Genr in this context I believe refers to "general" and asit to asistencia or attendance. My preference would be for main examination in any case however.

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Note added at 7 mins (2006-02-01 22:22:36 GMT)
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Both exist as the references show>

MIT Department of Physics - General ExamsThe purpose of the general examination is to assure the Department that its ... All portions of the general examination must be taken no later than the ...

Generals ExaminationThe General Examination is a formal requirement of the Graduate School. ... The program of study leading to the General Examination is designed by the ...
www.cs.washington.edu/education/grad/generals/ - 17k

The General Examination. This focuses on organ systems other than the skin. Use the skills you have learned in the other clinical disciplines. ...
www.vet.ed.ac.uk/clive/ cal/DiagDerm/Examination/general.htm - 15k - Cached - Similar pages

What are the main examination rules? Candidates have ten years to pass all 14 examinations from the date of registration. There are two examination sessions ...
www.ey.com/global/content.nsf/ Russia_E/PEC_-_ACCA_-_Rules - 39k - Cached - Similar pages

The number of candidates to be admitted to the Main Examination will be about twelve ... The Main Examination will consist of a written examination and an ...
www.upsc.gov.in/exams/ notifications/csp2006/sec1plan.htm - 5k

] GAZETTED PROBATIONERS' EXAMINATION 2005File Format: Microsoft Word 2000 - View as HTML
(2) and Main Examination for selection of candidates for various services and ... The number of candidates to be admitted to the Main Examination is in the ...

Hope these help

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Note added at 50 mins (2006-02-01 23:05:53 GMT)
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If the exam is at the end of an academic year the term "final examination" is also commonly used. Depends on your context.