Solution:

The pills can run for an hour.

Explanation:
If you had ninety minutes in mind, then you are wrong. You took the first pill at the zero minute. Then you took the second pill after 30 minutes and the third pill after 30 + 30 i.e. 60 minutes or an hour.

Solution:

Move the coins as given in the figure and you will get the required result.

Solution:

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

cannot be 1 (as number cannot be included)

Solution:

Colors:
Y B R G
G R B Y
B Y G R
R G Y B


Signs:
x + - /
- / x +
/ - + x
+ x / -

Solution:

It can be done as shown in the picture below.

Solution:

7 Races.

Solution:

The attached picture shows you how you can do it. If you were able to deduce any other way, feel free to comment.

Solution:

LOTTO

Explanation:
Just flip the two rows 1 and 2 vertically, you will find the word "Lotto".

Solution:

Move and then pour all juice from second glass to fifth glass.

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 competition was held on 11 November 2013. The logic is simple. In America, the dates are mentioned as Month/Day/Year and in Britain, dates are written as Day/Month/Year. But on 11 November 2013, the date and month will be the same. And thus both will write in the same manner i.e. 11/11/2013. If it would have been any other date, the evaluators would have been able to identify it.