Solution:

9862

Sum of digits of all other numbers is 21 , but sum of digits of 9862 is 25

Solution:

74658

* 8 + 6 =14
* 5 - 4 = 1
* 7 = 2*4 - 1
* 4 + 6 = 10
* 7+4+6+5+8 = 30

Solution:

Yes it is possible in Roman Numerals. In Roman Numerals,
9 = IX
10 = X
11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.

Solution:

Step one: First you will have to make 3 trips of 1,000 apples 333 miles. Then you will be left with 2,001 apples and 667 miles to go.

Step two: Next you will have to take 2 trips of 1,000 apples 500 miles. In this manner you will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).

Step three: At last, you will have to travel the last 167 miles with one load of 1,000 apples and you will be left with 833 apples when you reach the town

Solution:

On the back, since bullet train is accelerating, therefore,the person at the back will spend less time than one in front.

Solution:

Yes, you should switch the envelope. In the beginning when you picked up the envelope, you had a 1/3 probability of finding an offer letter in the envelope. There was 2/3 chance that the letter was there in the two envelopes on the table.

If you keep your selected envelope, you still have a 1/3 chance of finding an offer letter in that. However, since the interviewer has removed one empty envelope from the table, if you switch, you have a probability of 2/3 that the offer letter is inside that.

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

Solution:

he was genius.

Officials must have thought he was jumping with a hostage, they would never risk giving him a faulty parachute.

Solution:

The attached picture gives away the solution. If you can find another solution, do send us yours.

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

Solution:

The attached picture shows you how you can do it. If you were able to deduce any other way, feel free to comment.