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Yes, B.Tech lateral entry is possible in COEP for B.Sc. students. The eligibility criteria is given below.
Passed B.Sc. Degree from a University Grants Commission (UGC) or Association of Indian Universities recognized University with at least 45% marks (40% in case of candidates of Backward class categories and Persons with Disability belonging to Maharashtra State only) and passed HSC with Mathematics as a subject.
Provided that students belonging to this category shall clear the subjects of Engineering Graphics/Engineering Drawing and Engineering Mechanics of the first year Engineering Program along with second year subjects.
For more details, please visit: http://cetcell.mahacet.org/

The eligibility criteria of AFCAT is given below.
1. For Flying branch : Candidates must have scored a minimum of 60% marks each in Maths and Physics at 10+2 level. (AND) Graduation with a minimum of three years degree course in any discipline from a recognised University with a minimum of 60% marks or equivalent.
2. For GD Non Technical Administration & Logistics: Graduate Degree (min. Three years degree course) in any discipline from a recognised university with a minimum of 60% marks.
3. Age : 20-24 Years for flying branch and 20-26 years for GD Non Technical branch.
4. Marital status : Candidates must be unmarried below the age of 25 years. So you can be eligible for above branches f meeting the above criteria.

The Medical Diploma Courses that one can pursue after completing 10th class as you want to take admission in it are as follows:
Diploma Courses in Medical
A.N.M. (Nursing)
Advance Post Graduate Diploma in Stem Cells and Regenerative Medicine
Advanced Diploma in Clinical Diagnostic Techniques
Advanced Diploma in Dialysis Centre Management
Advanced Diploma in Ophthalmic Care Management
Advanced Diploma in Pharmaceutical Management
Advanced Diploma in Technical & Analytical Chemistry
Advanced Postgraduate Diploma in Clinical Research Management (APGDCRM)
Certificate Course in Prasava Vigyana
D.N.A.
D.N.B. (Obstetrics & Gynaecology)
D.Pharma.
Diloma Course in Abhyanga Mardan Tantra
Diploma in Anaesthesiology
Diploma in Community Medicine
Diploma in Dermatology
Diploma in Otorhinolaryngology
Diploma in Tuberculosis & Respiratory Medicine
Diploma in Vetrinary Pharmacy
Diploma Course in Ayurveda Sanskrit Padavika
Diploma in Acupuncture Therapy
Diploma in Advanced Medical Imaging Technology
Diploma in Alternative Medicines (D.A.S.M.)
Diploma in Alternative System of Medicine
Diploma in Anaesthesia (DA)
Diploma in Anesthesia
Diploma in Ayurveda Nursing and Pharmacy
Diploma in Ayurvedic Knowledge
Diploma in Ayurvedic Pharmacy
Diploma in Blood Banking Technology
Diploma in C.T. Scan Technician
Diploma in Cardiology Technician
Diploma in Cardiovascular Technician (DCVT)
Diploma in Child Care
Diploma in Child Health (DCH)
Diploma in Clinical & Community Psychology
Diploma in Clinical Analysis
Diploma in Clinical Diagnostic Techniques
Diploma in Clinical Pathology (DCP)
Diploma in Clinical Perfusion
Diploma in Clinical Research
Diploma in Community Health and Nutrition
Diploma in Counselling Psychology
Diploma in CVT Nursing
Diploma in Dental Hygienist
Diploma in Dental Material & Oral Hygiene
Diploma in Dental Mechanics
Diploma in Dental Technician (D.D.T.)
Diploma in Dermatology, Venerology and Leprosy (DDVL)
Diploma in Diabetology
Diploma in Dialysis Techniques
Diploma in Dietetics and Applied Nutrition
Diploma in Dietetics and Nutrition
Diploma in Dietetics, Health and Nutrition
Diploma in E.N.T.
Diploma in Electro Homoeopathy Medicine (D.E.H.M.)
Diploma in Electro-Homoeopathy
Diploma in Emergency and Trauma Care Technician
Diploma in Emergency Medicine
Diploma in Family Medicine (DFM)
Diploma in Forensic Medicine
Diploma in General Nursing and Midwifery (G.N.M.)
Diploma in Gynaecology and Obstetrics (DGO)
Diploma in Health Administrati