## Maths NCERT solutions list

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 FormulaExercise 1.1Exercise 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 formulaExercise 2.1Exercise 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 formulaExercise 3.1Exercise 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 formulaExercise 4.1Exercise 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 formulaExercise 5.1Exercise 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 formulaExercise 6.16.3Exercise 6.2 Exercise |

7. Coordinate Geometry• 7.1 Introduction • 7.2 Distance Formula • 7.3 Section Formula • 7.4 Area of a Triangle • 7.5 Summary Important formulaExercise 7.1Exercise 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 formulaExercise 8.1Exercise 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 formulaExercise 9.1Exercise 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 formulaExercise 10.1Exercise 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 formulaExercise 11.1Exercise 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 formulaExercise 12.1Exercise 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 formulaExercise 13.1Exercise 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 formulaExercise 14.1Exercise 14.2 Exercise 14.3 Exercise 14.4 |

15 Probability• 15.1 Introduction • 15.2 Probability — A Theoretical Approach • 15.3 Summary Important formulaExercise 15.1Exercise 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 formulaExercise 1.1 1.4Exercise 1.2 Exercise 1.3 Exercise |

2. POLYNOMIALS2.1 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 formulaExercise 2.1 2.4Exercise 2.2 Exercise 2.3 Exercise |

3. COORDINATE GEOMETRY3.1Introduction 3.2 Cartesian System 3.3 Plotting a Point in the Plane if its Coordinates are given 3.4 Summary Important formulaExercise 3.1 3.4Exercise 3.2 Exercise 3.3 Exercise |

4. LINEAR EQUATIONS IN TWO VARIABLES4.1 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 formulaExercise 4.1 4.4Exercise 4.2 Exercise 4.3 Exercise |

5. INTRODUCTION TO EUCLID’S GEOMETRY5.1 Introduction 5.2 Euclid’s Definitions, Axioms and Postulate 5.3 Equivalent Versions of Euclid’s Fifth Postulate 5.4 Summary Important formulaExercise 5.1Exercise 5.2 Exercise 5.3 |

6. LINES AND ANGLES6.1 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 formulaExercise 6.1 6.4Exercise 6.2 Exercise 6.3 Exercise |

7. TRIANGLES7.1 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 formulaExercise 7.1 7.4Exercise 7.2 Exercise 7.3 Exercise |

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 formulaExercise 8.1 8.4Exercise 8.2 Exercise 8.3 Exercise |

9. AREAS OF PARALLELOGRAMS AND TRIANGLES9.1 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 formulaExercise 9.1 9.4Exercise 9.2 Exercise 9.3 Exercise |

10. CIRCLES10.1 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 formulaExercise 10.1 10.4Exercise 10.2 Exercise 10.3 Exercise |

11. CONSTRUCTIONS11.1 Introduction 11.2 Basic Constructions 11.3 Some Constructions of Triangles 11.4 Summary Important formulaExercise 11.1Exercise 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 formulaExercise 12.1Exercise 12.2 Exercise 12.3 |

13. SURFACE AREAS AND VOLUMES13.1 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 formulaExercise13. 1 13.4Exercise 13.2 Exercise 13.3 Exercise |

14. STATISTICS14.1 Introduction 14.2 Collection of Data 14.3 Presentation of Data 14.4 Graphical Representation14.5 Measures of Central Tendency 14.6 Summary Important formulaExercise 14.1 14.4Exercise 14.2 Exercise 14.3 Exercise |

15. PROBABILITY15.1 Introduction 15.2 Probability – an Experimental Approach 15.3 Summary Important formulaExercise 15.1 15.2Exercise |

## 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 NumbersImportant formulaExercise 1.1 1.4Exercise 1.2 Exercise 1.3 Exercise |

2. Linear Equations in One VariableImportant formulaExercise 2.1 2.4Exercise 2.2 Exercise 2.3 Exercise |

3. Understanding QuadrilateralsImportant formulaExercise 3.1 3.4Exercise 3.2 Exercise 3.3 Exercise |

4. Practical GeometryImportant formulaExercise 4.1 4.4Exercise 4.2 Exercise 4.3 Exercise |

5. Data HandlingImportant formulaExercise 5.1 5.4Exercise 5.2 Exercise 5.3 Exercise |

6. Squares and Square RootsImportant formulaExercise 6.1 6.4Exercise 6.2 Exercise 6.3 Exercise |

7. Cubes and Cube RootsImportant formulaExercise 7.1 7.4Exercise 7.2 Exercise 7.3 Exercise |

8. Comparing QuantitiesImportant formulaExercise 8.1 8.4Exercise 8.2 Exercise 8.3 Exercise |

9. Algebraic Expressions and IdentitiesImportant formulaExercise 9.1 9.4Exercise 9.2 Exercise 9.3 Exercise |

10. Visualising Solid ShapesImportant formulaExercise 10.1 10.4Exercise 10.2 Exercise 10.3 Exercise |

11. MensurationImportant formulaExercise 11.1 11.4Exercise 11.2 Exercise 11.3 Exercise |

12. Exponents and PowersImportant formulaExercise 12.1 12.4Exercise 12.2 Exercise 12.3 Exercise |

13. Direct and Inverse ProportionsImportant formulaExercise 13.1 13.4Exercise 13.2 Exercise 13.3 Exercise |

14. FactorisationImportant formulaExercise 14.1 14.4Exercise 14.2 Exercise 14.3 Exercise |

15. Introduction to GraphsImportant formulaExercise 15.1 15.4Exercise 15.2 Exercise 15.3 Exercise |

16. Playing with NumbersImportant formulaExercise 16.1 16.4Exercise 16.2 Exercise 16.3 Exercise |

## 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. IntegersImportant formulaExercise 1.1 1.4Exercise 1.2 Exercise 1.3 Exercise |

2. Fractions and DecimalsImportant formulaExercise 2.1 2.4Exercise 2.2 Exercise 2.3 Exercise |

3. Data HandlingImportant formulaExercise 3.1Exercise 3.2 Exercise Exercise |

4. Simple EquationsImportant formulaExerciseExercise Exercise Exercise |

5. Lines and AnglesImportant formulaExerciseExercise Exercise Exercise |

6. The Triangle and its PropertiesImportant formulaExerciseExercise Exercise Exercise |

7. Congruence of TrianglesImportant formulaExerciseExercise Exercise Exercise |

8. Comparing QuantitiesImportant formulaExerciseExercise Exercise Exercise |

9. Rational NumbersImportant formulaExerciseExercise Exercise Exercise |

10. Practical GeometryImportant formulaExerciseExercise Exercise Exercise |

11. Perimeter and AreaImportant formulaExerciseExercise Exercise Exercise |

12. Algebraic ExpressionsImportant formulaExerciseExercise Exercise Exercise |

13. Exponents and PowersImportant formulaExerciseExercise Exercise Exercise |

14. SymmetryImportant formulaExerciseExercise Exercise Exercise |

15. Visualising Solid ShapesImportant formulaExerciseExercise 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 NUMBERSImportant formulaExerciseExercise Exercise Exercise |

2. WHOLE NUMBERSImportant formulaExerciseExercise Exercise Exercise |

3. PLAYING WITH NUMBERSImportant formulaExerciseExercise Exercise Exercise |

4. BASIC GEOMETRICAL IDEASImportant formulaExerciseExercise Exercise Exercise |

5. UNDERSTANDING ELEMENTARY SHAPESImportant formulaExerciseExercise Exercise Exercise |

6. INTEGERSImportant formulaExerciseExercise Exercise Exercise |

7. FRACTIONSImportant formulaExerciseExercise Exercise Exercise |

8. DECIMALSImportant formulaExerciseExercise Exercise Exercise |

9. DATA HANDLINGImportant formulaExerciseExercise Exercise Exercise |

10. MENSURATIONImportant formulaExerciseExercise Exercise Exercise |

11. ALGEBRAImportant formulaExerciseExercise Exercise Exercise |

12. RATIO AND PROPORTIONImportant formulaExerciseExercise Exercise Exercise |

13. SYMMETRY CHAPTERImportant formulaExerciseExercise Exercise Exercise |

14. PRACTICAL GEOMETRYImportant formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |

2. Relations and Functions 2.1 Introduction 2.2 Cartesian Product of Sets2.3 Relations 2.4 Functions Important formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |

4. Principle of Mathematical Induction 4.1 Introduction 4.2 Motivation 4.3 The Principle of Mathematical Induction Important formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |

7. Permutations and Combinations 7.1 Introduction 7.2 Fundamental Principle of Counting 7.3 Permutations 7.4 Combinations Important formulaExerciseExercise Exercise Exercise |

8. Binomial Theorem 8.1 Introduction 8.2 Binomial Theorem for Positive Integral Indices 8.3 General and Middle Terms Important formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |

16. Probability 16.1 Introduction 16.2 Random Experiments 16.3 Event 16.4 Axiomatic Approach to Probability Important formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |

2. Inverse Trigonometric Functions 2.1 Introduction 2.2 Basic Concepts 2.3 Properties of Inverse Trigonometric Functions Important formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |

8. Application of Integrals 8.1 Introduction 8.2 Area under Simple Curves8.3 Area between Two Curves Important formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise 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 formulaExerciseExercise Exercise Exercise |