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Solution


Q.

If the number of seven-digit numbers, such that the sum of their digits is even, is m·n·10n; m, n∈{1,2,3,...,9}, then m + n is equal to __________.          [2025]

Ans.

(14)

Total 7 digit numbers = 9000000

7 digit numbers having sum of their digits is even

        =90000002=9·5·105

On comparing with m·n·10n, we get

         m = 9 and n = 5

∴    m + n = 14.