What does this mathematical rebus means ?

Fate has decided that you will only be pleased to meet me when you need me

Maybe that is why, when I am working, I start working

However annoying I may be to the regulars, the little ones are always inspired

I will always be waiting if you try to reach me

How many of you can guess my name, let me see

A bridge is about to collapse. There are four people P, Q, R and S on one of the sides. Before the bridge collapses, they want to cross it. Now since the bridge is too weak, it can only stand the weight of two people at a time. Also, it is night time and nothing is visible. They have just one torch with them.

Now P takes one minute to cross the bridge, Q takes two minutes to cross, R takes five minutes to cross and S takes ten minutes to cross.

The bridge will collapse in seventeen minutes. How will they be able to cross the bridge before it collapses?

I am white when I am dirty, and black when I am clean. What am I?

James ordered a fishing rod, priced at $3.56. Unfortunately, James is an Eskimo who lives in a very remote part of Greenland and the import rules forbid any package longer than 4 feet to be imported. The fishing rod was 4 feet and 1 inch, just a little too long, so how can the fishing rod be mailed to James without breaking the rules? Ideally James would like the fishing rod to arrive in one piece!

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

Check out the number list below and find what number comes next in the sequence.

111 , 113 , 117 , 119 , 123 , 137 , ?

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

A spaceship was lost. The detective was given a piece of paper. This was the location of the spaceship! This is what the slip had scribbled on it:
Juice, Umbrella, Potato, Ice, Tomato, Elephant, Rice.

Where is the spaceship?