Hello Sahi,

Generally for state entrance exams, the colleges that take admissions on the basis of their scores have two basis of admission,one through the state quota and the other through the all india quota.

For example if you see colleges of Tamil Nadu,they take admission both through TEANCET and Jee Mains for B.Tech program through state and all India quota respectively.

As for your question,yes general category students can apply through all India quota.