I have branches, but no fruit, trunk or leaves. What am I?

What occurs twice in a week, once in a year but never in a day?

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

In the picture, you can see a chess board. On the top left position, the K marks a knight. Now, can you move the knight in a manner that after 63 moves, the knight has been placed at all the squares exactly once excluding the starting square?

In a chess board, the queen piece can move horizontally, vertically and diagonally freely. The picture represents the same.Can you place 8 queens on the board in a manner that none of the queens can attack each other?

O_er_t_o_

Complete the missing letters of the given word.

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?