### 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

### Maths Trick Shortcut way of calculating the numbers

Maths Trick Shortcut way of calculating the numbers

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Trick No. 1 : Multiplying any number by 11
If you want to multiply any number by 11, start from right to left.

Write first digit(unit digit) as it is.

Add the first and second digit and Wright it at second place (tens place).

If the sum is greater than 9 then take the carry to the next sum.

Continue like this and finally write the last digit as it is.

Example:-
7857 x 11 =   First digit = 7

For Second  digit = 5+7 = 12  this is imply that second digit is 2 and 1 is taken as carry with the next step.

For third digit = 8+5 = 13 + 1(carry)=14  this is imply that third digit is 4 and 1 is taken as carry with the next step.

For fourth digit = 7+8+1(carry) = 16  this is imply that fourth digit is 6 and 1 is taken as carry with the next step.

For fifth digit = 7+1(carry) = 8  this is imply that fifth digit is 8

Arranging all these digits we get 7857 x 11 = 86427

Trick No. 2 : Multiplying any number by 99999…….

 Multiplication with 9999….. is always difficult because 9 is the last most digit on the multiplication table. But multiplication with 9  can be made very easy because it is nearest to 10. For this we follow the following steps.  To multiply any number by 9999….. , simple we put zeros after the given number as there are 9’s in the multiplication and from the result subtract the number itself.  Example:-        3456 x 9 = 34560 - 3456     = 31104       3456 x 99 = 345600 – 3456   = 342144   3456 x 999   = 3456000 - 3456  = 3452544   3456 x 999999 = 3456000000 – 3456 = 3455996544   This trick always provide you the correct result without any multiplication.

Trick No 3 :- Squaring any number of  9

 (9999)2 = 9999 x 9999 =  99980001   Trick:-  Write the given number(9999), subtract 1 from the given number we get 9998.   Now Subtract 9998 from 9999 we get 0001   Place 0001 after 9998 we get 99980001 [Result of the multiplication]

Trick No 4 :- Multiplying any number with equal number of 999…

 349 x 999 = 348651 Trick :-   349-1 = 348           999-348 = 651 So Result of the multiplication is  348651 ...............................................................    56789 x 99999 = 5678843211 Trick :- 56789-1 = 56788     99999-56788 = 43211 So result of the multiplication is 5678843211

Trick No 5 :- Method of finding the square of any two digit number  with sum of the unit digit = 10 and same tens digits.

 25 x 25 = 625 Trick :- Multiply unit digit = 5 x5 = 25 (2+1) x 2 = 6 Result of the multiplication is 625 53 x 57 = 3021 Trick :- Multiply unit digit = 3 x 7 = 21 (5+1) x 5 = 30 Result of the multiplication is 3021 98 x 92 = 9016 Trick :- Multiply unit digit = 8 x 2 = 16 (9+1) x 9 = 90 Result of the multiplication is 9016

Trick No 6 :- Method of finding the square of any two digit number

 (32)2 = 1024 Trick : square of unit digit = 2 x 2 = 4(unit digit) 3 x 2 x 2 = 12 ( take 2 as tens digit and 1 as carry) 3 x 3 = 9 + 1(carry) = 10 ( Last two digits) Result of the multiplication : 1024 (67)2 = 4489 Trick : square of unit digit = 7 x 7 = 49(unit digit 9 and 4 as carry) 6 x 7 x 2 = 84 + 4(carry) = 88 ( take 8 as tens digit and 8 as carry) 6 x 6 = 36 + 8(carry) = 44 ( Last two digits) Result of the multiplication : 4489

Trick No 7 :- Simple method of multiplication ( Useful for the starters)

36 x 29 = (30 + 6) x (20 + 9)
 x 30 6 20 20 x 30 = 600 20 x 6 = 120 9 9 x 30 = 270 9 x 6 = 54 Add = 870 = 174 1044

332 x 289 = (300 + 30 + 2) x (200 + 80 + 9)
 X 300 30 2 Add 200 60000 6000 400 66400 80 24000 2400 160 26560 9 2700 270 18 2988 Add 86700 8670 578 95948

Trick No 8 :- Trick for the square and square root

A number ending with 2, 3, 7, 8 is never a perfect square.
Square root of even number is even and square root of odd number is odd.

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