hi,

YES you can write APICET EXAM  and can do MBA in distance mode.

Andhra Pradesh is definitely not short of Distance education universities, and has various famous, prestigious universities including

 Acharya Nagarjuna University center for Distance Education, 

Center for Distance Education Sri Krishnadevaraya University,

 Dr. B. R. Ambedkar Open University,

 School of Distance Education – Andhra University, 

 Integral Institute of Advanced Management

Many of the universities and colleges are UGC recognized colleges, and AICTE approved universities,   Acharya Nagarjuna and Andhra University are approved by DEC and are UGC recognized, and so is Dr B. R. Ambedkar Open University. Similarly Sri Venkateshwara University is approved by the UGC for distance education.

ALL THE BEST