Explanation:

Let's solve the problem step by step:

- Calculate \( (61)^2 - (11)^2 \):

$$

(61)^2 = 3721 \quad \text{and} \quad (11)^2 = 121

$$

$$

(61)^2 - (11)^2 = 3721 - 121 = 3600

$$

- We are given this result is equal to \( (15 \times ?^2)^2 \).

$$

\sqrt{3600} = 60

$$

- We need to find a value for \( ?^2 \) such that:

$$

15 \times ?^2 = 60

$$

- Solving for \( ?^2 \):

$$

?^2 = \frac{60}{15} = 4

$$

- The square root of 4 is 2, so \( ? = 2 \).

- Hence, the correct option is Option 1: 2.

Based on this calculation, your choice of Option 1: 2 is indeed correct.