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

Can you find a number that lies one third of the distance between 1/3 and 2/3?

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.

Using mathematical symbols like +, -, and x in order to make the equations correct. Replace # with the above-given symbols.

9 # 8 # 7 # 6 # 5 # 4 = 91

On one occasion, A Boy collects 71 rupees in form of 20 paise and 25 paise. He collects a total of 324 coins.

Can you tell me how many 20-paisa and 25-paisa he got?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

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

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?