# NCERT Solutions for Class 11 Maths

• Last Updated : 23 Jun, 2022

If you’re reading this and stumbled upon this page to search for NCERT Class 11 Maths Solutions, then you’re at the right place. Class 11 is starting a new path where things can get pretty confusing and complicated because the Class 11th Maths Syllabus is altogether different from before. And finding solutions to such questions can get tougher when you don’t have any idea where to search for them. There are many websites that provide Solutions to NCERT Class 11 Maths problems but most of them provide solutions that are not easy to understand.

At GeeksforGeeks, you can find the solution to all your Maths questions in one place. We provide NCERT Class 11 Maths Solutions that are easy to understand. The Solutions provided by GeeksforGeeks can help you to build a deeper understanding of the concepts like Sets, Relations & Functions, Complex numbers, Conic sections, etc.

Our CBSE NCERT Solutions for Class 11 Maths provide a step-by-step and extensive explanation of all the problems covered in the NCERT textbook on topics such as set theory, calculus, geometry, and so on. They serve as a guide for students who wish to double-check their answers to problems and for children who desire a better comprehension of subjects. These NCERT Solutions for Class 11 Mathematics are compiled and curated by certified Math professionals who guarantee that students will build a strong foundation in Maths.

NCERT Answers for Class 11 Maths are incredibly beneficial to students studying for home examinations such as units, half-yearlies, and finals. Because the subjects of Class 11th and 12th are so closely related, pupils can begin their preparation for Class 12th indirectly. CBSE Class 11 Maths NCERT answers may also be very useful for competitive examinations like IIT-JEE, BITS PILANI, and so on.

We’ve also covered 1500+ Most Asked Questions in Mathematics, Chapterwise Important Formulas, and many other topics based on the New CBSE Class 11th curriculum to help learners strengthen their fundamental understanding. Students can use these notes and other study materials to help them prepare for their Final Exams. ## Chapter 1: Sets

The Chapter covers Class 11 Maths NCERT Solutions Chapter 1- Sets that explains the concept of sets along with their representation. The topics discussed are empty sets, equal sets, subsets, finite and infinite sets, power sets, and universal sets

There are six exercises in the Chapter, in which Exercise 1.1 is based on the introduction of sets and their representations; Exercise 1.2 is based on the concept of the empty set, finite and infinite sets, and equal sets; Exercise 1.3 is based on the concept of subsets, power set, and universal set; Exercise 1.4 is based on the concept of Venn diagrams and operations on sets.

Exercise 1.5 is based on the complement of a set and its properties and Exercise 1.6 is based on the concept of union and intersection of two sets.

Class 11th Maths CBSE Solutions of Chapter 1 are here:

More resources for CBSE Class 11 Maths Chapter 1

## Chapter 2: Relations and Functions

Class 11 Maths NCERT Solutions of Chapter 2 Relations and Function cover subjects such as determining whether a relationship is a function, identifying distinct types of functions, adding, subtracting, multiplying functions, and determining the range of these functions.

Class 11 Maths Chapter 2 relations and functions have 36 questions. 9 are moderately complicated, 15 are easy and 12 are tough sums. There are a total of four exercises, Exercise 2.1 and 2.2 deal with the problems based on the Cartesian Product of Sets and the introduction to Relations and Functions. However, further exercises like Exercise 2.3, 2.4, and miscellaneous consist of the questions based on the Introduction to Domain and Range, Piecewise Function, and Range of a Function.

Class 11th Maths CBSE Solutions of Chapter 2 are here:

More resources for CBSE Class 11 Maths Chapter 2

## Chapter 3: Trigonometric Functions

This Chapter covers NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions the concepts of angles, trigonometric functions, and equations. The topics discussed are positive and negative angles, measurement and conversion of angles, the definition of trigonometric functions, general solution of trigonometric equations, and domain and range of the trigonometric function.

There are five exercises in the Chapter, in which Exercise 3.1 is based on the introduction of angles, measurement of angles in degree and radian, and the relation between degree and radian; Exercise 3.2 is based on the concept of trigonometric functions, signs, domain, and range of trigonometric functions.

Exercise 3.3 is based on trigonometric functions of sum and difference of two angles; Exercise 3.4 is based on trigonometric equations (functions of a variable) and Miscellaneous Exercise is based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 3 are here:

More resources for CBSE Class 11 Maths Chapter 3

## Chapter 4: Principle of Mathematical Induction

As the name suggests, the Chapter explains the concept of the Principle of Mathematical Induction. The topics discussed are the process to prove the induction and motivating the application taking natural numbers as the least inductive subset of real numbers.

There is only one exercise in the Chapter which is based on the Principle of Mathematical Induction with its simple applications.

Class 11th Maths CBSE Solutions of Chapter 4 are here:

• NCERT Maths Solutions Class 11 Exercise 4.1 Set 1, Set 2 – 24 Questions & Solutions

More resources for CBSE Class 11 Maths Chapter 4

## Chapter 5: Complex Numbers and Quadratic Equations

As the name of the Chapter suggests, therefore, this chapter explains the concept of Complex numbers and quadratic equations and their properties. The topics discussed are the square root, algebraic properties, argand plane and polar representation of complex numbers, and Solutions of quadratic equations in the complex number system

There are four exercises in the Chapter, in which Exercise 5.1 is based on the introduction, algebraic functions, the modulus, and the conjugate of a complex number; Exercise 5.2 is based on the argand plane and polar representation of a complex number; Exercise 5.3 is based on the quadratic equations with real coefficients and miscellaneous exercise based on all the topics discussed in the Chapter.

NCERT Solutions for Class 11 Maths of Chapter 5 are here:

More resources for CBSE Class 11 Maths Chapter 5

## Chapter 6: Linear Inequalities

The Chapter explains the concept of Linear Inequalities. The topics discussed are Algebraic Solutions and graphical representation of Linear Inequalities in one variable and two variables respectively.

There are four exercises in the Chapter, in which Exercise 6.1 is based on the introduction to linear inequalities, algebraic solution, and graphical representation of linear inequalities in one variable, Exercise 6.2 is based on the graphical representation of Linear Inequalities in two variables.

Exercise 6.3 is based on the graphical method to find a solution to the system of Linear Inequalities in two variables and a miscellaneous exercise based on the problems of inequalities in one variable only.

Class 11th Maths CBSE Solutions of Chapter 6 are here:

More resources for CBSE Class 11 Maths Chapter 6

## Chapter 7: Permutations and Combinations

The present chapter explains the concepts of Permutation (an arrangement of a number of objects in a definite order) and Combination (a collection of the objects irrespective of the order).

The topics discussed are the fundamental principle of counting, factorial, permutations, combinations, and their applications. There are five exercises in the Chapter, in which Exercise 7.1 is based on the introduction to permutations and combinations along with the fundamental principle of counting.

Exercise 7.2 is based on the application of the permutation for all distinct objects and factorial notation; Exercise 7.3 is based on the application of the permutation when all the objects are not distinct and the derivation of the formula of permutation

Exercise 7.4 is based on the introduction to combinations where the order doesn’t matter and its applications and a miscellaneous exercise are based on the introduction to permutations and combinations and the fundamental principle of counting.

Class 11th Maths CBSE Solutions of Chapter 7 are here:

More resources for CBSE Class 11 Maths Chapter 7

## Chapter 8: Binomial Theorem

This Chapter discusses the Binomial Theorem for positive integers used to solve complex calculations. The topics discussed are the history, statement, and proof of the binomial theorem and its expansion along with Pascal’s triangle.

There are three exercises in the Chapter, in which Exercise 8.1 is based on the introduction to the binomial theorem, the theorem for positive integral indices, and Pascal’s triangle; Exercise 8.2 is based on the general and middle term in the binomial expansion and their simple applications and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 8 are here:

More resources for CBSE Class 11 Maths Chapter 8

## Chapter 9: Sequences and Series

The Chapter covers the NCERT solution for Class 11 Maths Chapter 9 – Sequences and Series that discusses the concepts of a sequence (an ordered list of numbers) and series (the sum of all the terms of a sequence).

The topics discussed are sequence and series, arithmetic and geometric progression, arithmetic, and geometric mean. There are five exercises in the Chapter, in which Exercise 9.1 is based on the introduction to sequence and series.

Exercise 9.2 is based on the arithmetic progression, arithmetic mean, and general term of the progression; Exercise 9.3 is based on the finite and infinite geometric progression, geometric mean, general term of the progression, the sum of n terms of geometric progression, and the relation between arithmetic and geometric mean.

Exercise 9.4 is based on the sum of the special series sums to n terms and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 9 are here:

More resources for CBSE Class 11 Maths Chapter 9

## Chapter 10: Straight Lines

In this chapter, we will cover NCERT Solutions for Class 11 Maths Chapter 10-Straight lines where we define the concept of the line, its angle, slope, and general equation

The topics discussed are the slope of a line, the angle between two lines, various forms of line equations, the general equation of a line, and the family of lines respectively. There are four exercises in the Chapter, in which – Exercise 10.1 is based on the introduction to straight lines, the slope of a line for given coordinates of two points, parallel and perpendicular lines with the axis, the angle between two lines, and collinearity of three points; Exercise 10.2 is based on the various form of equations of a line in terms of point-slope form, slope-intercept form, two-point form, intercept form and normal form.

Exercise 10.3 is based on the general line equation, an equation of the family of lines that passes through the two lines’ intersection point and the distance of a point from a line, and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 10 are here:

More resources for CBSE Class 11 Maths Chapter 10

## Chapter 11: Conic Sections

The topics discussed in the present Chapter are the sections of a cone, the degenerate case of a Conic Section along with the equations and properties of conic sections.

There are five exercises in the Chapter, in which – Exercise 11.1 is based on the introduction of a cone, sections of a cone (generated and degenerated), and a circle; Exercise 11.2 is based on the introduction to a parabola, its standard equations, and latus rectum.

Exercise 11.3 is based on the introduction to ellipse, its standard equations, eccentricity, latus rectum, focus, semi-major and semi-minor axis; Exercise 11.4 is based on the introduction to hyperbola, its standard equations, eccentricity, and latus rectum and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 11 are here:

More resources for CBSE Class 11 Maths Chapter 11

## Chapter 12: Introduction to Three-dimensional Geometry

As the name suggests, the Chapter explains the concepts of Geometry in three-dimensional space. The topics discussed are the coordinate axes and planes respectively, points coordinate, distance, and a section for points.

There are four exercises in the Chapter, in which Exercise 12.1 is based on the Introduction to three-dimensional geometry, coordinate axes, and coordinate planes in three dimensions and coordinates of a point in space; Exercise 12.2 is based on the distance between two points; Exercise 12.3 is based on the section formula to find a coordinate of a point that divides the line between a ratio and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 12 are here:

More resources for CBSE Class 11 Maths Chapter 12

## Chapter 13: Limits and Derivatives

The Chapter Limits and Derivatives explains the concept of calculus that deals with the study of change in the value of a function when the change occurs in the domain points. The topics discussed are the definition and algebraic operations of limits and derivatives respectively.

There are three exercises in the Chapter, in which Exercise 13.1 is based on the introduction to limits and derivatives, algebra of limits, limits of trigonometric functions, and polynomial and rational functions.

Exercise 13.2 is based on the algebra of derivative of functions, derivative of polynomial and trigonometric functions, and a miscellaneous exercise based on the intuitive idea of derivatives, limits, and derivatives and limits of trigonometric functions.

Class 11th Maths CBSE Solutions of Chapter 13 are here:

More resources for CBSE Class 11 Maths Chapter 13

## Chapter 14: Mathematical Reasoning

As the name suggests, the Chapter explains the concepts of Mathematical Reasoning (a critical skill to analyze any given hypothesis in the context of mathematics). The topics discussed are statements, inductive reasoning, and deductive reasoning.

There are six exercises in the Chapter, in which Exercise 14.1 is based on the simple statements, application of the “implies” condition; Exercise 14.2 is based on the negation and true-false statement and application of the “and/or” condition.

Exercise 14.3 is based on the compound statement, application of “and” and “or” condition; Exercise 14.4 is based on the If-then statement, application of “if and only if” condition; Exercise 14.5 is based on the If-then statement, application of “implied by” condition and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 14 are here:

More resources for CBSE Class 11 Maths Chapter 14

## Chapter 15: Statistics

This Chapter explains the concepts of Statistics (data collected for specific purposes), dispersion, and methods of calculation for ungrouped and grouped data. The topics discussed are range, mean deviation, variance and standard deviation, and analysis of frequency distributions.

There are four exercises in the Chapter, in which Exercise 15.1 is based on the range and mean deviation of mean and median for the data; Exercise 15.2 is based on the mean, variance, and standard deviation for the data and analysis of frequency distribution.

Exercise 15.3 is based on the data’s mean, variance, and coefficient of variance and a miscellaneous exercise based on all the topics discussed in the Chapter.

Class 11th Maths CBSE Solutions of Chapter 15 are here:

More resources for CBSE Class 11 Maths Chapter 15

## Chapter 16: Probability

The Chapter discusses the concept of Probability (a measure of uncertainty of various phenomena or a chance of occurrence of an event). The topics discussed are the random experiments, outcomes, sample spaces, event, and their type.

There are four exercises in the Chapter, in which Exercise 16.1 is based on the introduction of probability, possible outcomes, and sample spaces; Exercise 16.2 is based on the introduction of events, the occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events.

Exercise 16.3 is based on the probability of an event and random experiments and a miscellaneous exercise is based on the advanced probability problems and axiomatic probability

Class 11th Maths CBSE Solutions of Chapter 16 are here:

More resources for CBSE Class 11 Maths Chapter 16

## Important Resources for CBSE Class 11th provided by GeeksforGeeks:-

Question 1: Is Class 11 Maths tough?

Math is one of the subjects that many students are afraid of. However, if you create interest via continuous practice, you will ultimately master it. Trying to transition from Class 10 to Class 11 in math, particularly in CBSE, is tough since the pattern and type of questions change.

Because students are inexperienced with these new concepts, this frequently results in a drop in internal scores. Keeping on to new theories and concepts takes some time. You can only get through this change with practice. Chapters such as trigonometry, permutation, and combination may appear difficult at first, but with practice, they will become easy.

Question 2: Which book is best for Class 11 Maths?

No book, however, can replace the NCERT Class 11 Maths textbook. This is your bible, and you must keep it with you at all times. NCERT provides over half of the question paper, and all competitive exams are based on NCERT.

However, once you’ve finished with NCERT, you can move on to RS Agarwal’s Senior Secondary School Mathematics: for Class 11 and RD Sharma’s Mathematics for Class 11.

Question 3: What are some important tips for Class 11 final examinations to score good marks?