Can you solve below mathematical equation?

2^1234 - 2^1233

Cristina was born in 1888. She just had her 30th birthday today how did that happen?

One of the leprechaun is missing if you see the two pictures attached to this question. Where did he go? When he comes back, do you know where has he been?

Which is the smallest number that you can write using all the vowels exactly once?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

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

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

Can you find the hidden animal in the picture below?

I am the first thing you need while camping.
I am always with the person named Marcos Valencia and Carrick.
But Pogba Zlatan and Rooney think I am wasteful and do not need me.
I am the second to the last thing to add when you are making a patch.

What am I?