# NCERT Solutions for Class 11 Maths

NCERT solutions for class 11 maths comprise a step-wise and detailed description of all the questions covered by the NCERT book on topics such as set theory, calculus, geometry, etc. They act as a guide to students who want to cross-check their results to questions as well as to kids who want a better understanding of concepts. These NCERT solutions class 11 maths are prepared by certified math experts who ensure that the matter is presented at a gradually increasing level of difficulty thus, enabling kids to build a strong foundation.

NCERT solutions for class 11 maths are extremely helpful for students preparing for the home exams such as units, half yearlies, and finals. As the subject matter of class 11th and 12th are closely interlinked it helps students to indirectly start their preparation for class 12th. CBSE class 11 maths NCERT solutions can also be very helpful for competitive exams such as IIT-JEE, BITS PILANI, etc.

## NCERT Solutions Class 11 Maths PDF Download

The NCERT solutions class 11 maths are crafted for kids to promote the development of their cognitive and logical skills. All the NCERT solutions are available for free pdf download and are very easy to use. The solutions given below have been arranged chapter-wise and can be referred to when attempting problems of a particular topic.

### Class 11 Maths NCERT Solutions Chapter 1 to 16

The knowledge that you gain from class 11th is especially important as it is put directly to use in class 12th also. Thus, periodically revisiting these solutions for revision of topics and extra practice is crucial. Download the class 11 NCERT textbook given below to develop in-depth mathematical knowledge.

ā Download Class 11 Maths NCERT Book

## NCERT Solutions Class 11 Maths Chapter 1 - Sets

NCERT solutions for class 11 maths sets teach students meticulously about set theory and how to create sets. This chapter also includes the various types of sets, subsets, Venn diagrams, and their analysis, as well as complements of sets.

### Important Formulas in NCERT Solutions Class 11 Maths Chapter 1

- (A ∪ B)′ = A′ ∩ B′
- ( A ∩ B )′ = A′ ∪ B′
- n (A ∪ B) = n (A) + n (B)
- If A ∩ B ≠ φ, then n (A ∪ B) = n (A) + n (B) – n (A ∩ B)

where A and B are sets

### Class 11 Maths Chapter 1 Sets

**Topics Covered:** Class 11 Maths NCERT Solutions cover topics such as writing numbers in the form of sets, verifying empty, finite, infinite, equal sets, identifying subsets, performing various operations on sets, and finding complements of sets.

**Total Questions:** Class 11 maths chapter 1 Sets has 64 questions in total out of which 18 are easy, 37 are medium and 9 are tough problems.

## NCERT Solutions Class 11 Maths Chapter 2 - Relations and Functions

NCERT solutions for class 11 maths relations and functions describe the meaning of a relation and a function. This involves a study of the graphs of a function along with performing various algebraic operations on them.

Class 11 Maths NCERT Solutions Chapter 2 Exercise PDFs |
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### Class 11 Maths Chapter 2 Relations and Functions

**Topics Covered:** Stating if a relation is a function, identifying different types of functions, adding, subtracting, multiplying functions, and finding the range of these functions are topics covered under Class 11 Maths NCERT Solutions.

**Total Questions:** Class 11 maths chapter 2 relations and functions have 36 questions. 9 are moderately complicated, 15 are easy and 12 are tough sums.

### NCERT Solutions Class 11 Maths Chapter 2 Summary

NCERT solutions for class 11 maths chapter 2 gives kids an understanding of the various terms related to functions and relations such as domain, image, range, as well as teaches children certain concepts enabling them to execute algebraic operations on functions.

## NCERT Solutions Class 11 Maths Chapter 3 -Trigonometric Functions

NCERT solutions for class 11 maths trigonometric functions is an important topic as it is required for higher studies. This chapter deals with the domain and range of trigonometric functions, the sum and difference of two angles within trigonometric functions, as well as the application of trigonometric identities.

### Important Formulas in NCERT Solutions Class 11 Maths Chapter 3

- cos (x – y) = cos x cos y + sin x sin y
- cos ( π/2 − x ) = sin x
- cos (2π – x) = cos x
- sin (x – y) = sin x cos y – cos x sin y
- sin (– x) = – sin x
- 1 + cot
^{2}x = cosec^{2 }x - cos
^{2 }x + sin^{2 }x = 1

### Class 11 Maths Chapter 3 Trigonometric Functions

**Topics Covered:** Finding the values of all trigonometric functions if one is given, proving if an expression is true or not based on trigonometric identities, as well as identifying the principal and general solutions of trigonometric functions are essential topics that are explained in detail in the Class 11 Maths NCERT Solutions.

**Total Questions:** There are 61 questions in total in the Class 11 maths chapter 3 trigonometric functions. 21 are easy identity-based sums, 12 are of an intermediate level and 28 are tough ones that require a student to apply his critical thinking skills.

## NCERT Solutions Class 11 Maths Chapter 4 - Principle of Mathematical Induction

NCERT solutions for class 11 maths principle of mathematical induction gives a step-wise explanation on how to prove a certain statement for k + 1 iterations if it stands true for 1 number. It is a short yet important lesson.

Class 11 Maths NCERT Solutions Chapter 4 Exercise PDFs |
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### Class 11 Maths Chapter 4 Principle of Mathematical Induction

**Topics Covered:** Class 11 Maths NCERT Solutions consist of questions that require students to use formulas to prove that a statement is true for all numbers if it satisfies the condition imposed on the number 1.

**Total Questions:** Class 11 maths chapter 4 principle of mathematical induction has 24 problems. 5 are simple, 13 are slightly tougher and 6 are difficult sums.

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

NCERT solutions for class 11 maths complex numbers and quadratic equations educate students on the relationship between complex numbers and quadratic equations. They learn about performing various arithmetic operations on complex numbers, and how to express complex numbers in the polar form as well as the methods for solving quadratic equations that involve complex numbers.

Class 11 Maths NCERT Solutions Chapter 5 Exercise PDFs |
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### Important Formulas in NCERT Solutions Class 11 Maths Chapter 5

- z
_{ 1}+ z_{ 2}= (a + c) + i (b + d) where z_{1}= a + ib, z_{2}= c + id - z
_{ 1}z_{ 2}= (ac – bd) + i (ad + bc) - Polar form of a complex number (z = x + iy) is r (cosθ + i sinθ) where r = √(x
^{2}+ y^{2})

### Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

**Topics Covered:** Finding the modulus and conjugate of a complex number, representing a complex number in the polar form on the argand plane, solving a quadratic equation, and analyzing the discriminant of a quadratic equation are topics falling under Class 11 Maths NCERT Solutions.

**Total Questions:** There are 42 sums in Class 11 maths chapter 5 complex numbers and quadratic equations. 14 are simple questions based on formulas, 17 are complex and 11 are of an intermediate level.

## NCERT Solutions Class 11 Maths Chapter 6 - Linear Inequalities

NCERT solutions for class 11 maths linear inequalities shed light on the graphical meaning of the algebraic solutions to linear equations in one and two variables. Students can build their visualization skills with the help of the solutions to this chapter.

Class 11 Maths NCERT Solutions Chapter 6 Exercise PDFs |
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### Class 11 Maths Chapter 6 Linear Inequalities

**Topics Covered:** Solving linear inequalities, finding the graphical solution to linear equations in two variables, and interpreting word problems so as to translate them to mathematical equations are encompassed under Class 11 Maths NCERT Solutions.

**Total Questions:** Class 11 maths chapter 6 linear inequalities have a pool of 65 questions. 15 are difficult word problems, 26 are medium level and 24 are simple interpretational sums.

### NCERT Solutions Class 11 Maths Chapter 6 Summary

The NCERT solutions class 11 maths chapter 6 helps students to correctly interpret the meaning of a linear equation as well as apply them to real-life problems. This enables them to derive reasonable conclusions and solve similar issues that involve the use of linear equations with efficiency.

## NCERT Solutions Class 11 Maths Chapter 7 - Permutations and Combinations

NCERT solutions for class 11 maths permutations and combinations introduce students to the fundamental principle of counting. This chapter teaches them how to differentiate between permutations and combinations while dealing with several practical applications of the topic.

### Important Formulas in NCERT Solutions Class 11 Maths Chapter 7

^{n}P_{r}= n! / (n - r)!^{n}C_{r}= n! / r! (n - r)!

where n is the number of things taken r at a time

### Class 11 Maths Chapter 7 Permutations and Combinations

**Topics Covered:** Solving placement word problems based on the formulas of permutations and combinations are the topics broadly covered in Class 11 Maths NCERT Solutions. This includes permutations and combinations with non-distinct or distinct objects.

**Total Questions:** Class 11 maths chapter 7 permutations and combinations has 45 exemplar sums out of which 12 are easily solvable, 19 are moderate and 14 are difficult problems that require logical thinking.

## NCERT Solutions Class 11 Maths Chapter 8 - Binomial Theorem

NCERT solutions for class 11 maths binomial theorem is a concept that is required to solve and simplify several questions related to not only the aforementioned chapter but also sister topics such as probability. Thus, kids need to be well-versed with the binomial theorem and how to expand expressions using this formula.

Class 11 Maths NCERT Solutions Chapter 8 Exercise PDFs |
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### Class 11 Maths Chapter 8 Binomial Theorem

**Topics Covered:** Expanding expressions using the binomial theorem, finding a particular term, as well as pinpointing the middle term in an exponentiated expression, are topics in the Class 11 Maths NCERT Solutions.

**Total Questions:** Class 11 maths chapter 8 binomial theorem includes 36 well-researched questions that are split into 14 easy, 6 medium and 16 difficult sums.

## NCERT Solutions Class 11 Maths Chapter 9 - Sequences and Series

NCERT solutions for class 11 maths sequences and series give kids an insight into arithmetic and geometric progressions as well as how they are related to one another. This lesson also details a step-by-step explanation of how to work with special series.

### Important Formulas in NCERT Solutions Class 11 Maths Chapter 9

- General term of an A.P: a
_{n}= a + (n – 1) d. - General term of a G.P: a
_{n}= ar^{n – 1}. - Sum of n terms in an A.P: S
_{n}= n/2 [2a + (n-1)d]. - Sum of n terms in a G.P: S
_{n}= a (1 - r^{n})/ 1 - r

### Class 11 Maths Chapter 9 Sequences and Series

**Topics Covered:** Writing the terms of a given sequence, finding the sum of n terms in arithmetic and geometric progressions, using the general term to solve problems, verifying the relationship between A.P and G.P along with special series are the essential topics covered in the Class 11 Maths NCERT Solutions.

**Total Questions:** Class 11 maths chapter 9 Sequences and series has 106 questions which can be divided into 38 formula-based simple sums, 23 of moderate complexity, and 45 higher-order thinking problems.

## NCERT Solutions Class 11 Maths Chapter 10 - Straight Lines

NCERT solutions for class 11 maths straight lines elucidates certain key geometrical concepts related to a line. These involve teaching kids about the slope of a line, the angle between two lines, collinearity of three points, the distance between two lines, along all the different forms of the equation of a line.

Class 11 Maths NCERT Solutions Chapter 10 Exercise PDFs |
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### NCERT Solutions Class 11 Maths Chapter 10 Study Tips

NCERT solutions class 11 maths chapter 10 is an easy lesson however, it can get confusing due to the large number of formulas that kids need to learn. The following study tips can help with the learning process.

- Understanding the derivation and concept behind the formulas.
- Constant practice and solving numerous problems on the same.

### Class 11 Maths Chapter 10 Straight Lines

**Topics Covered:** Finding the slope of a line when the coordinates of two points are given, determining the parallelism and perpendicularity of lines is included in the Class 11 Maths NCERT Solutions. Additionally, the point-slope form of the equation of a line, its two-point, slope-intercept, normal form as well as the general equation of a line are also essential parts of this chapter.

**Total Questions:** Class 11 maths chapter 10 straight lines has 76 fantastic problems that can be subdivided into 25 straightforward questions, 17 complicated and 34 moderately tough sums.

## NCERT Solutions Class 11 Maths Chapter 11 - Conic Sections

NCERT solutions for class 11 maths conic sections take a deeper look at several figures such as a cone, circle, hyperbola, and parabola as well as the various aspects associated with it. Kids learn about the different elements of these figures and how to accurately determine their measures.

### Important Formulas in NCERT Solutions Class 11 Maths Chapter 11

- Equation of a Circle with center (h, k): (x – h)
^{ 2}+ (y – k)^{ 2}= r^{ 2} - Equation of a Parabola: y
^{ 2}= 4ax - Equation of an Ellipse: x
^{2}/a^{2}+ y^{2}/b^{2}= 1 - Equation of a Hyperbola: x
^{2}/a^{2}- y^{2}/b^{2}= 1

### Class 11 Maths Chapter 11 Conic Sections

**Topics Covered:** Class 11 Maths NCERT Solutions encapsulate topics such as finding the equation of a circle and a hyperbola given certain constraints, determining the focus, axis, and equation of a parabola, using the standard equation of an ellipse to determine the focus as well as the length of the major and minor axes.

**Total Questions:** The total number of questions in class 11 maths chapter 11 conic sections is 70. 21 out of these are difficult problems while 30 are easy and 19 are of a medium level.

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

NCERT solutions for class 11 maths introduction to three-dimensional geometry helps children get a grasp on geometrical concepts such as the distance formula, and the section formula. It helps students get a good understanding of how to apply these formulas to effectively solve problems.

Class 11 Maths NCERT Solutions Chapter 12 Exercise PDFs |
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### Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

**Topics Covered:** Class 11 Maths NCERT Solutions has questions based on important topics such as finding the distance between two points and using the section formula to divide a line segment in a given ratio.

**Total Questions:** Class 11 maths chapter 12 introduction to three-dimensional geometry has 20 sums. 7 are formula-based easy problems, 8 are tough requiring kids to use their mathematical skills and 5 are intermediate.

## NCERT Solutions Class 11 Maths Chapter 13 - Limits and Derivatives

NCERT solutions for class 11 maths limits and derivatives provide students with an understanding of how derivatives and limits are related to each other. Children first learn about limits and the methods to solve them followed by finding the derivative of a function using limits.

Class 11 Maths NCERT Solutions Chapter 13 Exercise PDFs |
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### Class 11 Maths Chapter 13 Limits and Derivatives

**Topics Covered:** Class 11 Maths NCERT Solutions incorporates topics such as finding the limit of a function at a point, algebra of limits, limits of trigonometric functions, using the limit formula to find the derivative of a function, and algebra of derivatives.

**Total Questions:** Class 11 maths chapter 13 limits and derivatives has 73 questions. 16 are of moderate complexity, 28 are fairly simple formula-based sums and 29 are demanding problems.

### NCERT Solutions Class 11 Maths Chapter 13 Summary

NCERT solutions class 11 maths chapter 13 gives a bird’s eye view of the relationship between derivatives and limits as well as how to use limits in order to find the first derivative of different functions.

## NCERT Solutions Class 11 Maths Chapter 14 - Mathematical Reasoning

NCERT solutions for class 11 maths mathematical reasoning help kids in harnessing and enhancing their reasoning skills. This lesson calls for students to read sentences and draw logical inferences from them.

### Class 11 Maths Chapter 14 Mathematical Reasoning

**Topics Covered:** Class 11 Maths NCERT Solutions explain in detail topics such as compound statements, the negation, and implication of statements, how to validate statements as well as contrapositive and converse statements.

**Total Questions:** There are 25 problems in the Class 11 maths chapter 14 mathematical reasoning. 17 are very simple, 3 are of medium level and 5 are challenging questions.

## NCERT Solutions Class 11 Maths Chapter 15 - Statistics

NCERT solutions for class 11 maths statistics detail the techniques to solve various statistical problems that center around the measures of dispersion, standard deviation, variance, frequency distribution table, and continuous or discrete frequency table.

Class 11 Maths NCERT Solutions Chapter 15 Exercise PDFs |
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### NCERT Solutions Class 11 Maths Chapter 15 Study Tips

NCERT solutions class 1 maths chapter 15 is very important from an examination point of view. The following tips can help streamline the studying process for students.

- Revise Statistics from previous classes.
- Understand and learn the formulas.
- Practice all questions.

### Class 11 Maths Chapter 15 Statistics

**Topics Covered:** Finding the range, mean deviation, and mean of grouped as well as ungrouped data fall under the scope of the Class 11 Maths NCERT Solutions. Apart from this other topics included are the discrete and continuous frequency table along with subtopics such as standard deviation, variance, mean deviation about the median, and analysis of the frequency distribution table.

**Total Questions:** Class 11 maths chapter 15 statistics has 34 questions in total. 14 are easy sums that can be solved using the formulas, 15 are intermediate and 5 are complicated higher-order thinking problems.

## NCERT Solutions Class 11 Maths Chapter 16 - Probability

NCERT solutions for class 11 maths probability builds on previous classes and introduces kids to probability elements such as random experiments, outcomes, sample space, different types of events, and other associated concepts that form the backbone of this chapter.

Class 11 Maths NCERT Solutions Chapter 16 Exercise PDFs |
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### Class 11 Maths Chapter 16 Probability

**Topics Covered:** Class 11 Maths NCERT Solutions gives kids a detailed elucidation of topics such as types of events, algebra of those events, complementary events, exhaustive events, axiomatic approach to probability, and probability of occurrence of an event.

**Total Questions:** There are 54 well-structured questions in the Class 11 maths chapter 16 probability. Out of these 21 are straightforward questions, 19 are complex, and 14 need focus as they are challenging.

## Important Formulas in NCERT Solutions Class 11 Maths

Formulas cover several expressions, axioms, and theorems that were constructed using some logical rules. They are used to describe a general relationship between two or more quantities. Thus, to attempt questions efficiently kids need to learn them. An overview of the important formulas covered in NCERT solutions for class 11 maths is given below:

**Coordinate Geometry**

- Distance Formula = √[(x
_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2}] - Slope Intercept: y = mx + c
- Parallel lines slopes: m
_{1}= m_{2}

**Algebra**

- Distributive property: p * (q + r) = pq + pr
- Commutative property: p + q = q + p
- Additive Inverse: p + (-p) = 0

**Trigonometry**

- (sinx)(siny) = ½ [cos(x-y) - cos(x+y)]
- (cosx)(cosy) = ½ [cos(x-y) + cos(x+y)]

## Importance of NCERT Solutions Class 11 Maths

Class 11 Maths NCERT Solutions are extremely helpful for CBSE students because it helps to build a robust foundation for all mathematical topics covered in 11th grade. Given below are a few of the advantages of the NCERT solutions:

**Exam Preparation**- Students belonging to class 11 have to prepare for their home exams and competitive exams (IIT-JEE, BITS PILANI, etc.). NCERT solutions provide a step-wise implementation of all solutions that help kids understand how to write an exam so that they can get the best score possible. It also outlines the tips and tricks required to solve complex problems within seconds that are very useful for competitive exams.**Crystal Clear Concepts**- As the subject matter of classes 11 and 12 are closely related hence, kids need to ensure that they have no doubts so that they can successfully clear both the grades. The NCERT Class 11 Maths Solutions gives a brief and precise explanation of all questions enabling children to develop an in-depth knowledge of all topics.**Revision**- The NCERT solutions give students an opportunity to revise their entire syllabus quickly and efficiently. As children do not have enough time to solve all questions during examination days, they can go through these solutions and recall all the important concepts, theorems, and formulas necessary to attempt similar types of questions. Thus, during the exam, they are confident and do not feel flustered.

## FAQs on NCERT Solutions for Class 11 Maths

### Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths?

The questions provided in the NCERT solutions class 11 maths have been curated by experts to give students a holistic learning experience. Thus, it is necessary for students to practice all problems step-by-step so as to develop a strong mathematical foundation.

### Why are NCERT Solutions Class 11 Maths Important?

In order to succeed in examinations, kids need a reliable source of information that can act as a guide. The NCERT solutions class 11 maths work to give students the best quality of knowledge that can be used to get a very good score thus, they are extremely important for kids.

### Do I Need to Make Notes while Referring to NCERT Solutions Class 11 Maths?

Notes are the best way to recall certain pointers regarding any questions. In addition to this, they speed up the revision process during examination days. Hence, all students are advised to make notes while studying the NCERT solutions class 11 maths.

### What are the Best Ways to Learn Concepts Covered in NCERT Solutions Class 11th Maths?

Understanding a topic and practicing questions on it regularly are the best ways to learn the concepts covered in NCERT solutions class 11th maths. Students can get the most out of these solutions by regularly revising the subject matter ensuring that they get good marks in their examinations.

### How are NCERT Solutions Class 11 Maths Promoting Problem Solving in Students?

NCERT solutions class 11 maths employ the technique of breaking problems down into smaller packets to simplify analysis. As students start getting an idea of how to solve sums using these methods they can inevitably sharpen their problem-solving skills.

### What are the Important Topics Covered in NCERT Solutions Class 11 Maths?

All topics covered in NCERT solutions class 11 maths are important as they are interlinked with the syllabus of class 12th. These topics not only make their way in the class 11 test papers but are also required to successfully attempt the class 12 board exams. Thus, students should not skip any chapter while studying.

### Can We Use Different Methods to Solve Problems Apart From Those Mentioned in NCERT Solutions Class 11 Maths?

As long as the method is universally recognized, the steps are constructed logically and the answer is correct a student can use any method apart from those in the NCERT solutions class 11 Maths. However, shortcuts cannot be utilized and all the problems have to be attempted with a step-wise solution.

### How Many Chapters are there in Class 11 Maths NCERT Solutions?

There are a total of 16 chapters in the class 11 maths NCERT solutions that have been designed to give students a deep-seated knowledge of topics such as calculus, trigonometry, probability, statistics, etc. Kids can study these solutions and master the chapters in no time.

### Why Choose Cuemath for Class 11 Maths NCERT Solutions?

Cuemath is the best online educational platform for class 11 maths NCERT solutions. The explanations of questions and the methods used to solve them have been carefully thought out by mathematical experts from IITs. The solutions are short, accurate, and easy to understanding ensuring that kids get the maximum benefit from them.

### Why Should I Practice NCERT Solutions Class 11 Maths Regularly?

Practice yields perfection. If students revise the NCERT solutions class 11 maths regularly they will be well-prepared for any examination, be it school or competitive. During the test kids can breeze through the question paper without feeling stressed thus, improving their chances of giving a triumphant exam.

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