I am an odd number. Take away a letter and I become even. What number am I?

How do you go from 98 to 720 using just one letter?

We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

Chocolate costs 6 rupees and a Toy costs 5 rupees. If you have 32 rupees in total, how many chocolates and how many Toys can be purchased with that amount?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

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

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?