Solution:

a) Immediately

Explanation:
"Temperature difference" is the driving force for the heat transfer.
Since the coffee is initially very hot and hence it will be cool down at a very fast rate.
If we add cream immediately : The temperature will initially go down for sure but then will cool down at the slower rate as coffees mixed with cream is cooler than coffee alone and therefore heat cool down rate is less. Also, the cream will increase the mass of the content in the cup and hence larger mass will take more time to cool down.
Hence cream should be added immediately

Solution:

Anybody will prefer the shop in the eastern market for sure. There are two reasons for it:
Firstly, since there are only two barbers in the town, the one running the shop in eastern market must have gotten his hair done by the one running the shop in the northern market and vice versa. Thus, if the barber in the eastern market has a shabby haircut, it must be due to the incompatibility.
Secondly, the neat and clean shop can be due to the scarcity of customers as well. While the untidy place refers to the fact that so many customers get their hair done in that shop.

Thus any one will opt for the barber shop in the eastern market.

Solution:

It will take the man 58 minutes to reach the top.

Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.

Solution:

28 =>1+2+4+7+14

cannot be 1 (as number cannot be included)

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

There are three roses and four bees.

Solution:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

Solution:

They were playing tennis.

Tiger Phil
30 - 30
40 - 30 (Phil hit a bad shot)
Game won - 30 (Tiger hit an awesome shot)

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.

Solution:

step 3 is wrong

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.