Correct Answer: Option C

Explanation

\(413_7\) to base 5 

convert first to base 10

\(417_7 = 4 × 7^2 + 1 × 7^1 + 3 × 7^0\)
= 4 × 49 + 1 × 7 + 3 × 1
= 196 + 7 + 3

= \(206_{10}\)

convert this result to base 5

\(∴ 413_7 = 1311_5\)
 

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