Solution:

20 units, 12 units & 15 units

As hard as it may sound, we have to just apply some basic algebraic equations to solve it.
Let the three sides be X, Y and Z. Now, the area of different surfaces is given:
X * Y = 240
Z * Z = 300
Y * Z = 180

Multiplying the obtained equations:
(X*Y) (X*Z) (Y*Z) = 240 * 300 * 180
X^2 * Y ^2 * Z^2 = 12960000
(X*Y*Z)^2 = 12960000
X*Y*Z = 3600

Now we know that X*Y = 240

Thus Z = 3600/240 = 15.

If we put the given values in the same manner, we get the three sides:
X = 20 units
Y = 12 units
Z = 15 units

Solution:

On the back, since bullet train is accelerating, therefore,the person at the back will spend less time than one in front.

Solution:

There are 3 fruits (1 grapes, 1 apples, and 1 oranges).

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Solution:

None

The sum of numbers from 0-9(0,1,2,3,4,5,6,7,8,9) is 45 and therefore can be divisible by 3 and 9.

Solution:

XIX is the answer which refers to nineteen in roman numeric system. On taking out one i.e. I, we will get XX that is equal to twenty.

Solution:

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

Solution:

41312432

Solution:

Solution is below

Solution:

zero

I had 3 green socks and 1 Pink sock.

=> chances of pair of green socks = 1/2
chances of pair of mixed socks = 1/2
chances of pair of green socks = NULL

Solution:

All Digits [0-9] follow the following pattern: There is one occurrence of all digits in every 10 numbers Example. Digit-9 occurred one time between 10 and 19 in 9, between 20 and 29 in 29
However, for tens(91,92,93...99) and hundreds (900,901.... 999), the occurrence is much more. Since we have included 1000, Therefor 1 is the most occurred digit.
Note: Despite three '0s' in 1000, 0 is not most occurred digit as they don't have tens and hundreds like other digits.