Can you solve below mathematical equation?

2^1234 - 2^1233

A Car driver was heading down a street in Washington. He went right past a stop sign without stopping, he turned left where there was a 'no left turn' sign and he went the wrong way on a one-way street. Then he went on the right side of the road past a cop car. Still, he didn't break any traffic laws. Why not?

You throw me out when you want to use me and you take me in when you don't want to use me.

Who Am I?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

In my garden, I have many trees but only one of them is the mango tree. In these mango trees, there are some mangoes(as expected).

But after a strong wind, there are neither mangoes on the tree nor on the ground. Explain?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

A seven-year-old kid challenged his classmates that he can make the number one disappear by adding something to it.

How can he do that?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

The following sentence is false. The preceding sentence is true.
Are these two sentences true or false?

What is the word or phrase?