# NCERT Solutions For Class 12

NCERT Solutions for class 12 all subjects in PDF format are available to free download. Students who are preparing for IIT – JEE mains and advance, the study material is also available for practice, Mathematics solutions are given in English and Hindi Medium.Other subjects like Physics, Chemistry, Biology, Accounts, Business Studies, Economics, etc. will be uploaded in Hindi Medium for the new academic session 2020-21 following the latest CBSE Curriculum 2020-2021.

NCERT Books for class 12 are design not only for CBSE exams, you can also crack competitive exams using these books. Purchasing too many books puzzle the students. It is just advice that concentrate on your course book (that is NCERT) and later on go for other practice books including NCERT Exemplar Problems.

Contents

## NCERT Sols for Class 12

NCERT Solutions for Class 12 Maths, Phy, Chem, Bio with study material and notes for revision are given below. You can also download contents for Business studies, P. E. and English in PDF.

### Preparing For Competitive Exams

Preparing for competitive exams should be done side by side but priority should be given to CBSE Exams. Scoring good marks never resemble to good study. If you are preparing for your exams by studying the concepts of topic, you may easily clear the competitive exams also. Students who has studied well in both the class 11th and 12th, clearing the competition is not a big job for him.

#### Study Material For Class 12 Physical Education

Online study material for Class 12 Physical Education is also available on websites to free download. These study material contains the notes, important questions and their answers. Segregation of questions with answers are also provided in the end of each chapter.

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

1. 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.
2. Chapter 2 Inverse Trigonometric Functions –  Finding principle value, solving identities using properties
3. 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
4. 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
5. 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.
6. 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
7. 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
8. Chapter 8 Application of Integrals –  Finding area of region of simple curve, curve and line. Finding area between two curves.
9. 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
10. 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
11. 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
12. Chapter 12 Linear Programming – Finding maximum or minimum value of Z using bounded or unbounded region of graphical inequality.  Solving Diet, Manufacturing & Transport problems.
13. 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

##### About Class 12 Biology

Class 12 Biology is basically the study of life. It contains the description of various life forms including human beings. In Biology, we starts with identification, nomenclature and classification and extent it to the complexity of body structure and life span.

It is one of the most interesting subjects if we relate everything with our environment or daily life. Knowing the behavior and habitats of various animals, we can understand the nature in better way. During the studying Biology in class 12, we must relate everything with nature or each other. We should focus on physiology anatomy of living being.Download NCERT Books 2020-21 and Offline apps based on new CBSE Syllabus. Ask your queries related to NIOS or CBSE Board through Discussion Forum.

### How To Prepare For Maths In Class 12?

Solve each and every questions including examples given in NCERT Books. In case of doubt you may refer NCERT Solutions given on different website. If you have done NCERT Textbook and Exemplar Problem Book, you can solve every question in other books also.

### Is There Any NCERT Book For Physical Education Class 12?

There is no NCERT Book published so far for Physical Education. Syllabus for Physical Education Class 12 is described CBSE. Private publishers are printing the books following these syllabus.

### How To Prepare For Class 12 Physics Exams?

Read carefully your course book, underlining the important terms and topics. Derive all the formulae, you are using in class 12, whether it in course or not. After completing each chapter, go through NCERT Exemplar Book of same chapter or topic. For CBSE final exams, must do CBSE Sample Papers and Previous Years Papers.

### Why Is Education Learn Academy One Of The Best Websites In NCERT Solutions For Class 12?

There is simplicity in website. No login and password. There is no registration of Mobile number. No messaging or calling for business sale. Moreover, best online support.