What is both possible and impossible at the same time?

Jenifer and Jesica are having a conversation.

Jenifer: I am definitely not over 30.
Jesica: I am 28 and you are surely 5 years older to me at least.
Jenifer: No, you are at least 29.

You are told that both of them are lying throughout in the conversation. Can you find their respective ages?

Find the number of squares in the below-given picture.

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

Here is what you have to do. You have to throw a ball as hard as you can but it must return back to you even if it does not bounce at anything. Also, you have nothing attached to the ball. There is no one on the other end to catch that ball and throw it back at you.

How will you do it?

These types of puzzles are known as charades. What you have to do is find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.

Just for example, if my first refers to 'off' and my second refers to 'ice', then my whole will be office.

My first is present - future's past -
A time in which your lot is cast.

My second is my first of space
Defining people's present place.

My whole describes a lack of site -
A place without length, breadth, or height.

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

I am the fastest animal but cannot climb the tree. What am I?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, "Oh! I am really sorry, I thought this was my room."
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.

Solve the equation in the image by looking at the pattern closely.