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The number of ordered pairs (m,n) where ...

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

A

A. `1250`

B

B. `2500`

C

C. `625`

D

D. `500`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `6^(m)+9^(n)`
Unit digit of `6^(m)` is `=6`
Unit digit of `9^(n)` will be `=9` or `1`
For multiple of `5` unit digit of `9^(n)` must be `=9`
It occur when `n=` odd
Total number or ordered pair `=50xx25=1250`
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