Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

There was once a college that offered a class on probability applied to the real world. The class was relatively easy, but there was a catch. There were no homework assignments or tests, but there was a final exam that would have only one question on it. When everyone received the test paper it was a blank sheet of paper with a solitary question on it: 'What is the risk?'.Most students were able to pass, but only one student received 100% for the class! Even stranger was that he only wrote down one word!
What did he write?

A dying old man wants to divide his entire land between his only two sons. Since his only wish is to treat them as equal as both of them have been too good to him, he wants to divide his land equally between them. The problem is that the land is significantly irregular in shape and thus there is no choice of cutting them into two equal halves.

Can you help him divide the land in a manner that both of his sons will be happy?

While sitting in the Car, John suddenly finds that one of the wheels was missing. John noticed that a killer is approaching towards him. John cannot get out of the car.

How will John escape?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

Akbar called Birbal and asked him to draw a line on the floor. He asked Birbal to make that line smaller without erasing it. Birbal smiled and did it before Akbar could blink his eyes.

How did he managed to do it?

The centre of the third figure is empty. What digit should fit inside?

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?