Correct option is C. $$22222222$$
$$\textbf{Apply the Divisibility rule of 11 for the given options}$$
Divisibility rule of $$11$$: A number is said to be divisible by $$11$$ if the difference between the sum of the digits at the odd places and the sum of the digits at the even places is $$0$$ or a multiple of $$11$$.
For $$1011011$$, difference between sum of digits digits at odd and even places
$$= (1 + 1 + 0 + 1) - (0 + 1 + 1)$$
$$= 1$$ which is not $$0$$ nor a multiple of $$11$$
For $$1111111$$, difference between digits at odd and even places
$$= (1 + 1 + 1+ 1) - ( 1 + 1+ 1)$$
$$= 1$$ which is not $$0$$ nor a multiple of $$11$$
For $$22222222$$, difference between digits at odd and even place
$$= (2 + 2 + 2 + 2 + 2) - (2 + 2 + 2 + 2)$$
$$ = 0$$
Therefore, $$22222222$$ is divisible by $$11$$
For $$3333333$$, difference between digits at odd and even places
$$= (3 + 3 + 3 + 3) - (3 + 3 + 3)$$
$$ = 3$$ which is not $$0$$ nor a multiple of $$11$$
$$\therefore$$ $$\textbf{Option C is correct}$$.