Observe the following pattern and find the missing numbers.

11² = 121

101² = 10201

1001² = 1002001

100001² = 1 .......2.........1

10000001² = ..........................

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.
∴ 100001²= 10000200001
10000001² = 100000020000001

Thanks