What has no start, end, or centre?

Can you find out the remainder when 3^300 is divided by 5?

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

Eight Chelsea player makes the following statements :

1. Seven of us are lying here.
2. Six of us are lying here.
3. Five of us are lying here.
4. Five of us are lying here.
5. Four of us are lying here.
6. Three of us are lying here.
7. My name is Torres.
8. My name is Lampard.

The last two are Lampard and Torres or maybe Torres and Lampard.
So can you deduce which of the last two is Lampard or Torres?

Why 1729 is a magic number? Answer Logically.

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

Its something that each of us devours,
Not just us but birds, beats, trees, and flowers,
Frets iron and nibbles steel,
Toil hard stones to meal,
Exterminates king, collapse town,
And blows the mountains down.