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

Let $AB, CD, EF, GH,$ and $JK$ be five diameters of a circle with center at $O$. In how many ways can three points be chosen out of $A, B, C, D, E, F, G, H, J, K,$ and $O$ so as to form a triangle?

How many integers in the set $(100,101,102, \ldots, 999)$ have at least one digit repeated?