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 X Maths Formulas | Basics | Assignments | SP


CBSE Class 10th Maths Assignments and Sample Papers

CBSE syllabus, sample paper, unit test and assignments for mathematics for class IX and X. Chapter Wise assignments for classes IX & X  for mathematics. Chapter-wise basic concepts & formulas for classes IX & X, Assignment pdf for math for classes IX & X

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Mathematics MCQ Class 10

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Maths Practical (Class IX) For 2022-23

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Maths Practical (Class X) For 2022-23

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RESOURCE CENTRE MATHEMATICS

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TEACHER'S NOTES
SUBJECT:  MATHEMATICS CLASS 10



NCERT BOOK WITH SOL.


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 Class X

 Mathematics Class X

Important Formulas and 

Basic Concepts

Chapter-wise CBSE Syllabus

 Chapter 1 Number System

Syllabus: Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of   

Assignment

Multiple Choice Questions on Ch-1

 Chapter 2 Polynomials

Syllabus: Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

Basic Concepts

Assignment

Multiple Choice Questions on Ch-2

Chapter 3 Pair of Linear equations in two variables

Syllabus: Pair of linear equations in two variables and graphical method of their solution, consistency/ inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.

Basic Concepts

Assignment

Multiple Choice Questions on Ch-3

 Chapter 4 : Quadratic Equations

Syllabus: Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorisation, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

Basic Concepts

Assignment 

Multiple Choice Questions  on Ch-4

 Chapter 5: Arithmetic Progression

Syllabus:  Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

Basic Concepts

Assignment

Multiple Choice Questions  on Ch-5

 Chapter 6 : Similarity of Triangles

Syllabus:  Definitions, examples, counter examples of similar triangles. 

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 

2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 

3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar. 

4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar. 

5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

Basic Concepts

Assignment

B.P.T.

Ratio of Area of two similar Triangles

Pythagoras Theorem and Converse of Pythagoras Theorem

Multiple Choice Questions  on Ch-6

 Chapter 7 : Coordinate Geometry

Syllabus: Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

Basic Concepts

Assignment

Multiple Choice Questions  on Ch-7

 Chapter 8 : Trigonometry

INTRODUCTION TO TRIGONOMETRY

Syllabus: Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 300 , 450 and 600 . Relationships between the ratios.

TRIGONOMETRIC IDENTITIES

 Periods Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

Basic Concepts

Assignment

Multiple Choice Questions on Ch-8

 Chapter 9 : Application of Trigonometry

Syllabus: 

HEIGHTS AND DISTANCES:

Angle of elevation, Angle of Depression,  Periods Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

Assignment

Multiple Choice Questions on Ch-9

 Chapter 10 : Tangent to a circle

Syllabus: Tangent to a circle at, point of contact 

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 

2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.


Basic Concepts

Assignment

Multiple Choice Questions on Ch-10

 Chapter 12 : Area related to circle

Syllabus:  Periods Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.

Basic Concepts

Assignment

Multiple Choice Questions  on Ch-12

 Chapter 13 : Surface area and volume

Syllabus: Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Basic Concepts

Assignment

Multiple Choice Questions on Ch-13

 Chapter 14 : Statistics

Syllabus: Mean, median and mode of grouped data (bimodal situation to be avoided).

Basic Concepts

Assignment

Multiple Choice Questions  on Ch-14

 Chapter 15 : Probability

Syllabus: Classical definition of probability. Simple problems on finding the probability of an event.

Basic Concepts

Assignment

Multiple Choice Questions  on Ch-15

CBSE Syllabus (Mathematics) for classes 9th, 10th,(2022-23)    Click Here

Deleted Syllabus for class 10 Session 2022-23



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