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### Lecture 3: Straight Lines Part- 3

01:06:23

Published    26-Mar-2017      Bilingual

## COMPLETE CRASH COURSE MATHEMATICS COMPETITIVE EXAM NDA

Study Khazana delivers Competitive Exam NDA, twenty video lectures by Puneet Dogra on Mathematics Complete Crash Course with complete solutions using sample paper based on 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 UNDERSTAND BY ALGEBRA?

• Concept of a set
• operations on sets
• Venn diagrams. De Morgan laws
• Cartesian product relation
• equivalence relation
• Representation of real numbers on a line
• Complex numbers – basic properties
• modulus argument
• Cube roots of unity
• Binary system of numbers
• Conversion of a number in decimal system to binary system and vice-versa.
• Arithmetic
• Geometric and Harmonic Progressions
• Quadratic equations with real coefficients
• Solution of linear in equations of two variables by graphs
• Permutation and Combination
• Binomial theorem and its application
• Logarithms and their applications.

## WHAT DO YOU UNDERSTAND BY TRIGONOMETRY?

• Angles and their measures in degrees and in radians
• Trigonometrical ratios
• Trigonometric identities Sum and difference formulae
• Multiple and Sub-multiple angles
• Inverse trigonometric functions
• Applications – Height and distance
• Properties of triangles.

## WHAT DO YOU UNDERSTAND BY MATRICS AND DETERMINANTS?

• Types of matrices
• Operations on matrices
• Determinant of a matrix
• Basic properties of determinants
• Adjoint and inverse of a square matrix
• Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

## WHAT DO YOU UNDERSTAND BY ANALYTICAL GEOMETRY?

• Rectangular Cartesian Coordinate system
• Distance formula
• Equation of a line in various forms
• Angle between two lines
• Distance of a point from a line
• Equation of a circle in standard and in general form
• Standard forms of parabola
• Ellipse and hyperbola
• Eccentricity and axis of a conic

## WHAT DO YOU UNDERSTAND BY DIFFERENTIAL CALCULUS?

• Concept of a real-valued function – domain
• range and graph of a function
• Composite functions
• Derivative of function at a point
• Derivatives of sum
• Product and quotient of functions
• Derivative of a function with respect to another function
• Derivative of a composite function
• Second order derivatives
• Increasing and decreasing functions
• Application of derivatives in problems of maxima and minima.   WHAT DO YOU UNDERSTAND BY CALCULUS DIFFERENTIAL EQUATION?
• Integration as inverse of differentiation
• Integration by substitution and by parts
• Standard integrals involving algebraic expressions
• Trigonometric
• Exponential and hyperbolic functions
• General and particular solution of a differential equation           WHAT DO YOU UNDERSTAND BY VECTOR ALGEBRA?
• Vectors in two and three dimensions
• Magnitude and direction of a vector
• Unit and null vectors addition of vectors
• Scalar multiplication of vector

## WHAT DO YOU UNDERSTAND BY STATISTICS AND PROBABILITY?

• Statistics: Classification of data
• Frequency distribution
• Cumulative frequency distribution – examples
• Graphical representation – Histogram
• Pie Chart
• Frequency Polygon – examples
• Measures of Central Tendency – Mean Median and Mode
• Variance and standard deviation – determination and comparison
• Correlation and regression
• Random experiment
• Outcomes and associated sample space
• Events
• Mutually exclusive and exhaustive events
• Impossible and certain events
• Union and Intersection of events
• Complimentary
• elementary and composite events
• Conditional probability
• Bayes’ theorem – simple problems
• Random variable as function on a sample space
• Binomial distribution
• Examples of random experiments giving rise to Binominal 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 NDA 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 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.

#### value for money

great...it was a nice learning and it nearly took me to a different level

#### Nice videos sir

nice sir....but would have been better if the time period of the course was of 6 months ..thanks sir...good videos

#### maths

why had you given short tricks for log? you had not included tricks of 3D , set, relation and function more.

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