Can you find out which number multiplied by itself will give the output as 12345678987654321?

Which English verb becomes past tense just by rearranging the letters?

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?

Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?