NCERT Solutions Class 12 Maths 2023 for all chapters is available here for free download. Students can access the Class 12 solutions for NCERT Maths Chapter-wise from the pdf links provided in this article. Maths Class 12 NCERT Solutions pdf is helpful for the candidates who have to appear in the board exam. CBSE prescribes the NCERT textbook in class 12 for Maths. The NCERT Maths book for class 12 is designed by expert teachers and academicians. Students can get all the solutions and answers from NCERT Solutions. The solution of class 12 NCERT Maths is as per the latest syllabus and curriculum. These solutions can be used by kids as a reference if they get stuck while solving questions or can act as a source to clarify concepts. Read the article to download the NCERT Solutions for Class 12 Maths PDF.
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NCERT Solutions Class 12 Maths 2023- Download Pdf
CBSE conducts the annual board exam for students studying in class 12. NCERT Solutions for Class 12 Maths provide a solid conceptual base for all the topics included in CBSE Class 12 Maths Syllabus. It covers all the important theorems and formulae with detailed explanations to promote a better conceptual understanding in students. Therefore, it is recommended for the students to download the Maths Solutions for class 12 and practice the sample questions. These solutions for the exercise questions are given at the end of each chapter.
NCERT Solutions For Class 12 Maths Chapter 1: Relations and Functions
Chapter 1 of the NCERT textbook deals with relations and functions, types of relation, types of functions, the composition of functions and invertible function, binary operations, and miscellaneous examples. Students can learn about various types of Sets, Types of relations: reflexive, symmetric, transitive, and equivalence relations in this chapter. Apart from this, questions based on binary operations, invertible elements, and commutative operations are also included in this chapter.
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NCERT Solutions For Class 12 Maths Chapter 2: Inverse Trigonometric Functions
In chapter 2 of NCERT Maths is about Inverse trigonometric functions, which are simply defined as the inverse functions of the basic trigonometric functions which include sine, cosine, tangent, cotangent, secant, and with its cosecant functions. This is an important chapter of Algebra. Students can learn how to use inverse functions in trigonometry to get the angle with any of the trigonometry ratios. Trigonometric Functions are very important and mostly used in the field of engineering, physics, geometry, and navigation.
Important Formulas for NCERT Solutions Class 12 Maths Chapter 2
- sin–1 (–x) = – sin–1 x
- tan–1 x + cot–1 x = π/2
- sin–1 x + cos–1 x = π/2
- cos–1 (–x) = π – cos–1 x
- cot–1 (–x) = π – cot–1 x
NCERT Solutions For Class 12 Maths Chapter 3: Matrices
In chapter 3 of the NCERT book, students are introduced to the Matrix is a rectangular array of real or complex numbers in the form of m horizontal lines which are called rows, and n vertical lines which are called columns. Students are also taught about the definition of a matrix, types of matrices, equality of matrices, operations on matrices such as the addition of matrices and multiplication of a matrix by a scalar, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, properties of the transpose of the matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, the inverse of a matrix by elementary operations and miscellaneous examples.
Important Formulas for NCERT Solutions Class 12 Maths Chapter 1
- – A = (–1)A
- A – B = A + (–1) B
- A + B = B + A
- (A + B) + C = A + (B + C)
- k(A + B) = kA + kB (where A, B and C are matrices).
NCERT Solutions For Class 12 Maths Chapter 4: Determinants
Chapter 4 of the NCERT textbook is about the Determinants. Students are taught about the definition and meaning of determinants, remarks based on the order of determinants, properties of determinants, finding the area of a triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, the inverse of a matrix, applications of determinants and matrices, and miscellaneous examples. The determinant is a scalar value that can be measured from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix A is denoted set(A), set A, or |A|.
NCERT Solutions For Class 12 Maths Chapter 5: Continuity And Differentiability
Chapter 5 of the NCERT Maths is about continuity, algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of implicit functions, a derivative of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, mean value theorem via miscellaneous examples.
Important Formulas for NCERT Solutions Class 12 Maths Chapter 5
- Chain Rule: df/dv = (dt/dx) * (dt/dx)
- d/dx (sin-1x) = 1/√(1 – x2)
- d/dx (cos-1x) = – 1/√(1 – x2)
- d/dx (tan-1x) = 1/(1 + x2)
- d/dx (cot-1x) = 1/(1 + x2)
- d/dx (sec-1x) = 1/x √(1 – x2)
NCERT Solutions For Class 12 Maths Chapter 6: Application of Derivatives
Chapter 6 Derivative is an interesting topic in class 12 Maths. Students will learn different applications of derivatives used in various fields such as Science, Engineering, and other fields. A derivative can be defined as the rate of change of one quantity with respect to another. Where the rate of change of function is defined as dy/dx = f(x) = y’ and the ratio of dy/dx is used as one of the applications of derivatives in real life. The concept of derivatives has been used in many ways, such as when a matter of change of temperature or rate of change of shapes and sizes. Where the derivative function is used to calculate the highest and lowest point of the curve in a graph, with the help of the graph, you can also know its turning point as well.
NCERT Solutions For Class 12 Maths Chapter 7: Integrals
NCERT solutions for class 12 maths integrals introduce the students to the concept of the anti-derivative also known as an integral. A detailed definition of indefinite integral, integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, comparison between differentiation and integration, methods of integration such as integration by substitution, integration using partial fractions, integration by parts, integration using trigonometric identities, integration of some integral functions, definition, and meaning of definite integrals, definite integral as the limit of a sum, fundamental theorem of calculus, evaluation of definite integrals by substitution, some properties of definite integrals and miscellaneous examples.
NCERT Solutions For Class 12 Maths Chapter 8: Application Of Integrals
In this chapter, students are introduced with the integrals starting with definition, area under simple curves, area of the region bounded by a curve and a line, area between two curves, and miscellaneous examples. This is an important chapter that gives students a precise and comprehensive knowledge of calculus. The Calculus is used to find the area under simple curves, especially lines, parabolas; area of circles /ellipses.
NCERT Solutions For Class 12 Maths Chapter 9: Differential Equations
In this chapter of NCERT class 12 Maths, students are introduced to the Definition, order, and degree, general and particular solutions of a differential equation. Solution of differential equations by the method of separation of variables, solutions of homogeneous differential equations of the first order and first degree of the type: ??/?? = ?(y/x). Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constant. Students can get access to the NCERT Class 12 Maths Solutions Chapter 9 from this article.
NCERT Solutions For Class 12 Maths Chapter 10: Vector Algebra
Chapter 12 NCERT Maths is about some of the basic concepts about vectors, various operations on vectors, and their algebraic and geometric properties. When considered together, these two types of properties give a full realization to the concept of vectors and lead to their vital applicability in various areas. Students must download the NCERT Class 12 Maths Chapter 12 from the pdf link given in this article.
NCERT Solutions For Class 12 Maths Chapter 11: Three Dimensional Geometry
Chapter 12 of NCERT Class 12 Maths covers the topics like Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. Distance of a point from a plane. The main use of vectors is to describe the physical quantities having directions and magnitude associated with them. The various types of vectors included in this class 12 vector algebra are Zero Vector, Unit Vector, Coinitial Vectors, Collinear Vectors, Equal Vectors, Negative of a Vector. Scroll down to download the NCERT Solutions for Class 12 Maths Chapter 11 pdf.
NCERT Solutions For Class 12 Maths Chapter 13: Probability
This is the final chapter of NCERT Class 12 Maths textbook. Probability is defined as the extent to that an event is likely to occur. It is a number of events to occur from the total number of event that occurs. The probability formula is defined as the likelihood of an event to happen be equal to the given ratio of the number which results and the total number of outcomes. And where Conditional Probability is the likelihood of an event or outcome occurring is defined as the occurrence of a previous event or outcome.
NCERT Solutions for Class 12 Maths All Chapters
NCERT Maths Class 12 Solutions are given below for all chapters. Students can click on the link of the respective chapter number to download Class 12 Maths NCERT chapter-wise solutions.
| Name of the Chapter | PDF Link |
| Chapter 1 Relations and Functions | Download PDF |
| Chapter 2 Inverse Trigonometric Functions | Download PDF |
| Chapter 3 Matrices | Download PDF |
| Chapter 4 Determinants | Download PDF |
| Chapter 5 Continuity and Differentiability | Download PDF |
| Chapter 6 Applications of Derivatives | Download PDF |
| Chapter 7 Integrals | Download PDF |
| Chapter 8 Applications of Integrals | Download PDF |
| Chapter 9 Differential Equations | Download PDF |
| Chapter 10 Vector Algebra | Download PDF |
| Chapter 11 Three dimensional Geometry | Download PDF |
| Chapter 12 Linear Programming | Download PDF |
| Chapter 13 Probability | Download PDF |
Other Important Links on CBSE Class 12
