Maths NCERT solutions

Maths NCERT solutions

Maths NCERT solutions list

Here is the list of maths NCERT solutions for Class 6th to 12th
1.Maths NCERT solutions for class 10th CBSE and other Boards Exam
2.Maths NCERT solutions for class 9th CBSE and other Boards Exam
3.Maths NCERT solutions for class 8th CBSE and other Boards Exam
4.Maths NCERT solutions for class 7th CBSE and other Boards Exam
5.Maths NCERT solutions for class 6th CBSE and other Boards Exam
6.Maths NCERT solutions for class 11th CBSE and other Boards Exam
7.Maths NCERT solutions for class 12th CBSE and other Boards Exam

Maths NCERT solutions is an important milestone in your life as you take some serious decisions about your future based on your performance. Indeed, Mathematics forms a vital component of Class 6th to 12th as well as every competitive exams’ syllabus.

Benefits of accessing class 6th to 12th maths NCERT solutions are not only confined to your success in Maths, but it also lays a foundation for other super important subjects. Getting a good grip over exhaustive details of some chapters of Maths like Calculus, differential equations etc can be of great help while understanding the derivations and concepts behind the numericals of Science. You can easily download FREE CBSE Class 12th NCERT Maths Solutions PDF of each and every chapter of Mathematics. The solutions for each exercise have been curated and reviewed by some of the best teachers across India. It covers all the answers to the questions from each chapters from the NCERT Mathematics textbook. Class 6th to 12th maths NCERT solutions covers crucial and intricate chapters. The chapters are designed in a sequential and logical manner, which allows you to understand the concepts easily.

Maths NCERT solutions Class 10

Content of Class 10th Mathematics
1. Real Numbers
• 1.1 Introduction
• 1.2 Euclid’s Division Lemma
• 1.3 The Fundamental Theorem of Arithmetic
• 1.4 Revisiting Irrational Numbers
• 1.5 Revisiting Rational Numbers and Their Decimal Expansions
• 1.6 Summary
Important Formula
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise 1.4
2. Polynomials
• 2.1 Introduction
• 2.2 Geometrical Meaning of the Zeroes of a Polynomial
• 2.3 Relationship between Zeroes and Coefficients of a Polynomial
• 2.4 Division Algorithm for Polynomials
• 2.5 Summary
Important formula
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise 2.4
3. Pairs of linear equations in two variables
• 3.1 Introduction
• 3.2 Pair of Linear Equations in Two Variables
• 3.3 Graphical Method of Solution of a Pair of Linear Equations
• 3.4 Algebraic Methods of Solving a Pair of Linear Equations
•• 3.4.1 Substitution Method
•• 3.4.2 Elimination Method
•• 3.4.3 Cross-Multiplication Method
• 3.5 Equations Reducible to a Pair of Linear Equations in Two Variables
• 3.6 Summary
Important formula
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
4. Quadratic Equations
• 4.1 Introduction
• 4.2 Quadratic Equations
• 4.3 Solution of a Quadratic Equation by Factorisation
• 4.4 Solution of a Quadratic Equation by Completing the Square
• 4.5 Nature of Roots
• 4.6 Summary
Important formula
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
5. Arithmetic Progressions
•5.1 Introduction
• 5.2 Arithmetic Progression
• 5.3 nth Term of an AP
• 5.4 Sum of First n Terms of an AP
• 5.5 Summary
Important formula
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
6. Triangles
• 6.1 Introduction
• 6.2 Similar Figures
• 6.3 Similarity of Triangles
• 6.4 Criteria for Similarity of Triangles
• 6.5 Areas of Similar Triangles
• 6.6 Pythagoras Theorem
• 6.7 Summary
Important formula
Exercise 6.1
Exercise 6.2
Exercise
6.3
7. Coordinate Geometry
• 7.1 Introduction
• 7.2 Distance Formula
• 7.3 Section Formula
• 7.4 Area of a Triangle
• 7.5 Summary
Important formula
Exercise 7.1
Exercise 7.2
Exercise 7.3
8. Introduction to Trigonometry
• 8.1 Introduction
• 8.2 Trigonometric Ratios
• 8.3 Trigonometric Ratios of Some Specific Angles
• 8.4 Trigonometric Ratios of Complementary Angles
• 8.5 Trigonometric Identities
• 8.6 Summary
Important formula
Exercise 8.1
Exercise 8.2
Exercise 8.3
Exercise 8.4
9. Some Applications of Trigonometry
• 9.1 Introduction
• 9.2 Heights and Distances
• 9.3 Summary
Important formula
Exercise 9.1
Exercise 9.2
10 Circles
• 10.1 Introduction
• 10.2 Tangent to a Circles
• 10.3 Number of Tangents from a Point on a Circle
• 10.4 Summary
Important formula
Exercise 10.1
Exercise 10.2
Exercise 10.3
Exercise 10.4
11 Constructions
• 11.1 Introduction
• 11.2 Division of a Line Segment
• 11.3 Construction of Tangents to a Circle
• 11.4 Summary
Important formula
Exercise 11.1
Exercise 11.2
Exercise 11.3
12 Areas Related to Circles
• 12.1 Introduction
• 12.2 Perimeter and Area of a Circle — A Review
• 12.3 Areas of Sector and Segment of a Circle
• 12.4 Areas of Combinations of Plane Figures
• 12.5 Summary
Important formula
Exercise 12.1
Exercise 12.2
Exercise 12.3
13 Surface Areas and Volumes
• 13.1 Introduction
• 13.2 Surface Area of a Combination of Solids
•13.3 Volume of a Combination of Solids
• 13.4 Conversion of Solid from One Shape to Another
• 13.5 Frustum of a Cone
• 13.6 Summary
Important formula
Exercise 13.1
Exercise 13.2
Exercise 13.3
Exercise 13.4
14 Statistics
• 14.1 Introduction
• 14.2 Mean of Grouped Data
• 14.3 Mode of Grouped Data
• 14.4 Median of Grouped Data
• 14.5 Graphical Representation of Cumulative Frequency Distribution
• 14.6 Summary
Important formula
Exercise 14.1
Exercise 14.2
Exercise 14.3
Exercise 14.4
15 Probability
• 15.1 Introduction
• 15.2 Probability — A Theoretical Approach
• 15.3 Summary
Important formula
Exercise 15.1
Exercise 15.2
Exercise 15.3

Maths NCERT solutions Class 9th

Whether you choose to be an engineer or a doctor, you will have to deal with Mathematics in every area. Making the concepts of maths concrete can immensely help you in securing good marks in the CBSE Class 6th to 12th exam as well as in various competitive exams.

Content of Class 9th Mathematics
1. Number system
1.1 Introduction
1.2 Irrational Numbers
1.3 Real Numbers and their Decimal Expansions
1.4 Representing Real Numbers on the Number Line
1.5 Operations on Real Numbers
1.6 Laws of Exponents for Real Numbers
1.7 Summary
Important formula
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise
1.4
2. POLYNOMIALS
2.1 Introduction
2.2 Polynomials in One Variable
2.3 Zeroes of a Polynomial
2.4 Remainder Theorem
2.5 Factorisation of Polynomials
2.6 Algebraic Identities
2.7 Summary
Important formula
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise
2.4
3. COORDINATE GEOMETRY
3.1Introduction
3.2 Cartesian System
3.3 Plotting a Point in the Plane if its Coordinates are given
3.4 Summary
Important formula
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise
3.4
4. LINEAR EQUATIONS IN TWO VARIABLES
4.1 Introduction
4.2 Linear Equation
4.3 Solution of a Linear Equation
4.4 Graph of a Linear Equation in Two Variables
4.5 Equations of Lines Parallel to x-axis and y-axis
4.6 Summary
Important formula
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise
4.4
5. INTRODUCTION TO EUCLID’S GEOMETRY
5.1 Introduction
5.2 Euclid’s Definitions, Axioms and Postulate
5.3 Equivalent Versions of Euclid’s Fifth Postulate
5.4 Summary
Important formula
Exercise 5.1
Exercise 5.2
Exercise 5.3
6. LINES AND ANGLES
6.1 Introduction
6.2 Basic Terms and Definitions
6.3 Intersecting Lines and Non-intersecting Lines
6.4 Pairs of Angles
6.5 Parallel Lines and a Transversal
6.6 Lines Parallel to the same Line
6.7 Angle Sum Property of a Triangle
6.8 Summary
Important formula
Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise
6.4
7. TRIANGLES
7.1 Introduction
7.2 Congruence of Triangles
7.3 Criteria for Congruence of Triangles
7.4 Some Properties of a Triangle
7.5 Some More Criteria for Congruence of Triangles
7.6 Inequalities in a Triangle
7.7 Summary
Important formula
Exercise 7.1
Exercise 7.2
Exercise 7.3
Exercise
7.4
8. QUADRILATERALS
8.1 Introduction
8.2 Angle Sum Property of a Quadrilateral
8.3 Types of Quadrilaterals
8.4 Properties of a Parallelogram
8.5 Another Condition for a Quadrilteral to be a Parallelogram
8.6 The Mid-point Theorem
8.7 Summary
Important formula
Exercise 8.1
Exercise 8.2
Exercise 8.3
Exercise
8.4
9. AREAS OF PARALLELOGRAMS AND TRIANGLES
9.1 Introduction
9.2 Figures on the same Base and Between the same Parallels
9.3 Parallelograms on the same Base and between the same Parallel
9.4 Triangles on the same Base and between the same Parallel
9.5 Summary
Important formula
Exercise 9.1
Exercise 9.2
Exercise 9.3
Exercise
9.4
10. CIRCLES
10.1 Introduction
10.2 Circles and its Related Terms : A Review
10.3 Angle Subtended by a Chord at a Point
10.4 Perpendicular from the Centre to a Chord
10.5 Circle through Three Points
10.6 Equal Chords and their Distances from the Centre
10.7 Angle Subtended by an Arc of a Circle
10.8 Cyclic Quadrilaterals
10.9 Summary
Important formula
Exercise 10.1
Exercise 10.2
Exercise 10.3
Exercise
10.4
11. CONSTRUCTIONS
11.1 Introduction
11.2 Basic Constructions
11.3 Some Constructions of Triangles
11.4 Summary
Important formula
Exercise 11.1
Exercise 11.2
12. HERON’S FORMULA
12.1 Introduction
12.2 Area of a Triangle – by Heron’s Formula
12.3 Application of Heron’s Formula in finding Areas of Quadrilaterals
12.4 Summary
Important formula
Exercise 12.1
Exercise 12.2
Exercise 12.3
13. SURFACE AREAS AND VOLUMES
13.1 Introduction
13.2 Surface Area of a Cuboid and a Cube
13.3 Surface Area of a Right Circular Cylinder
13.4 Surface Area of a Right Circular Cone
13.5 Surface Area of a Sphere
13.6 Volume of a Cuboid
13.7 Volume of a Cylinder
13.8 Volume of a Right Circular
13.9 Volume of a Sphere
13.10 Summary
Important formula
Exercise13. 1
Exercise 13.2
Exercise 13.3
Exercise
13.4
14. STATISTICS
14.1 Introduction
14.2 Collection of Data
14.3 Presentation of Data
14.4 Graphical Representation14.5 Measures of Central Tendency
14.6 Summary
Important formula
Exercise 14.1
Exercise 14.2
Exercise 14.3
Exercise
14.4
15. PROBABILITY
15.1 Introduction
15.2 Probability – an Experimental Approach
15.3 Summary
Important formula
Exercise 15.1
Exercise
15.2

Maths NCERT solutions Class 8th

NCERT Solution for maths of Class 6th to 12 plays a vital role in your exam preparation as it has detailed chapter wise solutions for all exercises. First and foremost, you should imprint this in your mind that NCERT books are the biggest tool that you can have to get well-versed with the fundamentals.

1.Rational Numbers
Important formula
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise
1.4
2. Linear Equations in One Variable
Important formula
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise
2.4
3. Understanding Quadrilaterals
Important formula
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise
3.4
4. Practical Geometry
Important formula
Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise
4.4
5. Data Handling
Important formula
Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise
5.4
6. Squares and Square Roots
Important formula
Exercise 6.1
Exercise 6.2
Exercise 6.3
Exercise
6.4
7. Cubes and Cube Roots
Important formula
Exercise 7.1
Exercise 7.2
Exercise 7.3
Exercise
7.4
8. Comparing Quantities
Important formula
Exercise 8.1
Exercise 8.2
Exercise 8.3
Exercise
8.4
9. Algebraic Expressions and Identities
Important formula
Exercise 9.1
Exercise 9.2
Exercise 9.3
Exercise
9.4
10. Visualising Solid Shapes
Important formula
Exercise 10.1
Exercise 10.2
Exercise 10.3
Exercise
10.4
11. Mensuration
Important formula
Exercise 11.1
Exercise 11.2
Exercise 11.3
Exercise
11.4
12. Exponents and Powers
Important formula
Exercise 12.1
Exercise 12.2
Exercise 12.3
Exercise
12.4
13. Direct and Inverse Proportions
Important formula
Exercise 13.1
Exercise 13.2
Exercise 13.3
Exercise
13.4
14. Factorisation
Important formula
Exercise 14.1
Exercise 14.2
Exercise 14.3
Exercise
14.4
15. Introduction to Graphs
Important formula
Exercise 15.1
Exercise 15.2
Exercise 15.3
Exercise
15.4
16. Playing with Numbers
Important formula
Exercise 16.1
Exercise 16.2
Exercise 16.3
Exercise
16.4

Maths NCERT solutions Class 7th

The philosophy with which the maths ncert solution class 10 syllabus was developed, and which the website has tried To realise in the present post. More specifically, while creating the post, the Following broad guidelines have been kept in mind.

The matter needs to be linked to what the child has studied before, and to Her experiences. The language used in the post, including that for ‘word problems’, must be Clear, simple and unambiguous. Concepts/processes should be introduced through situations from the Children’s environment.

1. Integers
Important formula
Exercise 1.1
Exercise 1.2
Exercise 1.3
Exercise
1.4
2. Fractions and Decimals
Important formula
Exercise 2.1
Exercise 2.2
Exercise 2.3
Exercise
2.4
3. Data Handling
Important formula
Exercise 3.1
Exercise 3.2
Exercise
Exercise
4. Simple Equations
Important formula
Exercise
Exercise
Exercise
Exercise
5. Lines and Angles
Important formula
Exercise
Exercise
Exercise
Exercise
6. The Triangle and its Properties
Important formula
Exercise
Exercise
Exercise
Exercise
7. Congruence of Triangles
Important formula
Exercise
Exercise
Exercise
Exercise
8. Comparing Quantities
Important formula
Exercise
Exercise
Exercise
Exercise
9. Rational Numbers
Important formula
Exercise
Exercise
Exercise
Exercise
10. Practical Geometry
Important formula
Exercise
Exercise
Exercise
Exercise
11. Perimeter and Area
Important formula
Exercise
Exercise
Exercise
Exercise
12. Algebraic Expressions
Important formula
Exercise
Exercise
Exercise
Exercise
13. Exponents and Powers
Important formula
Exercise
Exercise
Exercise
Exercise
14. Symmetry
Important formula
Exercise
Exercise
Exercise
Exercise
15. Visualising Solid Shapes
Important formula
Exercise
Exercise
Exercise
Exercise

Maths NCERT solutions Class 6th

For each concept/process give several examples and exercises, but not of The same kind. This ensures that the children use the concept/process again And again, but in varying contexts. Here ‘several’ should be within reason, Not overloading the child. Encourage the children to see, and come out with, diverse solutions to Problems. As far as possible, give the children motivation for results used.

1. KNOWING OUR NUMBERS
Important formula
Exercise
Exercise
Exercise
Exercise
2. WHOLE NUMBERS
Important formula
Exercise
Exercise
Exercise
Exercise
3. PLAYING WITH NUMBERS
Important formula
Exercise
Exercise
Exercise
Exercise
4. BASIC GEOMETRICAL IDEAS
Important formula
Exercise
Exercise
Exercise
Exercise
5. UNDERSTANDING ELEMENTARY SHAPES
Important formula
Exercise
Exercise
Exercise
Exercise
6. INTEGERS
Important formula
Exercise
Exercise
Exercise
Exercise
7. FRACTIONS
Important formula
Exercise
Exercise
Exercise
Exercise
8. DECIMALS
Important formula
Exercise
Exercise
Exercise
Exercise
9. DATA HANDLING
Important formula
Exercise
Exercise
Exercise
Exercise
10. MENSURATION
Important formula
Exercise
Exercise
Exercise
Exercise
11. ALGEBRA
Important formula
Exercise
Exercise
Exercise
Exercise
12. RATIO AND PROPORTION
Important formula
Exercise
Exercise
Exercise
Exercise
13. SYMMETRY CHAPTER
Important formula
Exercise
Exercise
Exercise
Exercise
14. PRACTICAL GEOMETRY
Important formula
Exercise
Exercise
Exercise
Exercise

Maths NCERT solutions Class 11th

All proofs need to be given in a non-didactic manner, allowing the learner to see the flow of reason. The focus should be on proofs where a short and clear argument reinforces mathematical thinking and reasoning. Whenever possible, more than one proof is to be given by maths ncert solution.

Proofs and solutions need to be used as vehicles for helping the learner develop a clear and logical way of expressing her arguments. All geometric constructions should be accompanied by an analysis of the construction and a proof for the steps taken to do the required construction. Accordingly, the children would be trained to do the same while doing constructions.

Content
1. Sets
1.1 Introduction
1.2 Sets and their Representations
1.3 The Empty Set
1.4 Finite and Infinite Sets
1.5 Equal Sets
1.6 Subsets
1.7 Power Set
1.8 Universal Set
1.9 Venn Diagrams
1.10 Operations on Sets
1.11 Complement of a Set
1.12 Practical Problems on Union and Intersection of Two Sets
Important formula
Exercise
Exercise
Exercise
Exercise
2. Relations and Functions
2.1 Introduction
2.2 Cartesian Product of Sets2.3 Relations
2.4 Functions
Important formula
Exercise
Exercise
Exercise
Exercise
3. Trigonometric Functions
3.1 Introduction
3.2 Angle
3.3 Trigonometric Functions
3.4 Trigonometric Functions of Sum and Difference of Two Angles
3.5 Trigonometric Equations
Important formula
Exercise
Exercise
Exercise
Exercise
4. Principle of Mathematical Induction
4.1 Introduction
4.2 Motivation
4.3 The Principle of Mathematical Induction
Important formula
Exercise
Exercise
Exercise
Exercise
5. Complex Numbers and Quadratic Equations
5.1 Introduction
5.2 Complex Numbers
5.3 Algebra of Complex Numbers
5.4 The Modulus and the Conjugate of a Complex Number
5.5 Argand Plane and Polar Representation
5.6 Quadratic Equations
Important formula
Exercise
Exercise
Exercise
Exercise
6. Linear Inequalities
6.1 Introduction
6.2 Inequalities
6.3 Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
6.4 Graphical Solution of Linear Inequalities in Two Variables
6.5 Solution of System of Linear Inequalities in Two Variables
Important formula
Exercise
Exercise
Exercise
Exercise
7. Permutations and Combinations
7.1 Introduction
7.2 Fundamental Principle of Counting
7.3 Permutations
7.4 Combinations
Important formula
Exercise
Exercise
Exercise
Exercise
8. Binomial Theorem
8.1 Introduction
8.2 Binomial Theorem for Positive Integral Indices
8.3 General and Middle Terms
Important formula
Exercise
Exercise
Exercise
Exercise
9. Sequences and Series
9.1 Introduction
9.2 Sequences
9.3 Series
9.4 Arithmetic Progression (A.P.)
9.5 Geometric Progression (G.P.)
9.6 Relationship Between A.M. and G.M.
9.7 Sum to n terms of Special Series
Important formula
Exercise
Exercise
Exercise
Exercise
10. Straight Lines
10.1 Introduction
10.2 Slope of a Line
10.3 Various Forms of the Equation of a Line
10.4 General Equation of a Lin10.5 Distance of a Point From a Line
Important formula
Exercise
Exercise
Exercise
Exercise
Conic Sections
11.1 Introduction
11.2 Sections of a Cone
11.3 Circle
11.4 Parabola
11.5 Ellipse
11.6 Hyperbola
Important formula
Exercise
Exercise
Exercise
Exercise
12. Introduction to Three Dimensional Geometry
12.1 Introduction
12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space
12.3 Coordinates of a Point in Space
12.4 Distance between Two Points
12.5 Section Formula
Important formula
Exercise
Exercise
Exercise
Exercise
13. Limits and Derivatives
13.1 Introduction
13.2 Intuitive Idea of Derivatives
13.3 Limits
13.4 Limits of Trigonometric Functions
13.5 Derivatives
Important formula
Exercise
Exercise
Exercise
Exercise
14. Mathematical Reasoning
14.1 Introduction
14.2 Statements
14.3 New Statements from Old
14.4 Special Words/Phrases
14.5 Implications
14.6 Validating Statements
Important formula
Exercise
Exercise
Exercise
Exercise
15. Statistics
15.1 Introduction
15.2 Measures of Dispersion
15.3 Range
15.4 Mean Deviation
15.5 Variance and Standard Deviation
15.6 Analysis of Frequency Distributions
Important formula
Exercise
Exercise
Exercise
Exercise
16. Probability
16.1 Introduction
16.2 Random Experiments
16.3 Event
16.4 Axiomatic Approach to Probability
Important formula
Exercise
Exercise
Exercise
Exercise

Maths NCERT solutions Class 12th

Add such small anecdotes, pictures, cartoons and historical remarks at several places which the children would find interesting.Include optional exercises for the more interested learners. These would not be tested in the examinations.

Give answers to all exercises, and maths ncert solutions/hints for those that the children may require. Whenever possible, propagate constitutional values. The post has particularly been created With the view to giving children space to explore mathematics, Maths NCERT solution and develop the abilities To reason mathematically.

Content
1. Relations and Functions
1.1 Introduction
1.2 Types of Relations
1.3 Types of Functions
1.4 Composition of Functions and Invertible Function
1.5 Binary Operations
Important formula
Exercise
Exercise
Exercise
Exercise
2. Inverse Trigonometric Functions
2.1 Introduction
2.2 Basic Concepts
2.3 Properties of Inverse Trigonometric Functions
Important formula
Exercise
Exercise
Exercise
Exercise
3. Matrices
3.1 Introduction
3.2 Matrix
3.3 Types of Matrices
3.4 Operations on Matrices
3.5 Transpose of a Matrix
3.6 Symmetric and Skew Symmetric Matrices
3.7 Elementary Operation (Transformation) of a Matrix
3.8 Invertible Matrices
Important formula
Exercise
Exercise
Exercise
Exercise
4. Determinants
4.1 Introduction
4.2 Determinant
4.3 Properties of Determinants 4.4 Area of a Triangle
4.5 Minors and Cofactors
4.6 Adjoint and Inverse of a Matrix
4.7 Applications of Determinants and Matrices
Important formula
Exercise
Exercise
Exercise
Exercise
5. Continuity and Differentiability
5.1 Introduction
5.2 Continuity
5.3 Differentiability
5.4 Exponential and Logarithmic Functions
5.5 Logarithmic Differentiation
5.6 Derivatives of Functions in Parametric Forms
5.7 Second Order Derivative
5.8 Mean Value Theorem
Important formula
Exercise
Exercise
Exercise
Exercise
6. Application of Derivatives
6.1 Introduction
6.2 Rate of Change of Quantities
6.3 Increasing and Decreasing Functions
6.4 Tangents and Normals
6.5 Approximations
6.6 Maxima and Minima
Important formula
Exercise
Exercise
Exercise
Exercise
7. Integrals
7.1 Introduction
7.2 Integration as an Inverse Process of Differentiation
7.3 Methods of Integration
7.4 Integrals of some Particular Functions
7.5 Integration by Partial Fractions
7.6 Integration by Parts
7.7 Definite Integral
7.8 Fundamental Theorem of Calculus
7.9 Evaluation of Definite Integrals by Substitution
7.10 Some Properties of Definite Integrals
Important formula
Exercise
Exercise
Exercise
Exercise
8. Application of Integrals
8.1 Introduction
8.2 Area under Simple Curves8.3 Area between Two Curves
Important formula
Exercise
Exercise
Exercise
Exercise
9. Differential Equations
9.1 Introduction
9.2 Basic Concepts
9.3 General and Particular Solutions of a Differential Equation
9.4 Formation of a Differential Equation whose General Solution is given
9.5 Methods of Solving First order, First Degree Differential Equations
Important formula
Exercise
Exercise
Exercise
Exercise
10. Vector Algebra
10.1 Introduction
10.2 Some Basic Concepts
10.3 Types of Vectors
10.4 Addition of Vectors
10.5 Multiplication of a Vector by a Scalar
10.6 Product of Two Vectors
Important formula
Exercise
Exercise
Exercise
Exercise
11. Three Dimensional Geometry
11.1 Introduction
11.2 Direction Cosines and Direction Ratios of a Line
11.3 Equation of a Line in Space
11.4 Angle between Two Lines
11.5 Shortest Distance between Two Lines
11.6 Plane
11.7 Coplanarity of Two Lines
11.8 Angle between Two Plane11.9 Distance of a Point from a Plane
11.10 Angle between a Line and a Plane
Important formula
Exercise
Exercise
Exercise
Exercise
12. Linear Programming
12.1 Introduction
12.2 Linear Programming Problem and its Mathematical Formulation
12.3 Different Types of Linear Programming Problems
Important formula
Exercise
Exercise
Exercise
Exercise
13. Probability
13.1 Introduction
13.2 Conditional Probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes’ Theorem
13.6 Random Variables and its Probability Distributions
13.7 Bernoulli Trials and Binomial Distribution
Important formula
Exercise
Exercise
Exercise
Exercise