Explanation:

- In each number pair, the second number is obtained by squaring the square root of the first number and reducing it by 1.

- Option 1: $\sqrt{100}=10$; ${10}^2-1=99$. Here, 81 is not equal to 99.

- Option 2: $\sqrt{36}=6$; $6^2-1=35$. Result is 16, which is incorrect by the pattern assumed.

- Option 3: $\sqrt{49}=7$; $7^2-1=48$. Result is 25, not true.

- Option 4: $\sqrt{81}=9$; $9^2-1=80$. Result is 49, correct by assumed pattern.

- The odd one out is Option 4, as the operation $n^2-1$ does not yield the second number.