$10, 20, 40, 50, 70,80, 90$
In BST search we if we go from say $10$ to $40$ while searching for $60$, we will never encounter $20$. So, $10, 20, 40$ and $50$ visited, means they are visited in order. Similarly, $90, 80$ and $70$ are visited in order. So, our required answer will be
$\frac{No. \ of \ possible \ permutations \ of \ 7 \ numbers}{No.\ of \ possible \ permutations \ of \ numbers \ smaller \ than \ 60 \ \times \ No. \ of \ possible \ permutations \ of \ numbers \ larger \ than \ 60}$
(Since only one permutation is valid for both the smaller set of numbers as well as larger set of numbers)
$= \frac{7!}{4!3!}$
$=35$