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 X (Ch-2) | Polynomials

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Board - CBSE



CHAPTER 2  :  Polynomials


Chapter:-  2: Polynomials


This lesson is divided into seven modules and it is completed in seven class meetings.


All definitions and important terms related to the polynomials. Polynomial Chapter 2 Class IX


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


Demonstration and Lecture method


  • Basic concepts and definitions related to the topic polynomials.
  • Explanation of remainder and factor theorem.
  • Relationships between zeroes and coefficients of quadratic polynomials and cubic polynomials.
  • Explanation of division algorithm.
  • Method of finding all zeroes of cubic and bi-quadratic polynomials.

Lesson Plan For CBSE  Class 10 (Chapter 2) For Mathematics Teacher

Start the session by checking their previous knowledge, by asking the questions related to the topic. After this explain the topic to the students. Click Here

S. No


[Click Here For Complete Explanation]


Introduction and motivation

Teacher will start the session by giving many examples of Algebraic Expressions. Now teacher will explain which types of Algebraic Expressions are called Polynomials. After this teacher will introduce the definition of Polynomial and explain the different components of polynomials.

Polynomial: An algebraic expression in which the exponent of the variable is a whole number is called a polynomial.

Example: 3x2 + 5,  4x3 - 8x2 + 5x - 3,  5x4 + 3x2   are some examples of polynomial .


Important Definitions

Now teacher will explain the Important Definitions like Degree, coefficients and zeroes of the polynomials and their graphical representations.

Degree of constant polynomial is zero and degree of zero polynomial is undefined.

After this teacher will explain the different types of polynomial on the bases of degree and on the basis of number of terms. 

 Teacher will also give examples  and explanations of definitions of the polynomials like linear, quadratic, cubic, bi-quadratic, monomial, binomial, and tri-nomial .



Finding Zeroes from the Graph

Students will be given the knowledge of finding the number of zeroes from the graph of the polynomial.

Number of zeroes of a polynomial is equal to the number of times the graph of that polynomial meet the x - axis.

Graph of a quadratic polynomial is always parabolic.


Zeroes of Quadratic Polynomial

Now teacher will explain the Factor method of finding the zeroes of quadratic polynomials and will explain the Relationship between zeroes and coefficients. 

Teacher will also provide some problems to the students to check whether students can apply the method or not.


Now teacher will explain the method of finding the quadratic polynomial from the zeroes and explain the topic by taking some examples.


Division Algorithm

By taking some examples, teacher will explain the method of dividing one polynomial by another. To verify the result of division teacher will explain the Division Algorithm.

Dividend = Divisor  Quotient + Remainder


Zeroes of Bi-Quadratic Polynomial

Now teacher will explain the method of finding all zeroes of bi quadratic polynomials by using factor theorem and division algorithm. Method will be well explained by taking examples. 

Teacher can also give some problems to the students to check whether they will understand the concept or not.


Zeroes of Cubic Polynomial

Now concept of cubic polynomial is also be introduced. Students will be given the knowledge of cubic polynomial, its general form, its zeroes and the relationship between zeroes and coefficient.


  • After studying this lesson students will be able  to explain the relationship between zeroes and coefficients. 
  • Students should know the method of division of one polynomial with another and the division algorithm. 
  • Students should be able to factorize the quadratic, cubic and bi-quadratic polynomials and become able to find their zeroes.

  • Review questions given by the teacher. 
  • Student can prepare the presentation on the topic relationship between zeroes and coefficients for quadratic as well as cubic polynomials. 
  • Solve NCERT problems with examples, 
  • Solve assignment on Multiple Choice Questions (MCQ) given by the teacher.

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at  cbsemathematics.com


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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