$10^{10}$ < n < $10^{11}$
As the sum of the digits of n = 2, n can be any one out of
11000000000
10100000000
10010000000
.
.
.
10000000001 … (10 such numbers)
or n can be 20000000000
There are 11 such values of n.
Hence,Option(1)11 is the correct choice.