IS IT POSSIBLE TO LOVE SOMEONE WITHOUT A REASON?

No it's not possible..

Talking about love here, when you love someone, something attracts you to the person, either the beauty, character, personality, the way he/she walks, talks etc...
You might not be able to tell the exact reason that made you fall in love with the person but you should know something attracted you to him/her and that's your reason..
Even those who lust for women have reason then why would love not come with a reason..

Sometimes we get so carried away by the way we feel about a particular person and it makes us see and think that "I just love this person for no reason" not true...

Think and check what drew you to that person...