 # NCERT Solutions for Class 12 Maths in Hindi Medium and English Medium (गणित) | 12th Class Maths NCERT Book Solutions PDF Download

NCERT Solutions for Class 12 Maths will give you a glimpse of all the topics in the Class 12 Maths Syllabus. Step by Step Explanations given for the topics of Class 12 Maths makes it easy for you better understand the concepts. In addition to the NCERT Solutions for Class 12 Maths, you can also find other preparation resources like CBSE Class 12 Maths Notes, Exemplar Problems, Previous Question Papers, etc. Download the handy study material over here and stand out on your board or any other competitive exams compared to your peers.

## CBSE NCERT Solutions for Class 12 Maths Updated for 2021-22

Class 12 CBSE Maths NCERT Solutions will not just confine you to your success in academics but also lays a strong foundation for other important subjects. Our 12th Class Maths NCERT Solutions PDFs include questions from all the exercises in NCERT Maths Textbooks. Use them as a quick reference and clear ambiguities if any in a fraction of seconds.

### NCERT Solutions for Class 12 Maths in English Medium

Chapter 1 Relations and Functions

Chapter 2 Inverse Trigonometric Functions

Chapter 3 Matrices

Chapter 4 Determinants

Chapter 5 Continuity and Differentiability

Chapter 6 Application of Derivatives

Chapter 7 Integrals

Chapter 8 Application of Integrals

Chapter 9 Differential Equations

Chapter 10 Vector Algebra

Chapter 11 Three Dimensional Geometry

Chapter 12 Linear Programming

Chapter 13 Probability

### NCERT Solutions for Class 12 Maths in Hindi Medium (गणित)

NCERT Solutions for Class 12th Maths can be extremely helpful for students as they can get an idea of the kind of questions appearing in the exams. Solving the Questions from these 12th Class Maths NCERT Solutions one can develop a strong foundation of maths basics that are essential for higher classes. Study effectively and learn how to present answers in a better way to score well. To self-evaluate your preparation standards you can simply rely on MCQ Questions for Class 12 Maths with Answers and identify the areas of need.

### 12th Class Maths All Chapters Brief

Students who are willing to attempt the Class 12 Maths Exam should know the Syllabus and Marks Distribution beforehand. Have a glimpse of all the chapters existing here and prepare accordingly. They are as follows

#### Chapter 1 Relations and Functions

1st Chapter in NCERT Textbook deals majorly with the topics relations and functions, types of relations such as reflexive, symmetric, transitive, and equivalence, types of functions namely One to one and onto functions, binary operations and miscellaneous examples, the composition of functions and invertible function, etc.

#### Chapter 2 Inverse Trigonometric Functions

Inverse Trigonometric Functions Chapter includes several topics such as the basic concept of inverse trigonometric functions, properties of inverse trigonometric functions, Definition, range, domain, principal value branch, miscellaneous examples explained thoroughly.

#### Chapter 3 Matrices

In this Chapter 3 of Class 12 Maths Textbook we will discuss majorly matrix definition, types of matrices, equality of matrices, operations on matrices, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, symmetric and skew-symmetric matrices, properties of multiplication of matrices, transpose of a matrix, properties of the transpose of the matrix, the inverse of a matrix by elementary operations, elementary operation or transformation of a matrix, and miscellaneous examples.

#### Chapter 4 Determinants

In this Chapter students will get to know the definition & meaning of determinants, order of determinants, properties of determinants, applications of determinants, minors and cofactors of determinants, finding the area of a triangle using determinants, adjoint of a matrix, the inverse of a matrix, and matrices and miscellaneous examples.

#### Chapter 5 Continuity and Differentiability

This Chapter 5 gives students knowledge on topics like continuity definition & meaning, differentiability definition, and meaning, derivative of implicit functions, derivatives of composite functions, derivatives of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, second-order derivatives, derivatives of functions in parametric forms, mean value theorem via miscellaneous examples.

#### Chapter 6 Applications of Derivatives

Chapter 6 includes derivatives definition, rate of change of quantities, approximations, tangents and normals, maxima and minima, increasing and decreasing functions, first derivative test, maximum and minimum values of a function in a closed interval, and miscellaneous examples.

#### Chapter 7 Integrals

Ch 7 Integrals include topics like definite & indefinite integral definition, integration the inverse process of differentiation, geometrical interpretation of indefinite integral, comparison between differentiation and integration, properties of indefinite integral,  integration using partial fractions, integration by parts, methods of integration such as integration by substitution, integration using trigonometric identities. Along with these concepts, it also includes topics such as fundamental theorem of calculus, definite integral as the limit of a sum, evaluation of definite integrals by substitution, some properties of definite integrals and miscellaneous examples.

#### Chapter 8 Applications of Integrals

This Chapter is a continuation of the chapter we discussed earlier and begins with the definition of integrals, area under simple curves, area between two curves, area of the region bounded by a curve and a line, and miscellaneous examples.

#### Chapter 9 Differential Equations

Here you will learn about the topics differential equations definition, a concept related to differential equations, degree & order of a differential equation, general and particular solutions of a differential equation, formation of a differential equation whose general solution is given, procedure to form a differential equation that will represent a given family of curves. Apart from these know the methods of solving first order, differential equations with variable separable, first-degree differential equations, linear differential equations, homogeneous differential equations, the procedure for solving first-order linear differential equations and miscellaneous examples.

#### Chapter 10 Vector Algebra

This chapter deals with the topics basic concepts regarding vector algebra, how to find the position vector, direction cosines, types of vectors, addition of vectors, properties of vector addition, components of a vector, vector joining two points, section formula. Furthermore, it even explains the topics like multiplication of a vector by a scalar, product of two vectors, scalar or dot product of two vectors, properties of scalar product, vector or cross product of two vectors, projection of a vector on a line, and miscellaneous examples.

#### Chapter 11 Three Dimensional Geometry

It covers information like Direction cosines and direction ratios of a line joining two points, coplanar and skew lines, Cartesian equation and vector equation of a line, Cartesian and vector equation of a plane, the shortest distance between two lines, the distance of a point from a plane.

#### Chapter 12 Linear Programming

In this chapter, we will discuss the concepts like Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. In addition, you will know the concepts like the Graphical method of solution for problems in two variables, feasible and infeasible solutions, feasible and infeasible regions (bounded), optimal feasible solutions(up to three non-trivial constraints).

#### Chapter 13 Probability

This Chapter includes topics like Conditional probability,  independent events, multiplication theorem on probability, total probability, Random variable, and its probability distribution, Bayes’ theorem. Along with these concepts, you will also become familiar with topics such as the mean of a random variable, the variance of a random variable, Bernoulli trials, and binomial distribution with miscellaneous examples.

### CBSE Class 12 Maths Unitwise Weightage for 1st Term

 No. Units Marks I Relations and Functions 08 II Algebra 10 III Calculus 17 V Linear Programming 05 Total 40 Internal Assessment 10 Total 50

### 12th Class Maths Unitwise Weightage for Second Term

 Unit Unit Name Marks III Calculus 18 IV Vectors and Three-Dimensional Geometry 14 VI Probability 08 Total 40 Internal Assessment 10 Total 50

### Key Features of CBSE Class 12th Mathematics NCERT Book Solutions

• 12th Grade Students can easily practice and revise the syllabus using these NCERT Solutions.
• You can save your time as you will find the required Math Formulas and Equations all in one place.
• Tips & Tricks mentioned in the CBSE Class 12 Maths NCERT Solutions can be quite helpful and you can answer extremely difficult questions too with ease.
• You can use them during your last-minute revision and get to know the subjects on a deeper level.
•  Answering the Questions in 12th Std Maths NCERT Book Solutions on a regular basis will improve your accuracy and speed while attempting the exams.

### FAQs on Class 12 Maths NCERT Solutions

1. Which is the best resource to find the CBSE NCERT Solutions for Class 12 Maths?

NCERTSolutions.guru is the best resource to find the NCERT Solutions for 12th Class Maths for All Chapters given by experts.

2. How many Chapters are there in the CBSE Class 12th Mathematics Textbook?

There are 13 Chapters in total in the Class 12th Mathematics Textbook.

3. Are NCERT Solutions Class 12 Maths sufficient to crack Board Exams?

Yes, NCERT Solutions of Class 12 Maths are more than enough to crack the Board Exams.

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