Three coins are tossed.

$\therefore$ The sample space =$2^3=8$ possible outcome

$S=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$

Let A be the event "Exactly one head"

$A=\{HTT,THT,TTH\}$

Let B be the event "Exactly two heads"

$B=\{HHT,HTH,THH\}$

$\therefore A \cap B \neq \phi$ and $A\cup B\neq S$

$\therefore$ A and B are mutually exclusive but not exhaustive.