Divisible by 11...

The divisibility rule of 11 is that the difference between the sums of alternative digits are divisible by 11. To solve the problem we have to arrange the digits to follow the rule and at the same time give the largest number. Obvious the highest digit should be 9 and then follow by the largest remaining numbers whenever possible.

The largest number has the following sums of alternative digits.

$\begin{matrix} 9+7+5+4+3= & 28 \\ -(8+6+2+1)= & -17 \\ Difference= & 11 \end{matrix}$

The largest number is $\boxed {987652413}$ .