Following are the steps while calculating the answer

4 digit numbers divisible by $11=\frac{8999}{11}=819,4$ digit numbers divisible by $13=\frac{8999}{13}=692$ or $693$

Number of integers common to 11 and 13 (as questionis 11 or 13) $=\frac{8999}{(13\times 11)}=62$ or $63$

To subtract numbers which are common to $11\&17;13\&17;11,13\&17$

$11\&17=\frac{8999}{(11\times 17)}=47$ or $48$ terms

$13\&17=\frac{8999}{(13\times 17)}=40$ or $41$

$11,13,17=\frac{8999}{(11\times 13\times 17)}=3$ or $4$ terms

Total ( you can approximate as the answers are far apart)= 819+693-63-48-41+4= 1364

Closest answer is option (2)