Result verification of old course 10th of 1977

Matric examinations were being conducted by universities and the universities examination section is supposed to maintain all the old records. In Pre computer age, the universities were marinating physical records of all the persons who appeared for the examination in that university. Now they are recording and keeping them on their computers. So getting duplicate copies of old certificates is not a problem.
You have all the details with you. You know the university in which you studied your matric. Go to the website of that university and see the procedure given by them. Some universities are having online application facility and some are asking to apply physically.
You can go to the administrative office of the university and meet the concerned person in the examinations section and apply as mentioned by them. You have to pay some money for the fees.

You have got the entire details of the relevant facts of your Matriculation Examination. Your school might be attached to a Board. If I don't err, your school located at Maunbehat existing in Darbhanga should be attached to Bihar School Examination Board. Those were the days when the records were being maintained through the records but with the time this has been phased out. All the earlier records have been transferred to the computer.
Hence to have your old mark sheet of Matriculation, you need to write an application to the secretary of the concerned Board to issue you a mark sheet for the said examination. Better take a forwarding comment of the existing Headmaster/ Principal of the school and send the same through the registered post to the secretary/ controller examination of the Board along with the requisite fee prescribed for getting the fresh mark sheet.