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Q.
The number of ordered pairs $(m, n), m, n \in\{1,2$, $\ldots, 50\}$ such that $6^m+9^n$ is a multiple of 5 is
Permutations and Combinations
Solution:
As the last digit of $6^m, m \in N$ is $6,6^m+9^n$ will be divisible by 5 if the unit's digit of $9^n$ is 4 or 9 . This is possible when $n$ is odd.
$\therefore $ required number of ordered pairs $=50 \times 25=$ 1250.