There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?

Replace the incorrect term by the correct term in the given sequence: 3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40 where odd terms and even terms follow the same pattern.

A boy plays with a ball, and he drops it from a height of $1.5$ m. Every time the ball hits the ground, it bounces back to attain a height $\frac{4}{5}$th of the previous height. The ball does not bounce further if the previous height is less than $50$ cm. What is the number of times the ball hits the ground before the ball stops bouncing?

A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel)?

From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is $80 + 0.1m$, where $m = 1, 2, 3, ... 100$ and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is $69 + 0.15n$ for any $n$. On which date in the year 2021 are the prices of these two fuels equal?

Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed?