No, there is no chance to get admission in any of the IIMs without clearing the CAT exam. CAT exam is especially conducted for admissions in IIMs by different IIMs every year. Its score is adopted by some other private colleges for giving admission but it's mainly conducted for IIMs and in any of the IIMs no other MBA exam is considered to shortlist student for the second round.

After CAT exam every IIM prepares a merit list to call students for next round of interview and WSAT based on your aggregate score which comprises of many parameters such as CAT marks, 10th, 12th and graduation percentage, work experience, engineer or non-engineer, gender whose weight varies for all different IIMs. After the second round again a new merit list is made on the basis of other aggregate scores which also includes the marks of interview and WSAT.

If you have a dream to pursue your MBA degree from IIM then you should start preparing for CAT 2018 from now only which is going to held in the month of Oct/Nov in 2018.

All the best!!