# NCERT Solutions for Class 12 Maths

## CBSE, Karnataka Board PUC Class 12 Maths Solutions Guide

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## CBSE, Karnataka Board PUC Class 12 Maths Textbook Solutions

Questions and answers for the Class 12 Maths Textbook on this page. NCERT Solutions for Class 12 Maths Digest CBSE, Karnataka Board PUC will help students understand the concepts better.

## NCERT Solutions for Class 12 Maths Chapterwise List | Class 12 Maths Digest

The answers to the NCERT books are the best study material for students. Listed below are the chapter-wise NCERT Maths Class 12 Solutions CBSE, Karnataka Board PUC.

## Chapters covered in NCERT Solutions for Class 12 Maths

### NCERT Solutions for Class 12 Mathematics Chapter 1: Relations and Functions

Concepts covered in Relations and Functions are Composition of Functions and Invertible Function, Concept of Binary Operations, Introduction of Relations and Functions, Inverse of a Function, Types of Functions, Types of Relations

#### NCERT Class 12 Mathematics Chapter 1: Relations and Functions exercises

ExerciseNo. of questionsPages
Exercise 1.1255 to 7
Exercise 1.21710 to 11
Exercise 1.31718 to 19
Exercise 1.42224 to 26
Exercise 1.52029 to 31

### NCERT Solutions for Class 12 Mathematics Chapter 2: Inverse Trigonometric Functions

Concepts covered in Inverse Trigonometric Functions are Basic Concepts of Inverse Trigonometric Functions, Graphs of Inverse Trigonometric Functions, Inverse Trigonometric Functions - Principal Value Branch, Inverse Trigonometric Functions (Simplification and Examples), Properties of Inverse Trigonometric Functions

#### NCERT Class 12 Mathematics Chapter 2: Inverse Trigonometric Functions exercises

ExerciseNo. of questionsPages
Exercise 2.11441 to 42
Exercise 2.22047 to 48
Exercise 2.31751 to 52

### NCERT Solutions for Class 12 Mathematics Chapter 3: Matrices

Concepts covered in Matrices are Addition of Matrices, Elementary Transformations, Equality of Matrices, Introduction of Matrices, Introduction of Operations on Matrices, Inverse of a Matrix by Elementary Transformation, Invertible Matrices, Matrices Notation, Multiplication of a Matrix by a Scalar, Multiplication of Matrices, Multiplication of Two Matrices, Negative of Matrix, Order of a Matrix, Proof of the Uniqueness of Inverse, Properties of Matrix Addition, Properties of Multiplication of Matrices, Properties of Scalar Multiplication of a Matrix, Properties of Transpose of the Matrices, Subtraction of Matrices, Symmetric and Skew Symmetric Matrices, Transpose of a Matrix, Types of Matrices

#### NCERT Class 12 Mathematics Chapter 3: Matrices exercises

ExerciseNo. of questionsPages
Exercise 3.11864 to 80
Exercise 3.23680 to 83
Exercise 3.32388 to 90
Exercise 3.42297 to 100
Exercise 3.513100 to 101

### NCERT Solutions for Class 12 Mathematics Chapter 4: Determinants

Concepts covered in Determinants are Applications of Determinants and Matrices, Area of a Triangle, Determinant of a Matrix of Order 3 × 3, Determinant of a Square Matrix, Determinants of Matrix of Order One and Two, Elementary Transformations, Introduction of Determinant, Inverse of a Square Matrix by the Adjoint Method, Minors and Co-factors, Properties of Determinants, Rule A=KB

#### NCERT Class 12 Mathematics Chapter 4: Determinants exercises

ExerciseNo. of questionsPages
Exercise 4.113108 to 109
Exercise 4.219119 to 121
Exercise 4.39122 to 123
Exercise 4.47126
Exercise 4.518131 to 132
Exercise 4.616136 to 137
Exercise 4.719141 to 143

### NCERT Solutions for Class 12 Mathematics Chapter 5: Continuity and Differentiability

Concepts covered in Continuity and Differentiability are Algebra of Continuous Functions, Concept of Continuity, Concept of Differentiability, Continuous Function of Point, Derivative - Exponential and Log, Derivatives of Composite Functions - Chain Rule, Derivatives of Functions in Parametric Forms, Derivatives of Implicit Functions, Derivatives of Inverse Trigonometric Functions, Exponential and Logarithmic Functions, Higher Order Derivative, Infinite Series, Logarithmic Differentiation, Mean Value Theorem, Proof Derivative X^n Sin Cos Tan, Second Order Derivative

#### NCERT Class 12 Mathematics Chapter 5: Continuity and Differentiability exercises

ExerciseNo. of questionsPages
Exercise 5.137159 to 161
Exercise 5.29166
Exercise 5.315169
Exercise 5.410147 to 174
Exercise 5.518178 to 179
Exercise 5.611181
Exercise 5.717183 to 184
Exercise 5.88186
Exercise 5.923191 to 192

### NCERT Solutions for Class 12 Mathematics Chapter 6: Application of Derivatives

Concepts covered in Application of Derivatives are Approximations, Graph of Maxima and Minima, Increasing and Decreasing Functions, Introduction to Applications of Derivatives, Maxima and Minima, Maximum and Minimum Values of a Function in a Closed Interval, Rate of Change of Bodies or Quantities, Simple Problems on Applications of Derivatives, Tangents and Normals

#### NCERT Class 12 Mathematics Chapter 6: Application of Derivatives exercises

ExerciseNo. of questionsPages
Exercise 6.119197 to 199
Exercise 6.222205 to 206
Exercise 6.332211 to 213
Exercise 6.423216 to 2016
Exercise 6.548231 to 234
Exercise 6.625242 to 244

### NCERT Solutions for Class 12 Mathematics Chapter 7: Integrals

Concepts covered in Integrals are Comparison Between Differentiation and Integration, Definite Integral as the Limit of a Sum, Definite Integrals Problems, Evaluation of Definite Integrals by Substitution, Evaluation of Simple Integrals of the Following Types and Problems, Fundamental Theorem of Calculus, Geometrical Interpretation of Indefinite Integrals, Indefinite Integral by Inspection, Indefinite Integral Problems, Integrals of Some Particular Functions, Integration as an Inverse Process of Differentiation, Integration Using Trigonometric Identities, Introduction of Integrals, Methods of Integration: Integration by Parts, Methods of Integration: Integration by Substitution, Methods of Integration: Integration Using Partial Fractions, Properties of Definite Integrals, Some Properties of Indefinite Integral

#### NCERT Class 12 Mathematics Chapter 7: Integrals exercises

ExerciseNo. of questionsPages
Exercise 7.122299
Exercise 7.240304 to 305
Exercise 7.324307
Exercise 7.425315 to 316
Exercise 7.523322 to 323
Exercise 7.624327 to 328
Exercise 7.712330
Exercise 7.86334
Exercise 7.924338 to 340
Exercise 7.108340
Exercise 7.1121347
Exercise 7.1244352 to 354

### NCERT Solutions for Class 12 Mathematics Chapter 8: Application of Integrals

Concepts covered in Application of Integrals are Area Between Two Curves, Area of the Region Bounded by a Curve and a Line, Area Under Simple Curves

#### NCERT Class 12 Mathematics Chapter 8: Application of Integrals exercises

ExerciseNo. of questionsPages
Exercise 8.113365 to 366
Exercise 8.27371 to 372
Exercise 8.320375 to 376

### NCERT Solutions for Class 12 Mathematics Chapter 9: Differential Equations

Concepts covered in Differential Equations are Basic Concepts of Differential Equation, Differential Equations with Variables Separable Method, Formation of a Differential Equation Whose General Solution is Given, General and Particular Solutions of a Differential Equation, Homogeneous Differential Equations, Linear Differential Equations, Order and Degree of a Differential Equation, Procedure to Form a Differential Equation that Will Represent a Given Family of Curves, Solutions of Linear Differential Equation

#### NCERT Class 12 Mathematics Chapter 9: Differential Equations exercises

ExerciseNo. of questionsPages
Exercise 9.112382 to 383
Exercise 9.212385
Exercise 9.312391
Exercise 9.423395 to 397
Exercise 9.517406 to 407
Exercise 9.619413 to 414
Exercise 9.723419 to 421

### NCERT Solutions for Class 12 Mathematics Chapter 10: Vector Algebra

Concepts covered in Vector Algebra are Addition of Vectors, Basic Concepts of Vector Algebra, Components of Vector, Direction Cosines, Geometrical Interpretation of Scalar, Introduction of Product of Two Vectors, Introduction of Vector, Magnitude and Direction of a Vector, Multiplication of a Vector by a Scalar, Position Vector of a Point Dividing a Line Segment in a Given Ratio, Projection of a Vector on a Line, Properties of Vector Addition, Scalar (Or Dot) Product of Two Vectors, Scalar Triple Product of Vectors, Section Formula, Vector Joining Two Points, Vector (Or Cross) Product of Two Vectors, Vectors and Their Types, Vectors Examples and Solutions

#### NCERT Class 12 Mathematics Chapter 10: Vector Algebra exercises

ExerciseNo. of questionsPages
Exercise 10.119428
Exercise 10.219440 to 441
Exercise 10.318447 to 448
Exercise 10.412454 to 455
Exercise 10.519458 to 459

### NCERT Solutions for Class 12 Mathematics Chapter 11: Three Dimensional Geometry

Concepts covered in Three Dimensional Geometry are Angle Between Line and a Plane, Angle Between Two Lines, Angle Between Two Planes, Coplanarity of Two Lines, Direction Cosines and Direction Ratios of a Line, Distance of a Point from a Plane, Equation of a Line in Space, Equation of a Plane in Normal Form, Equation of a Plane Passing Through Three Non Collinear Points, Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point, Intercept Form of the Equation of a Plane, Introduction of Three Dimensional Geometry, Plane Passing Through the Intersection of Two Given Planes, Relation Between Direction Ratio and Direction Cosines, Shortest Distance Between Two Lines, Three - Dimensional Geometry Examples and Solutions, Vector and Cartesian Equation of a Plane

#### NCERT Class 12 Mathematics Chapter 11: Three Dimensional Geometry exercises

ExerciseNo. of questionsPages
Exercise 11.111467 to 478
Exercise 11.213477 to 478
Exercise 11.331493 to 494
Exercise 11.423497 to 499

### NCERT Solutions for Class 12 Mathematics Chapter 12: Linear Programming

Concepts covered in Linear Programming are Different Types of Linear Programming Problems, Graphical Method of Solving Linear Programming Problems, Introduction of Linear Programming, Linear Programming Problem and Its Mathematical Formulation, Mathematical Formulation of Linear Programming Problem

#### NCERT Class 12 Mathematics Chapter 12: Linear Programming exercises

ExerciseNo. of questionsPages
Exercise 12.110513 to 514
Exercise 12.214519 to 526
Exercise 12.38526 to 582

### NCERT Solutions for Class 12 Mathematics Chapter 13: Probability

Concepts covered in Probability are Bayes’ Theorem, Bernoulli Trials and Binomial Distribution, Conditional Probability, Independent Events, Introduction of Probability, Mean of a Random Variable, Multiplication Theorem on Probability, Probability Examples and Solutions, Properties of Conditional Probability, Random Variables and Its Probability Distributions, Variance of a Random Variable

#### NCERT Class 12 Mathematics Chapter 13: Probability exercises

ExerciseNo. of questionsPages
Exercise 13.124538 to 540
Exercise 13.222546 to 548
Exercise 13.314555 to 557
Exercise 13.421569 to 571
Exercise 13.515576 to 578
Exercise 13.621582 to 584

NCERT solutions of class 12th maths

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## NCERT Solutions for Class 12 Maths

Class 12 NCERT solutions answers all the questions given in the NCERT textbooks in a step-by-step process. Our Maths tutors have helped us put together this for our Class 12 Students. The solutions on Shaalaa will help you solve all the NCERT Class 12 Maths questions without any problems. Every chapter has been broken down systematically for the students, which gives fast learning and easy retention.

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## NCERT Solutions for Class 12 Maths CBSE, Karnataka Board PUC

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Our CBSE, Karnataka Board PUC NCERT solutions for Maths Class 12 cover everything from Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations, Vector Algebra, Three Dimensional Geometry, Linear Programming, Probability and the other topics.

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