laravel eloquent select first row of each group by

I have subjects table and tutorials table in sqlite database. I am trying to select current tutorial. There are my tables

subjects table
    -------------------
    |  id |   name    |
    -------------------
    |  1  | Chemistry |
    |  2  | Physic    |
    -------------------
tutorials table
    -----------------------------------------
    | id  |    name   | subj_id | completed |
    -----------------------------------------
    |  1  | chapter 1 |   1     |     1     |
    |  2  | chapter 2 |   1     |     0     |
    |  3  | chapter 3 |   1     |     0     |
    |  4  | chapter 1 |   2     |     1     |
    |  5  | chapter 2 |   2     |     1     |
    |  6  | chapter 3 |   2     |     0     |
    |  7  | chapter 4 |   2     |     0     |
    -----------------------------------------

My current eloquent is

  $query->where('completed', false)->groupBy('subj_id')->get();

It return

-----------------------------------------
| id  |    name   | subj_id | completed |
-----------------------------------------
|  3  | chapter 3 |   1     |     0     |
|  7  | chapter 4 |   2     |     0     |
-----------------------------------------

what i wish to select is id 2 and 6.

-----------------------------------------
| id  |    name   | subj_id | completed |
-----------------------------------------
|  2  | chapter 2 |   1     |     0     |
|  6  | chapter 3 |   2     |     0     |
-----------------------------------------

How can I get id 2 and 6. I am using sqlite.