What goes up but never comes down?

I’m tall when I’m young, and I’m short when I’m old. What am I?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

Jenifer is learning to drive her car. She went down a one way lane and in the wrong direction. But she do not break any law.

How come ?

There is a place where if I stand up straight, I will still be considered sideways.

I am 5 letters long.
My first two tell you who I am
My first 3 could be a medicine
My last three reversed could be a young boy.
My 4th, 3rd and 2nd in that order could be a fruit drink.
If you have me you may hang me round your neck
WHAT AM I ?

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

You are playing as white and given four rooks to checkmate the black king in four moves with the following rules 1. You can place one rook every move and ensure the black king should be in check position.2. After four moves the black king should be in the checkmate position.