How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

In a school, 280 students studied chemistry, 254 students studied physics and 280 students studied biology.

97 students studied chemistry as well as physics, 138 students studied physics as well as biology and 152 students studied chemistry as well as biology.

73 students studied all the three branches.

Can you find out the total number of students?

How many triangles are there on the puzzle below?

'S' refers to the number of seconds in a day and 'H' refers to the number of hours in ten years. Which quantity out of these two is greater?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

Rectify the following equality 101 - 102 = 1 by moving just one digit.

Replace the question mark with the correct number in below Picture:

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10