Why 1729 is a magic number? Answer Logically.

An apple seller is hosting a competition. He offers 1000 apples and 10 boxes to the people who pass by. The challenge is to put those 1000 apples in the 10 boxes in such a manner that if he asks for any amount of apples, the person can directly give him the boxes or a combination of boxes. If the person can do it, he promises to give a thousand apples for free.

If you happen to pass by the apple seller, will you be able to win a thousand apples?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

There is a five-letter word which has 3 consonants(all are same) and 2 different vowels.
Also, something wrong is associated with the word.

Can you name it?

Suppose you are a girl candidate and sitting in an interview. Suddenly the interviewer asks you, 'What if one morning you wake up and find out that you are pregnant?

How will you reply to such a question?

No matter how little or how much you use me, you change me every month. What am I?

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

What word is pronounced the same if you take away four of its five letters?

A spy was in Canada trying to steal insider information on how to set up new Maple Syrup factories in their country. He was introduced to the operations manager of the biggest factory in Canada. However, the manager was suspicious and decided to test him with a question before he trusted him. So he asked, “What would you be sure to find in the middle of Toronto?” The spy thought fast and came up with an answer for the manager. What was his answer?

A Scientist was fifty years old in the year 2000 but he was forty years old in the year 2010. How can this be possible?

PS: It has a logical answer.