Question

Observe the following pattern and find the missing number.

${101}^2=10201$
${1001}^2=1002001$
${10001}^2=\text{\_\_\_\_\_\_\_\_\_}$

• A. $10000201$
• B. $1020001$
• C. $100020001$
• D. $102001$

Answer 1

The correct option is C $100020001$

We observe that, on the RHS, both the equalities have $1$ as its first and last digit. And the middle digit is $2$. Number of zeros between the leftmost digit $1$ and the middle digit $2$ and the middle digit $2$ and the rightmost digit $1$ is the same as the number of zeros in the given number.
$\therefore {10001}^2=100020001$