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# NCERT Solutions for Class 12-science Maths CBSE

TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics caters to all the needs of a CBSE 12th grader with its wholesome package of study material consisting of videos, CBSE sample paper Class 12, revision notes, most important questions, and subjective and objective questions. CBSE Class 12 syllabus notes are drafted in the simplest way possible, which is the reason why the material can be referred by all students whenever they feel the need for it. Our skilled and experienced academic team covers all requirements of students by following the updated CBSE curriculum. These CBSE Class 12 Maths notes help a student in scoring full marks in their examination and ensure a strong approach for a student with CBSE Class 12 syllabus and JEE exams as well.

## NCERT solutions for CBSE Class 12 Maths

NCERT Solutions for CBSE Class 12 Mathematics Chapter 1 - Relations and Functions

In this chapter, study the different types of relations including reflexive relations, symmetric relations, equivalence relations, and transitive relations with NCERT Solutions for Class 12 Mathematics. You’ll also learn about concepts related to functions such as composite functions and the inverse of a function. Also, use the free textbook Solutions to understand how to solve problems related to binary operations.

Chapter 1 - Relations and Functions Exercise Ex. 1.1

Determine whether the relations are reflexive, symmetric and transitive with NCERT Solutions for CBSE Class 12 Maths. There are many MCQs from this chapter that can help students practise better. Refer to CBSE Class 12 Maths notes and check your answers and understanding of how to write stepwise solutions.

Chapter 1 - Relations and Functions Exercise Ex. 1.2

The concept of function from the CBSE Class 12 syllabus is of paramount importance. Study more about function and different types of functions with CBSE Class 12 Maths textbook solutions.

Chapter 1 - Relations and Functions Exercise Ex. 1.3

Explore Composition of Functions and Invertible Function with NCERT Solutions for CBSE Class 12 Maths. Refer to CBSE sample papers Class 12 to understand different kinds of questions and solutions from this exercise by our subject experts.

Chapter 1 - Relations and Functions Exercise Ex. 1.4

Always be a step ahead in CBSE Class 12 Maths by learning about Binary functions. Determine whether the given function is binary and check your answers on TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

Chapter 1 - Relations and Functions Miscellaneous Exercise

TopperLearning’s NCERT Solutions for CBSE Class 12 Maths help you by giving step-wise solutions for all the questions in this exercise. Use our doubt solver “Undoubt” when you’re puzzled. Clear your concerns by practising More by using video lectures, MCQs, and CBSE Class 12 Maths sample paper.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 2 - Inverse Trigonometric Functions

Go through NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions solved by our expert Maths teachers as per the latest NCERT (CBSE) Book guidelines in free textbook Solutions. Get solutions for all exercise questions from your textbook and understand how to prove the important properties of inverse trigonometric functions with NCERT Solutions for Class 12 Mathematics.

Chapter 2 - Inverse Trigonometric Functions Exercise 2.1

Learn about Inverse trigonometric solutions and the process of principal value with detailed stepwise solutions with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. Questions from this exercise can be asked in the MCQs category. Hence, it would be a great idea to refer to TopperLearning’s extra MCQs and CBSE Class 12 Maths sample papers for practice.

Chapter 2 - Inverse Trigonometric Functions Exercise 2.2

Understand the Properties of Inverse Trigonometric Functions and simplify them in the basic forms in CBSE Class 12 Maths. You can find all the solutions on TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. Refer to CBSE Class 12 Maths notes for some extra practice material.

Chapter 2 - Inverse Trigonometric Functions Miscellaneous Exercise

Increase your confidence by attempting all kinds of questions from this chapter with absolutely no worries as TopperLearning provides you with NCERT Solutions for CBSE Class 12 Maths. In case of any difficulties, use our doubt solver "Undoubt" platform.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 3 - Matrices

Get detailed and step-wise answers for questions on Matrices with NCERT Solutions for Class 12 Mathematics. Find out what is a symmetric matrix, a skew-symmetric matrix, and a square matrix. Understand the elementary operations of a matrix. Learn how to find the inverse of the given matrices by using elementary transformations and more.

Chapter 3 - Matrices Exercise 3.1

Learn the basics of matrices and types of matrices in CBSE Class 12 Maths and tally all your solutions with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. There are different kinds of questions like MCQs, objective, and subjective questions that can be practised with TopperLearning’s CBSE Class 12 Maths.

Chapter 3 - Matrices Exercise 3.2

Just like when we learnt about numbers and then performed various operations on them, we now shall take the same step with Matrices too in CBSE Class 12 syllabus. Perform operations like addition, multiplication and subtraction understanding the properties associated with it as you refer to NCERT Solutions for CBSE Class 12 Maths.

Chapter 3 - Matrices Exercise 3.3

What is the Transpose of a Matrix? How to identify Symmetric and Skew Symmetric Matrices? Know more about these new terminologies in the CBSE Class 12 syllabus. Attempt all the questions and refer to the solutions with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

Chapter 3 - Matrices Exercise 3.4

Understand how to find the inverse of a matrix by elementary operations with stepwise solutions from TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

Chapter 3 - Matrices Miscellaneous Exercise

Get ready to attempt all kinds of mixed questions in this final exercise in CBSE Class 12 Maths. Be rest assured as TopperLearning will help you with all the solutions on TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 4 - Determinants

Using the NCERT solutions, you can revise the important topic of determinants, their properties, and their applications in the CBSE syllabus for Class 12 Maths. Study with the free textbook Solutions to understand how you can use determinants to find the inverse of a square matrix or area of a triangle. Learn to solve linear equations using the matrix method and practise the correct steps to prove the given linear equations with TopperLearning’s NCERT Solutions for Class 12 Mathematics.

Chapter 4 - Determinants Exercise 4.1

Enlighten yourself with all the basic terminologies of Determinants, which is based on the concept of Matrices, with CBSE Class 12 Maths textbook solutions.

TopperLearning’s CBSE Class 12 notes along with CBSE Class 12 Maths Sample papers give you a good understanding of all the concepts and questions from this exercise.

Chapter 4 - Determinants Exercise 4.2

Learn about the properties of Determinants and perform various operations on them with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. Understand the information provided in the question and check each step of the calculation as stated in TopperLearning’s videos for CBSE Class 12 Maths textbook solution.

Chapter 4 - Determinants Exercise 4.3

Calculate the area of the triangle using Determinants and evaluate your answers with CBSE Class 12 Maths textbook solution. Practise more problems with the weekly tests and CBSE Class 12 sample paper 2020-21.

Chapter 4 - Determinants Exercise 4.4

Get acquainted with the steps to find out minors and co-factors in a determinant in a detailed manner and check your answers on TopperLearning with  NCERT Solutions for CBSE Class 12 Maths.

Chapter 4 - Determinants Exercise 4.5

Learn more about Matrices and find inverse and adjoint of a matrix with detailed solutions on TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. The video solutions and weekly tests are the best way to practise CBSE Class 12 Maths.

Chapter 4 - Determinants Exercise 4.6

Know more about Applications of Determinants and Matrices through this exercise and tally your answers by checking TopperLearning’s  NCERT Solutions for CBSE Class 12 Maths. Questions from this exercise can be found in the subjective section of CBSE Class 12 sample papers 2020-21.

Chapter 4 - Determinants Miscellaneous Exercise

Get ready for CBSE online Class 12 by attempting a mixed bag of questions on Determinants. TopperLearning’s NCERT Solutions for CBSE Class 12 Maths assist you with all the solutions so that you can use them to explore the problem-solving techniques in Maths and learn to study independently.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 5 - Continuity and Differentiability

Use Chapter 5 NCERT solutions to study the important topic of differential calculus. In this chapter, you can revise topics such as logarithmic functions, exponential functions, Mean Value Theorem, and Rolle’s Theorem. With the NCERT textbook solutions, our Maths experts will help you understand mathematical concepts such as differentiability, continuity, and relations in the CBSE syllabus for Class 12 Maths.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.1

Revise the ways to check limits and continuity of a function on the given points in this exercise and refer to solutions with deep conceptual insight on TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.2

Grasp one of the most crucial concepts of CBSE Class 12 Maths and learn to differentiate the functions with respect to x with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. This exercise tests students’ knowledge of the basics of differentiation.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.3

TopperLearning’s CBSE Class 12 Maths solutions assist you with finding derivatives for implicit functions and inverse trigonometric functions. Get adequate practice with TopperLearning’s video solutions, weekly tests, most important questions, and CBSE Class 12 Maths sample papers.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.4

How do we differentiate between exponential functions?
Answers and detailed stepwise solutions are available for your assistance  TopperLearning’s CBSE Class 12 Maths textbook solutions. Solve every problem and some extra questions with TopperLearning’s CBSE Class 12 Maths material, and increase your precision.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.5

Get a grip and complete clarity of Logarithmic differentiation and check your solutions with TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.6

Strengthen your knowledge about derivatives by learning about Derivatives of Functions in Parametric Forms with TopperLearning’s solutions for NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.7

What is a second-order derivative? The answer to this question along with all the solutions for this exercise is available on TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 5 - Continuity and Differentiability Exercise Ex. 5.8

Questions from this exercise are based on Mean Value Theorem and are asked for 3-4 marks.  Hence, make sure you go through TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 5 - Continuity and Differentiability Miscellaneous Exercise

Dive in deeper to understand different questions based on derivatives through some unique problems and their solutions with TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics. With self-study, you will be confident enough to solve problems correctly in your exam. Get as much practice as you want with TopperLearning’s video solutions, weekly test, most important questions, and CBSE Class 12 Maths sample papers.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 6 - Applications of Derivatives

In the NCERT Solutions for Class 12 Mathematics, our Maths experts have made sure that you have all the support to revise concepts such as maxima, minima, approximation, rate of change, etc. NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives will not just help you to prepare for your Class 12 board exams, but also give a boost to your JEE preparation with free textbook solutions.

Chapter 6 - Applications of Derivatives Exercise Ex. 6.1

The concept of Rate of Change of Quantities has been evaluated in this exercise. The solutions to all the questions are provided by TopperLearning at NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 6 - Applications of Derivatives Exercise Ex. 6.2

Analyse Increasing and Decreasing Functions using differentiation in CBSE Class 12 Maths. Gain complete clarity by referring to solutions from TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 6 - Applications of Derivatives Exercise Ex. 6.3

How to use differentiation to find the equation of the tangent line and the normal line to a curve at a given point? The solution to this concept can be found by using our NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 6 - Applications of Derivatives Exercise Ex. 6.4

In this exercise of CBSE Class 12 Maths, we will use differentials to approximate values of certain quantities with NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 6 - Applications of Derivatives Exercise Ex. 6.5

The concept of the derivative is useful for estimating the maximum or minimum values of various functions in  CBSE Class 12 Maths. With TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics by your side, it is easy to understand all the steps of the solutions.

Chapter 6 - Applications of Derivatives Miscellaneous Exercise

Get extensive knowledge of all kinds of questions from this chapter in the final exercise with TopperLearning’s apt NCERT Solutions for CBSE Class 12 Mathematics. Several questions from here can be asked for 3-4 marks in the subjective section. Not only this, the questions are ideal practice for JEE exams. In case of doubts, get in touch instantly with our team of subject experts using the doubt solver “Undoubt”.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 7 - Integrals

This chapter covers integral calculus and as per CBSE exam guidelines, calculus topics carry high weightage in Class 12 Maths board exam. TopperLearning’s NCERT Chapter 7 solutions will come in handy as they will help you understand how to solve questions using the technique of integration by parts. Also, revise how to find integrals and how to integrate the functions given in your exercise questions with our NCERT Solutions for Class 12 Mathematics.

Chapter 7 - Integrals Exercise Ex. 7.1

Discover the basics of Integration along with its terms and the formulae that lay the foundation of complex questions in the CBSE Class 12 syllabus. TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics are on-point solutions with conceptual insight.

Chapter 7 - Integrals Exercise Ex. 7.2

There are some additional techniques or methods for finding the integrals by reducing them into standard forms in CBSE Class 12 syllabus. Solve all the questions from this exercise and refer to TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics for answers. Doubts and difficulties disappear with more practice and because of Topper Learning’s most important questions, weekly tests, and CBSE sample paper Class 12.

Chapter 7 - Integrals Exercise Ex. 7.3

How to find the solution of an integrand that involves some trigonometric functions? Answer to these questions and to all the problems from this exercise are provided in the NCERT Solutions for CBSE Class 12 Mathematics on TopperLearning in the most detailed and apt manner.

Chapter 7 - Integrals Exercise Ex. 7.4

Learn more about deducing answers for Integrals of Some Particular Functions with TopperLearning’s video solutions and practice material at NCERT Solutions for CBSE Class 12 Mathematics. Refer to our CBSE sample paper Class 12 to understand the different kinds of questions that can be asked from this exercise along with the solutions, given by our subject experts.

Chapter 7 - Integrals Exercise Ex. 7.5

TopperLearning makes the concept of integrations with some unique formulae for solving Integration by partial fractions in its NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 7 - Integrals Exercise Ex. 7.6

TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics elaborate one more method of integration that is quite useful in integrating products of functions. There are some most important questions asked from this section in CBSE Class 12 sample paper 2020-21

Chapter 7 - Integrals Exercise Ex. 7.7

This exercise discusses some special types of standard integrals based on the technique of integration by parts with all the solutions ready on TopperLearning’s NCERT Solutions for CBSE Class 12 Mathematics.

Chapter 7 - Integrals Exercise Ex. 7.8

Evaluate the definite integrals as a limit of sums in this short exercise with elaborate solutions available on TopperLearning’s CBSE Class 12 Maths textbook solution.

Chapter 7 - Integrals Exercise Ex. 7.9

TopperLearning’s CBSE Class 12 Maths textbook solutions for this exercise provides you with the best approach for solving the questions, which are based on the concept of Definite Integral and theorems of integral calculus. Explore some more questions in TopperLearning’s study material.

Chapter 7 - Integrals Exercise Ex. 7.10

One of the methods of finding the indefinite integral is the method of substitution. So, we apply the same for Definite Integral as well. Tally all your solutions with CBSE Class 12 Maths textbook solutions on TopperLearning.

Chapter 7 - Integrals Exercise Ex. 7.11

There are some properties that will be useful in evaluating definite integrals more easily. TopperLearning’s CBSE Class 12 Maths solution not only lists out the properties but also gives a thorough solution for each question.

Chapter 7 - Integrals Miscellaneous Exercise

TopperLearning’s CBSE Class 12 Maths textbook solutions will give you all the guidance you need to solve each and every question from the master exercise where you can apply all the concepts you learnt in this vast chapter. Check your knowledge with some extra practice questions, video solutions, weekly tests, and CBSE Class 12 sample paper 2020-21.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 8 - Applications of Integrals

This chapter covers integral calculus and as per CBSE exam guidelines, calculus topics carry high weightage in your Class 12 Maths board exam. The NCERT Chapter 7 solutions will come in handy to understand how to solve questions using the technique of integration by parts. Also, revise how to find integrals and how to integrate the functions given in your exercise questions using free textbook solutions.

Chapter 8 - Applications of Integrals Exercise Ex. 8.1

Find out the Area under Simple Curves using the process of Integration. This application of Integrals can be understood better with all the solutions on TopperLearning’s CBSE Class 12 Maths textbook solutions.

Chapter 8 - Applications of Integrals Exercise Ex. 8.2

Ideally, integration is the process of calculating area by dividing cutting the region into many small stripes of the elementary areas and then adding the elementary areas. Hence, we calculate the Area between Two Curves using the concept of integration in the CBSE Class 12 Maths Solutions.

Chapter 8 - Applications of Integrals Miscellaneous Exercise

Check your method and ask your queries after going through TopperLearning’s study material, which comprises video solutions, important questions, and weekly tests. Refer to TopperLearning’s CBSE sample paper Class 12 to understand different kinds of questions associated with this exercise and also study the solutions, written by our subject experts.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 9 - Differential Equations

Use TopperLearning’s NCERT Solutions for Chapter 9 to understand the basics of differential equations. Study the steps used by Maths experts to form a differential equation. Practise the methods used to solve first-order first-degree differential equations. Also, understand how to prove that a given equation is a homogeneous differential equation with NCERT Solutions for Class 12 Mathematics.

Chapter 9 - Differential Equations Exercise Ex. 9.1

Learn about basic concepts like the order of a differential equation and the degree of a differential equation, and solve problems from this exercise. Refer to answers associated with reasons at TopperLearning’s CBSE Class 12 Maths solutions and gain absolute clarity on this exercise.

Chapter 9 - Differential Equations Exercise Ex. 9.2

TopperLearning’s CBSE Class 12 Maths solutions offer the solutions to all the complex problems from this exercise making it simple to understand with stepwise solutions.

Chapter 9 - Differential Equations Exercise Ex. 9.3

Figure out how a Differential Equation whose General Solution is given is formed, with TopperLearning’s CBSE Class 12 Maths Solutions.

Chapter 9 - Differential Equations Exercise Ex. 9.4

How to solve a differential equation? What are the methods of Solving First Order, and First Degree Differential Equations? Find answers to these questions with TopperLearning’s CBSE Class 12 Maths Solutions.

Chapter 9 - Differential Equations Exercise Ex. 9.5

Understand how to prove a given differential equation homogeneous with these simple steps as shown in TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

Chapter 9 - Differential Equations Exercise Ex. 9.6

Simplify the given question using the concept of linear differential equations and find answers quickly. Tally all your answers with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths and reach out to our experts using our doubt solver “Undoubt”.

Chapter 9 - Differential Equations Miscellaneous Exercise

Get ready to solve all types of questions from this chapter and assess your knowledge with TopperLearning’s NCERT Solutions for CBSE Class 12 Maths. TopperLearning offers several questions and abundant study material so that you ace your CBSE Class 12 syllabus and exam preparation. Refer to TopperLearning’s CBSE sample paper Class 12 to understand different kinds of questions from this exercise along with the solutions, given by our subject experts.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 10 - Vector Algebra

NCERT solutions for this chapter help you revise the concept of vectors, the properties of vectors, and more. Refer to the solutions as you solve problems about the various types of vectors such as unit vector, collinear vector, equal vectors, etc. Understand how to find the direction cosines of a vector. Also, learn to classify scalar and vector quantities with TopperLearning’s NCERT Solutions for Class 12 Mathematics.

Chapter 10 - Vector Algebra Exercise Ex. 10.1

Revise all the basic concepts of three-dimensional space, vectors, types of vectors, etc. and increase your exam score with TopperLearning’s study material. Practise better with the most important questions and CBSE sample paper Class 12.

Chapter 10 - Vector Algebra Exercise Ex. 10.2

Perform various operations like addition, multiplication, etc. on vectors and refer to TopperLearning’s CBSE Class 12 Maths textbook solutions for step by step solutions to the questions.

Chapter 10 - Vector Algebra Exercise Ex. 10.3

Get familiar with the different types of product of vectors in this exercise and study the complete solutions with CBSE Class 12 Maths textbook solutions by TopperLearning. Refer to CBSE sample paper Class 12 to understand different kinds of questions associated with this exercise and take a look at the solutions, written by our subject experts.

Chapter 10 - Vector Algebra Exercise Ex. 10.4

Boost your scores by solving every kind of problem from this exercise with the help of TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

Chapter 10 - Vector Algebra Miscellaneous Exercise

Vector Algebra is considered to be the most scoring chapter in CBSE Class 12 Maths. Solve a mixed bag of questions to develop excellence in Maths with TopperLearning’s useful study material.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 11 - Three Dimensional Geometry

In this chapter, study in detail the direction cosines of a line and the equation of a plane in different forms with free textbook solutions. The NCERT Chapter 11 solutions will help you with step-wise answers to find the vector equation of a line. Revise the concept of the derivation of cartesian form from a vector form with TopperLearning’s NCERT Solutions for Class 12 Mathematics. Also, learn to find the angle between two lines as per the given data.

Chapter 11 - Three Dimensional Geometry Exercise Ex. 11.1

Solve this exercise and get introduced to Three-dimensional geometry. You can refer to TopperLearning’s CBSE Class 12 Maths textbook solutions to understand the calculation part.

Chapter 11 - Three Dimensional Geometry Exercise Ex. 11.2

Discover all the important terminologies regarding the equation of a line in space. Gain access to detailed solutions with conceptual insights with CBSE Class 12 Maths textbook solutions by TopperLearning.

Chapter 11 - Three Dimensional Geometry Exercise Ex. 11.3

Evaluate your knowledge by understanding details about planes in the given questions and get a simplified output that can be checked thoroughly with NCERT Solutions for CBSE Class 12 Maths on TopperLearning.

Chapter 11 - Three Dimensional Geometry Miscellaneous Exercise

Get access to all solutions of the exercise and find the precision to boost your score with TopperLearning’s NCERT Solutions for Class 12 Mathematics.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 12 - Linear Programming

This chapter involves solving optimisation problems using graphical methods. Practise the different types of real-life problems in this chapter to understand the concept of linear programming. Using the chapter solutions at TopperLearning’s NCERT Solutions for Class 12 Mathematics, you’ll be able to answer questions about finding the minimum cost, maximum profit, minimum use of resources, etc.

Chapter 12 - Linear Programming Exercise Ex. 12.1

We shall study some linear programming problems and their solutions by graphical method only in this exercise. Revise all the necessary terms and methods with TopperLearning’s video solutions and elaborate study material under CBSE Class 12 notes.

Chapter 12 - Linear Programming Exercise Ex. 12.2

Master the concept of Different Types of Linear Programming Problems and methods to solve them with TopperLearning’s finest NCERT Solutions for CBSE Class 12 Maths.

Chapter 12 - Linear Programming Miscellaneous Exercise

Get a good grasp on all types of questions from this chapter and compare your solutions to TopperLearning’s NCERT Solutions for CBSE Class 12 Maths.

NCERT Solutions for CBSE Class 12 Mathematics Chapter 13 - Probability

Through the NCERT solutions for Class 12, Chapter 13, revise topics such as conditional probability, Bayes’ theorem, and the theorem of total probability. Study the concept of the binomial distribution with TopperLearning’s CBSE syllabus for Class 12 Maths to solve problems related to probability. Also, practise problems to understand how to find the probability distribution of a random variable as per given data.

Chapter 13 - Probability Exercise Ex. 13.1

With the knowledge from previous grades, dive in deeper to understand the properties of conditional probability and compare your solutions with TopperLearning’s NCERT Solutions for Class 12 Mathematics.

Chapter 13 - Probability Exercise Ex. 13.2

Solve these questions by using the multiplication Theorem on Probability. Get a complete insight on the concepts with TopperLearning’s CBSE Class 12 Maths textbook solution.

Chapter 13 - Probability Exercise Ex. 13.3

Attempt questions based on Bayes' Theorem and the theorem on total probability. Increase your scores by referring to stepwise solutions with CBSE Class 12 Maths textbook solution by TopperLearning.

Chapter 13 - Probability Exercise Ex. 13.4

Gain access to all the correct solutions of the exercise and boost your exam score with TopperLearning’s NCERT Solutions for Class 12 Mathematics.

Chapter 13 - Probability Exercise Ex. 13.5

Get acquainted with Bernoulli Trials and Binomial Distribution and use the same for solving questions from this exercise.

Chapter 13 - Probability Miscellaneous Exercise

Get an extensive understanding of all kinds of questions from this chapter in the final exercise with TopperLearning’s accurate NCERT Solutions for CBSE Class 12 Mathematics.

## CBSE Class 12 Chapter-wise Marks Weightage

Aim your preparation for CBSE online Class 12  in the right direction by taking into account the weightage of each chapter. Prepare for your board exams with TopperLearning’s finest study material and increase your scores.

Course Structure CBSE Class 12 (2021-22)

One Paper                                                                                                      Max Marks: 80

 No. Units No. of Periods Marks 1 Relations and Functions 30 08 2 Algebra 50 10 3 Calculus 80 35 4 Vectors and Three-Dimensional Geometry 30 14 5 Linear Programming 20 05 6 Probability 30 08 Total 240 80 Internal Assessment 20

## MATHEMATICS – Standard Question Paper Design Class 12 (2021-2022)

Familiarise yourself with the format of the CBSE sample paper Class 12 so that your preparation and practice for the exam are perfect. In order to add to notes and assessment, TopperLearning also provides CBSE Class 12 sample paper 2020-21. The whole package can be accessed 24x7 allowing no interruption in your exam preparation.

QUESTION PAPER DESIGN CLASS 12 (2021 - 22)

Time: 3 hours                                                                                                                                  Max. Marks: 80

 Sr No. Typology of Questions Total Marks % Weightage 1 Remembering: Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers. Understanding: Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas 44 55 2 Applying: Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way. 20 25 3 Analysing : Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Evaluating: Present and defend opinions by making judgments about information, the validity of ideas, or quality of work based on a set of criteria. Creating: Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions 16 20 Total 80 100

 INTERNAL ASSESSMENT 20 MARKS Periodic Tests ( Best 2 out of 3 tests conducted) 10 Marks Mathematics Activities 10 Marks

## Benefits of NCERT Solutions Class 12 Maths

Class 12 Maths NCERT solutions are invaluable because it gives you the methods used by experts to answers the NCERT textbook questions as per your CBSE Class 12 syllabus. By going through the chapter-wise solutions, you’ll be able to understand the different types of problems based on linear programming, integral calculus, inverse trigonometric functions, and more.

## Frequently Asked Questions (FAQs) - CBSE Class 12 Mathematics

1.Why should I get TopperLearning NCERT Solutions for Class 12?

The study material is developed by a skilled and experienced team of subject experts who specialise in simplifying concepts for students. TopperLearning’s NCERT Solutions for CBSE Class 12 Maths has a detailed, stepwise approach accompanied by conceptual insights and repetitive mention of formulae to ensure full coverage of the CBSE syllabus for Class 12 Maths. It has everything that a student requires for exam preparation, thus ensuring success.

2. Which is the best book for CBSE 12th grade preparation?

The NCERT textbook itself is the best book for the preparation for the board exam. You can refer to some extra questions available in TopperLearning’s study material for more practice.

3. Is the CBSE Class 12 syllabus difficult?

CBSE Class 12 syllabus is not difficult but vast but can be simplified and covered with the right amount of practice.

4. How can I ask doubts?

We have our doubt solver, “Undoubt” where Maths experts are readily available to solve all your doubts promptly.

5. Can I score 100 per cent marks in CBSE Maths and CBSE Class 12 Science?

Yes, with the right amount of hard work and practice, you can certainly score full marks in the subjects.

6. How many chapters are there in CBSE Class 12 Maths?

There are 13 chapters including paper 1 and paper 2. Solutions of all the exercises for NCERT textbooks are available in TopperLearning’s study material.

7. Where can I access the deleted syllabus of CBSE Class 12?

It was reduced in 2020. The deleted syllabus of CBSE Class 12 is included in the current syllabus and you can also find solutions for the questions from the deleted syllabus in TopperLearning’s notes for CBSE online Class 12.

8. Can I find solutions for CBSE Class 12 Science?

TopperLearning caters to every need of a student and so the solutions for CBSE Class 12 Science are of course available. We also have solutions for CBSE Class 12 English making sure students are completely prepared for their exams.

9. Are the CBSE Class 12 Maths solution accepted on the boards?

Yes. Our academic experts have made sure that the solutions of the CBSE syllabus for Class 12 Maths are accurate and correct. The methods are just as in NCERT textbooks. CBSE syllabus for Class 12 Maths solutions are well accepted by the CBSE board schools.

10. Are there any sample papers for extensive practice?

Yes of course. We have CBSE sample papers Class 12 that act as an add on feature and help you with sample solutions as well for practice.