### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

### Class XII Maths Formulas | Basics | Assignments | SP

 Chapter-wise Basics and Formulas

CBSE syllabus, sample papers, unit tests and solutions of sample papers, CBSE syllabus for class XII for all subjects, chapter-wise basic concepts of mathematics for class XII, chapter-wise planning in mathematics for class XII.

 Mathematics MCQ Class XII Click Here Maths Practical (Class XI) For 2021-22 Click Here Maths Practical (Class XII) For 2021-22 Sample Question Papers Term-1 (2021-22) Maths Project Work For Class XII Click Here

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## TEACHERS NOTESSUBJECT: MATHEMATICS CLASS XII

 CLASS 12 (Non- Medical and Applied Mathematics)
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 NCERT Mathematics Book with solutions NCERT Book NCERT Sol. NCERT Book NCERT Sol.
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## CLASS XII

Complete explanation with CBSE Syllabus 2022-23

## MATHS FORMULASMATHS ASSIGNMENTSMATHS (MCQ)BASIC POINTS IN DETAIL

CHAPTER 1: Relations and Functions

Syllabus: Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions

Basic & Formulas

Multiple Choice Questions Ch-1

CHAPTER 2: (Inverse Trigonometric Functions)

Syllabus: Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Basics & Formulas

Assignment 1

Multiple Choice Questions Ch-2

CHAPTER 3: (Matrices)
Syllabus: Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. On-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Basics & Formula's

Sol. of Important Questions Ch-3

Multiple Choice Questions Ch-3

CHAPTER 4: Determinants

Syllabus: Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint 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.

Basics & Formulas

Multiple Choice Questions Ch-4
CHAPTER 5: Continuity and Differentiability
Syllabus: Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin−1 𝑥 , cos−1 𝑥 and tan−1 𝑥, 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.

Basics & Formulas

Limit & Continuity

Assignment 1

Multiple Choice Questions Ch-5

CHAPTER 6: Application of Derivatives

Syllabus: Applications of derivatives: rate of change of bodies, increasing/decreasing functions, 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).

Basics & Formulas

Multiple Choice Questions Ch-6

 CHAPTER 7: Integral (Indefinite and Definite)Syllabus: 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. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.Indefinite IntegralDefinite IntegralMultiple Choice Questions Ch-7 CHAPTER 8: Application of IntegralsSyllabus: Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)Basic & Formula'sConic Section - 1 (Circle and Parabola)Conic Section - 2 (Ellipse and Hyperbola)Multiple Choice Questions Ch-8 CHAPTER 9: Differential EquationsSyllabus : Definition, order and degree, general and particular solutions of a differential equation. 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: + py = q, where p and q are functions of x or constants. + px = q, where p and q are functions of y or constantsMultiple Choice Questions Ch-9 CHAPTER 10: Vector AlgebraSyllabus: 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.Basics & Formulas CHAPTER 11: Three Dimensional GeometryDirection cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.Basics & FormulasAssignmentMultiple Choice Questions Ch-11 CHAPTER 12: Linear Programming problems (LPP)Syllabus: Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).Basics & Formula'sMultiple Choice Questions  Ch-12 CHAPTER 13: ProbabilitySyllabus: Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.Probability - 1Probability - 2Multiple Choice Questions Ch-13

 STUDY MATERIAL CLASS 12 CBSE  Syllabus (Mathematics) For  (Classes 11 & 12)  2022-23 : Click here Deleted portion in mathematics for 2022-23 : Click Here