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Mathematics — Grade 12, Part II
NCERT
Contents
7 chaptersCh. 1INTEGRALS38 sections
- Chapter 7: Integrals35 words
- 7.1 Introduction334 words
- 7.2 Integration as an Inverse Process of Differentiation534 words
- 7.2.1 Some properties of indefinite integral465 words
- EXERCISE 7.1270 words
- 7.3 Methods of Integration184 words
- 7.3.1 Integration by substitution516 words
- EXERCISE 7.2156 words
- 7.3.2 Integration using trigonometric identities206 words
- EXERCISE 7.3150 words
- 7.4 Integrals of Some Particular Functions676 words
- EXERCISE 7.4154 words
- 7.5 Integration by Partial Fractions761 words
- EXERCISE 7.5181 words
- 7.6 Integration by Parts559 words
- EXERCISE 7.6128 words
- 7.6.2 Integrals of some more types385 words
- EXERCISE 7.7124 words
- 7.7 Definite Integral501 words
- 7.8 Fundamental Theorem of Calculus51 words
- 7.8.1 Area function238 words
- 7.8.2 First fundamental theorem of integral calculus248 words
- 7.8.3 Second fundamental theorem of integral calculus401 words
- EXERCISE 7.8134 words
- 7.9 Evaluation of Definite Integrals by Substitution348 words
- EXERCISE 7.9139 words
- 7.10 Some Properties of Definite Integrals499 words
- EXERCISE 7.10122 words
- Miscellaneous Examples316 words
- Miscellaneous Exercise on Chapter 7157 words
- Summary214 words
- Summary: partial fractions145 words
- Summary: integration by substitution70 words
- Summary: integrals of some special functions105 words
- Summary: integration by parts51 words
- Summary: some special types of integrals124 words
- Summary: first fundamental theorem of integral calculus54 words
- Summary: second fundamental theorem of integral calculus42 words
Ch. 2APPLICATION OF INTEGRALS8 sections
Ch. 3DIFFERENTIAL EQUATIONS19 sections
- Chapter 9: Differential Equations38 words
- 9.1 Introduction387 words
- 9.2 Basic Concepts405 words
- 9.2.1. Order of a differential equation164 words
- 9.2.2 Degree of a differential equation342 words
- EXERCISE 9.1204 words
- 9.3. General and Particular Solutions of a Differential Equation518 words
- EXERCISE 9.2418 words
- 9.4. Methods of Solving First Order, First Degree Differential Equations292 words
- 9.4.1 Differential equations with variables separable613 words
- EXERCISE 9.3368 words
- 9.4.2 Homogeneous differential equations606 words
- EXERCISE 9.4462 words
- 9.4.3 Linear differential equations669 words
- EXERCISE 9.5380 words
- Miscellaneous Examples622 words
- Miscellaneous Exercise on Chapter 9569 words
- Summary193 words
- Historical Note269 words
Ch. 4VECTOR ALGEBRA28 sections
- Chapter 10: Vector Algebra36 words
- 10.1 Introduction302 words
- 10.2 Some Basic Concepts277 words
- Position Vector245 words
- Direction Cosines393 words
- 10.3 Types of Vectors330 words
- EXERCISE 10.1472 words
- 10.4 Addition of Vectors418 words
- Properties of vector addition285 words
- 10.5 Multiplication of a Vector by a Scalar299 words
- 10.5.1 Components of a vector409 words
- 10.5.2 Vector joining two points262 words
- 10.5.3 Section formula475 words
- EXERCISE 10.2456 words
- 10.6 Product of Two Vectors141 words
- 10.6.1 Scalar (or dot) product of two vectors326 words
- Observations on the dot product237 words
- Two important properties of scalar product317 words
- 10.6.2 Projection of a vector on a line366 words
- Observations on projection, angles and inequalities384 words
- EXERCISE 10.3607 words
- 10.6.3 Vector (or cross) product of two vectors417 words
- Observations on the cross product432 words
- EXERCISE 10.4664 words
- Miscellaneous Examples376 words
- Miscellaneous Exercise on Chapter 10481 words
- Summary320 words
- Historical Note241 words
Ch. 5THREE DIMENSIONAL GEOMETRY16 sections
- Chapter 11: Three Dimensional Geometry38 words
- 11.1 Introduction290 words
- 11.2 Direction Cosines and Direction Ratios of a Line762 words
- 11.2.1 Direction cosines of a line passing through two points456 words
- EXERCISE 11.1474 words
- 11.3 Equation of a Line in Space263 words
- 11.3.1 Equation of a line through a given point and parallel to a given vector428 words
- Derivation of cartesian form from vector form589 words
- 11.4 Angle between Two Lines581 words
- 11.5 Shortest Distance between Two Lines227 words
- 11.5.1 Distance between two skew lines488 words
- Cartesian form361 words
- 11.5.2 Distance between parallel lines451 words
- EXERCISE 11.2632 words
- Miscellaneous Exercise on Chapter 11339 words
- Summary246 words
Ch. 6LINEAR PROGRAMMING8 sections
- Chapter 12: Linear Programming42 words
- 12.1 Introduction374 words
- 12.2 Linear Programming Problem and its Mathematical Formulation450 words
- 12.2.1 Mathematical formulation of the problem654 words
- 12.2.2 Graphical method of solving linear programming problems1,453 words
- EXERCISE 12.1596 words
- Summary222 words
- Historical Note195 words
Ch. 7PROBABILITY16 sections
- Chapter 13: Probability45 words
- 13.1 Introduction428 words
- 13.2 Conditional Probability629 words
- 13.2.1 Properties of conditional probability388 words
- EXERCISE 13.1427 words
- 13.3 Multiplication Theorem on Probability493 words
- 13.4 Independent Events838 words
- EXERCISE 13.2376 words
- 13.5 Bayes' Theorem166 words
- 13.5.1 Partition of a sample space434 words
- 13.5.2 Theorem of total probability1,102 words
- EXERCISE 13.3582 words
- Miscellaneous Examples460 words
- *Miscellaneous Exercise on Chapter 13*468 words
- Summary165 words
- *Historical Note*295 words