What does an Island and the letter T have in common?

A woman is sitting in her hotel room and hears a knock at the door. She opens the door to see a man whom she’s never met before. He says, “I’m sorry, I have made a mistake, I thought this was my room.” He then goes down the corridor and into the elevator. The woman goes back into her room and calls security. What made the woman so suspicious of the man?

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

What Does this text mean:

important=important

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

It is raining today at 11:59 am. What is the probability of sunny weather after 72 hours?

Which tank will fill first?

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?

Rahul decided to meet Simran so he boards a local train from Bombay station. Just after the station, there is a 1km long tunnel. The train starts and is now accelerating. Rahul is a claustrophobic guy, so what is the best position for him to sit?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.