Solution:

I am Stamp.

Solution:

Birbal drew another line that was larger than the pre-drawn line. Now the pre drawn line was smaller.

Solution:

3/7

Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.

Solution:

16-days

In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)

Solution:

Just 2

Day One: You make your first cut at the 1/7th mark and give that to the worker.
Day Two: You cut 2/7ths and pay that to the worker and receive the original 1/7th in change.
Day three: You give the worker the 1/7th you received as change on the previous day.
Day four: You give the worker 4/7ths and he returns his 1/7th cut and his 2/7th cut as change.
Day Five: You give the worker back the 1/7th cut of gold.
Day Six: You give the worker the 2/7th cut and receive the 1/7th cut back in change.
Day Seven: You pay the worker his final 1/7th.

Solution:

Karate Kid (car + at + tea + kid)

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:

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

Solution:

If the man killed himself, he would not have been able to rewind the cassette. Thus it is clear someone else killed him.

Solution:

The mules is moving in circular path and hence outside legs travels more distance than inner legs.

Solution:

Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.

So either A or B will speak up first depending on the situation.