Solution:

60 minutes

Explanation:
Roy will be able to consume all the five tablets in an hour.

Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.

Solution:

It can be possible if she was living in B.C. not A.D.

Solution:

1 Hour.

Suppose he takes the first tablet at 12:00 pm. Then the second will be consumed by him at 12:15, third at 12:30, fourth at 12:45 and fifth at 1:00.

Solution:

Edge Of Tomorrow

Explanation:
Well since tomorrow is written on an edge, the name of the movie is Edge of Tomorrow.

Solution:

There are six 'F' in this sentence. Are you astonished? Read the sentence again and this time, count them on your fingers carefully.

Solution:

All (all months have twenty eight days atleast)

Solution:

New Year Resolution (Popular Screen Resolution of the year)

Solution:

Need for Speed.

Explanation:
Clearly, ds/dt refers to speed. Concluding with whats written already, the movie name is Need for Speed.

Solution:

The deaf beggar as the sister of the person who died.

Solution:

12/27

Explanation:
This is really simple if you know the concept. You just have to increase the fraction by multiplying with a number. In that way, you will increase the numerator and you will be able to find the required fraction. Here, we are multiplying the numerator and denominator of both the numbers with 9. Now if you simplify, the number will remain the same and thus dont think we changed the fraction.

1/3 * 9/9 = 9/27
2/3 * 9/9 = 18/27

Its easy to find the one third fraction on the way now i.e. 12/27.