### 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

### DIVISIBILITY TEST- CBSE Mathematics

Divisibility test for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 with examples and explanation
Divisibility Test :-
This topic contains the divisibility test by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 with examples for more understanding.
Divisibility Test by 2:-
·  If unit digit of a number is even ( 0, 2, 4, 6, 8) then that number is divisible by “2”
·   All even numbers are divisible by “2”.
Example 1:-
· Let given number is  258694
· Unit digit  of  this  number is   “4”  it is even. Therefore 258694  is  also  divisible   by  “2”
Example 2:-
·  Let given number is  2586947
·  Unit digit of this number is    “7”, it is odd. So  the number 2586947 is not  divisible by “2”.
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 3:-
·  If sum of the digits of a given number is  divisible by “3” then that number is also divisible  by “3”.
Example 1:-
·   Let given number is :-345897
·  Sum of the digits:   3+4+5+8+9+7 = 36
·  36 is divisible by “3”, so 345897 is also divisible by “3”
Example 2:-
· Let given number is :-  985897
·  Sum of the digits:   9+8+5+8+9+7 = 46
·   46 is not divisible by “3”, so 985897 is also not divisible by “3”
DIVISIBILITY TEST- CBSE Mathematics

Divisibility Test by 4:-
·  Take last two digits of of a given number and divide it by “4”, if it is divisible by “4”, then the given number is also divisible by “4”.
·  If last two digits of a given number is “00” then that number is also divisible by “4”.
Example 1:
·  Let given number is  37984
·  Last two digits :  8, 4,   84 is divisible by “4”. So 37984 is also divisible by “4”
Example 2:
·  Let given number is  839842
·  Last two digits :  4, 2,   42 is not divisible by “4”. So 839842 is also not divisible by “4”
Example 3:
· Let given number is  9739800
·  Last two digits :  00  , yes 9739800  is also divisible by “4”

Divisibility Test by 5:-
·  If last digits of a given number is either “0” or “5” then the given number is also divisible by “5”.
Example 1:
·  Let given numbers are    379520,  789735
·  Last digit  “0”  and “5” . Yes above both numbers are divisible by 5
Example 2:
·  Let given number is  379523
·   Last digit  “3”  So above  number is not  divisible by 5
Divisibility Test by 6:-
·  If a number is divisible by both “2” and “3” then that number is also divisible by 6.
Example 1:

Let given number is  357846
·   Last digit is “6”, it is even. So it is divisible by “2”
·   Sum of the digits: 3+5+7+8+4+6 = 33,  “33” is divisible by “3”. So 357846 is also divisible by “3”
·  Here we find that 357846 is divisible by both “2” and “3”. Hence 357846 is also divisible by “6”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test 7:-
·  Take last digit of a given number.
·  Now subtract the double of this digit from the remaining number.
·   Now see whether the result is divisible by "7" or not.
·  If judgment is still difficult then repeat the above process again and again,  till you left with two digit number then make the judgment.
Example 1:-
·         Let given number is  21875
·         Last digit “5”. Double of 5 is = 10
·         Now find 2187-10 = 2177
·         Last digit “7”. Double of “7”  is = 14
·         Now find 217 - 14 = 203
·         Last digit “3”. Double of 3 is = 6
·         Now find 20-6 = 14
·         Since 14 is divisible by “7” so 21875 is also divisible by “7”
Example 2:
·         Let given number is  789423
·         Last digit “3”. Double of 3 is = 6
·         Now find 78942 – 6   78936
·         Last digit “6”. Double of 6 is  = 12
·         Now find  7893-12 = 7881
·         Last digit “1”. Double of 1 is = 2
·         Now find 788-2 = 786
·         Last digit “6”. Double of 6 is = 12
·         Now find 78-12 = 76
·         76  is not divisible by “7” so  number 35789423 is not divisible by “7”
DIVISIBILITY TEST- CBSE Mathematics

Divisibility Test by 8:-
·   Take last three digits of   a given number and divide it by “8”, if it is divisible by “8” then the given number is also divisible by “8”.
Example 1:
·    Let given number is :  5793512
·    Last three digits : 5, 1, 2,
·   512 is divisible by “8” (512/8 = 64) so 5793512 is also divisible by “8”
Example 2:
·   Let given number is :  5793515
·   Last three digits : 5, 1, 5,
·  515 is not divisible by “8”,  so 5793515 is also not divisible by “8”
DIVISIBILITY TEST- CBSE Mathematics

Divisibility Test by 9:-
·   If sum of the digits of a given number is divisible by “9” then that number is also divisible by “9”.
Example 1:
·   Let given number is :  63918
·   Sum of the digits:  6+3+9+1+8 = 27
·   27 is divisible by “9”, so this number is also divisible by 9”
Example 2:
·   Let given number is :  63925
·   Sum of the digits:  6+3+9+2+5 = 25
·   25 is not divisible by “9”, so number 63925 is also not divisible by “9”
Divisibility Test by 10:-
·  If last digits of a given number is  “0”  then the given number is also divisible by “10”.
Example 1:
·   Let given number is :  63910
·  Last digit is “0”, so 63910 is divisible by “10”
Example 2:
·   Let given number is :  63917
·   Last digit is “7”  so  63917 is not divisible by “10”
DIVISIBILITY TEST- CBSE Mathematics
Divisibility Test by 11:-
·  Mark the digits of a given number odd or even, starts from the right side (unit digit).
·  Add the digits at odd position.
·  Add the digits at even places.
·  Find the difference between the two sums.
·  If difference is either “0” or divisible by “11” then that number is also divisible by 11.
·  If the difference is not divisible by 11 then that number is not divisible by 11.
Example 1:
· Let given number is :  659175
· Sum of the digits at even place = 7+9+6 = 22
· Sum of the digits at odd places = 5+1+5 = 11
· Difference:   22-11 = 11
· Since difference is divisible by “11” so the number 659175 is also divisible by “11”
Example 2:
· Let given number is :  959171
· Sum of the digits at even place = 1 + 1 + 5 = 7
· Sum of the digits at odd places = 7+9+9 = 25
·  Difference:   25-7= 18
·  Since difference”18” is not divisible by “11” so the number 959171 is not divisible by “11”
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