Solution:

1611

Explanation:
The number on the right side is formed as (sum of digits of the 1st number)(number1/number2)
example,
24 $ 6 = 64 (2+4 = 6) (24/6 = 4)
35 $ 5 = 87 (3+5=8) (35/5 = 7)
63 $ 7 = 99 (6+3 =9) (63/7 =9)

Simillarly,
88 $ 8 = (8+8 = 16) (88/8 = 11)

Solution:

7

Explanation:
8th is bald man head, check the video below.

Solution:

Treasure Map Is Hidden Inside The Hanging Room Floor.

Explanation.
Just reverse the text "roolF mooR gnignaH ehT edisnI neddiH sI paM erusaerT".

Solution:

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

Solution:

Read the question carefully again. New Year do falls after Christmas but that happens if two different years. The question is put up against the year 2050 and thus there will be 51 weeks and 2 days in between them as New Year will appear on 1 January 2050 and Christmas will happen on 25 December 2050.

Solution:

The last marble will be yellow.

Since marbles can only be taken out in pairs and you started off with an odd number of yellows there is always going to be one yellow left over that you'll keep putting back in the box until it's left on it's own.

Solution:

What must be kept in mind before you start calculating through any method is that the weights can be put on both the pans.

So the weights - 1, 3, 7, 12, 43, 76, 102

The oldest man that can be weighed using these weights is a man aged 122 years

Solution:

She is near the trunk of the tree as shown below.

Solution:

They use the bricks and dirt from the tunnel to stand on it.

Solution:

1/36

Explanation:
The number of possibilities for the first as well as the second dice are 6 and 6 respectively. Therefore the total possibilities or outcome are 6 * 6 = 36.
Out of 36 outcomes, we need only one case i.e. the first gives 2 and the second gives 5.
Therefore, the probability will be 1 on 36 or 1/36.

Solution:

Yes it is possible in Roman Numerals. In Roman Numerals,
9 = IX
10 = X
11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.