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1) Firstly, explain your situation to them.
2) If you have photocopies of your 10th and 12th marks card then you could submit them. Also tell them you'll submit the duplicates of your marks cards at the earliest.
3) Your school and college will have a record of your 10th and 12th scores. So, approach your school and college from where you've graduated and ask them for a letter stating you've completed your education from that college/school.
4) Apply to your respective board for a duplicate marks card while also mentioning the reason for it. You might have to pay a fee for it which depends on the board. The sooner you apply for it the better.

List of Documents required at the time of PG Admission 2019-2020The applicants shall be required to produce the following documents in original with two sets of self-attested photocopies at the time of admission: Admit card of Entrance Exam, if admission is through entrance mode and Admission form generated by logging on to dash board using their registered email id and password. Class X Certificate (Marks sheet or certificate) indicating date of birth and Parents names* (The names of applicants claiming reservation under OBC/EWS/ SC/ST /CW/ PwD must match with the names that appear on the corresponding reservation certificates; similarly their parents names must match in both sets of certificates). Class XII Marks Sheet. Four passport size photographs, consolidated marksheet and Degree Certificate of qualifying examination on the basis of which the candidate is seeking admission. Marks sheets of all semesters and provisional certificate may be submitted and accepted in those cases only where degree is not issued by their university, subject to producing proof thereof.OBC/EWS/ SC/ST /CW/ PwD Certificate (in the name of the Applicant) issued by the competent authority. OBC (Non-Creamy Layer) Certificate (in the name of the Applicant) issued after March 31, 2019 by the competent authority, and wherein the caste is in the OBC central list issued by http://ncbc.nic.in. EWS Certificate from competent authority certifying that the applicant can claim reservation under this category. One identity proof issued by the Competent Authority as notified by Government of India. The candidates are required to submit two undertakings as provided in below mentioned link:
http://du.ac.in/adm2019/pdf/Undertaking_Ragging.pdf

Yes, you can go for MA program even after graduating in BSc (PCM).
MA is a postgraduate academic degree that is awarded in a non-science subject. An MA is a 2-year degree program that can be done in subjects like English, Hindi and any regional or foreign language.
The basic eligibility criterion to be fulfilled by students for applying to MA course is completion Bachelors degree in any stream. Admission to the course is based on entrance exams along with merit obtained by students in Bachelors degree. However the eligibility may vary from university to university.
Eligibility for Master of Arts (MA)
Interested aspirants who wish to pursue Master of Arts degree must fulfill the below mentioned eligibility criteria:
Pass with a minimum of 55% aggregate marks at graduation level.English needs to be one of the mandatory subject at graduation level.Graduation must be done from a recognized college.Entrance Examination can be conducted by university as well.
Some of the colleges for pursuing MA are :
Lovely Professional University, JalandharLoyola College, ChennaiChrist University, BangaloreFergusson College, PuneStella Maris College, Chennai

A candidate seeking admission for the Post Graduate Program should have passed the full time (not by correspondence or part time) Graduate Degree Exam in Science (12th + 3 years degree entire 5 years in science only) with Physics/Chemistry/Mathematics Microbiology or Biochemistry as the main subject or one of them as second subject in the three year degree or Agriculture / Food Science/ Polymer Science or Engineering / Technology degree of a AICTE/ recognised University with minimum second class.Those with equivalent overseas qualification would also be eligible for admission; the candidate needs to have consistently high academic performance and sound general knowledge.