Solution:

Q

Explanation:
First Square:
6 + 4 + 4 = 14
N is the 14th letter.

Second Square:
4 + 1 + 7 = 12
L is the 12th letter.

Third Square:
5 + 6 + 10 = 21
U is the 21st letter.

Fourth Square:
14 + 2 + 1 = 17
Q is the 17th letter.

Solution:

4

Explanation:
Now if you go on calculating 2^300, you will lose so much time and it might not even be feasible to carry out so long of calculations. Thus we will make use of a trick here. We will calculate the remainder of each power of 2 till we come across a pattern.

2^1 divided by 4 leaves the remainder 2.
2^2 divided by 4 leaves the remainder 0.
2^3 divided by 4 leaves the remainder 0.
2^4 divided by 4 leaves the remainder 0.

You can see that all the following powers of two will be divisible by 4. Therefore the remainder when 2^300 is divided by 4 will be 0 only.

Solution:

First fill the 8 liters jug complete - 4, 8, 0
Fill the 5 liters jug with 8 liters jug - 4, 3, 5
Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0
Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3
Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3
Fill the 5 liters jug from the 8 liters jug - 1, 6, 5
Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.

Solution:

Paradise

Solution:

The guy threw a boomerang in the air from his window. It flew away and looped around to return back with high velocity. It hit his head and he died on the spot due to the injury. This can be the only logical explanation.

Solution:

3816547290

Solution:

192

Explanation:
I started with the number 192.
Adding the reversed 291 to 192 gave me 483.
Similarly,
483 + 384 = 867
867 + 768 = 1635
1635 + 5361 = 6996

Solution:

If you look closely, you will find a sequence in every alternating number.
192, 222 and 252 form one series where 30 is added each time.
021, 324 and 627 form one series where 303 is added each time.

Thus the next two numbers will be 282 and 930.

Solution:

3

Explanation:
Number in the series = (Top Left Number * Bottom Left Number)/(Top Right Number * Bottom Right Number)
= (30 * 2) / (4*5)
= 3

Solution:

10,15,9,20,12

Explanation:
The score obtained on the first throw is 10.
The score obtained on the second throw is 15.
The score obtained on the third throw is 9.
The score obtained on the fourth throw is 20.
The score obtained on the fifth throw is 12.