APICET

No, but try in the counselling if you're not an OC student and maybe you can.
I got TS-ICET rank of 706 in 2017 and I still didn't get OU or CBIT and I was an OC.

It will be held in either this week or 1st or 2nd week of July. Since OU affiliated colleges schedule for MBA starts from July last week so keep fingers crossed, they will let you know when are the prior at least 1-2 days in advance if you have registered for counselling.

Hello Narendra,
The counseling dates for the APICET has been arranged in the first week of June
I hope you haven't missed that out
All the best.

No, unfortunately not. XLRI only accepts XAT score.

Dear Narendra,
The APICET 2018 counselling date has been declared. During the counselling session, qualified candidates of ICET will be invited where they can be allotted a seat as per their option. For the convenience of the students, a web based counseling procedure takes place.
Regards.

Hello Navath,
Well, JNTU is somehow difficult there is 50-50 chance to get admission there, but yes, you can get admission is Maharaja Agrasen and Surajamal for sure.