A 'Secure Code' is defined as a sequence of different digits chosen from all non-negative single digit integers; we need to find the ratio of the number of 4-digit secure codes to the number of 3digit secure codes.

The non - negative single digit integers are 0 to 9 i.e. 10


Since the digits are to be different, the number of 4-digit secure codes and the number of 3-digit secure codes would be $\(\underline{10} \times \underline{9} \times \underline{8} \times \underline{7}=5040 \& \underline{10} \times \underline{9} \times \underline{8}=720\)$ respectively.

So, the required ratio is $\(\frac{Number of 4-digit Secure Codes }{Number of 3-digit Secure Codes }=\frac{5040}{720}=\frac{7}{1}=7: 1\)$

Hence the answer is (B).