MYSQL count based on conditions in same column
As far as you don't show us your desired result let me show some approaches to your question.

Your first example:

SELECT COUNT(student_id) count
FROM   tbl_result
WHERE  subject_id IN ('7112',  '6118');


give a result of 5, it doesn't matter if you use COUNT(*) or COUNT(student_id).

| count |
|:-----:|
|   5   |


If you want to know which students then you can use GROUP BY student_id, but then you should add student_id to the SELECT statement:

SELECT subject_id, COUNT(id) count
FROM   tbl_result
WHERE  subject_id IN ('7112',  '6118')
GROUP BY subject_id;


Result:

| subject_id | count |
|:----------:|:-----:|
|    6118    |   3   |
|    7112    |   2   |


For the second one use the same syntax adding more conditions:

SELECT subject_id, COUNT(id) count
FROM   tbl_result
WHERE  subject_id IN ('7112',  '6118')
AND    score &gt; 49
GROUP BY subject_id;


Result:

| subject_id | count |
|:----------:|:-----:|
|    6118    |   3   |
|    7112    |   1   |

SELECT COUNT(*) count
FROM   tbl_result
WHERE  subject_id IN ('7112',  '6118')
AND    score &gt; 49;

| count |
|:-----:|
|   4   |


Rextester here