(i) 22222 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 6 and sum of digits in even places = 4 

∴ The difference of the sum of alternative digits of a number is 2, which is not divisible by 11. 

Hence, 22222 is not divisible by 11.

(ii) 444444 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 12 and sum of digits in even places = 12 

∴ The difference of the sum of alternative digits of a number is 0, which is divisible by 11. 

Hence, 444444 is divisible by 11.

(iii) 379654 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 17 and sum of digits in even places = 17 

∴ The difference of the sum of alternative digits of a number is 0, which is divisible by 11. 

Hence, 379654 is divisible by 11.

(iv) 1057982 

We know that if the difference of the sum of alternative digits of a number, i.e. digits which are in odd places together and digits in even places together, is divisible by 11 then that number is divisible by 11. 

Here, sum of digits in odd places = 17 and sum of digits in even places = 15 

∴ The difference of the sum of alternative digits of a number is 2, which is not divisible by 11. 

Hence, 1057982 is not divisible by 11.