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Explanation:

From the digits 0, 1, 2, … , 9, there are 4 digits that can create confusion are 1, 6, 8 and 9

Numbers with 0 in unit’s place cannot be counted because reversing them will give an invalid code.

Codes for which confusion can arise:

Possible number of digits in ten’s place = 4

Possible number of digits in unit’s place, such that the 2 digits are distinct = 3

Total number of ways = 4 × 3 = 12

However, the numbers 69 and 96 do not create confusion when written upside down.

∴ Total number of ways for codes for which confusion can arise = 12 − 2 = 10

Total codes possible with digits from 0 to 9:

Possible number of digits in ten’s place = 9 (0 cannot be used)

Possible number of digits in one’s place, such that the 2 digits are distinct = 9

Total number of all possible codes = 9 × 9 = 81

∴ Number of codes with no confusion = 81 – 10 = 71

Hence, option (c).

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