# NCERT Solutions For Class 11 Maths

## NCERT Solutions for Class 11 Maths – Download Chapter wise PDF

NCERT Solutions for Class 11 Maths provided here have been put together by our subject experts. The solutions have been mainly crafted to simplify all Class 11 Math problems, which are given in the textbooks prescribed in CBSE syllabus (2021-2022). These NCERT Solutions of Class 11 Maths are organized systematically and cover all the 16 chapters included in the syllabus. Therefore, the NCERT Class 11 Maths Solutions offer comprehensive learning and also help students to develop better math skills along with logical and reasoning skills. The difficult problems have been simplified and explained here in these solutions to make learning much more comfortable.

NCERT Solutions of Maths is an essential resource for students preparing for Class 11 Maths exam. NCERT Solutions for Class 11 can clear all your doubts with the help of materials like, sample solved questions, shortcut tips, summary, notes, etc.

In most of the competitive engineering exams or common entrance tests conducted for admissions in Engineering institutes, the questions are designed as per the syllabus of textbooks. Therefore, the students are advised to practice these NCERT Solutions for Class 11 Maths exercises worksheets on a regular basis to score better marks in exams. Also, students are suggested to solve the exemplar problems and solutions available with us online. These Class 11 Maths Solutions provide proper guidance and a thorough learning experience. The students can go through chapter-wise solutions from the table provided below.

## NCERT Solutions Class 11 Maths Chapters – Free PDF Download

Access and download NCERT Class 11 exemplar problems chapter-wise here.

Students having trouble in solving problems of NCERT Class 11 Maths can refer to the solutions given below for better guidance and a quick review.

## NCERT Solutions for Class 11 Maths Chapter 1 Sets – Term I

This chapter discusses the concept of Sets along with their representation. The topics included in the chapter are Empty set, Finite and Infinite sets, Equal sets, Subsets, Power set and Universal set. The chapter also helps students learn to draw Venn diagrams as well as to get familiar with the concepts of Union and Intersection of sets. The Difference of sets and Complement of a set, along with its properties are also covered in this chapter. There are 6 exercises along with a miscellaneous exercise in the chapter, providing a sufficient number of questions to the students to solve and in turn, understand the concept.

Topics Covered in Class 11 Maths Chapter 1 Sets for First Term:

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets.

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## NCERT Solutions for Class 11 Maths Chapter 2 Relations & Functions – Term I

In this chapter, students taught about the concepts of Ordered pairs, Cartesian product of sets, the number of elements in the cartesian product of two finite sets, the definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Along with the topic of relation, students get to learn about the topic of functions as well. Function as a special type of relation, pictorial representation of a function, domain, co-domain and range of a function, real-valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions with their graphs are the few topics that come under the concept of Functions. Students will learn to link pairs of objects from two sets and then introduce relations between the two objects in the pair. And then, they will learn about special relations which will qualify to be functions. There are 3 exercises along with a miscellaneous exercise present in the chapter which covers the topics mentioned above.

Topics Covered in Class 11 Maths Chapter 2 Relations and Functions for First Term:

Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself ( R x R only).Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs.

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## NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions – Term II

The chapter discusses positive and negative angles, method of measuring angles in radians as well as in degrees and conversion from one measure to another. The chapter also deals with the definition of Trigonometric Functions with the help of unit circle, general solution of trigonometric equations, signs, domain and range of Trigonometric Functions and their graphs. The chapter helps the students in learning the process of expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy along with their simple applications and deducing the identities, related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x. The problems in 4 exercises, along with a miscellaneous exercise, present in the chapter cover all the topics mentioned above.

Topics Covered in Class 11 Maths Chapter 3 Trigonometric Functions for Second Term:

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following:

$tan(x\pm y)=\frac{tanx\pm tany}{1\mp tanxtany},cot(x\pm y)=\frac{cotxcoty\mp 1}{cotx\pm coty}$

$sin\alpha \pm sin\beta =2sin\frac{1}{2}(\alpha \pm \beta )cos\frac{1}{2}(\alpha \mp \beta )$

$cos\alpha + cos\beta =2cos\frac{1}{2}(\alpha + \beta )cos\frac{1}{2}(\alpha – \beta )$

$cos\alpha – cos\beta =-2sin\frac{1}{2}(\alpha + \beta )sin\frac{1}{2}(\alpha – \beta )$

Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.

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

The chapter, Principle of Mathematical Induction, covers a number of topics that includes the process of proving the induction and motivating the application by looking at natural numbers as the least inductive subset of real numbers. Problems related to the Principle of Mathematical Induction, along with its simple applications are covered in the exercise given in the chapter.

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## NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations – Term I

The chapter discusses, in detail, about the need for complex numbers, especially √−1, to be motivated by the inability to solve some of the quadratic equations. The chapter also enables the students to learn about the algebraic properties of complex numbers, argand plane and polar representation of complex numbers. Statement of the fundamental theorem of algebra, solutions of quadratic equations (with real coefficients) in the complex number system and the square root of a complex number are also among the topics discussed in the chapter. There are 3 exercises and a miscellaneous exercise in this chapter that covers these topics.

Topics Covered in Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations for First Term:

Need for complex numbers, especially √−1, to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system.

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## NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities – Term II

The chapter Linear Inequalities, as the name suggests, deals with the concept of Linear Inequalities. The concepts of algebraic solutions of Linear Inequalities in one variable and their representation on the number line, graphical representation of Linear Inequalities in two variables as well as the graphical method of finding a solution of the system of Linear Inequalities in two variables are also covered in this chapter. A total of 3 exercises and a miscellaneous exercise is present in this chapter which includes all the topics covered in the chapter.

Topics Covered in Class 11 Maths Chapter 6 Linear Inequalities for Second Term:

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.

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## NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations – Term II

A permutation is an arrangement of a number of objects in a definite order taken at a time whereas Combination is a collection of the objects where the order doesn’t matter. The chapter discusses everything about the Fundamental principle of counting, factorial n. (n!), permutations, combinations, derivation of formulae and their connections along with simple applications. A total of 4 exercises and a miscellaneous exercise that includes questions covering all the topics present in the chapter.

Topics Covered in Class 11 Maths Chapter 7 Permutations and Combinations for Second Term:

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, formula for nPr and nCr, simple applications.

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

In this chapter, students study about Binomial Theorem for positive integers. This theorem can be used to solve complex calculations that are difficult to solve using repeated multiplication. The chapter discusses the history, statement and proof of the Binomial Theorem for positive integral indices. Pascal’s triangle, general and middle term in the binomial expansion and their simple applications are some topics that are explained, in detail, in this chapter. 2 exercises along with a miscellaneous exercise are present in the chapter to help students practise problems related to Binomial Theorem.

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## NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series – Term I

A sequence is an ordered list of numbers. The sum of all the terms of a sequence is a series. The chapter discusses the following topics which include Sequence and Series, Arithmetic Progression (A. P.), Arithmetic Mean (A.M.), Geometric Progression (G.P.), general term of a G.P., the sum of first n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), the relation between A.M. and G.M, formulae for the special series sums and more. There are 4 exercises and a miscellaneous exercise present in the chapter that helps the students in understanding the concepts given in the chapter by solving the questions in it.

Topics Covered in Class 11 Maths Chapter 9 Sequences and Series for First Term:

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M.

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## NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines – Term I

The chapter helps students recall two-dimensional geometry from earlier classes. Shifting of origin, the slope of a line and angle between two lines, various forms of equations of a line including the ones parallel to the axis, point-slope form, slope-intercept form, two-point form, intercept form, and normal form are some of the topics that are being discussed in the chapter. Other concepts that the chapter covers are the general equation of a line, equation of the family of lines passing through the point of intersection of two lines, the distance of a point from a line and more. There are 3 exercises and a miscellaneous exercise provided in the chapter to help the students solve and practise questions related to the chapter.

Topics Covered in Class 11 Maths Chapter 10 Straight Lines for First Term:

Brief recall of two dimensional geometry from earlier classes. Slope of a line and angle between two lines.

Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Distance of a point from a line.

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## NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections – Term II

This chapter discusses the concept of Conic Sections in detail. In Maths, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The topics covered include the sections of a cone, namely, circle, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerate case of a conic section. Standard equations and simple properties of circle, parabola, ellipse and hyperbola are also present in the chapter. There are 4 exercises in the 11 Maths NCERT Solutions PDF and a miscellaneous exercise in this chapter, solving which the students learn the topics mentioned above.

Topics Covered in Class 11 Maths Chapter 11 Conic Sections for Second Term:

Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

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## NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three-dimensional Geometry – Term II

A point in space has three coordinates. In this chapter, students of Class 11 shall learn the basic concepts of geometry in three-dimensional space. The chapter discusses the concept of coordinate axes and coordinate planes in three dimensions, coordinates of a point, distance between two points and section formula, in detail. There are 3 exercises in the chapter to help students solve and understand the concept in a better way. A miscellaneous exercise is also present at the end of the chapter that contains additional questions which cover all the topics in the chapter.

Topics Covered in Class 11 Maths Chapter 12 Introduction to Three-dimensional Geometry for Second Term:

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

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

### Limits – Term I and Derivatives – Term II

The chapter, Limits and Derivatives, provides an introduction to Calculus. Calculus is a branch of Maths dealing with the study of change in the value of a function as the points in the domain change. In this chapter, initially, students gain an intuitive idea of derivative (without actually defining it). Later, the chapter provides a simple definition of a limit and some algebra of limits. Finally, the chapter returns to a description of derivative and some algebra of derivatives. There are 2 exercises and a miscellaneous exercise that covers all the topics in the chapter.

Topics Covered in Class 11 Maths Chapter 13 Limits for First Term:

Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions

Topics Covered in Class 11 Maths Chapter 13 Derivatives for Second Term:

Derivative introduced as rate of change both as that of distance function and geometrically. Definition of Derivative, relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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

This chapter in the NCERT Solutions discusses some basic ideas of Mathematical Reasoning, especially in the context of Mathematics. Students, by now, must have already learnt inductive reasoning in the context of Mathematical Induction. In this chapter, some fundamentals of deductive reasoning are covered. The topics present in the chapter include mathematically acceptable statements, connecting words/ phrases – consolidating the understanding of “if and only if (necessary and sufficient) condition”, “implies”, “and/or”, “implied by”, “and”, “or”, “there exists”, validating the statements involving the connecting words, and more. 5 exercises and a miscellaneous exercise are present in the chapter to help the students in understanding the concept of Mathematical Reasoning thoroughly.

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## NCERT Solutions for Class 11 Maths Chapter 15 Statistics – Term I

We know that statistics deals with data collected for specific purposes. In this chapter, we shall learn some of the important measures of dispersion and their methods of calculation for ungrouped and grouped data. The topics that students learn in the chapter include measures of dispersion, range, mean deviation, variance and standard deviation of ungrouped/grouped data and analysis of frequency distributions with equal means but different variances. Students can learn more about the chapter by solving the problems given in 3 exercises along with an additional exercise in the chapter.

Topics Covered in Class 11 Maths Chapter 15 Statistics for First Term:

Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data.

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## NCERT Solutions for Class 11 Maths Chapter 16 Probability – Term II

The chapter discusses the concept of probability as a measure of uncertainty of various phenomena or simply, chances of occurrence of an event. In this chapter, students will learn the concepts such as random experiments; outcomes, sample spaces (set representation) and Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories studied in earlier classes. Probability of an event, the probability of ‘not’, ‘and’ and ‘or’ events are also covered in the chapter. To understand the concept of probability properly, students can solve the 3 exercises along with the miscellaneous exercise.

Topics Covered in Class 11 Maths Chapter 16 Probability for Second Term:

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

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We at CoolGyan’S, help students to discover better ways to solve math problems, using their logical skills. Use of these NCERT Solutions can be a good move towards refining Maths fluency and achieving greater success. Student’s can use these study materials as a reference and prepare efficiently for the exams. Ultimately, students will be able to perform well in the exams by solving NCERT Maths sample papers and will get an idea about the different types of questions asked, along with their difficulty level and the marking scheme.

### Key Benefits of Maths NCERT Solutions Class 11

CoolGyan’S NCERT Solutions offer a lot of benefits to the students.

• Firstly, students can learn NCERT or CBSE based Class 11 Maths within their comfort zone. They can do it right from their homes using their PCs and tablets if the internet is enabled, or they can always download and use our free app.
• Class 11 Maths NCERT Solutions PDF download option is available for free to help students prepare for their exams effectively.
• Students have the luxury to customize their learning experience by studying each topic at their own pace without worrying about time constraints.
• Additionally, CoolGyan’S has the best subject experts who can further guide students to learn the subject and its concepts in a fun and straightforward manner.

### CBSE Class 11 Maths Unit wise weightage for First Term

 No. Units Marks I Sets and Functions 11 II Algebra 13 III Coordinate Geometry 06 IV Calculus 04 V Statistics and Probability 06 Total 40 Internal Assessment 10 Total 50

#### Internal Assessment Class 11 Term I

 Internal Assessment Marks Periodic Tests 05 Marks Mathematics Activities: Activity file record +Term end assessment of one activity & Viva 05 Marks Total Marks 10 Marks

### CBSE Class 11 Maths Unit wise weightage for Second Term

 Unit Unit Name Marks I Sets and Functions (Cont.) 08 II Algebra (Cont.) 11 III Coordinate Geometry (Cont.) 09 IV Calculus (Cont.) 06 V Statistics and Probability (Cont.) 06 Total 40 Internal Assessment 10 Total 50

#### Internal Assessment Class 11 Term II

 Internal Assessment Marks Periodic Tests 05 Marks Mathematics Activities: Activity file record +Term end assessment of one activity & Viva 05 Marks Total Marks 10 Marks

Besides, students can bring in all their queries regarding other subjects, including Physics, Chemistry, and Biology as well. Meanwhile, CoolGyan’S also keeps track of all the progress that student’s make. To help students in this aspect, NCERT Solutions for Class 11 Maths PDF free download can be opted by a better academic performance. Feedback and counselling provided via periodic assessments. CoolGyan’S offers tips & tricks to prepare CBSE exams with NCERT Solutions along with Class 11 Maths revision notes and class-wise NCERT model question papers that help students to prepare for the board exams, state-level exams, entrance tests and other competitive exams.

Students can opt to learn Maths as well as other subjects by accessing our solutions anywhere and at any time. If students face any problems while referring to NCERT Class 11 Maths book or solutions, they can always approach the CoolGyan’S support team to clear all their doubts. Students can also download Class 11 Maths NCERT Solutions to get a better knowledge of the fundamental concepts which are important for the exams.

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## Frequently Asked Questions on NCERT Solutions for Class 11 Maths

### How CoolGyan’S NCERT Solutions for Class 11 Maths help us to score good marks in the exam?

The subject matter specialists at CoolGyan’S have framed the NCERT Solutions in accordance with the syllabus designed by the CBSE board. The essential explanation is provided for major points to make the concepts easier for the students while learning. Both chapter wise and exercise wise solutions are designed with the aim of helping students to ace the exam without fear. The solutions mainly help students to improve their problem-solving abilities which are important for the exam.

### Name the important concepts discussed in Chapter 11 of NCERT Solutions for Class 11 Maths.

Chapter 11 of NCERT Solutions PDF Class 11 Maths deals with concepts like parts of a cone which explains about parabola, ellipse, circle, degenerate conic sections and hyperbola. Other important topics like the relationship between semi-minor axis, semi-major axis, the distance of focus from the centre of the ellipse, standard equations of parabola and ellipse. This is one of the important chapters in Class 11 as it discusses the important concepts of conic sections which would be continued in higher classes as well.

### What are the main topics covered in relations and functions of NCERT Solutions for Class 11 Maths?

This chapter introduces students to the relations and their characteristics. The Cartesian product of sets and its relations are one of the important concepts explained here. The real-life model of cartesian products is explained in an understandable language to make it easier for students while studying. This chapter helps students to build a strong foundation of basic concepts which are important from the exam point of view.

### What will I study in Chapter 4 Mathematical Induction of NCERT Solutions for Class 11 Maths?

Mathematical Induction is a technique which is used to prove whether a given statement is right or wrong. The important fact is that the theorem should be true for every given natural number. Students will be familiar with the following points by studying this chapter.
1. Proving a statement or illustration is the main motive.
2. The proof should be true for all the values of natural numbers.
3. For initial value, the statement should be true.
4. For values till nth iteration, the statement should be true.
5. All the steps in the proof should be true and justified.