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In mathematics, relations and functions is one of the basic and important chapters that help to understand other numerous topics conveniently. There are tons of topics such as types of relations, one to one, composite functions, the inverse of a function and lastly binary operations that you will learn through our online class. However, most of the students find it hard to understand and end up facing problems with further topics. So, check out our Studykhazana online classes offered by Puneet Dogra in order to resolve your issues in respect of relations and functions with ease.

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### Lecture 2: Relations & functions Part-2

01:09:57

In this section, you will learn:
1) Definition of Inverse Trigonometric Functions
2) Range of Inverse Trigonometric functions
3) Domain of Inverse Trigonometric Functions
4) Principle branch values
5) Graph of Inverse Trigonometric Functions
6) Elementary properties of Inverse Trigonometric functions

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### Lecture 7: Inverse Trigonometry- 7

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In this section, you will learn:
1) Concept, notation, order, equality and types of matrices
2) Zero matrix, transpose of a matrix, symmetric and skew symmetric matrices.
3) Simple properties of addition, subtraction and scaler multiplication
4) Non-commutativity of multiplication of matrices
5) Existence of non-zero matrices whose product is the zero matrix
6) Concept of elementary row and column operations
7) Invertible matrices and proof of uniqueness of inverse, if it exist.

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### Lecture 7: Matrices Part - VII

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In this section you will learn the following:
1) Determinant of square matrix
2) Properties of determinants
3) Minors
4) Co-factors
5) Application of determinant in finding area of a triangle
6) Adjoint and Inverse of a square matric

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### Lecture 8: Determinant part- 8

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Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.Derivatives of logarithmic and exponential functions. 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 interpretation.

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### Lecture 11: Derivatives- 11

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In this section, you will learn the following:
1) Applications of derivatives
2) Rate of change of bodies
3) increasing/ decreasing functions
4) Tangents and Normal
5) Use of derivatives in approximation
6) Maxima and Minima
7) Simple word problem

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### Lecture 13: Maxima & Minima- VI

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Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

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### Lecture 24: Integration Part- 24

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Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

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### Lecture 3: Application of Integrations Part - 3

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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 solutions of 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 or constants.

dx/dy + px = q, where p and q are functions of y or constants.

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### Lecture 7: Differential Equation Part - 7

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Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. 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. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

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### Lecture 4: Vector Part - 4

01:21:57

In this section, you will learn the following:
1) Direction Cosines and direction ratios of a line joining two points.
2) Cartesian Equation and Vector Equation of a line.
3) Coplanar and skew lines
4) Shortest distance between two lines.
5) Cartesian and vector equation of a plane.
6) Angles between a) Two lines  b) Two Planes  c) a line and a plane
7) Distance of a point from a plane.

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### Lecture 6: 3D Part - VI

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In this section, you will learn the following:
1) Introduction
2) Related terminology like constraints, objective function, optimization and different types of linear programming problems.
3) Mathematical formulation of L.P Problems.
4) Graphical method of solution for problems in two variables: feasible and infeasible regions.
5) feasible and infeasible solutions
6) Optimal feasible solutions

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### Lecture 3: Linear Programming - III

00:27:19

Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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### Lecture 10: Probability Part- 10

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Published    27-Apr-2017      Bilingual

## MATHEMATICS COMPLETE COURSE OF CLASS 12TH CBSE

Study Khazana delivers CBSE Class 12th Mathematics, one hundred five video lectures by Puneet Dogra on Mathematics Complete Course with complete solutions using sample paper based on NCERT Syllabus. This chapter covers the following topic to make students understand the topic and covers the whole chapter with all the question and answers.

## WHAT DO YOU STUDY IN RELATIONS AND FUNCTIONS?

• Introduction of Relations and Functions
• Types of relations- reflexive, symmetric, transitive and equivalence relations
• One to one and onto functions,
• What is a composite function?
• Discuss inverse of a function.
• Explain Binary operations

## WHAT DO YOU STUDY IN INVERSE TRIGONOMETRICS FUNCTIONS?

• Definition of Inverse Trigonometric Functions
• Explain range and domain of inverse trigonometric function
• Discuss principal value branch
• Graphs of inverse trigonometric functions
• Elementary properties of inverse trigonometric functions

## WHAT DO YOU STUDY IN MATRICES?

• Concept of Matrices
• Define- Notation, order, equality,
• Types of matrices,
• Explain zero and identity matrix, transpose of a matrix,
• Discuss symmetric and skew symmetric matrices.
• Operation on matrices through Addition and multiplication and multiplication with a scalar
• Simple properties of addition, multiplication and scalar multiplication
• Non- commutatively of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices?
• 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)

## WHAT DO YOU STUDY IN DETERMINANTS?

• Determinant of a square matrix (up to 3 x 3 matrices),
• Properties of determinants, minors, co-factors and
• Applications of determinants in finding the area of a triangle
• Ad joint 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.     WHAT DO YOU STUDY IN CONTINUITY?
• Introduction of Continuity
• Derivative of composite functions,
• Explain chain rule,
• Derivatives of inverse trigonometric functions,
• Derivative of implicit functions
• Concept of exponential and logarithmic functions

## WHAT DO YOU STUDY IN DIFFERENTIABILITY?

• Introduction of differentiability,
• Derivatives of inverse trigonometric functions,
• Derivative of implicit functions
• Concept of exponential and logarithmic functions
• Derivatives of logarithmic and exponential functions
• Explain Logarithmic differentiation,
Derivative of functions expressed in parametric forms.
• Discuss Second order derivatives.
• Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

## WHAT DO YOU STUDY IN APPLICATION OF DERIVATIVES?

• Introduction of Applications of derivatives,
• Explain rate of change of bodies,
• Increasing and decreasing functions of derivatives
• Discuss tangents and normal’s
• Use of derivatives in 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)

## WHAT DO YOU STUDY IN INTEGRALS?

• Integration as inverse process of differentiation
• Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of different types and problems based on them
• Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)
• Basic Properties of definite integrals and evaluation of definite integrals.

## WHAT DO YOU STUDY IN APPLICATION OF INTEGRALS?

• Applications in finding the area under simple curves,
• Finding the area of- especially lines, circles/parabolas/ellipses (in standard form only),
• Area between any of the two above said curves (the region should be clearly identifiable).

## WHAT DO YOU STUDY IN DIFFERENTIAL EQUATIONS?

• Definition of Differential Equations
• Explain order and degree of equations
• Discuss 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 solutions of homogeneous differential equations of first order and first degree

## WHAT DO YOU STUDY IN VECTOR?

• Introduction of Vectors
• Discuss magnitude and direction of a vector.
• What are Direction cosines and direction ratios of a vector?
• Types of vectors (equal, unit, zero, parallel and collinear vectors),
• Explain 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.
• Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

## WHAT DO YOU STUDY IN INTRODUCTION TO 3D GEOMETRY?

• Direction cosines and direction ratios of a line joining two points
• Cartesian equation 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

## WHAT DO YOU STUDY IN LINEAR PROGRAMMING?

• Introduction of Linear Programming
• Objective and function of Linear Programming
• Different types of linear programming (L.P.)
• Mathematical formulation of L.P
• Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded),
• Feasible and infeasible solutions,

## WHAT DO YOU STUDY IN PROBABILITY?

• Explain- Conditional probability, multiplication theorem on probability
• Discuss about- independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable.
• Concept of Repeated independent (Bernoulli) trials and Binomial distribution.

## HOW WE HELP THE STUDENTS???

These video lectures will make the subject easy for students. The free lecture is available as a demo. We provide mock exams after completion of the full course. These lectures are recording of the live session taken. it will include question and answers of the students undertaken during the class. CBSE Class 12th previous question papers and sample papers are also given to the students for practice. Video Lectures classes are taken by Study Khazana’s best faculties. Video lectures contain examples and formulas related to different topics. We have doubt sessions on YouTube related to students queries asked on WhatsApp. These classes are based on NCERT Syllabus. We offer pen drives and online-offline study mode to the students. We also have Android and IOS Study Khazana mobile app for helping students to study anywhere at any time. #### Puneet Dogra

 Phone: 95********94 Email: pun********@gmail.com Address: Institute:

Hello, I am Puneet Dogra faculty of Study Khazana. I am a very passionate teacher. I am going to change your experience of learning maths. My way of teaching will surely lead you to your desired scores or may be more.Moreover I will give some magical tips to make maths much easier for you.

##### Qualification

My highest qualification is MSc. in Mathematics from DU.

##### Biography

I have experience of more than 5 years in teaching.

#### GOOD TEACHER VERY NICE

WOOWWW I LAERNT MATHS VERY EASILY

nice lecture

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