Meaning : Without hope because there seems to be no possibility of comfort or success.
Example :
In an agony of hopeless grief.
With a hopeless sigh he sat down.
Having or manifesting hope.
A line of people hopeful of obtaining tickets.Meaning : Of a person unable to do something skillfully.
Example :
I'm hopeless at mathematics.
Meaning : Certain to fail.
Example :
The situation is hopeless.
Meaning : (informal to emphasize how bad it is) beyond hope of management or reform.
Example :
She handed me a hopeless jumble of papers.
He is a hopeless romantic.