CAT (QA) PYQs

How many numbers with two or more digits can be formed with the digits $1,2,3,4,5,6,7,8,9,$ so that in every such number, each digit is used at most once and the digits appear in the ascending order?

In a tournament, there are $43$ junior level and $51$ senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is $153$, while the number of boy versus boy matches in senior level is $276$. The number of matches a boy plays against a girl is

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