Can you solve below mathematical equation?

2^1234 - 2^1233

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

A pet show was happening in my locality. I went down along with my kids. In that show, I noticed that all except two of the entries were cats. All except two were dogs and all except two were Monkeys.

Can you find out how many of each animals were present in that pet show?

Here is a conversation between a couple who both are software professionals.

Husband: Hey! What is your date of birth?
Wife Replied Angrily: It is 591062400
Husband after doing some calculations replied, "Got It".

What is the DOB of the wife?

The king of Octopuses has servants who have six, seven or eight legs. The distinguishing characteristics of the servants is that the one with seven legs always lie but the one with either six or eight legs speak the truth always.

One day, four servants meet and converse:

The black one says, 'We have 28 legs altogether.'

The green one says, 'We have 27 legs altogether.'

The yellow one says, 'We have 26 legs altogether.'

The red one says, 'We have 25 legs altogether.'


Can you identify the colour of the servant who is speaking the truth?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

Look at me. I can bring a smile to your face, A tear to your eye, Or even a thought to your mind. But, I can't be seen. What am I?

Transform the word THINK into BRAIN while changing only one letter at a time in a manner that each of the word in the process is a real word!!!

Can you write down eight eights so that they add up to one thousand?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?