Can you place three balls such that the equation shown in the picture holds true?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

A red house is made out of red bricks. A yellow house is made out of yellow bricks. And, a blue house is made out of blue bricks. So, what is a greenhouse made of?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

Why did the Girl throw the butter out of the window?

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?