# NCERT Solutions for Class 12-science Maths CBSE

Get the best notes for Class 12 Maths with expert solutions for problems in your NCERT textbook. Learn to quickly solve maths numericals as per your Class 12 Science Maths syllabus with the step-wise NCERT solutions by our experienced Maths teachers. With consistent practise of the solutions, you can get over your fear of Maths problems and score good marks in your board exams.

Our Class 12 Maths NCERT solutions include NCERT solutions for Class 12 Maths Chapter 3 Matrices, Class 12 Determinants NCERT solutions, NCERT for CBSE Class 12 Maths Chapter 5 and more. The chapter-wise solutions assist you with a clear understanding of the Maths concepts such as derivatives, linear equations, probability, etc.

If you have doubts in any of the chapters, our academic experts can help you through TopperLearning’s “Undoubt” section. Here, you can also seek answers for doubts related to Maths board exam preparation or Maths Class 12 syllabus. For thorough Maths preparation, you should also practise the CBSE Class 12 sample papers and previous years’ papers on TopperLearning.

## NCERT solutions for CBSE Class 12 Science Maths

### Chapter 1 - Relations and Functions

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

### 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. Get solutions for all exercise questions in your textbook and understand how to prove the important properties of inverse trigonometric functions.

### Chapter 3 - Matrices

Get detailed and step-wise answers for questions on Matrices. 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 4 - Determinants

Using the NCERT solutions, you can revise the important topic of determinants, its properties, and its applications. Study the chapter 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.

### 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 the mathematical concepts such as differentiability, continuity, and relations.

### Chapter 6 - Applications of Derivatives

In this chapter, our Maths experts will support you 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 strengthen your JEE preparation.

### Chapter 7 - 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.

### Chapter 8 - Applications of Integrals

In this chapter, you will get solutions around the specific applications of integrals such as finding the area under simple curves, finding the area of the region bounded by a line and a circle, etc. Also, practise problems wherein you need to find the area of a region bounded by two parabolas or a triangle.

### Chapter 9 - Differential Equations

Utilise the 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.

### Chapter 10 - Vector Algebra

NCERT solutions for this chapter helps you with a revision of the concept of vectors, the properties of vectors and more. Use the solutions to solve problems related to 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.

### Chapter 11 - Three Dimensional Geometry

In this chapter, study in detail about the direction cosines of a line and the equation of a plane in different forms. 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. Also, learn to find the angle between two lines as per the given data.

### 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, you’ll be able to answer questions involving finding the minimum cost, maximum profit, minimum use of resources, etc.

### 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 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.

## Why NCERT Solutions for Class 12 Science Maths are important?

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.

If you go through your Class 12 Science Maths syllabus, you’ll find several theorems, equations, etc. Most of the chapters present you with more of numerical questions and less of theory questions. What this means is that you need to understand how to solve the problems by gaining conceptual clarity to be able to score marks in your board exam.

NCERT CBSE Class 12 solutions can be used for revision of the important concepts or for practising problems related to challenging syllabus topics. Also, a good grasp of your Class 12 Maths concepts will be useful when you pursue higher education in engineering, management science, etc. Learning the concepts accurately with TopperLearning’s NCERT Class 12 solutions will help you to prepare well for your Maths board exam and for competitive exams like JEE.

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