Solution:

Mayank took birth on Sunday.

Mayank was born 25 days before Rohit and thus the birth date of Mayank will be 8 Feb 1970.
Republic Day fell on Monday.
Number of days if counted from 26 January to 8 February will be 13.

After 13 days of Monday, it will be Sunday.

Solution:

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

Solution:

17 min

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question.

Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together.

1 and 2 go cross
2 comes back
7 and 10 go across
1 comes back
1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes

Solution:

If two widows, each having a son married the son of the other widow, and then by the consummation of marriage, both the couples had a daughter, all the aforementioned relationships will turn to be true.

Solution:

7

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

Solution:

NONE, holes are empty.

Solution:

Can be found on the pic below.

Solution:

The Lady sitting in the chair has the detector attached to the back of her blouse.

Solution:

2100 miles.

Each vowel equivalent to 500 and each consonant equivalent to -200

Solution:

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

Solution:

At every floor, the detective had to open the window himself. If the man had committed suicide, then at least one of the windows must have been open. A person who is committing suicide won’t close the window behind him. Thus he knows that someone pushed him off the edge and closed the window afterwards.