Can you solve below mathematical equation?

2^1234 - 2^1233

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

Find the value of "?" in the ball picture Riddle below:

Can you quickly find which two matchstick figures are identical?

13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from the above-mixed cards to guarantee at least one 'four of a kind?

Find out which of the given views in the picture is accurately the top view of the given pyramid.

Decode this picture on T-Shirt and tell what it says ?

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?

Can you find the key in the picture below?