If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot…

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^{\mathrm{n}}$; $m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to _______

Solution

Total 7 digit nos. $=9000000$
7 digit nos. having sum of digits
Even $=4500000$
$=9.5 \cdot 10^5$
$\mathrm{m}=9, \mathrm{n}=5$
$\mathrm{m}+\mathrm{n}=14$

Asked in: JEE Main 2025 (03 Apr Shift 1)

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