In MYSQL, how can we store a date where the day, month or both month & day are zero?
day are zero?

To store such kind of dates where the day, month or both month & day are zero we must have to set mode of sql to allow_invalid_dates mode.

mysql> set sql_mode = 'allow_invalid_dates';
Query OK, 0 rows affected (0.00 sec)

mysql> insert into check_date(OrderDate) values('2017-00-00');
Query OK, 1 row affected (0.06 sec)

mysql> select * from check_date;
+-------------+
| OrderDate |
+-------------+
| 2017-00-00 |
+-------------+
1 row in set (0.00 sec)

Above query will insert the date in which both month & day values are zero.

mysql> insert into check_date(Orderdate) values ('2017-00-05');
Query OK, 1 row affected (0.07 sec)

mysql> select * from check_date;
+------------+
| Orderdate  |
+------------+
| 2017-00-00 |
| 2017-00-05 |
+------------+
2 rows in set (0.00 sec)

Above query will insert the date in which month value is zero.

mysql> insert into check_date(Orderdate) values ('2017-05-00');
Query OK, 1 row affected (0.02 sec)

mysql> select * from check_date;
+------------+
| Orderdate  |
+------------+
| 2017-00-00 |
| 2017-00-05 |
| 2017-05-00 |
+------------+
3 rows in set (0.00 sec)

Above query will insert the date on which day value is zero.