# NCERT Exemplar Class 12 Maths Solutions

NCERT Exemplar Class 12 Maths Solutions are the best way to practice all the important topics of Maths. NCERT Exemplar problems and solutions provide you with a proper method of self-assessment of your preparedness for CBSE Class 12th exams. Our experts provide solutions to each of the problems for all the chapters of NCERT Exemplar Maths book in the simplest form. It gives you a systematic approach towards solving maths problems on any topic and of any complexity.

NCERT Exemplar Class 11th Maths Book has a total of 13 chapters which deal with many important topics like probability, differential equations, inverse trigonometric functions, and many others. Class 12 exams are a very important milestone for you in terms of your career goals as well as securing a seat in a good college. Having to deal with so many subjects and goals, you may find yourself in a fix on how to go about managing time.

Instasolv makes learning maths easy and interesting. Once you go through Exemplar problems and solutions provided by our team of experts, you would be better equipped to solve many complex problems independently. Here you will find some best practices to follow and easy ways to remember all the important theorems and formulae.

## NCERT Exemplar Solutions for Class 12 Maths Problems

## NCERT Exemplar Class 12 Maths Solutions Chapter 1: Relations and Functions

The Relations and Functions chapter has a total of 62 NCERT Exemplar problems divided into 5 sections. Key topics discussed here are:

- Types of Relations and Functions
- Domain and Ranges
- Composition of functions and Invertible functions
- Binary operations on functions.

## NCERT Exemplar Class 12 Maths Solutions Chapter 2: Inverse Trigonometric Functions

The Inverse Trigonometric Functions chapter has a total of 55 exemplar problems divided in 5 sections. Some of the important concepts discussed here are:

- Properties of Inverse Trigonometric Functions
- Restriction on domain and ranges of Trigonometric Functions
- Graphical representation of the behavior of the functions

## NCERT Exemplar Class 12 Maths Solutions Chapter 3: Matrices

Matrices chapter has a total of 101 exemplar problems spread in 5 different kinds of exercise. It covers the following important aspects of matrices:

- Order of matrix
- Types and properties of matrices
- Transpose of a matrix and invertible matrices
- Mathematical operations on matrices like addition, subtraction

## NCERT Exemplar Class 12 Maths Solutions Chapter 4: Determinants

This chapter has 58 exemplar problems in sets of 5 exercises. The gist of important topics in this chapter is:

- Properties of the determinant
- Determinant matrix of order 1, 2, and 3
- Adjoint and inverse of a matrix
- Application of matrices
- Solving linear equations using the concept of the inverse of a matrix
- Minor and cofactor

## NCERT Exemplar Class 12 Maths Solutions Chapter 5: Continuity and Differentiability

Continuity and differentiability is the basis of differential calculus hence a very important chapter for class 12. It has 106 exemplar problems divided into 5 exercises including the following concepts:

- Continuity and differentiability
- Algebra of continuous functions
- Composite functions and its derivatives
- Implicit functions
- Exponential functions
- Logarithmic functions
- The parametric form of functions and its derivatives
- Mean value theorem

## NCERT Exemplar Class 12 Maths Solutions Chapter 6: Application of Derivatives

This chapter would make you adept in solving derivative problems which are based on the rate of change of quantity and increasing/decreasing functions. It has 64 exemplar problems divided into 4 sections, covering this topic extensively. The salient topics discussed here are:

- Maxima and minima
- Equation of tangent and normal to a curve
- Min and max values of a function in a closed interval

## NCERT Exemplar Class 12 Maths Solutions Chapter 7: Integrals

Chapter 7 is Integrals which is a very important topic in the field of Class 12th Maths. It has 63 exemplar problems spread in 4 exercises which have a mix of short. Long, objective, and fill in the blanks type of questions. The key learning from this chapter are:

- Integration explained as an inverse of differentiation
- Indefinite integral and its geometric representation
- Differentiation versus Integration
- Methods of Integration
- Definite integral as the limit of a sum
- First and second fundamental theorems of integral calculus

## NCERT Exemplar Class 12 Maths Solutions Chapter 8: Application of Integrals

Chapter 8 is built on the foundation of chapter 7, which discusses integral calculus. In this chapter, you learn how to apply integration rules to find the area enclosed within a curve, circles, arcs, ellipses, and parabolas. It has 3 exercises and 34 exemplar problems which concentrate on the following concepts:

- The area under simple curves
- The area bounded by a line and a curve
- The area between 2 curves

## NCERT Exemplar Class 12 Maths Solutions Chapter 9: Differential Equations

The chapter of NCERT Exemplar Class 12 Maths book has 97 exemplar problems divided into 5 sections. This familiarizes you with different concepts around differential equations and its applications. The topics in this chapter cover:

- Order of a differential equation
- Differential equation degrees
- Differential equations for family of curves
- Differential equations and separable variables
- Differential equations of homogeneous type
- Differential equations which are linear

## NCERT Exemplar Class 12 Maths Solutions Chapter 10: Vector Algebra

In this chapter, you will get to learn the basic concepts of vectors and operations on vectors. It has 45 exemplar problems spread across 5 different exercises. Main takeaways from this chapter are:

- Basics of vectors and types of vectors
- Addition and multiplication of vectors by a scalar
- Vector’s components.
- Scalar product of vectors
- Vector projection on a line.
- Cross product of vectors

## NCERT Exemplar Class 12 Maths Solutions Chapter 11: Three-dimensional Geometry

With the basis of chapter 10 of vectors, chapter 11 prepares you on how to apply vector algebra concepts to 3-dimensional geometry. This has 5 exercises and 49 exemplar problems which deal with:

- Direction cosine and many concepts around it like the relation between direction cosines of a line
- Angle and the shortest distance between 2 lines
- Skew lines and distance between them.
- Plane equations and different concepts around it like the angle between 2 planes, the distance between the plane and a point, intercept form.

## NCERT Exemplar Class 12 Maths Solutions Chapter 12: Linear programming

Linear programming has 45 exemplar problems divided into 5 exercises which are based on the following concepts:

- Mathematical formula of linear programming
- Solving linear programming using a graphical representation
- Various types of linear programming like diet problem, manufacturing problem, transportation problem

## NCERT Exemplar Class 12 Maths Solutions Chapter 13: Probability

The chapter contains 5 exercises with 108 exemplar problems. Probability is one of the most important topics from the point of view of CBSE exams as well as many competitive exams. Many other branches of mathematics also use the idea of probability. Key topics covered in this topic are:

- Conditional probability and its properties
- Multiplication formula for the probability
- Total probability theorem
- Bayes’ theorem
- Bernoulli law and binomial distribution
- Distribution of probability with random variables

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