It appears from your case that :
1) The admission to the Banaras Hindu University MBBS course for the academic session 2014 will be based on merit AND valid AIPMT 2014 score and rank.
2) The last date for submitting the offline and online application was 30/04/2014. AIPMT exam was not conducted on this date.
3) The APMTexam was held on 4-5-2014 as you said "the applicants took the AIPMTexam on 04/05/2014".
Now think:
Could the original last date (30-4-2014) - before which the AIPMTexam was NOT held - have served the purpose of preparing a merit list based on both, AIPMTexam score and merit?
Could they, without fixing the last date for submission of application to a date AFTER holding of AIPMT exam. have taken into consideration the valid AIPMT 2014 score alongwith merit on 30-4-2014 as the AIPMT exam was not held on that date?
Would not fixing of last date of submission date to 15-5-2014, facilitate them to include both, AIPMT exam score and also merit while preparing Merit List?
So, BHU seems to have taken a corrective step by extending the date. Your petition may not stand. Think again before spending on litigation.