Observe the following pattern and find the missing numbers.11^2 = 121101^2 = 102011001^2 = 1002001100001^2 = 1 .......2.........1 10000001^2 = ..........................

Dear Student

We observe that the square on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1 and middle digit is 2. And the number of zeros between left most digits 1 and the middle digit 2 and right most digit 1 and the middle digit 2 is same as the number of zeros in the given number.
∴ 100001^2= 10000200001
10000001^2= 100000020000001

Thanks