Explanation:

To determine the smallest integer that makes 1005x4 divisible by 8, we use the rule that the number formed by the last three digits must be divisible by 8.

- Last three digits form: 5x4

- Test potential values for x that make 5x4 divisible by 8.

- If x = 0: 504 ÷ 8 = 63 ? Divisible

- If x = 1: 514 ÷ 8 = 64.25 ? Not Divisible

- If x = 4: 544 ÷ 8 = 68 ? Divisible

- If x = 2: 524 ÷ 8 = 65.5 ? Not Divisible

Hence, the smallest integer is Option:1, 0.

Correct Answer: Option:1, 0