Solution:

The movie name is Divergent.

Its based on a popular fiction series by Veronica Roth. Easy to guess for book lovers.

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

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

Solution:

You must put labels on the tablets as A and B before using. In that case, if you pour tablets together, you will get 3A, 2A 1B, 1A 2B or 3B. If they are from the same bottles you can take one from another bottle and save the remaining two for another day. If you get two from same and one from other, you can draw one from another bottle and you will have two pairs of which you can eat one and save the other.

Solution:

The password is U472BMT.

Read aloud the line and you will sound something like "U Four Seven 2 B M T".

Solution:

I am Spice

Explanation:
Spice is hot if you remove first two alphabets then it will become "ice", which is really cold.

Solution:

The brain teaser can be solved as shown in the image below.

Solution:

Since Jasmine and Thibault ate equal amount, they should pay the same amount. But since that's not possible, they can decide with 'rock, paper, scissor' or an equivalent measure to determine who will pay the extra dollar. Now, let's assume tha Jasmine pays $1 extra after losing

Jasmine will pay $5, Thibault will pay $4 and Noah will pay $2.

If the pizza's cost was $11, we can simply keep the same offset and divide. Jasmine is paying 6% more, Thibault is paying 15% more and Noah is paying 27% more.
Keeping the offset same both Jasmine and Thibault will pay $5 each and Noah will pay $1.

Solution:

The teacher will use a simple trick to form a perfect impression. He will ask all his students to raise their hands on each of the question that is asked. But the only catch will be that those who knows the answer correctly will raise their right hand and others will raise their left hand.

In this way, the principal will see all the hands being raised for each question even though all won't be knowing the correct answer. The teacher will ask only those who know the answer and they will always be correct. So the principal will be impressed to full extent.

Solution:

8/(1−1/5)