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CBSE Worksheets for Class 12 Maths

CBSE Worksheets for Class 12 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 12 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 12 Maths Worksheets for the students of Class 12. All our CBSE NCERT Class 12 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 12 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 12 Maths Number of Worksheets: 42

CBSE Class 12 Maths Worksheets PDF

All the CBSE Worksheets for Class 12 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 12 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 12 Maths Worksheet. CBSE Worksheets for Class 12 Maths can also use like assignments for Class 12 Maths students.

CBSE Class 12 Definite Integrals Worksheets

• CBSE Class 12 Definite integrals Assignment 1
• CBSE Class 12 Definite integrals Assignment 2
• CBSE Class 12 Definite integrals Assignment 3
• Class 12 Maths CBSE Worksheets for Definite integrals Assignment 4
• CBSE Class 12 Maths Worksheets Definite integrals Assignment 5
• CBSE Worksheets for Class 12 Maths Definite integrals Assignment 6
• CBSE Maths Worksheets for Class 12 Definite integrals Assignment 7

CBSE Determinants Class 12 Worksheets

• CBSE Worksheets for Class 12 Maths Determinants Assignment 1
• CBSE Class 12 Maths Determinants Assignment 2
• CBSE Class 12 Maths Determinants Assignment 3
• CBSE Class 12 Maths Determinants Assignment 4
• CBSE Class 12 Maths Determinants Assignment 5
• CBSE Class 12 Maths Worksheets for Determinants Assignment 6
• CBSE  Class 12 Maths Worksheets for Determinants Assignment 7

CBSE Class 12 Integration Worksheets

• CBSE Worksheets for Class 12 Maths Integration Assignment 1
• CBSE Worksheets for Class 12 Maths Integration Assignment 2
• CBSE Worksheets for Class 12 Maths Integration Assignment 3
• CBSE Worksheets for Class 12 Maths Integration Assignment 4
• CBSE Class 12 Maths Integration Assignment 5
• CBSE Class 12 Maths Integration Assignment 6
• CBSE Class 12 Maths Integration Assignment 7

CBSE Class 12 Relations and Functions Worksheets

• CBSE Class 12 Maths Relations and Functions Assignment 1
• CBSE Class 12 Maths Relations and Functions Assignment 2
• CBSE Class 12 Maths Relations and Functions Assignment 3
• CBSE Class 12 Maths Relations and Functions Assignment 4
• CBSE Class 12 Maths Relations and Functions Assignment 5
• CBSE Class 12 Maths Relations and Functions Assignment 6

CBSE Class 12 Maths Linear Programming Worksheets

• CBSE Class 12 Maths Linear Programming Assignment 1
• CBSE Class 12 Maths Linear Programming Assignment 2
• CBSE Class 12 Maths Linear Programming Assignment 3
• CBSE Class 12 Maths Linear Programming Assignment 4

Application of Derivatives CBSE Class 12 Maths Worksheets

• CBSE Worksheets for Class 12 Maths Application of Derivatives

Application of Integrals CBSE Class 12 Maths Worksheets

• CBSE Worksheets for Class 12 Maths Application of Integrals

Continuity and Differentiation Class 12 Worksheets

• CBSE Worksheets for Class 12 Maths Continuity and Differentiability Assignment 01
• CBSE Class 12 Maths Continuity and Differentiability Assignment 02

Differential Equations CBSE Class 12 Mathematics Worksheets

• CBSE Class 12 Differential Equations Assignment 01
• CBSE Class 12 Differential Equations Assignment 02

CBSE Class 12 Inverse Trigonometric Functions Worksheets

• CBSE Class 12 Maths Inverse Trigonometric Functions Assignment 01
• CBSE Class 12 Maths Inverse Trigonometric Functions Assignment 02

Continuity Class 12 Maths Worksheets

• CBSE Class 12 Maths Continuity Assignment

Class 12 CBSE Maths Matrices Worksheets

• CBSE Class 12 Maths Matrices
• CBSE Class 12 Maths Matrices and determinants

Class 12 Vector Algebra CBSE Maths Worksheets

• CBSE Class 12 Maths Vector Algebra Assignment

Advantages of CBSE Class 12 Maths Worksheets

• By practising NCERT CBSE Class 12 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 12 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 12 Maths Worksheets encourages classroom activities.

Worksheets of CBSE Class 12 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 12 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 12 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 12 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 12 Maths revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 12 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 12 Maths Worksheets to secure good score.

CBSE Worksheets For Class 12

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• NCERT Solutions
• NCERT Class 12
• NCERT 12 Maths

NCERT Solutions For Class 12 Maths

Ncert solutions for class 12 maths – free 2023-24 cbse pdf download.

NCERT Solutions for Class 12 Maths provides a solid conceptual base for all the topics included in the CBSE Class 12 Maths Syllabus. It covers all the important theorems and formulae with detailed explanations to ensure better conceptual understanding in students. NCERT Solutions for Class 12 Maths will help students in preparation for undergraduate-level Engineering entrance exams like JEE Mains, BITSAT, VITEEE, etc., to be conducted for the year 2023-2024.

BYJU’S brings you NCERT Solutions for Class 12 Maths, designed by our subject experts to facilitate a smooth and precise understanding of concepts. These Class 12 Solutions of NCERT have detailed step-by-step explanations of problems given in the textbooks. Apart from solutions for each chapter of CBSE Class 12 Maths, BYJU’S also provides Class 12 Maths notes, solved exemplar problems, and previous year question papers, along with worksheets as study materials for students who are preparing for their Class 12 board exams.

NCERT Solutions for Class 12 Maths Chapter-Wise PDF

Chapter 1 relations and functions, chapter 2 inverse trigonometric functions, chapter 3 matrices.

• Chapter 4 Determinants

Chapter 5 Continuity and Differentiability

Chapter 6 applications of derivatives, chapter 7 integrals, chapter 8 applications of integrals, chapter 9 differential equations, chapter 10 vector algebra.

• Chapter 11 Three dimensional Geometry

Chapter 12 Linear Programming

Chapter 13 probability, class 12 maths ncert solutions exercises.

Students can download NCERT Solution of Maths of Class 12 , chapter-wise from the links given below.

Chapter 1 of 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. Here, you can find the exercise solution links for the topics covered in this chapter.

Topics Covered in Class 12 Maths Chapter 1 Relations and Functions: Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

Also, access the following resources for Class 12 Chapter 1 Relations and Functions at BYJU’S:

• Relations And Functions Class 12 Maths Notes Chapter 1
• Important Questions For Class 12 Maths Chapter 1 – Relations and Functions
• Maths Revision Notes for Class 12 Chapter 1 Relations and Functions
• NCERT Exemplar Solutions for Class 12 Maths Chapter 1 Relations and Functions

Chapter 2, Inverse Trigonometric Functions of NCERT Class 12 Maths, gives an account of various topics such as the remarks based on basic concepts of inverse trigonometric functions, properties of inverse trigonometric functions and miscellaneous examples. These concepts are explained very well through examples. Solutions to the exercises from the chapter can be accessed from here.

Topics Covered in Class 12 Maths Chapter 2 Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Also access the following resources for Class 12 Chapter 2 Inverse Trigonometric Functions at BYJU’S:

• Inverse Trigonometric Functions Class 12 Notes – Chapter 2
• Important Questions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions
• Maths Revision Notes for Class 12 Chapter 2 Inverse Trigonometric Functions
• NCERT Exemplar Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

In Chapter 3 of NCERT textbook, we shall see 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. Here, you can find the exercise solution links for the topics covered in this chapter.

Topics Covered in Class 12 Maths Chapter 3 Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Also access the following resources for Class 12 Chapter 3 Matrices at BYJU’S:

• CBSE Class 12 Maths Notes Chapter 3 Matrices
• Important Questions for Class 12 Maths Chapter 3 – Matrices
• Maths Revision Notes for Class 12 Chapter 3 Matrices
• NCERT Exemplar Solutions for Class 12 Maths Chapter 3 Matrices

Chapter 4 Determinants –

Chapter 4 of 12 Class NCERT Maths Solution discusses the topic of determinants. Students will get to learn about the definition and meaning of determinants, remarks based on order of determinants, properties of determinants, finding area of triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, inverse of matrix , applications of determinants and matrices, and miscellaneous examples. Below, we have links provided to each exercise solution covered in this chapter.

Topics Covered in Class 12 Maths Chapter 4 Determinants: Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Also access the following resources for Class 12 Chapter 4 Determinants at BYJU’S:

• Determinants Class 12 Notes – Chapter 4
• Important Question for Class 12 Maths Chapter 4 – Determinants
• Maths Revision Notes for Class 12 Chapter 4 Determinants
• NCERT Exemplar Solutions for Class 12 Maths Chapter 4 Determinants

Chapter 5 of NCERT textbook starts with the definition of continuity. Students go on to learn about continuity, algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of implicit functions, 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. Here, students can find the exercises explaining these concepts properly with solutions.

Topics Covered in Class 12 Maths Chapter 5 Continuity and Differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concept of exponential and logarithmic functions and their derivatives. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.

Also access the following resources for Class 12 Chapter 5 Continuity and Differentiability at BYJU’S:

• Continuity And Differentiability Class 12 Notes Chapter 5
• Important Questions for Class 12 Maths Chapter 5 – Continuity and Differentiability
• Maths Revision Notes for Class 12 Chapter 5 Continuity and Differentiability
• NCERT Exemplar Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

Chapter 6 of NCERT textbook provides definition of derivatives, rate of change of quantities, increasing and decreasing functions, tangents and normals, approximations, maxima and minima , first derivative test, maximum and minimum values of a function in a closed interval, and miscellaneous examples. Here, students can find the exercises explaining these concepts properly.

Topics Covered in Class 12 Maths Chapter 6 Applications of Derivatives: Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

Also access the following resources for Class 12 Chapter 6 Applications of Derivatives at BYJU’S:

• Application of Derivatives Class 12 Notes Chapter 6
• Important Questions for Class 12 Maths Chapter 6 – Applications of Derivatives
• Maths Revision Notes for Class 12 Chapter 6 Application of Derivatives
• NCERT Exemplar Solutions for Class 12 Maths Chapter 6 Application of Derivatives

In Chapter 7, Integrals, we shall see the 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. Here, we have given exercises with solutions based on these topics from the chapter.

Topics Covered in Class 12 Maths Chapter 7 Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type

Also access the following resources for Class 12 Chapter 7 Integrals at BYJU’S:

• Integrals Class 12 Notes Chapter 7
• Important Questions for Class 12 Maths Chapter 7 – Integrals
• Maths Revision Notes for Class 12 Chapter 7 Integrals
• NCERT Exemplar Solutions for Class 12 Maths Chapter 7 Integrals

In Chapter 8 of NCERT textbook, we continue the discussions about 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. From the below-given links, students can access the exercises with solutions explaining the concepts from this chapter.

Topics Covered in Class 12 Maths Chapter 8 Applications of Integrals: Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ ellipses (in standard form only), area between the two above-said curves (the region should be clearly identifiable).

Also, access the following resources for Class 12 Chapter 8 Applications of Integrals at BYJU’S:

• Application of Integrals Class 12 Notes Chapter 8
• Important Questions Class 12 Maths Chapter 8-Applications of Integrals
• Maths Revision Notes for Class 12 Chapter 8 Application of Integrals
• NCERT Exemplar Solutions for Class 12 Maths Chapter 8 Application of Integrals

In this chapter, students concentrate on the definition of differential equations, basic concepts related to differential equations, degree of a differential equation , 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, methods of solving first order, first degree differential equations, differential equations with variable separable, homogeneous differential equations, linear differential equations, procedure involved to solve first order linear differential equations, and miscellaneous examples. Solutions to the exercises from the chapter can be accessed from here.

Topics Covered in Class 12 Maths Chapter 9 Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx + Py = Q, where P and Q are functions of x 

Also access the following resources for Class 12 Chapter 9 Differential Equations at BYJU’S:

• Differential Equation Class 12 Notes Chapter 9
• Important Questions Class 12 Maths Chapter 9 – Differential Equations
• Maths Revision Notes for Class 12 Chapter 9 Differential Equations
• NCERT Exemplar Solutions for Class 12 Maths Chapter 9 Differential Equations

In this chapter, students are introduced to vector algebra. The concepts in this chapter include how to find position vector, some basic concepts related to vector algebra, direction cosines, types of vectors such as zero vector, unit vector, collinear vector, equal vector, negative of a vector, addition of vectors, properties of vector addition, multiplication of a vector by a scalar, components of a vector, vector joining two points, section formula, product of two vectors, scalar or dot product of two vectors, properties of scalar product, projection of a vector on a line, vector or cross product of two vectors and miscellaneous examples. From the below-given links, students can access the exercises with solutions explaining the concepts from this chapter.

Topics Covered in Class 12 Maths Chapter 10 Vector Algebra: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.

Also, access the following resources for Class 12 Chapter 10 Vector Algebra at BYJU’S:

• Vector Algebra Class 12 Notes – Chapter 10
• Important Questions Class 12 Maths Chapter 10 – Vectors
• Maths Revision Notes for Class 12 Chapter 10 Vector Algebra
• NCERT Exemplar Solutions for Class 12 Maths Chapter 10 Vector Algebra

Chapter 11 Three Dimensional Geometry

Chapter 11 of NCERT Class 12 Maths constitutes topics related to three dimensional geometry, direction cosines and direction ratios of a line, relation between the direction cosines of a line, direction cosines of a line passing through two points, equation of a line in space, equation of a line through a given point and parallel to a given vector, derivation of cartesian form from vector form, equation of a line passing through two given points, angle between two lines, shortest distance between two lines, distance between two skew lines, distance between two parallel lines, plane in cartesian form, equation of a plane in a normal form, equation of a plane perpendicular to a given vector and passing through a given point, equation of a plane passing through three non collinear points, intercept form of the equation of a plane, plane passing through the intersection of two given planes, coplanarity of two lines , angle between two planes, distance of a point from a plane, angle between a line and a plane and miscellaneous examples. Below, we have listed links to the solutions for the exercises from this chapter.

Topics Covered in Class 12 Maths Chapter 11 Three Dimensional Geometry: Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Also access the following resources for Class 12 Chapter 11 Three Dimensional Geometry at BYJU’S:

• Three Dimensional Geometry Class 12 Notes Chapter 11
• Important Questions Class 12 Maths Chapter 11-Three Dimensional Geometry
• Maths Revision Notes for Class 12 Chapter 11 Three Dimensional Geometry
• NCERT Exemplar Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

In this chapter, students are introduced to linear programming. The concepts covered in this chapter are linear programming problem and its mathematical formulation, mathematical formulation of the problem, graphical method of solving linear programming problems, different types of linear programming problems with miscellaneous examples. Students can find the exercises explaining these concepts properly with solutions.

Topics Covered in Class 12 Maths Chapter 12 Linear Programming: Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constrains).

Also access the following resources for Class 12 Chapter 12 Linear Programming at BYJU’S:

• Linear Programming Class 12 Notes Chapter 12
• Important questions Class 12 Maths Chapter 12 Linear Programming
• Maths Revision Notes for Class 12 Chapter 12 Linear Programming
• NCERT Exemplar Solutions for Class 12 Maths Chapter 12 Linear Programming

This chapter deals with probability. By reviewing the basic facts and formulae studied earlier in Class 11, we shall implement those formulas again in this chapter along with the advance concepts mentioned, i.e., conditional probability, properties of conditional probability , multiplication theorem on probability, multiplication rule of probability for more than two events, independent events, Bayes’ theorem, partition of a sample space, theorem on total probability, random variables and its probability distributions, probability distribution of random variable, mean of random variable, variance of random variable, Bernoulli trials and binomial distribution with miscellaneous examples. We have compiled here the solutions to exercises from this chapter that explain the concept thoroughly.

Topics Covered in Class 12 Maths Chapter 13 Probability: Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Also access the following resources for Class 12 Chapter 13 Probability at BYJU’S:

• Probability Class 12 Notes Chapter 13
• Important Questions for Class 12 Maths chapter 13 Probability
• Maths Revision Notes for Class 12 Chapter 13 Probability
• NCERT Exemplar Solutions for Class 12 Maths Chapter 13 Probability

CBSE Class 12 Maths 2023-24 Unit-Wise Weightage

Internal Assessment Class 12

NCERT Solutions Class 12 Maths Chapter 1 to 13

NCERT Solutions PDF Class 12 Maths acts as a vital tool for students in their exam preparation and home assignments. Maths plays a vital role in the success of students in Class 12 boards and competitive exams. Solutions PDF of Class 12 can be your best support for board exam preparations. It’s difficult to score in Mathematics simply by reading and memorizing the formulae. Instead, practice is the perfect method to succeed.

Learning from BYJU’S NCERT Solutions will help students of Class 12 to grasp the conceptual meaning of every problem quite effectively. CBSE Class 12th NCERT Maths Solutions provides in-depth answers to all the problems covered in the syllabus. All the above-mentioned chapters are equally important and can be mastered with consistent practice and hard work. The topics like probability, calculus, coordinate geometry, and trigonometry are easy, and with proper practice, students can easily score good marks for questions from these units. We have also provided solved examples at the end of every chapter to make concepts clear to our readers.

Key Features of CBSE Class 12 Maths NCERT Solutions

• Students can easily practise and revise concepts by referring to these solutions.
• It saves your time by providing all the necessary concepts and formulae in a proper sequence.
• The CBSE Class 12th Maths NCERT Solutions   PDF Download option promotes among students the logical approach, which is crucial to ace the exam.
• These solutions are extremely helpful for quick revisions during examinations.

Students are advised to follow the NCERT Class 12 books and solutions on a regular basis to get in-depth knowledge about all the concepts covered in the syllabus.

Frequently Asked Questions on NCERT Solutions for Class 12 Maths

How many chapters are there in ncert solutions for class 12 maths , can i get answers for miscellaneous exercises in the ncert solutions for class 12 maths , is ncert solutions for class 12 maths the best source of reference materials for the students, where can i download the ncert solutions for class 12 maths , leave a comment cancel reply.

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Get NCERT solutions for Class 12 Maths free with videos. Solutions of all exercise questions, examples, miscellaneous exercise, supplementary exercise are given in an easy to understand way

The chapters and the topics in them are

• Chapter 1 Relation and Functions – Types of Relation - Reflexive, Symmetric, Transitive & Equivalence relation, Type of functions - One-one (injective), Onto (surjective) & Bijective, Composition of functions and Inverse of a function, Binary Operation - Commutative, Associative, Identity and Inverse.
• Chapter 2 Inverse Trigonometric Functions –  Finding principle value, solving identities using properties
• Chapter 3 Matrices – Order of matrix, Types of matrices - Column matrix, Row matrix, Square matrix, Diagnol matrix, Scalar Matrix, Identity matrix, Equal matrices, Addition, Subtraction and Multiplication of matrices, Transpose of a Matrix, Symmetric, Skew Symmetric Matrices, Finding inverse of matrix by elementary operations
• Chapter 4 Determinants – Evaluating 2 x 2, 3 x 3 Determinant, Properties of Determinant, Area of triangle, Minors and Cofactors, Adjoint and inverse of matrix, Solution of system of linear equations using matrix method
• Chapter 5 Continuity and Differentiability – Finding whether function is continuous, composition of continuous functions is continuous, Finding Derivative using chain rules, logarithmic and exponential differentiation, Mean value of theorem, Rolle's Theorem.
• Chapter 6 Application of Derivatives – Finding rate of change, Increasing & decreasing functions, Point of Inflexion, Finding slope of tangent  and normal, Finding approximate of functions and numbers, Finding maxima & minima using first derivative & second derivative test and Finding absolute maxima and minima
• Chapter 7 Integrals – Finding integration by substitution, trigonometric identities, Partial Fractions & using special formulas. Finding definite integrals as Limit as a Sum, Finding definite integral using indefinite integral and finding Definite Integral using properties
• Chapter 8 Application of Integrals –  Finding area of region of simple curve, curve and line. Finding area between two curves.
• Chapter 9 Differential Equations – Degree and order of differential equations, General & Particular Solutions of Differential Equation, Forming differential equation when general solution is equation, Solving by variable separating, solving homogeneous differential equations, Linear Differential Equation
• Chapter 10 Vector Algebra – What is vector, Difference between vector and scalar, Types of vector - Unit vector, Equal vector, Addition of vectors, Components of vector, Scalar(Dot) product of vectors, Projection of vector on line, Vector (Cross) product of vectors, Finding area of parallelogram
• Chapter 11 Three Dimensional Geometry – Direction Ratio & Direction cosines of line, Finding equation of line - given point & parallel vector, though two points, Angle between two lines, Distance between two skew lines, Distance between two parallel lines, Finding equation of plane - normal form, perpendicular to given vector & passing through point, through 3 non-collinear points, intercept form, through two planes. Coplanarity of two planes, Angle between two planes, Distance between point and plane, Angle between Line & Plane
• Chapter 12 Linear Programming  – Finding maximum or minimum value of Z using bounded or unbounded region of graphical inequality.  Solving Diet, Manufacturing & Transport problems.
• Chapter 13 Probability – Conditional Probability, Multiplication Theorem of Probability, Independent events, Bayes Theorem, Random Variable & its Probability Distributions, Mean & Variance of Random Variable, Bernoulli Trials & Binomial Distribution

Each chapter is divided into two parts - Serial Order Wise and Concept Wise.

• In Serial  Order Wise, the chapter is taught according to the NCERT Book with exercises, examples and miscellaneous. You should follow this when you are searching for a particular question
• In Concept Wise, we have divided the Chapter into topics. Concept is explained first, and then questions are ordered from easy to difficult. You should always follow this method to do the chapter. This is the Teachoo (टीचू) way of doing a chapter.

In addition to that, Important Questions are marked for your reference.

And, we have also solved Past Year Papers, and Sample Papers with step by step marking as well

Click on a Chapter below to begin

Chapter 1 Class 12 Relation and Functions

Chapter 2 class 12 inverse trigonometric functions, chapter 3 class 12 matrices, chapter 4 class 12 determinants, chapter 5 class 12 continuity and differentiability, chapter 6 class 12 application of derivatives, chapter 7 class 12 integrals, chapter 8 class 12 application of integrals, chapter 9 class 12 differential equations, chapter 10 class 12 vector algebra, chapter 11 class 12 three dimensional geometry, chapter 12 class 12 linear programming, chapter 13 class 12 probability, important questions for exams class 12, solutions of sample papers and past year papers - for class 12 boards.

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NCERT Solutions for Class 12 Maths

Ncert solutions for class 12 maths – free pdf solutions.

Maths NCERT Solutions for Class 12 acts as a vital tool when students are preparing for their Board examinations and even while solving the home work or any assignments. It also helps students to crack any competitive exam such as IIT JEE, AIIMS, NDA, UPSC, NEET, BITSAT, VITEEE or any government exam. In short, any undergraduate engineering entrance exam or government exam requires NCERT solutions since they are your best ally and foot forward towards your exam preparations. Scoring in Maths can be very difficult process as it is not plain wrote-learning but practical application of the conceptual knowledge you have learned. This can be only done by mere practice and hardwork.

Class 12 NCERT Maths Solutions prepare a strong foundation of conceptual learning of all the chapters and topics covered in 12 th standard portion as prescribed by CBSE. The solution PDF compromises of important formulas, theorems and equations. Each point is further explained with detailed explanations so that students can grasp it easily and understand the concepts efficiently. Mathongo provides detailed step by step explanation of the problems. They are free download and in PDF format. They are designed by the best professors and teachers to ensure students get good marks in their examination.

The maths solutions of CBSE NCERT Class 12 gives in-depth clarity answers to all the questions asked in the NCERT textbook. All the topics of NCERT are equally important and must be studied thoroughly to attain good marks. Students should study chapters like probability, calculus, coordinate geometry, trigonometry with consistence as they can become very easy to solve with proper practice and then these units will help in fetching high marks.

NCERT Class 12 Maths Chapterwise Solutions

• 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 Applications of Integrals
• Chapter 9 Differential Equations
• Chapter 10 Vector Algebra
• Chapter 11 Three-Dimensional Geometry
• Chapter 12 Linear Programming
• Chapter 13 Probability

Why Go for Mathongo’s NCERT Maths Solutions for Class 12

Mathongo provides NCERT class 12 maths solution at free of cost online and it’s easily accessible in the form of PDF. Each PDF constitutes of the chapter in which exercise wise solutions are given. It is very easy for the students to locate any answer from the exercise.

All the solutions are made with the help of the best teachers and academicians. The solutions are plain easy and can be understood by anyone. The approaches and the methods used to solve the questions are also given in step by step method so that students score good in paper. For additional conceptual clarity, diagrams and formulas are also used.

Mathongo has provided the best solutions for class 12 maths Ncert textbooks. Students can refer these solutions which will help them in solving the previous year question papers. These NCERT maths class 12 solution will help the students to study more effectively and also present the answers in the most effective way to get the highest scores.

The back-end exercise questions given in NCERT books are very important for the class 12 finals. These exercises often test the conceptual clarity and the subject knowledge of the student. NCERT Solutions will help you to understand these concepts better. On the other hand, the students who have problem in solving maths and require assistance and guidance can also refer class 12 Ncert Maths Solutions to clarify the complex questions concepts.

Maths is all about practice. The more you practice, the better you will be. Ncert maths class 12 pdf download can help students to solve all their problems and also save their time as everything is at one place, one click away.

Which book is best for class 12 Maths?

The best book for not only class 12 Mathematics but for any class is the NCERT textbook which is prescribed by CBSE. The conceptual base required to solve HOTs (High Order Thinking Problems) is built by practicing NCERT maths book examples and exercise questions. Once the students have studied thoroughly the NCERT textbook, the students can through books like RD Sharma and RS Aggarwal for further practice. However, students must not underestimate the power of solving NCERT since majority of the questions in the boards come either directly from NCERT or are NCERT based.

Is NCERT enough for Class 12 board Maths?

NCERT textbook is well enough for class 12 board examinations for Maths. Solving questions from NCERT textbook helps student to grasp concepts easily. If they wish to practice more as Maths is all about practice, they can use other reference books or even solve question banks and past year question papers.

Is class 12 NCERT Maths difficult?

The idea of the subject being difficult or easy lies in the mind of the beholder. Some students since childhood have Maths phobia engraved in their minds. But I would like to clear that. NCERT Maths of class 12 is not difficult. Once you get the conceptual clarity, you can start solving solved examples and problems followed by exercise questions. The only way you can master Maths is by practicing variety of questions.

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NCERT Solutions for Class 12 Maths Exercises

• NCERT Solutions

NCERT Solutions for Class 12 Maths Exercises - PDF Solutions

Class 12 Maths syllabus is covering basic and advanced mathematical concepts and fundamental principles. To study this CBSE syllabus , you will need the assistance of the complete study material with all the exercise solutions. The experts of Vedantu have designed the NCERT Class 12 Maths All Exercises Solutions to download and refer to while studying the respective chapters. Follow how the experts have solved the questions and develop your mathematical skills accordingly.

NCERT Solutions for Class 12 Maths Chapter 1

NCERT Solutions for Class 12 Maths Chapter 2

Ncert solutions for class 12 maths chapter 3, ncert solutions for class 12 maths chapter 4, ncert solutions for class 12 maths chapter 5, ncert solutions for class 12 maths chapter 6, ncert solutions for class 12 maths chapter 7, ncert solutions for class 12 maths chapter 8, ncert solutions for class 12 maths chapter 9, ncert solutions for class 12 maths chapter 10, ncert solutions for class 12 maths chapter 11, ncert solutions for class 12 maths chapter 12, ncert solutions for class 12 maths chapter 13.

What could be better if you get the simpler and readymade solutions of your Class 12 NCERT textbook exercises? Moreover, all these are created by an experienced subject matter expert. Can you imagine how beneficial these could be? Sounds amazing, right! You must opt for these NCERT solutions for Class 12 Maths right away. You can download NCERT solutions Class 12 Maths from Vedantu official website (vedantu.com) by registering yourself with your phone number/ email address. You can also access the same study materials from Vedantu app as well. In that case, you need to download the Vedantu app first from Google play store.

You will get Class 12 Maths NCERT solutions written in a simple and lucid manner. Solve all the problems/ questions given in the exercises and evaluate your performance with these 100% accurate solutions so that you can learn how to write answers to the questions from any perspective during the final exam. Each of the answers in the Maths NCERT solutions Class 12 is student-friendly and customized by the experts. 

These NCERT solutions Class 12 Maths contain step-by-step answers to all the questions from the exercise which are considered as an invaluable aid to the students when it comes to regular study, exam preparation or doing homework. Class 12 Maths NCERT solutions will clear all your doubts in very less time. Hence your confidence will be boosted. By practising the questions from these books, you will be able to improve your time management skills. That will help you in solving all the questions in the stipulated time frame during the final exam. 

NCERT Solutions for Class 12 Maths are designed as per the latest CBSE curriculum and guidelines. Vedantu’s study materials are updated regularly as per the latest changes. Hence students of Class 12 who are referring to these materials will be able to score the best marks in the final exam. Once you start using these materials, the preparation for Class 12 exam and scoring the highest percentile amongst your peers will seem like a cakewalk at the end of the day.

Class 12 Maths Chapter 1 Relations and Functions

Chapter 1 Relations and Functions of NCERT Class 12 Maths Syllabus deals with types of relations and functions along with a few miscellaneous examples.

NCERT Solutions for Class 12 Maths Chapter 1 Exercises are given in the table below:

Class 12 Maths Chapter 2 Inverse Trigonometric Functions

In CBSE Class 12 Inverse Trigonometric Functions , there are only two exercises where you will study the restrictions on domains and ranges of trigonometric functions which enables the visibility of their inverses and observe their behaviour through graphical representations.

CBSE Class 12 Maths Chapter 3 Matrices

There are 4 exercises included in this chapter. The links to these exercises are provided in the table below.

CBSE Class 12 Maths Chapter 4 Determinants

There are six exercises which are included in the NCERT Class 12 Maths Chapter 4 Determinants. By solving these exercises, students will be familiar with the concepts of determination, cofactors and the application of determinants in finding the area of a triangle, minors, adjoint and inverse of a square matrix. 

The free PDFs of the NCERT Solutions for Class 12 Maths Chapter 4 exercises can be downloaded from the links provided below:

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

Class 12 Maths Chapter 5 Continuity and Differentiability explains the definition of continuity and meaning of differentiability.

The free PDFs of the NCERT Solutions for Class 12 Maths Chapter 5 exercises can be downloaded from the links provided below:

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

In this chapter, you will study the applications of the derivative in various disciplines such as engineering, science, and many other fields. For instance, you will learn how the derivative can be used to determine the rate of change of quantities and to find the equations of tangent and normal to a curve at a point. You will also learn the use of derivatives to find intervals of increasing or decreasing functions, maxima and minima, along with a few simple problems based on all these concepts. 

NCERT Solutions for Class 12 Maths Chapter 7 Integrals

Topics in this chapter include an introduction to indefinite integrals, integration as inverse to differentiation, its geometrical interpretation, and properties. 

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

Here, in this chapter, you will study some specific applications of integrals to find the area given under the simple curves, also, the area between lines and arcs of circles, parabolas and ellipses (standard forms only). There are two exercises in this chapter in which you will also deal with finding the area bounded by the above-said curves.

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

In Differential Equations, you will be studying some basic concepts related to the differential equation, general and particular solutions of a differential equation, formation of differential equations, number of methods to solve a question based on first order - first-degree differential equations and some applications of differential equations in different areas.

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

In Class 12 Maths Chapter 10  Vector Algebra, you will be studying some basic concepts of vectors, various operations on vectors, and the algebraic as well as geometric properties. You will also learn about the types of vectors such as zero, unit, equal and collinear vectors.

Other topics discussed in this chapter include the negative of a vector, operations of vectors such as addition, its properties, components and how to multiply a vector by a scalar. You will also learn about section formulae, vector joining two points, dot product of two vectors, product of two vectors, cross product of two vectors, and projection of a vector on a line.

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry

CBSE Class 12 Maths Chapter 11 Three Dimensional Geometry deals with the direction cosines and direction ratios of a line joining two points and also about the equations of lines and planes in space under different conditions. Along with that, you will also get to know about the angle between two lines, a line and a plane, two planes, the shortest distance between two skew lines and the distance of a point from a plane.

You will also learn about cartesian equations and vector equations of a line, skew and coplanar lines, and the cartesian and vector equations of a plane.

NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming

This chapter has only two exercises in which you will study some linear programming problems and their solutions by graphical method. Other concepts in this chapter are the mathematical formulation of linear programming problems, different types of linear programming problems, terms such as objective function, optimization and constraints, as well as feasible and infeasible regions and solutions.

NCERT Solutions for Class 12 Maths Chapter 13 Probability

Class 12 Maths Chapter 13 Probability will teach you the important concepts of the conditional probability of an event given that another event has occurred, which will, in turn, clarify the Bayes' theorem, multiplication rule of probability and independence of events. You will also learn the concept of a random variable and its probability distribution, mean and variance of a probability distribution, total probability theorem, Bernoulli trials and binomial distribution.

CBSE Class 12 Maths Weightage (2024-25)

Given below is the unit-wise mark distribution for CBSE Class 12 Maths exam for session 2024-25.

Importance of Chapter Wise List of Class 12 Maths All Exercises

The vivid exercises of a chapter in Class 12 Maths have questions that check your preparation level. This is where you will need the support of exercise solutions to learn the exact ways of answering fundamental questions.

The experts have framed the answers by following the fundamental principles explained in the chapters and the latest CBSE guidelines . The 12th Maths All Exercises Book Answers will enable students to focus on their preparation and proceed with the exam syllabus faster.

Benefits of NCERT Maths All Exercises Book Class 12 Solutions PDF

Resolve doubts on your own with these solutions faster.

Learn the ideal answering formats to follow and solve problems accurately.

Prepare chapters in no time by using the solutions as revision material.

Understand the concepts and principles of Class 12 Maths chapters from the simpler solutions easily.

Here is the list of exercise solutions for all chapters in the CBSE Class 12 Maths syllabus .

Download NCERT Maths All Exercises Book Class 12 Solutions PDF

Perform the NCERT Maths All Exercises Book Class 12 Solutions PDF free download according to your syllabus. Focus on how the experts have solved the exercise problems. Cover a syllabus faster and develop your problem-solving skills in a better way to score more in the exams.

Important Related Links for CBSE Class 12 Maths

NCERT Solutions for Class 12 Math in Hindi Chapter wise free pdf 

Important Questions for CBSE Class 12 Math

RS Aggarwal Class 12 Solutions for Math book

FAQs on NCERT Solutions for Class 12 Maths Exercises

1. How can I prepare a Class 12 Maths chapter?

Complete studying the theoretical part of a chapter and solve the exercises. Refer to the solutions to compare your answers and find out where you need to change your techniques.

2. What is the advantage of using Class 12 Maths solutions?

You will the precise answers compiled following the latest CBSE guidelines to follow and develop your answering skills.

3. Can I practise using the CBSE Class 12 Maths solutions?

The solutions are to the point and comply with the NCERT guidelines. You can surely practise solving problems using the solutions.

4. How can I resolve doubts about Class 12 Maths exercises?

Refer to the exercise solutions framed by the experts to resolve all your doubts in no time.

5. What is the best way to develop my concepts for the Class 12 Maths chapters?

Apart from the notes, you can use the simpler solutions developed by the experts to learn how to use the concepts and principles of an exercise in a Class 12 Maths chapter. This is how you can develop your concepts.

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions For Class 12 Maths (2023-2024)

NCERT Solutions for Class 12 Maths (2023-2024) has been written to help students like you who are appearing for different board exams as well as the JEE. It provides sound knowledge and understanding of all important concepts covered in each chapter in the Class 12 Maths NCERT textbook. There are 13 important chapters from the NCERT textbook. Both problems and their detailed solutions are provided. The solutions have been devised by India’s best teachers to help students grasp basic concepts better and faster.

NCERT Solutions for Class 12 Maths All Chapters 2023-2024

NCERT Maths Class 12 Solutions are given below for all chapter. Select chapter number to view Class 12 Maths NCERT chapter wise solutions.

• 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

If you are looking for Class 12 Maths NCERT Solutions, there is no better place to be than right here. We provide Maths NCERT solutions class 12 that are precise, to the point and absolutely error free. With NCERT reputed to be the best textbooks for school education, we make the solutions that are at par with the excellent textbooks.

Important Questions for Class 12 Maths Chapter wise 2023-24

Relations and Functions

• Concept of Relations and Functions
• Binary Operations
•   Inverse Trigonometric Functions
• Matrix and Operations of Matrices
• Transpose of a Matrix and Symmetric Matrix
• Inverse of a Matrix by Elementary Operations

Determinants

• Expansion of Determinants
• Properties of Determinants
• Inverse of a Matrix and Application of Determinants and Matrix

Continuity and Differentiability

• Differentiability

Application of Derivatives

• Rate Measure Approximations and Increasing-Decreasing Functions
• Tangents and Normals
• Maxima and Minima
• Types of Integrals

Differential Equation

• Formation of Differential Equations
• Solution of Different Types of Differential Equations

Vector Algebra

• Algebra of Vectors
• Dot and Cross Products of Two Vectors

Three Dimensional Geometry

• Direction Cosines and Lines

Linear Programming

Probability

• Conditional Probability and Independent Events
• Baye’s Theorem and Probability Distribution

NCERT Exemplar Class 12 Maths

• Chapter 3 Matrices
• Chapter 5 Continuity and Differentiability
• Chapter 6 Application of Derivatives
• Chapter 7 Integrals
• Chapter 8 Applications of Integrals
• Chapter 9 Differential Equations
• Chapter 10 Vector Algebra
• Chapter 11 Three Dimensional Geometry
• Chapter 12 Linear Programming
• Chapter 13 Probability

RD Sharma Class 12 Maths Solutions

Class 12 Maths NCERT Solutions

Class 12 Maths is key in the preparation for boards as well as JEE Main and Advance, and our solutions are made keeping in mind the very same thing. The solutions are concise, and also discuss alternative methods to solve some problems. We make it a point to provide the students the best help they can get, and the solutions reflect just that.

The National Council of Educational Research and Training ( NCERT ) is an autonomous organization of the Government of India that was established in 1961 as a literary, scientific and charitable society under the Societies’ Registration Act (Act XXI of 1860). Its headquarters are located at Sri Aurobindo Marg in New Delhi. It sets the curriculum for all schools that follow the Central Board of Secondary Education (CBSE) across the country. Class 12 Maths NCERT Solutions is the perfect guide to help you prepare for CBSE exams as well as engineering entrances like the JEE.

Your performance in the board exams will play a role in determining your admission into a good college or even your dream college! That will undoubtedly induce a lot of pressure upon you and you may tend to get demotivated or stressed out. To help you overcome such situations, LearnCBSE is a platform all the way helps you to crack your target. if you have any queries leave in the comments box.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

The chapter builds up on the concepts of relations, functions, domain and codomain introduced in Class 11. The students explore several real valued functions, and their graphs. The chapter comprises of four exercises that consolidate the concepts explained in the chapter.

NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

This chapter plays in the restricted range of trigonometric functions that enables them to be one on one, and hence makes inverse of the functions visible. This chapter explores the inverse trigonometric through two exercises that teach the students the behavior of the functions, their graphical representations, and the elementary properties. These prove to be of more value in integration later.

NCERT Solutions for Class 12 Maths Chapter 3 Matrix

This chapter takes you through the properties of one of the most important tools of Mathematics, namely Matrices. The students learn the basics of Matrices and Matrix Algebra..

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Correctly preceded by Matrix, this chapter deals with an important part of Matrices, namely Determinants. The chapter deals with determinants of orders upto 3, and their cofactors and inverses.This chapter also talks about the applications of determinants, like calculation of area of triangles, adjoint of matrices, consistency of a set of linear equations.

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

This chapter picks up after the Differentiation of Functions introduced in Class 11. The chapter explores the important concepts of Continuity, Differentiability and establishes the relationship between them. It also deals with the continuity and differentiability of Inverse Trigonometric Functions. It also introduces exponential and logarithmic functions.

NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

With Continuity and Differentiability marking the start of Calculus, this chapter deals with the differentiability of functions, and introduction to derivatives. It delves into the derivatives of specific functions, and their applications, namely the tangents and normal to curves, and the rate of change in some quantities. It also talks about increasing and decreasing functions.

NCERT Solutions for Class 12 Maths Chapter 7 Integrals

This is one of the most important and time consuming chapters in the whole Class 12 Mathematics. This chapter deals with integration of functions, and its applications in terms of calculation of areas. This marks the introduction to Integral Calculus. There are a total of 11 exercises in this chapter, making it a very practice driven part of the syllabus.

NCERT Solutions for Class 12 Maths Chapter 8 Application of Integrals

This chapter deals with the applications of integrals in calculating areas under simple curve, lines, parabolas and ellipses. The two exercises provide enough questions for practicing the area calculations.

NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations

This chapter introduces the concept of Differential equations, the general and particular solutions, and the order and degree of an equation. This also talks about the applications of differential equations in the six exercises.

NCERT Solutions for Class 12 Maths Chapter 10 Vector Equations

This chapter deals with the vector quantities, that is, the quantities with both magnitude and direction. The Vector algebra summarises the rules of addition of vector quantities, and other important properties. Vector Algebra plays a big role in Physics.

Class 12 Maths Chapter 11 Three Dimensional Geometry

This chapter utilises vectors to calculate the distance between lines, a point and a line, and a line and a plane, along with the angles between them.It also introduces the concept of direction cosines

Class 12 Maths Chapter 12 Linear Programming

This chapter explores the concept of linear programming problems, and their solutions using graphical method only.

Class 12 Maths Probability

This chapter deals with the concept of Conditional Probability and the encounters of the same in our daily lives. This explores Bayes’ Theorem, the multiplication rule, and the independence of events. This chapter is best understood by practicing as many questions as possible.

NCERT Solution

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