Solution:

Yes, some people are going get really tiny pieces but you were allowed for that right. Also, there is another way of doing it. Can you think of it?

Solution:

101

Assuming '?' is no. of runs needed by Ajit in 51st inning.
(50 * 50 + ?)/51 = 51
=>2500 + ? = 51 * 51
=> ? = 2601 - 2500
=> ? = 101 (Answer)

Solution:

Playing chess

Game needs two players so Brother-8 is playing chess with Brother-2

Solution:

This can be done if you draw a five pointed star and place the balls on the corners and intersection points. See the figure to understand better.

Solution:

I have just two tee shirts neither of which are green, blue or orange in color.

Solution:

This problem can be solved with algebra as well as logical reasoning. We are going to tell you how it is logically possible.

Be it any quantity that was present in the beginning and any liquid as well. We know that we have taken a spoonful from one glass and put it into another. Then, we have taken a spoonful from the other glass and put it into the first glass. So, at the end of it, the quantity of liquid in either glass remains same as it was in the beginning.

Therefore, we can conclude the fact that any amount of coke that is missing in the glass with coke will be present in the lemonade glass. Also, the same quantity of lemonade will be missing from the lemonade glass and will be present in the coke glass.

Solution:

Let us denote the four people with A, B, C and D.
A takes 1 minute to cross, B takes 2, C takes 5 and D takes 10.

A and B cross first spending 2 minutes.
A comes back with torch taking 1 minute.
C and D cross taking 10 minutes.
B comes back with torch taking 2 minutes.
Finally, A and B cross the bridge taking 2 minutes.

2 + 1 + 10 + 2 + 2 = 17 minutes

Thus, this is the way they all managed to cross that bridge that night.

Solution:

That person in the picture is the son of the man holding the picture.

Solution:

The two statements have given it out. If you read carefully, you will easily be able to deduce the answer.

We know that everybody is wearing a different color than their names. Now let us begin with the man who noticed the first i.e. Mr. Grey. He is wearing either Pink or Orange. But in the second statement, we already know that the person who is wearing Pink is somebody else. Thus Mr. Grey must be wearing a Orange shirt.

Mr. Pink cannot wear Pink shirt and Orange shirt has already been taken, thus he must be wearing a Grey shirt.

This leaves only one choice for Mr. Orange and he must be wearing a Pink shirt.

Solution:

Since each one of them gave one answer wrong, this means that each one of them gave two answers right.

Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.

Thus both Student A and Student B must be right with the first question and the answer to the first is two.

If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
Q1. Two
Q2. Three
Q3. Two