In how many ways can 7 examination papers be arranged so that paper 1 and paper 2 never come toghether?

In how many ways can 7 examination papers be arranged so that papers 6 and 7 are never together?

In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?

In how many ways can five examination papers be arranged so that Physics and Chemistry papers never come together?

In how many ways can 7 people be arranged at round table, so that two particular persons be together?

In how many ways can 5 keys be put in a ring?

In how many ways can 8 students be arranged at a round table so that 2 particular students may be together, if (i) students are arranged with respect to table?