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

Lesson Plan Math Class 12 Ch- 4 | Determinants


E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+2
Lesson Plan, Class XII Subject Mathematics, chapter 4, Determinants , for Mathematics Teacher. Effective way of Teaching Mathematics. Top planning by the teacher for effective teaching in the class. E lesson planning for mathematics.

Board – CBSE

CLASS –XII

SUBJECT- MATHEMATICS

CHAPTER 4  :-  Determinants


TOPIC:- Chapter : 4 : Determinants

DURATION:-  

This chapter is divided into seven modules and is completed in 15 class meetings.

PRE- REQUISITE KNOWLEDGE:-



TEACHING AIDS:- 

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:-   Lecture method

OBJECTIVES:-
  • Introduction and determinants of a square matrices up to 3x3 matrices.
  • Properties of determinants.
  • Minors and cofactors of determinants.
  • Application of determinants in finding the area of triangle.
  • Adjoint and inverse of the square matrices.
  • Consistency, inconsistency and the number of solutions of system of linear equations.
  • Method of solving system of linear equations in two or three variables having unique solutions using inverse of matrix method.
PROCEDURE :-
Start the session by asking the questions related to the matrices and system of linear equations in two variables. Now introduce complete topic determinants as follows.

S.No

Explanation of the Topics   

1

First of all teacher will start the session by asking certain questions of matrices. Then introduce the topic determinant.

Now teacher will help the students in finding the determinant of 2 x 2 matrices and  3 x 3 matrices.

Definition of Determinant

Determinant is a number associated with the square matrix.

To every square matrix A = [aij]  of order n, we can associate a number (real or complex) called determinant of the square matrix  A.

Determinant of matrix  [A] is denoted by |A|

2

Properties of Determinants

Now teacher will explain all the properties of determinants with the help of examples and apply them in different problems. Teacher will provide sufficient number of problems to the students for practice.

3

Concepts of minor and cofactor

Now teacher will introduce the concept of minor and Determinant  and will explain the method of finding the minors and cofactors. Students will be given sufficient method of finding the determinants by using the cofactors.

4

Area of Triangle

Now teacher will explain the method of finding the area of the triangles by using determinants.

5

Adjoint and Inverse of a Matrix

First of all teacher will explain the definition of Singular matrices, invertible matrices and Adjoint of a matrix.

Singular Matrix: A matrix whose determinant is equal to zero is called a singular matrix. If determinant is not equal to zero then it is called Non-Singular Matrix. 

Invertible Matrix: A matrix is said to be invertible if it is non-singular.

Now teacher will explain the method of finding the Adjoint and inverse of the square matrices.

6

Consistency and and Inconsistency of system of linear equations.

Teacher will Discuss and Explain the consistency, inconsistency and the number of solutions of the system of linear equations with two or three variables.

7

Solution of System of Linear Equations

Now teacher will explain the method of solving the system of linear equations in two or three variables by using Adjoint method of finding inverse of matrix method.



EXPECTED OUTCOMES:-

After studying this lesson students should know the 

1. Method of finding the determinants, minors, cofactors.

2. Adjoint and inverse of matrices by using Adjoint of the matrices. 

3. Students should be able to solve the problems by using the properties of the determinants. 

4. Students should knows the matrix method of solving the system of linear equations in two or three variables.

STUDENTS DELIVERABLES:-
  • Review questions given by the teacher. 
  • Students should prepare the presentation on the properties of determinants. 
  • Solve NCERT problems with examples.
  • Solve assignment given by the teacher.
EXTENDED LEARNING:-

Students can extend their learning in Mathematics through the RESOURCE CENTRE.  Students can also find many interesting topics on mathematics at cbsemathematics.com

ASSESSMENT TECHNIQUES:-
  • Assignment sheet will be given as home work at the end of the topic. 
  • Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
  • Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
  • Re-test(s) will be conducted on the basis of the performance of the students in the test.


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