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

Algebraic Identities Of Polynomials


Algebraic Identities Of Polynomials
Algebraic identities, for classes 7th, 8th, 9th, 10th, 11th, 12th,  Algebraic identities required for polynomials, square table, cubic table, method of making algebraic identities, pascal triangle.

In order the start solving the mathematical concepts with interest, students should have some knowledge of basic concepts. Some previous topics are also compulsory for the students because these concepts helps the students in understanding the next level. So here in this post we learn the following topics.

INDEX

1

Square Table

2

Cubic Table

3

Algebraic Identities


SQUARE TABLE

For fast calculation it is compulsory for the students to learn the square table. Square table help the students, while solving the problems and it also increase the interest of the students. 

SQUARE TABLE

    NUMBER

   SQUARE

    NUMBER

SQUARE

12

1

212

441

22

4

222

484

32

9

232

529

42

16

242

576

52

25

252

625

62

36

262

676

72

49

272

729

82

64

282

784

92

81

292

841

102

100

302

900

112

121

312

961

122

144

352

1225

132

169

402

1600

142

196

452

2025

152

225

502

2500

162

256

552

3025

172

289

602

3600

182

324

652

4225

192

361

702

4900

202

400

752

5625

**************

CUBIC TABLE

For fast calculation it is compulsory for the students to learn the cubic table. Cubic table helps the students, while solving the problems and it also increase the interest of the students. 

CUBIC    TABLE

NUMBER

CUBE

NUMBER

CUBE

13

1

113

1331

23

8

123

1728

33

27

133

2197

43

64

143

2744

53

125

153

3375

63

216

163

4096

73

343

173

4913

83

512

183

5832

93

729

193

6859

103

1000

203

8000

Algebraic Identities

Algebraic identities are very useful at every level for solving the algebraic problems. If you want to be perfect in algebra you should have the knowledge of Algebraic Identities
Up to 10th standard students should learn first 14 Algebraic Identities.
Last five Algebraic Identities are specially for the students 11th and 12th .

1

 (a + b)2         = a2 + b2 + 2ab

2

 (a - b)2          = a2 + b2 – 2ab

3

 (a + b)(a - b)  = a2 – b2

4

 (x + a)(x + b)  = x2 + (a + b)x + ab

5

 (a + b + c)2   = a2 + b2 + c2 + 2ab + 2bc + 2ca

6

(a + b)3     = a+ b+ 3ab(a + b)  or  a+ b+ 3a2b + 3ab2

7

 (a - b)3    = a- b- 3ab(a - b)  or  a- b - 3a2b + 3ab2

8

 a+ b3   = (a + b)(a+ b- ab)

9

 a- b3     = (a - b)(a+ b+ ab)

10

 a+ b+ c- 3abc = (a + b + c)(a2+ b+ c–  ab – bc - ca) 

If  a + b + c = 0 then a3+b3+c= 3abc

Some Special Identities

11

a2  + b2  = (a + b)- 2ab

12

a + b2   = (a - b)2  + 2ab

13

a+ b3  = (a + b)3- 3ab(a + b)

14

a- b3    = (a - b)+ 3ab(a - b)


Next Algebraic identities are useful for the students after 10th standard. 

1

This Algebraic Identity can be used while finding the square root of a complex number in chapter 5 class 11

(a2 + b2)2  =   (a- b2)2  + 4a2b2

2

These Algebraic Identities(2 to 5) can be derived with the help of Binomial Expansion Chapter 8 class 11

(a + b) = a+ 4a3b + 6a2b+ 4ab+  b4

3

(a - b) = a- 4a3b + 6a2b- 4ab+ b4

4

(a + b)5 = a+ 5a4b + 10a3b+ 10a2b+ 5ab+ b5

5

(a - b)5 = a - 5a4b + 10a3b - 10a2b+ 5ab - b5

We can find the algebraic identities with the higher order by using Binomial Expansion.

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