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

Internal Assessment (Mathematics) For Classes XI and XII


Unit wise distribution of chapters and method of Internal Assessment in Mathematics for CBSE Class XI and XII.
 Scheme of evaluation in classes 11 and 12, method of compiling final result and internal assessment for class 11 and 12. 

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CBSE Board divided the Whole Syllabus  into two parts, Part A (Theory Part) and Part B (Internal Assessment). 
First of all we discuss about Theory Part A. This part is based upon the academic curriculum decided by the CBSE. 
Part A  
Theory Examination  [mm = 80]
Whole of the syllabus is divided into sixteen chapters and all chapters are divided into six units. This syllabus is completed in 240 Periods(each of 35 min). Total marks in this part is 80.

For class XI
Unit-wise distribution of  chapters and unit-wise marks are given below.

Course Structure Mathematics Class – XI , CBSE Board Mathematics
Units
Unit Name with chapters and number of periods
Number of Periods
Marks
I
Sets and Functions
Chapter : 1  Sets                                                       [15]
Chapter : 2  Relations and Functions                     [15]
Chapter : 3  Trigonometric Functions                    [30]
60
23
II
Algebra
Chapter : 4 Principal of Mathematical Induction    [8]
Chapter : 5  Complex Numbers                                 [12]
Chapter : 6  Linear Inequality                                   [15]
Chapter : 7  Permutations and Combinations         [10]
Chapter : 8  Binomial Theorem                                 [8]
Chapter : 9  Sequence and Series                              [17]
70
30
III
Coordinate Geometry
Chapter : 10  Straight Lines                                      [15]
Chapter : 11 Conic Sections                                      [15]
Chapter : 12 
Introduction to three dimensional geometry           [10]
40
10
IV
Calculus
Chapter : 13  Limits and Derivatives                       [30]
30
5
V
Mathematical Reasoning
Chapter : 14 Mathematical Reasoning                    [10]
10
2
VI
Statistics and Probability
Chapter : 15  Statistics                                              [15]
Chapter : 16  Probability                                          [15]
30
10
Total
240
80

For class XII

Course Structure Mathematics Class – XII , CBSE Board Mathematics

Units
Unit Name with chapters and number of periods
Number of Periods
Marks
I
Relations and Functions
Chapter :1 Relations and Functions     [15]
Chapter : 2 
Inverse Trigonometric Functions          [10]
25
08
II
Algebra
Chapter : 3 Matrices                              [25]
Chapter : 4 Determinants                      [25]
50
10
III
Calculus
Chapter : 5 
Continuity and Differentiability                 [20]
Chapter : 6  Applications of Derivatives    [25]
Chapter : 7 Integral                                     [20]
Chapter : 8 Applications of Integrals         [10]
Chapter : 9 Differential Equations             [20]
95
35
IV
Vectors and Three Dimensional Geometry
Chapter : 10 Vectors                                   [15]
Chapter : 11 
Three Dimensional Geometry                   [15]
30
14
V
Linear Programming
Chapter : 12  Linear Programming         [10]
10
05
VI
Probability
Chapter : 13 Probability                           [30]
30
8
Total
240
80


Part B
Internal Examination (MM = 20 Marks)
Internal Assessment of 20 Marks, based on school based examinations will have following break-up:

Year – end assessment of activities 
12 Marks
Assessment of project work  /PPT
5 Marks
Viva-Voice
3 marks
Total
20

Year End Assessment of Activity Work
(a) Each student will be asked to perform two given activities during the allotted time.
(b) The assessment may be carried out by a team of two Mathematics Teachers, including the teacher who is taking practical classes.
(c) The break-up of 12 marks of assessment for a single activity may be as under :

Statement of objective of the activity
1 mark
Material Required
1 mark
Preparation for the activity
3 marks
Conduct of Activity
3 marks
Observation and analysis
3 marks
Result and conclusion
1 mark
Total
12 marks

d) The marks for two activities may be added first and then marks calculated out of 12.
e) Full record of activities may be kept by each student.

Evaluation of project work [Specially for class 12]
a) Every student will be asked to do at least one project based on the concepts learnt in the classroom.

b) Project may be carried out individually (or in a group of two or three students).
c) The weightage of 5 marks for the project may be as under :

Identification and statement of the project
1 mark
Planning the project
1 mark
Procedure adopted
1 mark
Observations from data collected
1 mark
Interpretation and application of the result
1 mark
Total
5 Marks


During this year (2020-21) every student should be asked to perform at least 10 activities in one academic year.

Sample sheet of compiling internal assessment

S. No.
Students Name
Marks obtained in two activities
Project work/PPT
Viva-Voice
Total
[12]
[5]
[3]
[20]
1

2

3


Calculation of the final result
Student should get at least 33% marks in theory part as well as in internal assessment.

Total score of the student is calculated out of 100 after adding the marks obtained in theory examination as well as in internal Assessment.

A sample of Result sheet is shown below

S. No.
Students Name
Marks obtained in Theory Examination
Marks Obtained in Internal Assessment
Total


[80]
[20]
[100]
1




2




3





Introduction of Applied Mathematics in 11 and 12 standard
Every student in class 11 and 12 (Commerce/Humanities/Medical) can apply for applied mathematics (code 241). Before this, this subject taught to the students as skill subject. Now it is an elective subject. All students who studied basic maths in class 10th can also apply for applied mathematics. Again I want to make it clear that subject mathematics (with code 041)  in classes 11 and 12 is only for those students who studied standard mathematics in class 10.

Changes in Mathematics Syllabus (2020-21)

Class IX - No change
Class X - No change
Class XI - No change
Class XII - A topic "Binomial Probability Distribution has been included in unit 6 (Probability)


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