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 sum of all four-digit numbers that can be formed with the distinct non-zero digits $a, b, c,$ and $d$, with each digit appearing exactly once in every number, is $153310 + n$, where $n$ is a single digit natural number. Then, the value of $(a + b + c + d + n)$ is

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