CAT (QA) PYQs

The number of integers greater than $2000$ that can be formed with the digits $0, 1, 2, 3, 4, 5$, using each digit at most once, is

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

The number of all natural numbers up to $1000$ with non-repeating digits is