CAT (QA) PYQs

The number of groups of three or more distinct numbers that can be chosen from 1,2, $3,4,5,6,7$ and $8$ so that the groups always include $3$ and $5$, while $7$ and $8$ are never included together is

How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before 3?

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in $1421$, including itself, is