NCERT Solutions for Class 12 Maths Free PDF Download
Class 12th Maths NCERT Solutions: NCERT introduced a lot of new topics and concepts in the NCERT textbook for Class 12 Maths. There are a total of thirteen chapters in class 12 for maths. Here Study Path provided you the best and precise NCERT solutions for class 12 maths. All these solutions have been prepared by our subject expert. Download the NCERT Solutions for class 12 maths for free in PDF format and solve them daily to improve your marks in the board exams. You can also download RD Sharma solutions and RS Aggarwal Solutions for free.
NCERT Solutions For Class 12 Maths
- 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 Chapter-wise Free PDF Download
In class 12, there are two textbooks for physics. As per the latest NCERT book, class 12 has fourteen chapters for physics. In the first part, there are 8 chapters while in the second part, there is a total of 6 chapters. NCERT Solutions for class 12 physics provided by Study Path covered all the chapters in the NCERT textbook. These solutions are written in a very clear and concise manner. Regular practice of these solutions helps you to understand each concept easily. Ultimately it helps you to get good marks in the board exams.
Chapter 1 – Relations and Functions
In this chapter, you will learn about relations, functions, domain, co-domain, range, etc. This chapter extends the topics that you have already learned in class 11. There are four exercises in the chapter and each of these discusses a different concept.
Chapter 2 – Inverse Trigonometric Functions
In this chapter, you will learn how to calculate the principal values of inverse trigonometric functions, properties of inverse trigonometric functions. Further, you will learn how the restrictions enables a trigonometric function to be one on one.
Chapter 3 – Matrices
In this chapter, you will know about the order of a matrix, types of matrices, equality of matrices, operations on matrices, etc.
Chapter 4 – Determinants
In chapter 3, we have studied about matrices and algebra of matrices. In this chapter, you will learn about the determinants of matrices up to order three. Further, you will know about minor, cofactors, adjoint and inverse of matrix. Moreover, you will also learn how yo calculate the area of triangles using determinants.
Chapter 5 – Continuity and Differentiability
This chapter extends the topics you have learned in class 11. This chapter explains about continuity, differentiability, and the relation between them. Further, you will get to know about exponential and logarithmic functions.
Chapter 6 – Application of Derivatives
In this chapter, you will be learning about the applications of derivates in various fields of life. This chapter explains the concept of tangents and normals, increasing decreasing functions, approximations, etc.
Chapter 7 – Integrals
Integral is one of the important and lengthy chapters of class 12 maths. In this chapter, you will learn about definite and indefinite integrals. Further, you will learn about different methods to solve integrations viz., substitution method, integration by partial fractions, etc.
Chapter 8 – Application of Integrals
Integrals have a lot of applications in every field of life. In this chapter, you will learn how to calculate the area under simple curves, the area of the region bounded by a curve and line, the area between two curves, etc.
Chapter 9 – Differential Equations
In this chapter, you will be learning about the degree and order of a differential equation, general and particular solutions of a differential equation, formation of differential equations, etc.
Chapter 10 – Vector Algebra
Any quantity that has both magnitude and directions is called Vector. In Vector Algebra you will learn about direction cosines, direction ratios, types of vectors, the addition of vectors, etc.
Chapter 11 – Three Dimensional Geometry
In three dimensional geometry, we will use the concepts of direction ratios and direction cosines that you have learned in chapter 10 along with some new concepts for solving the problems. In this chapter, you will learn how two calculate the distance between two points and much more.
Chapter 12 – Linear Programming
In this chapter, you will be learning about Linear Programming Problem and its Mathematical Formulation. Further, we will use the graphical method to solve lin linear programming problems.
Chapter 13 – Probability
Probability is an important topic in mathematics and has a lot of applications. In this chapter, you will learn about conditional probability, Bayes’ theorem, multiplication rule, Bernoulli trials and more.