How much do I need to score in the CAT/XAT to get into IIM, FMS, or XLRI with the following academics: X: 86%, XII: 73%, B.Tech: 6.89 CGPA?

The first and foremost thing is that you should be thorough with all your concepts and have decent academics. The selection process into XLRI does not focus much on the profile but your score should be decent. 

The main thing that plays a vital role while preparing for these exams is quality over quantity. You should set your target of at least 95-96 percentile in XAT to get a call for the interview. The cut-offs for different fields are as follows. 

Group Discussion: 

Be a part of group discussion in a positive way. Do not boast your knowledge and try to give chances to others as well. Only put forward the points required. This is the phase where panelists check your ability to react and discuss with others on some topic.

Interview:

After group discussion, you have an interview round where the group of panelists checks your general knowledge. You should be well versed with the three main questions, firstly your strengths and weaknesses, then next why you consider XLRI to be the best among other colleges, and the last why you want to pursue the particular course. During your interview never beat around the bush, if you do not know something, say so. This will create a better impact on the interviewers.