CAT (QA) PYQs

How many four digit numbers, which are divisible by $6$, can be formed using the digits $0, 2, 3, 4, 6$, such that no digit is used more than once and $0$ does not occur in the left-most position?

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

With rectangular axes of coordinates, the number of paths from $(1,1)$ to $(8,10)$ via $(4,6)$, where each step from any point $(x, y)$ is either to $(x$, $y+1)$ or to ( $x+1, y$ ), is