Question
If 10^m × 1000 × n = 75^25 × 25^32 × 32^75, where n is not divisible by 10, then the value of m is
- (a)101
- (b)111
- (c)121
- (d)131
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The right side = 3²⁵ × 5¹¹⁴ × 2³⁷⁵. The number of factors of 10 it contains is min(375, 114) = 114. Since 10^m × 10³ supplies 10^(m+3), we need m + 3 = 114, so m = 111.
UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).
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