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  • The number of ordered pairs (m,n) where <img alt="m, n \in \left \{ {1,2,3,....50} \right \}" src="https://entrancecorner.oncodecogs.com/gif.latex?m%2C%20n%20%5Cin%20%5Cleft%20%5C%7B%20%7B1%2C2%2C3

The number of ordered pairs (m,n) where m, n \in \left \{ {1,2,3,....50} \right \}such that 6^m+9^nis a multiple of 5 is 

Option: 1

1250


Option: 2

2500


Option: 3

625


Option: 4

500


Answers (1)

best_answer

6^m+9^n

Unit digit of 6^m is =6
Unit digit of 9^\pi will be =9 or 1
For multiple of 5 unit digit of 9^n must be =9
It occur when n= odd
Total number of ordered pair =50 \times 25=1250

Posted by

Ajit Kumar Dubey

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