I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

I speak without a mouth, and hear without ears. I have no-body, but I come alive with the wind. What am I?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

You walk into an old horror house. It has no power or plumbing. Once inside, you see three doors. Each door has a number on it. Behind each door is a way for you to die. Behind door number one, you die by getting eaten by a lion. Behind door number two, you die by getting murdered. Behind door number three, you die by an electric chair. You can’t turn back, so you have to go through a door. Which door do you go through?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

There was a strange boy who was born before his father. How can this be possible?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

A person was killed at a house party. When the police arrive, there are six people present in the house who are the friends of the victim. The name of the friends is Rohit, Aman, Nick, Gagan, and Randy.

Near the dead body, they find a few numbers written with blood by the victim on the floor. The numbers are 8, 5, 4, and 11.

The police arrests one of the friends for the murder. Whom did they arrest and why?