IIMB 2000 (QA) PYQs

A person hosts a party of 13 guests and places 5 of them on one table and the remaining on the other table, the tables being round. In how many ways can he arrange the guests?

If all letters of the word 'TRILOK' are arranged in all possible manner as they are in a dictionary, then find the rank of the word 'TRILOK'.

The number of ways of selecting two numbers $a$ and $b$, $a$ $\in \{ 2,4,6, \cdots,100\}$ and $\mathrm{b} \in\{1,3,5, \ldots, 99\}$ such that $2$ is the remainder when $\mathrm{a}+\mathrm{b}$ is divided by $23$ is