What number when divided in half becomes zero?

A man desired to get into his work building, however he had forgotten his code.
However, he did recollect five pieces of information
* Fifth number + Third number = 14
* The fourth number is one more than the second number.
* The first number is one less than twice the second number.
* The second number and the third number equals 10.
* The sum of all five numbers is 30.

What is the code ?

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?

Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

Manish has to secure 40% marks to pass his B.tech final exams.
He got just 40 marks and failed by 40-marks.

What is the maximum marks?

In case you were starting to feel confident, this one was meant for third graders in Vietnam. The answer is 66, but we don't blame you for scratching your head about how they got there.

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

Rearrange the letters in "new door" to make one word.