Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

This picture comprises of 31 hands and 155 fingers.

Solution:

Rhea will open just one present.
Cindy|Y - Y is the 25th alphabet
Duk|E - E is the 5th alphabet
Joh|N - N is the fifteenth alphabet
Rhe|A - A is the first alphabet

Solution:

19|9|9

Explanation:
This is simple. All the months have been coded with a distinctive way.
Let's see about January:
January = 1071 = 10|7|1
10 is the position of J, the first letter of January in alphabetical order.
7 is the number of letters used in forming the word January.
1 is the position of January in the calendar.

For February:
February = 682 = 6|8|2
6 is the position of F, the first letter of February in the alphabetical order.
8 are the number of letters used in forming the word.
2 is the position of February in the calendar.

Similarly, September = 19|9|9
19 is the position of S, the first letter of September in the alphabetical order.
9 are the number of letters used in forming the word.
9 is the position of September in the calendar.

Solution:

The husband had booked two tickets for departure and only one for the return. The travel agent told this information to the police and they immediately came to know that he had planned the murder right from the beginning.

Solution:

0

Explanation:
1 * 1 * 1 = One
2 * 2 * 2 = Eight
3 * 3 * 3 = Twenty seven
4 * 4 * 4 = Sixty Four
For all the above, you can see that the first letter of the sum is the code.
Thus 5 * 5 * 5 = One twenty five

Thus 555 = O.

Solution:

8 is the required number.

Here, by dividing in half, we will actually chop off the digit from the middle. Then you will be left with two zeroes.

Solution:

Never

Explanation:
In the question, the distance of x miles is given at a particular moment. The middle car is running at that time at 50 MPH. The distance will keep increasing with time as three are running at different speeds. It will increase by x miles every hour till a certain point of time and then it will start decreasing till the fastest car meets the slowest again.

As per question, all the cars stop then. Thus, the distance will never be x miles again.

Solution:

The teacher will use a simple trick to form a perfect impression. He will ask all his students to raise their hands on each of the question that is asked. But the only catch will be that those who knows the answer correctly will raise their right hand and others will raise their left hand.

In this way, the principal will see all the hands being raised for each question even though all won't be knowing the correct answer. The teacher will ask only those who know the answer and they will always be correct. So the principal will be impressed to full extent.

Solution:

If you remember the formulas, you will find out that the first option cannot exist.
Side A^2 + Side B^2 = Side C^2

Thus the only possible option here is the second one and of course, it will have a greater area then