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- CBSE Mathematics

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”
4444


THANKS FOR YOUR VISIT

PLEASE COMMENT BELOW


Comments

Popular Post on this Blog

Lesson Plan Maths Class 10 | For Mathematics Teacher

Lesson Plan Math Class X (Ch-8) | Trigonometry

Lesson Plan Maths Class X (Ch-5) | Arithmetic Progression