Solution:

The time at first observation:
1:12

The time at second observation:
3:24

Thus, two hours and twelve minutes have passed between the two observations.

Solution:

zero

I had 3 green socks and 1 Pink sock.

=> chances of pair of green socks = 1/2
chances of pair of mixed socks = 1/2
chances of pair of green socks = NULL

Solution:

30,450 miles.

Explanation:
For each 5 miles driven using this rotation, each tire will lose (2/29000)+(2/21000) of its tread.So, suppose we drive 5*N miles like this. Then, each tire will lose 2*N*((1/29000)+(1/21000)) of its tread. We wish to determine N so that the latter expression gets to be 1, representing all of each tire's tread. That happens when N=6090, which is when 5*N (the total miles driven) is 30,450.

Solution:

On Your lap.

Solution:

99 matches.

The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 99 matches were played.

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:

It can be done as shown in the picture below.

Solution:

The password is U472BMT.

Read aloud the line and you will sound something like "U Four Seven 2 B M T".

Solution:

2 minutes (duration between 9:59 and 10:01)

Solution:

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

Solution:

One of the cop will move clockwise while the other will move anti-clockwise every day. In such a manner, they will catch the thief in minimum seven days.