Solution:

I have three theories based on which it can be either Murder, Suicide, or Accident.

Case1 : Its a Murder
Reason1: If it's suicide then a person must have waited for the Cigarette to end.
Reason2: Blood is spattered on the right side and the pistol is also on the right side. which seems pistol is planted at the end.

Case2 : Its a Suicide
Reason1. The lamp was switched off and glasses were removed which indicates she done writing(probably suicide note). The murderer does not care about switching off glasses or removing glasses.
Reason2: The blood was just on the wall at the height of a person. If it's a murder the blood must have been scattering around.
Reason3: Burning cigarette and alcohol indicated depression level which often is the reason for suicide.

Case3 : Its a Accident
It's must be an accident. The girl was writing using the pen and suddenly she heard a sound. She must have a gun for safety which she takes out of the security. As a preventive measure, she switched off the light so that she can't be seen in the dark. Also removed the glasses as they are of no use in the dark. After a while, she realized that it's just a sound. So to calm her down she drinks and also lights a cigarette. suddenly she slipped and try to hold stool but failed and forced her head into the wall and died.

Solution:

In the corners of the square, tighten two ropes. Tighten another rope between them by putting rings on each rope. That rope should be tightened on the sheep's neck on the other end.

Solution:

Steps:
1) Light fire on first bar from both the ends and second bar from one end.

2) After 30 seconds(when first bar gets completely burned out) , burn the second bar from second end as well.

3) When second run completely gets burned , you know its 45 seconds.

Solution:

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

Solution:

It can be done as shown in the picture below.

Solution:

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

Solution:

It can be solved as below.

Solution:

1653

Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 49th over. In the last over, he can hit a six in the last ball as well as that will be the last ball of the match.
Thus runs for the last over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 49 + 36 = 1653

Solution:

The guard and the prisoner cross the river
The guard comes back
The guard and the girl cross the river.
The guard and the prisoner comes back.
The mother and the girl cross the river.
Mother comes back
The mother and the father cross the river
Father comes back
The guard and the prisoner cross the river
Mother comes back
The father and the mother cross the river
Father comes back
The father and the boy cross the river
The guard and the prisoner comes back
The guard and the boy cross the river
The guard comes back
The guard and the prisoner cross the river.

Solution:

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules

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.