The statement $$\sim[p \vee(\sim(p \wedge q))]$$ is equivalent to :

If $$\mathrm{S}_{n}=4+11+21+34+50+\ldots$$ to $$n$$ terms, then $$\frac{1}{60}\left(\mathrm{~S}_{29}-\mathrm{S}_{9}\right)$$ is equal to :

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :

Let the number $$(22)^{2022}+(2022)^{22}$$ leave the remainder $$\alpha$$ when divided by 3 and $$\beta$$ when divided by 7. Then $$\left(\alpha^{2}+\beta^{2}\right)$$ is equal to :