i) 6446 

If the difference between the sum of the digits at odd places and the sum of the digits at even places of a number is either 0 or a multiple of 11. 

Then the number is divisible by 11. 

Sum of the digits at odd places = 6 + 4 = 10 

Sum of the digits at even places = 4 + 6 = 10 

Difference 10 – 10 = 0 

So, 6446 is divisible by 11.

ii) 10934 

Sum of the digits at odd places = 4 + 9 + 1 = 14 

Sum of the digits at even places = 3 + 0 = 3 

Difference = 14 – 3 = 11 

is a 11 multiple by divisibility rule for 11. 

So, 10934 is divisible by 11.

iii) 7138965

Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24 

Sum of the digits at even places = 6 + 8 + 1 = 15 

Difference = 24 – 15 = 9 

is not a multiple by divisibility rule for 11 

So, 7138965 is not divisible by 11.

iv)726352 

Sum of the digits at odd places = 2 + 3 + 2 = 7 

Sum of the digits at even places = 5 + 6 + 7 = 18 

Difference = 18 – 7 = 11 

is a 11 multiple by divisibility rule for 11. 

So, 726352 is divisible by 11.