The largest 5 digit number which divisible by 99 .
it is divisible by 99 so it has to divisible by both 9 and 11.
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now divisibility rule when we divide by 9:-
if sum of all the digits of the number is divisible by 9 then the number is divisible by 9.
example :- let the number is 350703 . The sum of the digits (3+5+0+7+0+3) =18 which is divisible by 9 so number is divisible by 9.
Now divisibility rule when divide by 11:-
If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11
Example:- let the number is 82907 . Then the difference of the sum of alternative digits (7+8+9 -2)=22 which is divisible by 11 . so this number is divisible by 11.
Now coming to question ,
in all the option sum of all the digits are divisible by 9 . so they are all divisible by 9 .
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now we have to check which is divisible by 11 ?
option a)
99999 → here the difference of the sum of alternative digits (9+9+9 -9-9)=9 which is not divisible by 11 . so this number is not divisible by 11 so not divisible by 99.
option b)
99981→ here the difference of the sum of alternative digits (1+9+9 -9-8)=2 which is not divisible by 11 . so this number is not divisible by 11 so not divisible by 99.
option c)
99909→ here the difference of the sum of alternative digits (9+9+9 -0-9)=18 which is not divisible by 11 . so this number is not divisible by 11 so not divisible by 99.
option D)
99990→ here the difference of the sum of alternative digits (9+9-9-9)=0 which is divisible by 11 . so this number is divisible by 11 so it is divisible by 99.
so correct option is D.