Let n be a natural number. The number of consecutive zeros at the end of the expansion of n! is exactly 2. How many values of n are possible?

NDA 2025 Mathematics question

Let be a natural number. The number of consecutive zeros at the end of the expansion of is exactly 2. How many values of are possible?

Answer: (C)

The number of zeros at the end of equals the exponent of 5 in , i.e. \dfrac$

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Question ID VK-030135