Solution:

888

Explanation:
Part-1: Triangle
The triangle is an equilateral triangle.
The value of E and L is determined by the position in the English alphabets i.e E = 5 & L = 12. Together they form number 512

As we know that the equilateral triangle has 3 equal sides, therefore
X^3 = 512
X = 8
=> XXX = 888 ... (desired)

Part-1: X/3 = X
X is the 24th letter, therefore 24/3 = 8

Solution:

Upon reaching each room, he found out that the window facing the dead body was closed. He had to open the window himself. This tells that there was somebody else with him who closed the window. If he would have committed suicide, at least one window would have been open.

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 husband had booked two tickets for departure and only one for the return. The travel agent told this information to the police and they immediately came to know that he had planned the murder right from the beginning.

Solution:

It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.

Solution:

Jamie is a window cleaner who was tired after cleaning the windows on the 45th floor and thus leaped inside the building.

Solution:

On Your lap.

Solution:

The women is a of short stature. She can't reach the upper elevator buttons, but can push is with his umbrella.

Solution:

The mules is moving in circular path and hence outside legs travels more distance than inner legs.

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.

Solution:

2003.

Explanation:
Its a series of prime numbes.