The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

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

Can you find out the remainder when 3^300 is divided by 5?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

You can hear me, but you can't touch or see me.

What am I?

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?

Two guards were guarding the camp.Guard-1 was looking towards the south to make sure no threat is coming from the road.Guard-2 was looking at the north to make sure no threat is coming from the top. Suddenly Guard-1 ask the Guard-2 why he is smiling?How Guard-1 knows that Guard-2 is smiling?