How to filter specific entries from a MySql table
This is what you need.

SELECT DISTINCT `original_results`.`Reg.No`
FROM  `results` AS `original_results`
WHERE NOT EXISTS (
    SELECT DISTINCT `helper_results`.`Reg.No`
    FROM `results` AS `helper_results` 
    WHERE `helper_results`.`Reg.No` = `original_results`.`Reg.No` AND `helper_results`.`Pass/Fail` = 'pass'
)