Question

How many ordered pairs of (m,n) integers satisfy `(m)/(12)=(12)/(n)`?
A. `30`
B. `15`
C. `12`
D. `10`

Answer 1

Correct Answer - A
`(a)` `(m)/(12)=(12)/(n)`
`impliesmn=144impliesn=(144)/(m)`
We want to find here total number of divisors of `144`
`144=2^(4)3^(2)`
Total divisors are `(4+1)(2+1)=15`
But negative pairs are also possible hence `=30`