Hello,

Usually the cut offs are a bit higher for government colleges. It is higher even for reserved categories. But you may expect a government college with 68.4% in 12th only in some colleges that may not be in top rankings, but only in a few courses. You might get some less sought after course in off campus colleges through special drive cutoffs (usually 6th cutoff onwards). You may apply in some good private colleges also.

Chances are really very less, but you may apply for it.

ALL THE BEST