What is the centre of gravity?

What is the word or phrase?

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

You have a thousand Re. 1 coins with you. You have ten bags with you and you can put any number of coins in each of the bags. The condition is that if someone asks you for any amount between 1 and 1000, you must be able to give that amount by just giving the bag (you are not allowed to open the bag and give coins).

How will you do it?