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Class 11 NCERT Solutions - Chapter 1 Sets - Exercise 1.1
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NCERT Solutions for Class 11 Maths 2024-25 : Chapter Wise PDF Download

Last Updated : 21 Jul, 2024
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NCERT Solutions for Class 11 Maths provides solutions that are easy to understand. The Class 11 NCERT solutions for Maths provided by our expert team can help you to build a deeper understanding of concepts like Sets, Relations and functions, Complex numbers, Conic sections, etc.

In this Class 11th Maths Solutions, we’ve also covered topics based on the latest CBSE Class 11 Syllabus to help learners strengthen their fundamental understanding.

Students can use Class 11 Maths NCERT solutions notes and other Class 11 Maths study materials to prepare for their Final Exams.

NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Maths

Table of Content

  • NCERT Solutions for Class 11 Maths Chapter 1 Sets
  • NCERT Solutions for Class 11 Maths Chapter 2 Relations & Functions
  • NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions
  • NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations
  • NCERT Solutions for Class 11 Maths Chapter 5 Linear Inequalities
  • NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations
  • NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem
  • NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series
  • NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines
  • NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections
  • NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three-dimensional Geometry
  • NCERT Solutions for Class 11 Maths Chapter 12 Limits and Derivatives
  • NCERT Solutions for Class 11 Maths Chapter 13 Statistics
  • NCERT Solutions for Class 11 Maths Chapter 14 Probability

NCERT Solutions for Class 11 Maths Chapter 1 – Sets

Class 11 Maths NCERT Solutions PDF Chapter 1 Exercises
NCERT Solutions for Class 11 Maths Chapter 1- Sets Exercise 1.1
NCERT Solutions for Class 11 Maths Chapter 1- Sets Exercise 1.2
NCERT Solutions for Class 11 Maths Chapter 1- Sets Exercise 1.3
NCERT Solutions for Class 11 Maths Chapter 1- Sets Exercise 1.4
NCERT Solutions for Class 11 Maths Chapter 1- Sets Exercise 1.5
NCERT Solutions for Class 11 Maths Chapter 1- Sets Miscellaneous Exercise

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

Class 11 Maths NCERT Solutions PDF Chapter 2 Exercises
NCERT Solutions for Class 11 Maths Chapter 2- Relations And Functions Exercise 2.1
NCERT Solutions for Class 11 Maths Chapter 2- Relations And Functions Exercise 2.2
NCERT Solutions for Class 11 Maths Chapter 2- Relations And Functions Exercise 2.3
NCERT Solutions for Class 11 Maths Chapter 2- Relations And Functions Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 3 – Trigonometric Functions

Class 11 Maths NCERT Solutions PDF Chapter 3 Exercises
NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Exercise 3.1
NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Exercise 3.2
NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Exercise 3.3 Set 1 and Set 2
NCERT Solutions for Class 11 Maths Chapter 3- Trigonometric Functions Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 4 – Complex Numbers and Quadratic Equations

Class 11 Maths NCERT Solutions PDF Chapter 4 Exercises
NCERT Solutions for Class 11 Maths Chapter 4- Complex Numbers and Quadratic Equations Exercise 4.1
NCERT Solutions for Class 11 Maths Chapter 4- Complex Numbers and Quadratic Equations Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 5 – Linear Inequalities

Class 11 Maths NCERT Solutions PDF Chapter 5 Exercises
NCERT Solutions for Class 11 Maths Chapter 5- Linear Inequalities Exercise 5.1
NCERT Solutions for Class 11 Maths Chapter 5- Linear Inequalities Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 6 – Permutations and Combinations

Class 11 Maths NCERT Solutions PDF Chapter 6 Exercises
NCERT Solutions for Class 11 Maths Chapter 6- Permutations and Combinations Exercise 6.1
NCERT Solutions for Class 11 Maths Chapter 6- Permutations and Combinations Exercise 6.2
NCERT Solutions for Class 11 Maths Chapter 6- Permutations and Combinations Exercise 6.3
NCERT Solutions for Class 11 Maths Chapter 6- Permutations and Combinations Exercise 6.4
NCERT Solutions for Class 11 Maths Chapter 6- Permutations and Combinations Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 7 – Binomial Theorem

Class 11 Maths NCERT Solutions PDF Chapter 7 Exercises
NCERT Solutions for Class 11 Maths Chapter 7- Binomial Theorem Exercise 7.1
NCERT Solutions for Class 11 Maths Chapter 7- Binomial Theorem Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 8 – Sequences and Series

Class 11 Maths NCERT Solutions PDF Chapter 8 Exercises
NCERT Solutions for Class 11 Maths Chapter 8 – Sequences and Series Exercise 8.1
NCERT Solutions for Class 11 Maths Chapter 8 – Sequences and Series Exercise 8.2
NCERT Solutions for Class 11 Maths Chapter 8 – Sequences And Series Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 9 – Straight Lines

Class 11 Maths NCERT Solutions PDF Chapter 9 Exercises
NCERT Solutions for Class 11 Maths Chapter 9- Straight Lines Exercise 9.1
NCERT Solutions for Class 11 Maths Chapter 9- Straight Lines Exercise 9.2
NCERT Solutions for Class 11 Maths Chapter 9- Straight Lines Exercise 9.3
NCERT Solutions for Class 11 Maths Chapter 9- Straight Lines Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 10 – Conic Sections

Class 11 Maths NCERT Solutions PDF Chapter 10 Exercises
NCERT Solutions for Class 11 Maths Chapter 10- Conic Sections Exercise 10.1
NCERT Solutions for Class 11 Maths Chapter 10- Conic Sections Exercise 10.2
NCERT Solutions for Class 11 Maths Chapter 10- Conic Sections Exercise 10.3
NCERT Solutions for Class 11 Maths Chapter 10- Conic Sections Exercise 10.4
NCERT Solutions for Class 11 Maths Chapter 10- Conic Sections Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 11 – Introduction to Three-dimensional Geometry

Class 11 Maths NCERT Solutions PDF Chapter 11 Exercises
NCERT Solutions for Class 11 Maths Chapter 11- Introduction to Three Dimensional Geometry Exercise 11.1
NCERT Solutions for Class 11 Maths Chapter 11- Introduction to Three Dimensional Geometry Exercise 11.2
NCERT Solutions for Class 11 Maths Chapter 11- Introduction To 3 D Geometry Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 12 – Limits and Derivatives

Class 11 Maths NCERT Solutions PDF Chapter 12 Exercises
NCERT Solutions for Class 11 Maths Chapter 12- Limits and Derivatives Exercise 12.1
NCERT Solutions for Class 11 Maths Chapter 12- Limits and Derivatives Exercise 12.2
NCERT Solutions for Class 11 Maths Chapter 12- Limits And Derivatives Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 13 – Statistics

Class 11 Maths NCERT Solutions PDF Chapter 13 Exercises
NCERT Solutions for Class 11 Maths Chapter 13- Statistics Exercise 13.1
NCERT Solutions for Class 11 Maths Chapter 13- Statistics Exercise 13.2
NCERT Solutions for Class 11 Maths Chapter 13- Statistics Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 14 – Probability

Class 11 Maths NCERT Solutions PDF Chapter 14 Exercises
NCERT Solutions for Class 11 Maths Chapter 14- Probability Exercise 14.1
NCERT Solutions for Class 11 Maths Chapter 14- Probability Exercise 14.2
NCERT Solutions for Class 11 Maths Chapter 14- Probability Miscellaneous Exercise

NCERT Solutions for Class 11 Maths (Old CBSE Syllabus)

Chapter 1 – Sets

In this class 11 NCERT maths solutions, the concept of Sets and their representation is thoroughly explored. The topics covered in class 11th mathematics include Empty set, Finite and Infinite sets, Equal sets, Subsets, Power set, and Universal set.

 Class 11 Maths NCERT Solutions Chapter 1 Exercise
  • NCERT Maths Solutions Class 11 Exercise 1.1 – 6 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 1.2 – 6 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 1.3 – 9 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 1.4 – 12 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 1.5 – 7 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 1.6 – 8 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise Set 1, Set 2 – 16 Questions & Solutions

More resources for Class 11 Chapter 1 Sets
  • CBSE Class 11 Maths Notes of Chapter 1 
  • Class 11 RD Sharma Solutions of Chapter 1 Sets 
  • All important NCERT formulas for class 11 Chapter 1 Sets

Chapter 2 – Relations and Functions

In this NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions, students will be introduced to essential concepts such as Ordered pairs, Cartesian product of sets, and the formation of relations between elements.

 Class 11 Maths NCERT Solutions Chapter 2 Exercise
  • NCERT Maths Solutions Class 11 Exercise 2.1 – 10 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 2.2 – 9 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 2.3 – 5 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 12 Questions & Solutions

More resources for Class 11 Chapter 2 Relation and Functions
  • CBSE Class 11 Maths Notes of Chapter 2 
  • Class 11 RD Sharma Solutions of Chapter 2 Relations and Functions 
  • All important NCERT formulas for class 11 Chapter 2 Relations and Functions 

Chapter 3 Trigonometric Functions

In class 11 NCERT maths solutions Chapter 3 Trigonometric Functions we have covers positive and negative angles, methods of measuring angles in radians and degrees, and the conversion between the two measures.

 Class 11 Maths NCERT Solutions Chapter 3 Exercise
  • NCERT Maths Solutions Class 11 Exercise 3.1 – 7 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 3.2 – 10 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 3.3 – 25 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 3.4 – 9 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 10 Questions & Solutions

More resources for Class 11 Chapter 3 Trigonometric Functions
  • CBSE Class 11 Maths Notes of Chapter 3 
  • Class 11 RD Sharma Solution of Chapter 3 Trigonometric Functions
  • All important NCERT formulas for class 11 Chapter 3 Trigonometric Functions 

Chapter 4 – Principle of Mathematical Induction

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

 Class 11 Maths NCERT Solutions Chapter 4 Exercise
  • NCERT Maths Solutions Class 11 Exercise 4.1 Set 1, Set 2 – 24 Questions & Solutions

More resources for Class 11 Chapter 4 Principal of Mathematical Induction
  • CBSE Class 11 Maths Notes of Chapter 4
  • Class 11 RD Sharma Solution of Chapter 4 Principle of Mathematical Induction 
  • All important NCERT Maths formulas for class 11 Chapter 4 Principle of Mathematical Induction 

Chapter 5 – Complex Numbers and Quadratic Equations

The class 11 NCERT maths solutions Chapter 5 Complex Numbers and Quadratic Equations delves into the significance of complex numbers, particularly √−1, as a necessity arising from the inability to solve certain quadratic equations. Students will also explore the algebraic functions, argand plane, and the conjugate of a complex number.

 Class 11 Maths NCERT Solutions Chapter 5 Exercise
  • NCERT Maths Solutions Class 11 Exercise 5.1 Set 1, Set 2 – 14 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 5.2 – 8 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 5.3 – 10 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise Set 1, Set 2 – 20 Questions & Solutions

More resources for Class 11 Chapter 5 Complex Numbers and Quadratic Equations
  • CBSE Class 11 Maths Notes of Chapter 5 
  • Class 11 RD Sharma Solutions of Chapter 5 Complex Numbers and Quadratic Equations
  • All important NCERT Maths formulas for class 11 Chapter 5 Complex Numbers and Quadratic Equations 

Chapter 6 – Linear Inequalities 

The NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities  focuses on the concept of Linear Inequalities. It covers algebraic solutions of Linear Inequalities in one variable and their representation on the number line.

 Class 11 Maths NCERT Solutions Chapter 6 Exercise
  • NCERT Maths Solutions Class 11 Exercise 6.1 Set 1, Set 2 – 26 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 6.2 – 10 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 6.3 – 15 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 14 Questions & Solutions

More resources for Class 11 Chapter 6 Linear Inequalities
  • CBSE Class 11 Maths Notes Chapter of 6
  • Class 11 RD Sharma Solutions of Chapter 6 Linear Inequalities 
  • All important NCERT Maths formulas for class 11 Chapter 6 Linear Inequalities

Chapter 7 – Permutations and Combinations

A permutation refers to arranging a number of objects in a specific order, taken one at a time. On the other hand, a combination involves a collection of objects where the order is not significant.

The NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations discussed are the factorial, permutations, combinations, fundamental principle of counting, and their applications.

 Class 11 Maths NCERT Solutions Chapter 7 Exercise
  • NCERT Maths Solutions Class 11 Exercise 7.1 – 6 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 7.2 – 5 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 7.3 – 11 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 7.4 – 9 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 14 Questions & Solutions

More resources for Class 11 Chapter 7 Permutations and Combinations
  • CBSE Class 11 Maths Notes of Chapter 7 
  • Class 11 RD Sharma Solutions of Chapter 7 Permutations and Combinations
  • All important NCERT Maths formulas for Class 11 Chapter 7 Permutations and Combinations 

Chapter 8 – Binomial Theorem

This class 11 NCERT maths solutions Chapter 8 Binomial Theorem introduces students to the Binomial Theorem for positive integers. This powerful theorem serves as a tool to solve intricate calculations that would be challenging to tackle to the binomial theorem and its expansion along with Pascal’s triangle.

 Class 11 Maths NCERT Solutions Chapter 8 Exercise
  • NCERT Maths Solutions Class 11 Exercise 8.1 – 14 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 8.2 – 2 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 10 Questions & Solutions

More resources for Class 11 Chapter 8 Binomial Theorem
  • CBSE Class 11 Maths Notes Chapter 8 
  • Class 11 RD Sharma Solutions of Chapter 8 Binomial Theorem 
  • All important NCERT Maths formulas for Class11 Chapter 8 Binomial Theorem 

Chapter 9 – Sequences and Series

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

 Class 11 Maths NCERT Solutions Chapter 9 Exercise
  • NCERT Maths Solutions Class 11 Exercise 9.1 – 14 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 9.2 – 8 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 9.3 Set 1, Set 2 – 32 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 9.4 – 10 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise Set 1, Set 2 – 32 Questions & Solutions

More resources for Class 11 Chapter 9 Sequences and Series
  • CBSE Class 11 Maths Notes of Chapter 9 
  • Class 11 RD Sharma Solutions of Chapter 9 Sequences and Series
  • All important NCERT Maths formulas for Class 11 Chapter 9 Sequences and Series

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. 

 Class 11 Maths NCERT Solutions Chapter 10 Exercise
  • NCERT Maths Solutions Class 11 Exercise 10.1 – 14 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 10.2 Set 1, Set 2 – 20 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 10.3 Set 1, Set 2 – 18 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise Set 1, Set 2 – 24 Questions & Solutions

More resources for Class 11 Chapter 10 Straight Lines
  • CBSE Class 11 Maths Notes of Chapter 10 
  • Class 11 RD Sharma Solutions of Chapter 10 Straight lines
  • All important NCERT Maths formulas for Class 11 Chapter 10 Straight Lines

Chapter 11 – Conic Sections

In this chapter, the concept of Conic Sections is explored in depth. In Mathematics, a conic section refers to a curve formed by the intersection of the surface of a cone with a plane.

 Class 11 Maths NCERT Solutions Chapter 11 Exercise
  • NCERT Maths Solutions Class 11 Exercise 11.1 – 15 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 11.2 – 12 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 11.3 – 20 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 11.4 – 15 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 8 Questions & Solutions

More resources for Class 11 Chapter 11 Conic Sections
  • CBSE Class 11 Maths Notes of Chapter 11 
  • Class 11 RD Sharma Solutions of Chapter 11 Conic Sections
  • All important NCERT Maths formulas for Class 11 Chapter 11 Conic Sections

Chapter 12 – Introduction to Three-Dimensional Geometry

The Chapter NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three-dimensional Geometry explains the fundamental principles of geometry in three-dimensional space, where a point is defined by three coordinates.

 Class 11 Maths NCERT Solutions Chapter 12 Exercise
  • NCERT Maths Solutions Class 11 Exercise 12.1 – 4 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 12.2 – 5 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 12.3 – 5 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 6 Questions & Solutions

More resources for Class 11 Chapter 12 Introduction to Three-Dimensional Geometry
  • CBSE Class 11 Maths Notes of Chapter 12 
  • Class 11 RD Sharma Solutions of Chapter 12 Introduction to Three-dimensional Geometry
  • All important NCERT Maths formulas for Class 11 Chapter 12 Introduction to Three-dimensional Geometry 

Chapter 13 – Limits and Derivatives

The NCERT solutions for class 11 maths chapter 13 Limits and Derivatives explains the concept of calculus which 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. 

 Class 11 Maths NCERT Solutions Chapter 13 Exercise
  • NCERT Maths Solutions Class 11 Exercise 13.1 Set 1, Set 2 – 32 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 13.2 – 11 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise Set 1, Set 2 – 30 Questions & Solutions

More resources for Class 11 Chapter 13 Limits and Derivatives
  • CBSE Class 11 Maths Notes Chapter of 13 
  • Class 11 RD Sharma Solutions of Chapter 13 Limits and Derivatives
  • All important NCERT Maths formulas for Class 11 Chapter 13 Limits and Derivatives  

Chapter 14 – Mathematical Reasoning

The class 11 NCERT maths solutions chapter 14 Mathematical Reasoning 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.

 Class 11 Maths NCERT Solutions Chapter 14 Exercise
  • NCERT Maths Solutions Class 11 Exercise 14.1 – 2 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 14.2 – 3 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 14.3 – 4 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 14.4 – 4 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 14.5 – 5 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 7 Questions & Solutions

More resources for Class 11 Chapter 14 Mathematical Reasoning
  • CBSE Class 11 Maths Notes of Chapter 14 
  • Class 11 RD Sharma Solutions of Chapter 14 Mathematical Reasoning 
  • All important NCERT Maths formulas for Class 11 Chapter 14 Mathematical Reasoning 

Chapter 15 – Statistics

This NCERT Solutions for Class 11 Maths Chapter 15 Statistics 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.

 Class 11 Maths NCERT Solutions Chapter 15 Exercise
  • NCERT Maths Solutions Class 11 Exercise 15.1 – 12 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 15.2 – 10 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 15.3 – 5 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 7 Questions & Solutions

More resources for Class 11 Chapter 15 Statistics
  • CBSE Class 11 Maths Notes of Chapter 15 
  • Class 11 RD Sharma Solutions of Chapter 15 Statistics 
  • All Important NCERT Maths formulas for Class 11 Chapter 15 Statistics

Chapter 16 – Probability

The class 11 NCERT maths solutions chapter 16 Probability discusses the concept of Probability (a measure of uncertainty of various phenomena or a chance of occurrence of an event). In Class 11 Maths, the topics discussed are random experiments, outcomes, sample spaces, event, and their type.

 Class 11 Maths NCERT Solutions Chapter 16 Exercise
  • NCERT Maths Solutions Class 11 Exercise 16.1 – 16 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 16.2 – 7 Questions & Solutions
  • NCERT Maths Solutions Class 11 Exercise 16.3 – 21 Questions & Solutions
  • NCERT Maths Solutions Class 11 Miscellaneous Exercise – 10 Questions & Solutions

More resources for Class 11 Chapter 16 Probability
  • CBSE Class 11 Maths Notes of Chapter 16
  • Class 11 RD Sharma Solutions of Chapter 16 Probability 
  • All Important NCERT Maths formulas for Class 11 Chapter 16 Probability 

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

  • CBSE Maths Notes for Class 11
  • RD Sharma Solutions Maths Class 11
  • CBSE Class 11 Maths Formulas
  • CBSE Physics Class 11 Notes
  • CBSE Class 11 Chemistry Notes

These CBSE solutions are recommended by the National Council of Educational Research and Training (NCERT), available at (https://ncert.nic.in/).



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      Question 14: [Tex](1+ \frac{1}{1}) (1+ \frac{1}{2}) (1+ \frac{1}{3}) ..... (1+ \frac{1}{n}) [/Tex] = (n+1)Solution: We have, P(n) = [Tex](1+ \frac{1}{1}) (1+ \frac{1}{2}) (1+ \frac{1}{3}) ..... (1+ \frac{1}{n}) [/Tex] = (n+1) For n=1, we get P(1) = (1+ [Tex]\frac{1}{1} [/Tex]) = 2 = (1+1) = 2 So, P(
      12 min read

    Chapter 5: Complex Numbers and Quadratic Equations

    • Class 11 NCERT Solutions- Chapter 5 Complex Numbers And Quadratic Equations - Exercise 5.1 | Set 1
      For Q.1 to Q.10 express each complex number in form of a+ibQuestion 1. (5i)[Tex](\frac{-3i}{5})[/Tex] Solution: Let the given number be a, a= (5i)*[Tex](\frac{-3i}{5})[/Tex] a= [Tex]\frac{-15i^2}{5}[/Tex] a= (-3)*i2 a= (-3)*(-1) a= 3+0i Question 2. i9+i19 Solution: Let the given number be a, a = i9
      2 min read
    • Class 11 NCERT Solutions- Chapter 5 Complex Numbers And Quadratic Equations - Exercise 5.1 | Set 2
      Chapter 5 Complex Numbers And Quadratic Equations - Exercise 5.1 | Set 1For Q.11 to Q.13 find the multiplicative inverse of the given number Question 11. 4-3i Solution: Let's denote given number as a, the complement of a = [Tex]\overline{a} [/Tex] = [Tex]\overline{4-3i}[/Tex] [Tex]\overline{a} [/Tex
      2 min read
    • Class 11 NCERT Solutions- Chapter 5 Complex Numbers And Quadratic Equations - Exercise 5.2
      Find the modulus and the arguments of each of the complex numbers i. Exercises 1 to 2.Question 1. z = – 1 – i √3 Solution: We have, z = -1 - i√3 We know that, z = r (cosθ + i sinθ) Therefore, r cosθ = -1 ---(1) r sinθ = -√3 ----(2) On Squaring and adding (1) and (2), we obtain r2 (cos 2θ + sin 2θ) =
      6 min read
    • Class 11 NCERT Solutions- Chapter 5 Complex Numbers And Quadratic Equations - Exercise 5.3
      Solve each of the following equations:Question 1. x2 + 3 = 0 Solution: We have, x2 + 3 = 0 or x2 + 0 × x + 3 = 0 ---(1) Discriminant, D = b2 - 4ac from (1) , a = 1 , b = 0 and c = 3 D = (0)2 - 4*(1)*(3) D = -12 Since , x = [Tex]\frac{( -b ± \sqrt{D} }{2a}[/Tex] Therefore , x = [Tex]\frac{( -0 ± \sqr
      5 min read
    • Class 11 NCERT Solutions- Chapter 5 Complex Numbers And Quadratic Equations - Miscellaneous Exercise on Chapter 5 | Set 1
      Complex numbers are fundamental in higher mathematics and have a wide range of applications in engineering, physics, and applied sciences. Chapter 5 of the Class 11 NCERT textbook introduces the concept of complex numbers and their properties. This chapter also covers quadratic equations including t
      7 min read
    • Class 11 NCERT Solutions - Chapter 5 Complex Numbers And Quadratic Equations - Miscellaneous Exercise on Chapter 5 | Set 2
      Chapter 5 of Class 11 NCERT Mathematics deals with Complex Numbers and Quadratic Equations. This chapter introduces the concept of complex numbers, which are essential for solving certain types of quadratic equations that do not have real solutions. The chapter also covers the algebraic operations o
      6 min read

    Chapter 6: Linear Inequalities

    • Class 11 NCERT Solutions- Chapter 6 Linear Inequalities - Exercise 6.1 | Set 1
      Question 1. Solve 24x < 100, when (i) x is a natural number. (ii) x is an integer. Solution: (i) when x is a natural number. Clearly x>0 because from definition (N =1,2,3,4,5,6.....)Now we have to divide the inequation by 24 we get x<25/6But x is a natural number that is the solution will b
      8 min read
    • Class 11 NCERT Solutions - Chapter 6 Linear Inequalities - Exercise 6.1 | Set 2
      Chapter 6 Linear Inequalities - Exercise 6.1 | Set 1Question 13. 2 (2x + 3) – 10 < 6 (x – 2) Solution: Given, 2(2x + 3) – 10 < 6 (x – 2)By multiplying we get4x + 6 – 10 < 6x – 12On simplifying we get4x – 4 < 6x – 12– 4 + 12 < 6x – 4x8 < 2x4 < xThus, the solutions of the given eq
      8 min read
    • Class 11 NCERT Solutions - Chapter 6 Linear Inequalities - Exercise 6.2
      Solve the following inequalities graphically in two-dimensional plane:Question 1: x + y < 5 Solution: Now draw a dotted line x + y = 5 in the graph (because (x + y = 5) is NOT the part of the given equation) We need at least two solutions of the equation. So, we can use the following table to dra
      6 min read
    • Class 11 NCERT Solutions - Chapter 6 Linear Inequalities - Exercise 6.3
      Solve the following system of inequalities graphically:Question 1: x ≥ 3, y ≥ 2 Solution: For equation 1: Now draw a solid line x = 3 in the graph (because (x = 3) is the part of the given equation) we need at least two solutions of the equation. So, we can use the following table to draw the graph:
      15+ min read
    • Class 11 NCERT Solutions- Chapter 6 Linear Inequalities - Miscellaneous Exercise on Chapter 6
      Chapter 6 of Class 11 NCERT Mathematics delves into the topic of the Linear Inequalities. Linear inequalities are mathematical expressions that involve inequalities rather than equalities representing a range of possible values for the variable rather than a single solution. In this chapter, student
      13 min read

    Chapter 7: Permutations and Combinations

    • Class 11 NCERT Solutions - Chapter 7 Permutations And Combinations - Exercise 7.1
      Chapter 7 of the Class 11 NCERT Mathematics textbook, titled "Permutations and Combinations," introduces students to fundamental concepts in counting and arranging objects. This chapter focuses on the principles of permutations and combinations, which are essential for solving various problems in pr
      6 min read
    • Class 11 NCERT Solutions - Chapter 7 Permutations And Combinations - Exercise 7.2
      Chapter 7 of the Class 11 NCERT Mathematics textbook, titled "Permutations and Combinations," delves into the principles of counting and arranging objects. This chapter covers the concepts of permutations and combinations, which are crucial for solving problems involving the arrangement and selectio
      4 min read
    • Class 11 NCERT Solutions- Chapter 7 Permutations And Combinations - Exercise 7.3
      Theorem 1: The number of permutations of n different objects taken r at a time, where 0 < r ≤ n and the objects do not repeat is n(n-1)(n – 2). . .(n – r + 1), which is denoted by nPr = [Tex]\frac{n!}{(n-r)!}[/Tex] Theorem 2: The number of permutations of n different objects taken r at a time, wh
      15 min read
    • Class 11 NCERT Mathematics Solutions- Chapter 7 Permutations And Combinations - Exercise 7.4
      Chapter 7 of the Class 11 NCERT Mathematics textbook, "Permutations and Combinations," explores fundamental concepts of counting and arrangement. Exercise 7.4 focuses on applying these concepts to solve problems related to permutations and combinations, enhancing students' ability to handle various
      6 min read
    • Class 11 NCERT Solutions- Chapter 7 Permutations And Combinations - Miscellaneous Exercise on Chapter 7
      Chapter 7 of the Class 11 NCERT Mathematics textbook delves into the Permutations and Combinations essential topics in the probability and combinatorics. This chapter explores the fundamental principles of the counting and arrangement which are crucial for the solving various problems in the mathema
      11 min read

    Chapter 8: Binomial Theorem

    • Class 11 NCERT Solutions- Chapter 8 Binomial Theorem - Exercise 8.1
      The Binomial Theorem provides a method to expand expressions that are raised to a power such as the (x + y)n. It is a crucial concept in algebra, particularly useful for expanding the polynomials and solving combinatorial problems. In this chapter, students learn to apply the Binomial Theorem to sim
      9 min read
    • Class 11 NCERT Solutions - Chapter 8 Binomial Theorem - Exercise 8.2
      Question 1. Find the coefficient of x5 in (x+3)8 Solution: The (r+1)th term of (x+3)8 is given by Tr+1 = 8Cr(x)8-r(3)r (eq1). Therefore for x5 we need to get 8-r =5 (Because we need to find x5. Therefore, power ox must be equal to 5) So we get r=3. Now, put r=3 in eq1. We get, Coefficient of x5 = 8C
      5 min read
    • Class 11 NCERT Solutions- Chapter 8 Binomial Theorem - Miscellaneous Exercise on Chapter 8
      Question 1. Find a, b, and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290, and 30375, respectively.Solutions: As, we know that (r+1)th term of (a+b)n is denoted by, Tr+1 = nCr an-r br Here, it is given that first three terms of the expansion are 729, 7290 and
      11 min read

    Chapter 9: Sequences and Series

    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Exercise 9.1
      Chapter 9 of the NCERT Class 11 Mathematics textbook covers Sequences and Series which are fundamental concepts in algebra and mathematical analysis. Exercise 9.1 specifically deals with the problems that help students understand and solve various types of sequences and series. Mastery of these prob
      6 min read
    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Exercise 9.2
      Chapter 9 of the NCERT Class 11 Mathematics textbook focuses on the Sequences and Series a fundamental topic in algebra. Exercise 9.2 deals with the various problems related to arithmetic and geometric progressions in which are key concepts in understanding the behavior and relationships of the sequ
      9 min read
    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Exercise 9.3 | Set 1
      Question 1. Find the 20th and nth terms of the G.P 5/2, 5/4, 5/8, ... Solution: According to the question G.P: 5/2, 5/4, 5/8, ... So, first term(a) = 5/2 So, the common ratio(r) = [Tex]\frac{a_1}{a}=\frac{\frac54}{\frac52}= \frac12[/Tex] Find: 20th and nth terms of the given G.P So, the nth term of
      10 min read
    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Exercise 9.3 | Set 2
      Question 17. If the 4th, 10th and 16th terms of a G.P. are x, y, and z, respectively. Prove that x, y, z are in G.P. Solution: Let the first term of G.P. be a and common ratio be r. According to the question a4 = ar3 = x ......(1) a10 = ar9 = y ......(2) a16 = ar15 = z ......(3) Now divide eq(2) by
      10 min read
    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Exercise 9.4
      Find the sum to n terms of each of the series in Exercises 1 to 7.Question 1. 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + … Solution: Given: Series = 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + … To find nth term, we have nth term, an = n ( n + 1) So, the sum of n terms of the series: [Tex]S_n=\displaystyle\sum^n_{k=1}a_k=
      4 min read
    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Miscellaneous Exercise On Chapter 9 | Set 1
      Question 1. Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term. Solution: Let the first term and common difference of the A.P. be a and d respectively. (m+n)th term of the A.P. = a+(m+n−1)d (m−n)th term of the A.P. = a+(m−n−1)d Thus, L.H.S = a+(m+n−1)d + a+(
      11 min read
    • Class 11 NCERT Solutions- Chapter 9 Sequences And Series - Miscellaneous Exercise On Chapter 9 | Set 2
      Question 17. If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P. Solution: We are given, a, b, c and d are in G.P. Therefore, we have b2 = ac … (1) c2 = bd … (2) ad = bc … (3) We need to prove (an + bn), (bn + cn), (cn + dn) are in G.P. i.e., => (bn+ cn)2 = (an + bn)
      14 min read
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