Answer
The order of increasing boiling point is :
$dimethyl ether \lt dimethylamine \lt ethanol $
Work Step by Step
Boiling point increases with increasing intermolecular hydrogen bonding. $ethanol $ has the maximum intermolecular hydrogen bonding, and $dimethyl ether$ has the least. So the order of increasing boiling point is :
$dimethyl ether \lt dimethylamine \lt ethanol $
