Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

Prove that twice of ten is the same as twice of eleven.

There are three boxes of different sizes with three cupcakes inside each of the boxes in Christina's kitchen. At night her daughter wakes up and goes to the kitchen. She opens a box and eats all three cakes.

But in the morning Christina finds out that each box still had three cupcakes. How?

You have 10 balls with you. A friend of yours out of nowhere asks you to place those ten balls in five lines such that each of the lines has exactly 4 balls on them. He needs to check your intelligence. Prove him by doing the task.

What has to be broken before you can use it?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

If your uncle’s sister is not your aunt, what relation is she to you?

Below, you can see some coding:
January = 1017
February = 628
March = 1335
April = 145
May = 1353
June = 1064
July = 1074
August = 186

Now deciphering the way it has been coded, can you find out how September will be coded?

Can anyone tell me a word in the English dictionary which has a silent 'z'?