(a) 5445:- Sum of the given digits at odd places = 5 + 4 = 9
Sum of the given digits at even places = 4 + 5 = 9
Difference = 9 – 9 = 0
As the difference between the sum of the digits at odd places and sum of the digits at even place is 0.
Therefore, 5445 is divisible by 11.
(b) 10824:-
Sum of the given digits at odd places = 4 + 8 + 1 = 13
Sum of the given digits at even places = 2 + 0 = 2
Difference = 13 – 2 = 11
The difference between the sum of the digits at odd places and the sum of the digit at even places is 11. Which is divisible by 11. Therefore 10824 is divisible by 11.
(c) 7138965:-
Sum of the given digits at odds places = 5 + 9 + 3 + 7 = 24
Sum of the given digits at even places = 6 + 8 + 1 = 15.
Difference = 24 – 15 = 9.
The difference between the sum of the digits at odd places and the sum of digits at even place is 9,
Which is not divisible by 11.
∴ 7138965 is not divisible by 11.
(d) 70169308:-
Sum of the digits at odd places = 8 + 3 + 6 + 0 = 17
Sum of digits at even places = 0 + 9 + 1 + 7 = 17
Difference = 17 – 17 = 0
As the difference between the sum of the digits at odd places and the sum of the digits at even place is 0.
Therefore, 70169308 is divisible by 11.
(e) 10000001:-
Sum of the digits at odd places=1 1
Sum of the digits even place = 1
Difference = 1 – 1 = 0
As the difference the sum of the digits at odd places and the sum of the digits at even places is 0. therefore 10000001 is divisible by 11.
(f) 901153:-
Sum of the digits at odd places = 3 + 1 + 0 = 4.
Sum of the digits at even places = 5 + 1 + 9 = 15
Difference = 15 – 4 = 11
The difference between the sum of the digits at odd places and the sum of the digits at even places is 11, Which is divisible by 11.
Therefore, 901153 is divisible by 11.
