under certain conditions, division of objects into groups, division of objects into groups of equal sizes, permutations of alike objects, distribution of alike objects, number of integral solutions of linear equations and inequations, circular permutations, selection of one or more objects, number of divisors and the sum of the divisors of a given natural number, and rearrangements.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 7 of CBSE Class 11 Maths Solutions –

• Chapter 7: Important Questions

• Chapter 7: Important Formulas

• Chapter 7: Revision Notes

• Chapter 7: NCERT Exemplar Solutions

• Chapter 7: RD Sharma Solutions

NCERT Solutions Chapter 8 Class 11 Binomial Theorem

Persian Mathematician Omar Khayyam, in the 11th century, provided the general formula for (a + b)n, where n is a positive whole number. This equation or its expansion has been provided in this chapter Binomial hypothesis. Chapter 8 of Class 11 Maths NCERT Solutions is “Binomial Theorem”. In the earlier days, computations were difficult for higher powers like 93⁸ or 305⁴. To solve this, the binomial theorem was used. This theorem simplifies the expression of (a + b)n, where n is an integer or a rational number. This chapter talks about the binomial theorem, remarks, binomial theorem for positive integral indices, pascal’s triangle, general term and middle terms in expansion of (a + b)n, middle term, binomial theorem for any index, binomial coefficients, properties of binomial coefficient, some important results, and multinomial expansion.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 8 of CBSE Class 11 Maths Solutions –

• Chapter 8: Important Questions

• Chapter 8: Important Formulas

• Chapter 8: Revision Notes

• Chapter 8: NCERT Exemplar Solutions

• Chapter 8: RD Sharma Solutions

NCERT Solutions Class 11 Maths Chapter 9 Sequences and Series

The topics of Geometric Progression, Arithmetic Progression, General Term of a G.P, Sum to n terms of a G.P etc., are included in the chapter Sequence and Series. This chapter carries a high weightage in the exam. So make sure to practise all the exercises included. The eighth chapter begins with the definition of sequence, real sequence, series, and progression. It continues with the topics arithmetic progression, properties of an arithmetic progression, geometric progression, properties of a geometric progression, means, arithmetic mean, arithmetic means between two numbers, geometric mean, geometric means between two numbers, arithmetic, geometric and harmonic means between two numbers, sigma notations, theorems, sum of n terms of some special sequences (sum of first n natural numbers, sum of squares of first n natural numbers, sum of cubes of first n natural numbers), arithmetic-geometric series, sum of n terms of an arithmetic-geometric series, sum to infinity, harmonic progression, and harmonic mean. This chapter has several formulas that students need to memorize to easily solve problems that are asked from this chapter in the Class 11 Maths. 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 9 of CBSE Class 11 Maths Solutions –

• Chapter 9: Important Questions

• Chapter 9: Revision Notes

• Chapter 9: NCERT Exemplar Solutions

• Chapter 9: RD Sharma Solutions

Class 11 Maths Chapter 10 NCERT Solutions Straight Lines

In this chapter, you will study some important topics like the Slope of a line, the angle between two lines, Collinearity between two points, horizontal and vertical lines and much more. Make sure you practise sums from all the three exercises included in this chapter. Chapter 10 of CBSE Class 11 Maths Solutions includes the topics distance formula, section formula, centroid, incentre, excentre, area of triangle, slope formula, condition of collinearity of three points, equation of a straight line in various forms, position of the point x1y1 relative to the line ax+by+c=0, ratio in which a given line divides the line segment joining two points, length of perpendicular from a point on a line, reflection of a point about a line, angle between two straight lines in terms of their slopes, parallel lines, perpendicular lines, straight lines making angle a with given line, bisector of the angles between two lines, methods to discriminate between the acute bisector and the obtuse angle bisector, to discriminate between the bisector of the angle containing a point, condition of concurrency, family of straight lines, a pair of straight lines through origin, and general equation of second degree representing a pair of straight lines. 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 10 of CBSE Class 11 Maths Solutions –

• Chapter 10: Important Questions

• Chapter 10: Important Formulas

• Chapter 10: Revision Notes

• Chapter 10: NCERT Exemplar Solutions

• Chapter 10: RD Sharma Solutions

NCERT Solutions Class 11 Maths Chapter 11 Conic Sections

Conics include curves such as circles, ovals under its broad aegis while parabolas and hyperbolas are referred to as conic segments. In addition to adding to your knowledge about the various geometric figures, you will also get to learn about their significance and application on the x, y and z axes. The topics in Chapter 11 of Class 11 Maths NCERT Solutions are conic sections, section of right circular cone by different planes, general equation of a conic: focal directrix property, distinguishing various conics, definition and terminology of parabola (focal distance, focal chord, double ordinate, latus rectum), position of a point relative to a parabola, line & a parabola, parametric representation, tangents to the parabola y² = 4ax, normal to the parabola y² = 4ax, pair of tangents, director circle, chord of contact, chord with a given middle point, standard equation and definitions (eccentricity, foci, equations of directrices, major axis, minor axis, principal axis, vertices, focal chord, double ordinate, latus rectum, centre), auxiliary circle/eccentric angle, parametric representation, position of a point with respect to an ellipse, line and an ellipse, tangents, normal, director circle, standard equation and definition of hyperbola (eccentricity, foci, equations of directrix, transverse axis, conjugate axis, principal axis, vertices, focal chord, double ordinate, latus rectum), rectangular or equilateral hyperbola, conjugate hyperbola, auxiliary circle, parametric representation, position of a point ‘P’ with respect to a hyperbola, line and a hyperbola, tangents (slope form, point form, parametric form), normal, director circle, rectangular hyperbola, equation of a circle in various forms, intercepts made by a circle on the axes, parametric equations of a circle, position of a point with respect to a circle, line and a circle, tangent, family of circles, normal, pair of tangents from a point, length of a tangent and power of a point, director circle, chord of contact, equation of the chord with a given middle point, equation of the chord joining two points of circle, common tangents to two circles, orthogonality of two circles, radical axis and radical centre.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 11 of CBSE Class 11 Maths Solutions –

• Chapter 11: Important Questions

• Chapter 11: Revision Notes

• Chapter 11: NCERT Exemplar Solutions

NCERT Solutions Maths Chapter 12 Class 11 Introduction to Three Dimensional Geometry

Conic sections pave the way for 3D geometry as we learn about the applications of the conical segments here as well.  Coordinate geometry has been extensively dealt with in this chapter and students also get to practise from the three exercises. This chapter talks about coordinate axes, coordinate planes, coordinates of a point in space, distance between two points, and section formula. It also talks about the coordinate system in three-dimensional geometry, rectangular coordinate system, direction ratios of a line and direction cosine, the relation between the direction cosines of a line, direction cosines of a line passing through two points and some fun facts about three-dimensional space. 

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 12 of CBSE Class 11 Maths Solutions –

• Chapter 12: Important Questions

• Chapter 12: Important Formulas

• Chapter 12: Revision Notes

• Chapter 12: NCERT Exemplar Solutions

• Chapter 12: RD Sharma Solutions

NCERT Solutions Class 11 Maths Chapter 13 Limits and Derivatives

Calculus, a very important concept of Mathematics, associated with the study of change in the value of a function with the change of points in the domain is explained in this chapter. Students, through this chapter, are introduced to the vast world of calculus, which finds a host of applications across various fields. As the name suggests, Chapter 13 of Class 11 Maths talks about limits, algebra of limits, limits of polynomials and rational functions, limits of trigonometric functions, derivatives, standard limits and derivatives. There are several important theorems in this chapter, that students need to learn and understand to do well in their Class 11 Maths exam.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 13 of CBSE Class 11 Maths Solutions –

• Chapter 13: Important Questions

• Chapter 13: Important Formulas

• Chapter 13: Revision Notes

• Chapter 13: NCERT Exemplar Solutions

• Chapter 13: RD Sharma Solutions

Class 11 Maths Chapter 14 NCERT Solutions Mathematical Reasoning

This chapter mostly deals with deductive reasoning and students find it to be very engaging as they are required to deduce solutions to problems on the basis of scenarios provided. In this chapter, the basics of mathematical reasoning, logic, statement (proposition), open and compound statement, elementary operation of logic, disjunction, negation, conditional sentence (implication), biconditional sentence (bi-implication), table for basic logical connections, truth value and truth table, tautology and contradiction, quantifiers and quantified statements, implications, contrapositive and converse, validating statements, and by contradiction are the topics included.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 14 of CBSE Class 11 Maths Solutions –

• Chapter 14: Important Questions

• Chapter 14: Important Formulas

• Chapter 14: Revision Notes

• Chapter 14: NCERT Exemplar Solutions

• Chapter 14: RD Sharma Solutions

Class 11 Maths Chapter 15 NCERT Solutions Statistics

Statistics is an integral component of higher mathematics. Topics such as range, mean deviation, Measures of dispersion, Standard deviation, Mean deviation for ungrouped data, etc., are dealt with in detail in this chapter. In this chapter, terminologies like statistics, limit of the class, class interval, primary and secondary data, variable or variate, frequency, discrete frequency distribution, continuous frequency distribution, and cumulative frequency distribution are explained. Topics such as graphical representation of frequency distribution (histogram, bar diagram, pie diagrams, frequency polygon, cumulative frequency curve/ogive), measures of central tendency (arithmetic mean – for unclassified data, frequency distribution, classified data, combined mean, weighted arithmetic mean, properties of arithmetic mean; geometric mean; harmonic mean), median (for simple distribution, unclassified frequency distribution, classified data), quartiles, mode (for raw data, classified distribution, classified data), relation between mean, median and mode, symmetrical and skew distribution, measures of dispersion (range, mean deviation, standard deviation, variance), and analysis of frequency distributions are also explained in detail in this chapter.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 15 of CBSE Class 11 Maths Solutions –

• Chapter 15: Important Questions

• Chapter 15: Important Formulas

• Chapter 15: Revision Notes

• Chapter 15: NCERT Exemplar Solutions

• Chapter 15: RD Sharma Solutions

NCERT Solutions Class 11 Maths Chapter 16 Probability

Probability is computing the level of the conviction of occasions under perfect conditions. A much-used concept in various spheres of life, students should make sure they understand the underlying core concerts and the applications in order to attempt a maximum number of questions from this chapter. This chapter starts with probability, approach to probability, random experiments, event, types of event, impossible and sure events, simple event, compound event, algebra of events, complementary event, event (A or B), Event “A and B”, Event “A but not B”, mutually exclusive events, exhaustive events, axiomatic approach to probability, probabilities of equally likely outcomes, probability of the event “A or B”, probability of the event “A and B”, and the probability of the event “Not A”.

Along with this, students can also download additional study materials provided by Vedantu, for Chapter 16 of CBSE Class 11 Maths Solutions –

• Chapter 16: Important Questions

• Chapter 16: Important Formulas

• Chapter 16: Revision Notes

• Chapter 16: NCERT Exemplar Solutions

• Chapter 16: RD Sharma Solutions

NCERT Solutions are a preferred study resource among students and with Vedantu you can download the same for absolutely zero cost. Keep your required study materials handy and prepare well for your exams.

Class 11 Maths Solutions for Students

What makes the NCERT class 11 Maths solutions worth downloading and use for learning purposes is the way it is being drafted. Subject experts of Vedantu have drafted every chapter of the Maths subject according to guidelines set by the CBSE board. So if students and parents are thinking that these solutions won't help then they need to check it out.

The best part is the free download of the PDF format of the solution. Students don't have to pay a penny for the solution. Each chapter is freely available and can be downloaded with a single click.

Chapter-wise Weightage of Marks Class 11 Maths

The chapter-wise weightage of marks for Class 11 Maths is as follows –

From this, we can see that the unit Sets and Functions has the highest weightage in terms of marks, and the lowest weightage is of the unit Mathematical Reasoning. Students should prepare for their exam on the basis of the weightage of marks of the units and pay more attention to units with more weightage as it is more likely that questions would be asked from these units in the exam.

Marking Scheme for Class 11 Maths First Term 

Marking Scheme for Class 11 Maths Second Term

They can also download the Class 11 Maths sample papers provided by Vedantu, as these papers can help them get an idea about the exam format. They can also learn to manage their time and identify their strong and weak areas and work on them accordingly.

Solution for Future Reference

One of the benefits of downloading NCERT solutions for class 11 maths is they can be used for future reference. The class 11 Maths subjects carry chapters that are essential in preparing for engineering entrance exams. So once you download the PDF format, you can save it and use it for future reference. Therefore, students can exercise each chapter on a regular basis for scoring better marks. In other words, these solutions provide proper guidance and a proper learning experience.

Covering All Chapters in One Solution

The NCERT solutions for class 11 maths cover all 16 chapters in one set. You can either download all the sets at once or different chapters. Chapters covered are- Relations & Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, and others. Subject experts have explained every chapter in clear language to make students understand.

Help in Exam Preparation

These solutions for class 11 Maths are systematic. Moreover, it helps in time management for the final exam. The step-by-step explanations will allow students to grasp the concept behind each topic. Since each chapter contains questions, students can practice the same for the exam. The ultimate aim is to score high in the exam.

Key Benefits of NCERT Solutions Class 11 Maths

• Students can learn the NCERT solution class 11 Maths within their comfort zone. Once downloaded, they can prepare as per the timeline on desktop and mobile. Since it is available for free, students can further relax.

• Students can customize their learning experience by completing each topic at their own pace.

• Not just Maths, but students can opt for other subject solutions in PDF format and do the learning.

• Students can understand all the concepts from the 16 chapters of Class 11 Maths easily, with the help of Vedantu’s Class 11 Maths NCERT Solutions. The solutions are designed in a simple, straightforward language and all the solutions are given step by step, for the ease of students.

• The NCERT Solutions help students prepare for their Class 11 Maths exam quicker, as whenever they get stuck at any question, they can simply refer to the solutions, understand the answer and move to the next question.

All the chapters and their concepts are explained in detailed format, so students don't get confused. Since maths is a complex subject, students have the freedom to practice at their own pace and prepare for future exams.

Vedantu Gives You Competitive Edge

Vedantu’s NCERT Solutions for Class 11 Maths and other subjects’ experts familiarize the students with these topics so that the speed of learning is improved drastically. Thus, it helps in efficient time management skills for better results in the exams. You get to practice all the exercise questions and improve your mathematical skills. Register for our free webinar class with the best Mathematics tutor in India. Also, the Vedantu Learning App will benefit you by providing access to free live masterclasses and free conceptual videos. You will also have access to all the PDFs of study materials and solutions. Additionally, you will be provided absolutely FREE Online Tests. You will have all the required standard study materials handy and this will make the process of learning easier for you.