JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Permutations and Combinations

Only five digits are available and none may repeat, so a number built from $0,2,4,6,8$ has at most five digits. Every five-digit number exceeds $10,000$ and no number with fewer digits does, so exactly the five-digit arrangements are counted. The leading place cannot hold $0$, leaving $4$ choices, and the remaining four places take the remaining four digits in $4!$ ways. The count is $4\times 4!=96$.