What is the missing number in the following sequence? $$$2,\,12,\,60,\,240,\,720,\,1440,\,\_\_\_,\,0$$$

In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs $$750$$ to each male senior citizen in the town and Rs $$1000$$ to each female senior citizen. Altogether, there were $$300$$ senior citizens eligible for this gift. However, only $$8/9$$^th of the eligible men and $$2/3$$^rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

If $$pqr \ne 0$$ and $${p^{ - x}} = {1 \over q},{q^{ - y}} = {1 \over r},\,{r^{ - z}} = {1 \over p},$$ what is the value of the product $$𝑥𝑦𝑧$$?

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?