Slow query need suggestion on rewrite or index

[zxmgh]

Since there is a index on table1 (col1, col2), and

select count(1) from table1;

--9746801

select COUNT(distinct col1)
from table1

--390

select COUNT(distinct col2)
from table1

--1

select COUNT(distinct col3)
from table1

--857

select COUNT(1)
from table1
where col3<=sysdate;

--971876

Do you know it will help if I modify the current index to
table1 (col3, col1, col2) or add a new index just on col3?

Thanks